# vibran (c41b2)

Vibration Analysis

The vibrational analysis section of CHARMM has been designed

to be a general purpose normal mode generation and analysis facility.

Also included is an extensive set of vector analysis and comparison

features and entropy calculation.

Support programs such as the iterative diagonalization program,

or the restartable large matrix diagonalization program are compatable

with this facility. Also included are routine to generate trajectories

which can be used for examining modes on the picture system.

In order to process commands with the vibrational analysis routines,

The energy terms must all be defined, and the structure must be determined

(

(

Systems with atoms fixed by the CONStraint FIX command can be treated

by using the REDU FIX option.

Within the vibrational analysis command mode, all miscellaneous

(MISCOM), coordinate manipulation (CORMAN), and internal coordinate (IC)

commands are allowed.

Keywords used to define Hydrogen bonds and nonbonded interactions

may be included in the command that invokes VIBRAN.

* Syntax | Syntax of the VIBRan command and all commands

* Normal modes | Description of normal modes

* I/O | Description of the read and write commands.

* Diagonalization | Description of the diagonalization command.

* Quasiharmonics | Description of the quasiharmonics command.

* Reduce | Reduced basis normal mode analysis

* Dimb | Iterative diagonalization (DIMB).

* Explore | Command to explore the energy hypersurface

* Fluctuations | Description of the fluctuation command.

* Princ-Axis-Flucts | Description of the PAFL command.

* Projections | Description of the projection command.

* Optimize | Perform a minimization (and calculate free energy change)

* Mode-definition | What vectors may be specified

* Rayleigh | Compute Rayleigh quotients for selected modes

* PED | Compute Potential Energy Distribution for a mode

* Edit | Description of the edit facility.

* Basis | Generate entire basis sets.

* Fill | Description of the fill command.

* Second derivatives | Generation, storage, and uses of second derivatives

* Block | Block Normal Mode method(BNM).

* MBH | Mobile Block Hessian method (MBH).

* GANM | Gaussian(Anisotropic) Network Model

* VSA | Vibrational Subsystem Analysis

The vibrational analysis section of CHARMM has been designed

to be a general purpose normal mode generation and analysis facility.

Also included is an extensive set of vector analysis and comparison

features and entropy calculation.

Support programs such as the iterative diagonalization program,

or the restartable large matrix diagonalization program are compatable

with this facility. Also included are routine to generate trajectories

which can be used for examining modes on the picture system.

In order to process commands with the vibrational analysis routines,

The energy terms must all be defined, and the structure must be determined

(

**»**energy Needs.). At present, SHAKE and images(

**»**images .) are not supported.Systems with atoms fixed by the CONStraint FIX command can be treated

by using the REDU FIX option.

Within the vibrational analysis command mode, all miscellaneous

(MISCOM), coordinate manipulation (CORMAN), and internal coordinate (IC)

commands are allowed.

Keywords used to define Hydrogen bonds and nonbonded interactions

may be included in the command that invokes VIBRAN.

* Syntax | Syntax of the VIBRan command and all commands

* Normal modes | Description of normal modes

* I/O | Description of the read and write commands.

* Diagonalization | Description of the diagonalization command.

* Quasiharmonics | Description of the quasiharmonics command.

* Reduce | Reduced basis normal mode analysis

* Dimb | Iterative diagonalization (DIMB).

* Explore | Command to explore the energy hypersurface

* Fluctuations | Description of the fluctuation command.

* Princ-Axis-Flucts | Description of the PAFL command.

* Projections | Description of the projection command.

* Optimize | Perform a minimization (and calculate free energy change)

* Mode-definition | What vectors may be specified

* Rayleigh | Compute Rayleigh quotients for selected modes

* PED | Compute Potential Energy Distribution for a mode

* Edit | Description of the edit facility.

* Basis | Generate entire basis sets.

* Fill | Description of the fill command.

* Second derivatives | Generation, storage, and uses of second derivatives

* Block | Block Normal Mode method(BNM).

* MBH | Mobile Block Hessian method (MBH).

* GANM | Gaussian(Anisotropic) Network Model

* VSA | Vibrational Subsystem Analysis

Top

Syntax for vibrational analysis command and subcommands

[SYNTAX VIBRational analysis]

Main command:

VIBRan [hbond-spec] [nbond-spec] [nmode-spec] [IHBFRQ 0] [INBFRQ 0]

nmode-spec ::= NMODe integer

(this specification allocates space on the heap and its )

(default is NATOM*3. For large systems, if normal modes are)

(to be used, it should be set to the largest number needed.)

(Its default value is set to 1 if NATOM is greater than 50)

hbond-spec !

nbond-spec !

Subcommands:

miscellaneous-command-spec !

IC ic-subcommand-spec ! see

COOR coor-subcommand-spec !

READ { NORMal-modes [FILE] unit-spec [APPEnd] [mode-spec] }

WRITe { NORMal-modes [mode-spec] [CARD] } unit-spec

{ SECOnd-derivatives [RAISe] [MASS]

[CARD [FINIt [STEP val] [TOL val] [atom-selection] ]] }

{ TRAJectory mode-spec magnitude-spec [PHAS real] [SHAKe]

[SEQUential-files] [NCYC integer] [STEP real]

[SUPErpose] [RANDom] [ISEEd integer] }

PRINt NORMal-modes [mode-spec] [magnitude-spec] [INTDer [FINIt]]

[VECTors] [DOTProducts] [DIPOles] [STATistics]

[atom-selection]

PROJect { mode-definition [mode-spec] [magnitude-spec] }

{ TRAJectory [NUNIts integer] FIRStunit integer [NSKIp integer]

[BEGIn integer] [STOP integer] [NOMAss]

[WRITe WUNIt integer coord-spec [SPIRal]] }

OPTImize { mode-definition [mode-spec] [magnitude-spec] }

{[BEGIn integer] [STOP integer] [mode-spec] [ENERgy]

[PARAmeters] [CMPN] [TMPR real] [IUNO integer]}

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe]

[FINIte [STEP real] [DSCF] [NSDD integer] [REST]]

[ENTRopy [TEMPerature real] [SIGMa real]]

QUASIharmonics [NUNIts integer] FIRStunit integer [NSKIp integer]

atom-selection [FCUToff real]

[NFREquencies integer] [NADD integer]

<NOTP|TEMP real [THERmo [RESI]]> <CORDiag|STPDiag|AUTOmatic>

[NORMalize] [MEANasref] [NOMAss]

REDUce IUNBas int [IUNTrans int] [BIG] [NFREq integer] [RAISe]

[FIX [[FINIte] [NSDD integer] [REST]]] [CMPAct]

RBQUasi IUNBas int [IUNTrans int] [NFREq integer] TEMP real

[NUNIts integer] FIRStunit integer [NSKIp integer]

DIMB IUNMode int [IUNRead int] [PARDim int] [NFREq int]

[NADD int] [RAISe] [CUTF1 real] [ITERation int]

[SAVFreq int] [TOLErance real] [STRENgth real]

[DWINdow] [BIG] [SCILib]

EXPLore [mode-spec] [magnitude-spec] unit-spec

[GRID int] [COMP] [SHAKe]

[ [ADJUst] [BOLTzmann temp] [GAUSs factor] ]

FLUCtuations { ATOM [atom-selection] } [mode-spec] [magnitude-spec]

{ IC } [QUANtum] [VERBose]

{ USER [atom-selection] }

PAFLuctuations { ATOM } [atom-selection] [mode-spec] [magnitude-spec]

{ GROUP [MASS] } [QUANtum] [VERBose] [COORdinate] [SAVE]

{ USER } [CONTinue]

RAYLeigh [mode-spec] [SAVE]

PED [mode-spec] [magnitude-spec] [TOL real]

THERmodynamic [mode-spec] [TEMPerature real] [STEP real] [FCUToff real]

EDIT { INCL mode-definition [ORTHog] [TO mode] } [atom-selection]

{ REMOve [mode-spec] mode-definition [NONOrm] }

{ DELEte [mode-spec] }

{ ORTHogonalize [PURGe] [mode-spec] [TOL real] }

{ SHAKe mode-spec }

{ ZERO mode-spec }

{ MOVE MODE n [TO m] [SCALe real] [NONOrm] }

{ ADD MODE n [TO m] [SCALe real] [NONOrm] }

{ MULT MODE n SCALe real }

{ SET MODE n SCALe real [NONOrm] }

{ COPY MODE n TO m }

BASIS { IC { FIRSt BOND } } [NOORthonorm]

{ { FIRSt ANGLe } }

{ { DIHEdral } }

{ { SECOnd ANGLe } }

{ { SECOnd BOND } }

{ }

{ TR atom-selection [BALAnce] }

FILL { DIFF } [mode-spec] [magnitude-spec] [APPE]

{ COMP }

CORREL [ MAXTimesteps int ] [ MAXSeries int ] [ MAXAtoms ] [ COVAriance]

MASS ! turn on mass weighting flag (default)

NOMAS ! turn off mass weighting flag

VSA [atom-selection]

BLKS { INIT }

{ ADDBlock atom-selection}

MBH [RAISe] [FINIte [STEP REAL]]

[ENTRopy [TEMPerature real] [SIGMa real]]

END

unit-spec ::= UNIT unit-number

mode-spec ::= MODE integer [ THRU integer ]

mode-definition ::=

{ { TRAN } { X } } [NONOrm] [NOTR]

{ { ROTA } { Y } }

{ { Z } }

{ }

{ SPHEre { X } [IX int] }

{ { Y } [IY int] }

{ { Z } [IZ int] }

{ { R } [IR int] }

{ { TX } }

{ { TY } }

{ { TZ } }

{ }

{ COMP }

{ DIFF }

{ FORC }

{ USER integer }

{ BOND atom atom }

{ ANGL atom atom atom }

{ DIHE atom atom atom atom }

{ CBND atom atom }

{ CANG atom atom atom }

atom::= {residue-number atom-name}

{ segid resid atom-name }

{ BYNUm atom-number }

magnitude-spec ::= { TEMP real TFRE real } [NONOrm]

{ KCAL real TFRE real }

{ RMS real }

{ MRMS real }

{ FACT real }

coord-spec ::= { FILE }

{ CARD }

{ PDB [OFFIcial] }

miscellaneous-command-spec

ic-subcommand-spec

coor-subcommand-spec

Syntax for vibrational analysis command and subcommands

[SYNTAX VIBRational analysis]

Main command:

VIBRan [hbond-spec] [nbond-spec] [nmode-spec] [IHBFRQ 0] [INBFRQ 0]

nmode-spec ::= NMODe integer

(this specification allocates space on the heap and its )

(default is NATOM*3. For large systems, if normal modes are)

(to be used, it should be set to the largest number needed.)

(Its default value is set to 1 if NATOM is greater than 50)

hbond-spec !

**»**hbonds .nbond-spec !

**»**nbonds .Subcommands:

miscellaneous-command-spec !

**»**miscom .IC ic-subcommand-spec ! see

**»**intcorCOOR coor-subcommand-spec !

**»**corman .READ { NORMal-modes [FILE] unit-spec [APPEnd] [mode-spec] }

WRITe { NORMal-modes [mode-spec] [CARD] } unit-spec

{ SECOnd-derivatives [RAISe] [MASS]

[CARD [FINIt [STEP val] [TOL val] [atom-selection] ]] }

{ TRAJectory mode-spec magnitude-spec [PHAS real] [SHAKe]

[SEQUential-files] [NCYC integer] [STEP real]

[SUPErpose] [RANDom] [ISEEd integer] }

PRINt NORMal-modes [mode-spec] [magnitude-spec] [INTDer [FINIt]]

[VECTors] [DOTProducts] [DIPOles] [STATistics]

[atom-selection]

PROJect { mode-definition [mode-spec] [magnitude-spec] }

{ TRAJectory [NUNIts integer] FIRStunit integer [NSKIp integer]

[BEGIn integer] [STOP integer] [NOMAss]

[WRITe WUNIt integer coord-spec [SPIRal]] }

OPTImize { mode-definition [mode-spec] [magnitude-spec] }

{[BEGIn integer] [STOP integer] [mode-spec] [ENERgy]

[PARAmeters] [CMPN] [TMPR real] [IUNO integer]}

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe]

[FINIte [STEP real] [DSCF] [NSDD integer] [REST]]

[ENTRopy [TEMPerature real] [SIGMa real]]

QUASIharmonics [NUNIts integer] FIRStunit integer [NSKIp integer]

atom-selection [FCUToff real]

[NFREquencies integer] [NADD integer]

<NOTP|TEMP real [THERmo [RESI]]> <CORDiag|STPDiag|AUTOmatic>

[NORMalize] [MEANasref] [NOMAss]

REDUce IUNBas int [IUNTrans int] [BIG] [NFREq integer] [RAISe]

[FIX [[FINIte] [NSDD integer] [REST]]] [CMPAct]

RBQUasi IUNBas int [IUNTrans int] [NFREq integer] TEMP real

[NUNIts integer] FIRStunit integer [NSKIp integer]

DIMB IUNMode int [IUNRead int] [PARDim int] [NFREq int]

[NADD int] [RAISe] [CUTF1 real] [ITERation int]

[SAVFreq int] [TOLErance real] [STRENgth real]

[DWINdow] [BIG] [SCILib]

EXPLore [mode-spec] [magnitude-spec] unit-spec

[GRID int] [COMP] [SHAKe]

[ [ADJUst] [BOLTzmann temp] [GAUSs factor] ]

FLUCtuations { ATOM [atom-selection] } [mode-spec] [magnitude-spec]

{ IC } [QUANtum] [VERBose]

{ USER [atom-selection] }

PAFLuctuations { ATOM } [atom-selection] [mode-spec] [magnitude-spec]

{ GROUP [MASS] } [QUANtum] [VERBose] [COORdinate] [SAVE]

{ USER } [CONTinue]

RAYLeigh [mode-spec] [SAVE]

PED [mode-spec] [magnitude-spec] [TOL real]

THERmodynamic [mode-spec] [TEMPerature real] [STEP real] [FCUToff real]

EDIT { INCL mode-definition [ORTHog] [TO mode] } [atom-selection]

{ REMOve [mode-spec] mode-definition [NONOrm] }

{ DELEte [mode-spec] }

{ ORTHogonalize [PURGe] [mode-spec] [TOL real] }

{ SHAKe mode-spec }

{ ZERO mode-spec }

{ MOVE MODE n [TO m] [SCALe real] [NONOrm] }

{ ADD MODE n [TO m] [SCALe real] [NONOrm] }

{ MULT MODE n SCALe real }

{ SET MODE n SCALe real [NONOrm] }

{ COPY MODE n TO m }

BASIS { IC { FIRSt BOND } } [NOORthonorm]

{ { FIRSt ANGLe } }

{ { DIHEdral } }

{ { SECOnd ANGLe } }

{ { SECOnd BOND } }

{ }

{ TR atom-selection [BALAnce] }

FILL { DIFF } [mode-spec] [magnitude-spec] [APPE]

{ COMP }

CORREL [ MAXTimesteps int ] [ MAXSeries int ] [ MAXAtoms ] [ COVAriance]

MASS ! turn on mass weighting flag (default)

NOMAS ! turn off mass weighting flag

VSA [atom-selection]

BLKS { INIT }

{ ADDBlock atom-selection}

MBH [RAISe] [FINIte [STEP REAL]]

[ENTRopy [TEMPerature real] [SIGMa real]]

END

unit-spec ::= UNIT unit-number

mode-spec ::= MODE integer [ THRU integer ]

mode-definition ::=

{ { TRAN } { X } } [NONOrm] [NOTR]

{ { ROTA } { Y } }

{ { Z } }

{ }

{ SPHEre { X } [IX int] }

{ { Y } [IY int] }

{ { Z } [IZ int] }

{ { R } [IR int] }

{ { TX } }

{ { TY } }

{ { TZ } }

{ }

{ COMP }

{ DIFF }

{ FORC }

{ USER integer }

{ BOND atom atom }

{ ANGL atom atom atom }

{ DIHE atom atom atom atom }

{ CBND atom atom }

{ CANG atom atom atom }

atom::= {residue-number atom-name}

{ segid resid atom-name }

{ BYNUm atom-number }

magnitude-spec ::= { TEMP real TFRE real } [NONOrm]

{ KCAL real TFRE real }

{ RMS real }

{ MRMS real }

{ FACT real }

coord-spec ::= { FILE }

{ CARD }

{ PDB [OFFIcial] }

miscellaneous-command-spec

**»**miscom .ic-subcommand-spec

**»**intcor .coor-subcommand-spec

**»**corman .Top

Normal Modes

There are two ways that normal modes are stored internally

in CHARMM. The most common usage is as one double precision mass

weighted array. A series of such arrays usually span an orthonormal

basis (as would be the case upon diagonalization). The second method

is to represent a normal mode as three non mass weighted coordinate

displacement arrays, stored in double precision. The program automatically

converts between them as necessary. Whenever interconversion is to be

done, a "magnitude specification" may be given. This specification

requires a step type and step length. The valid step types are;

FACT (simple factor)

TEMP (put mode at this temperature)

KCAL (put in the specified Kcals)

MRMS (step along until this mass weighted RMS is obtained)

RMS (step along until this RMS is reached).

When specifying TEMP or KCAL, a terminal frequency (cm-1) may be specified

(default TFRE is 5.0) which prevents excessive stepping along very low

frequency or translation-rotation modes.

The procedure used in going from double precion to coordinate

displacement arrays is;

1) Normalize double precision vector (unless NONOrm keyword is used)

2) Mass weight by dividing by root(mass)

3) Multiply by appropriate scale factor from step type and length

To convert from single precision into double precision, the

procedure is;

1) Save inner product (as initial step length)

2) Mass weight by multiplying by root(mass)

3) Normalize vector (unless NONO keyword is used)

4) Compute scale factor using initial step length and step type

Whenever a magnitude-specification is called for, some

interconversion will take place. The conversion from double precision

to coordinate displacements takes place in the subcommands;

PRINt NORMal-modes

WRITe TRAJectory

PROJect

FILL

EXPLore

FLUCtuations

The interconversion from coordinated displacements to double precision

takes place in the subcommands;

PROJect

EDIT NORMal-modes

The Normal Mode data structure of double precision arrays is local

to the Vibrational analysis section of CHARMM, and the storage space for

these arrays is released when exiting to CHARMM via the END command.

Normal Modes

There are two ways that normal modes are stored internally

in CHARMM. The most common usage is as one double precision mass

weighted array. A series of such arrays usually span an orthonormal

basis (as would be the case upon diagonalization). The second method

is to represent a normal mode as three non mass weighted coordinate

displacement arrays, stored in double precision. The program automatically

converts between them as necessary. Whenever interconversion is to be

done, a "magnitude specification" may be given. This specification

requires a step type and step length. The valid step types are;

FACT (simple factor)

TEMP (put mode at this temperature)

KCAL (put in the specified Kcals)

MRMS (step along until this mass weighted RMS is obtained)

RMS (step along until this RMS is reached).

When specifying TEMP or KCAL, a terminal frequency (cm-1) may be specified

(default TFRE is 5.0) which prevents excessive stepping along very low

frequency or translation-rotation modes.

The procedure used in going from double precion to coordinate

displacement arrays is;

1) Normalize double precision vector (unless NONOrm keyword is used)

2) Mass weight by dividing by root(mass)

3) Multiply by appropriate scale factor from step type and length

To convert from single precision into double precision, the

procedure is;

1) Save inner product (as initial step length)

2) Mass weight by multiplying by root(mass)

3) Normalize vector (unless NONO keyword is used)

4) Compute scale factor using initial step length and step type

Whenever a magnitude-specification is called for, some

interconversion will take place. The conversion from double precision

to coordinate displacements takes place in the subcommands;

PRINt NORMal-modes

WRITe TRAJectory

PROJect

FILL

EXPLore

FLUCtuations

The interconversion from coordinated displacements to double precision

takes place in the subcommands;

PROJect

EDIT NORMal-modes

The Normal Mode data structure of double precision arrays is local

to the Vibrational analysis section of CHARMM, and the storage space for

these arrays is released when exiting to CHARMM via the END command.

Top

I/O For Normal modes

The VIBRAN section supports its own I/O commands. Commands to

read, write and print coordinates (

and internal coordinates (

identical with those in the main program. This section can read and

write the Normal Mode data structure and write out the second

derivative matrix in several ways (for external use) and normal mode

trajectories (for the movie programs). Also, useful information about

normal modes may be printed using the PRINT NORM command.

READ { NORMal-modes [CARD] unit-spec [APPEnd] [mode-spec] }

WRITe { NORMal-modes [CARD] [mode-spec] } unit-spec

{ SECOnd-derivatives [RAISe] [MASS] -

[CARD [FINIt [STEP val] [TOL val] [atom-selection] ]] }

{ TRAJectory mode-spec magnitude-spec [PHAS real] [SHAKe] -

[SEQUential-files] [NCYC integer] [STEP real]

[SUPErpose] [RANDom] [ISEEd integer] }

PRINt NORMal-modes [mode-spec] [magnitude-spec] [INTDer [FINIt]] -

[VECTors] [DOTProducts] [DIPOles] [STATistics] -

[atom-selection]

By default, normal mode vectors are read and written in binary (FILE)

format, but ascii (CARD) can be specified. When writing, a unit must be

specified, and a contiguous subset of modes may be specified using the

mode-spec. When reading modes, all selected modes (from mode-spec) of the

modes in the normal mode file will be read (assuming there is enough space).

Note, when modes are selected on input, the selection is relative to the

ordering of modes in the input file and does NOT correspond to the destination

of these modes.

If the available space is exhausted, a warning is issued, and further

reading stops. Existing modes will be deleted when the READ NORM command

is executed unless the append option is used, in whichcase, the new

modes are added sequentially at the end. No modification of modes is

done upon reading (i.e. normalization, or orthogonalization).

When printing Normal Modes, a variety of options may be specified.

A contiguous subset of modes may be specified (the default is all modes), and

an appropriate magnitude may be specified ( modes:Normal Modes.).

For each specified mode, the frequency (cm**-1), eigenvalue (Kcal/gram/A**2),

force projection (Kcal/mole/A), % translation-rotation, and magnitude

information will be printed. In addition, internal derivatives (or optionally

by finite differences with the FINIte keyword) of the internal coordinate

data structure (INTD keyword), displacements in coordinate space (VECTors

keyword), dipole derivatives (DIPOles keyword), dotproducts with other modes

can be printed (DOTProducts keyword), and some vector statistics (STATistics

keywords).

The Second Derivative matrix may be written out in binary

or card format for input to other programs. In particular, there is a

program that extracts normal modes from a large secular equation (DIAGIT).

There is also a restartable diagonalization program for medium sized systems.

The RAISe keyword will shift the translation-rotation modes to high

frequency (currently 5000 cm-1). This option only work with the card output

format. The MASS keyword will calculate and write out M**(-1/2) * H * M**(-1/2)

which is the matrix used in the eigensolver with the DIAG command.

Finally, this command may be used to test the second derivative

energy surface determination by a comparison of finite derivatives and

analytic derivatives. This is done with the FINIte and CARD keywords.

Two values are also looked for, the finite difference step size (STEP,

def=0.005), and the difference tolerence for printing (TOL, def=0.0001).

Trajectory files may be written out for a set of modes with

a given magnitude factor. The modes for all specified modes may be

written out in one file, or in separate files for different modes

where sequential unit numbers are used starting with the specified

unit number. The SEQU keyword will cause sequential files to be written.

By default, one cycle of 12 frames will be written. The keywords

NCYC and PHASe can be specified to alter the number of cycles and the

phase angle between frames within a cycle. The PHASe keyword should be

an integer divisor of 360.0 ( a PHASe value of 7.2 will result in 50

frames per cycle). The total number of frames is given by NCYC * 360/PHASe.

If it is desired to specify a particular time step between frames,

the STEP keyword will specify this value in picoseconds. The total

number of frames will remain unchanged will remain unchanged.

If a movie of 10 modes and displaying one picosecond of each mode is

desired with 500 frames per picosecond (about 25 seconds of film time),

then the appropriate input could be:

WRIT TRAJ MODE 7 THRU 16 STEP 0.002 PHAS 3.6 NCYC 5 TEMP 2000.0

It is also possible to write out a trajectory that consists of a

superposition of a number of normal modes. The STEP parameter needs to be

specified, together with PHAS and NCYC, to set the length of the trajectory

in ps. By default, all normal modes in the trajectory have an initial phase

of 0. Random initial phases can be specified by using the keyword RANDom

and specifying a seed for the random number generator (default ISEED =

314159). A movie of 50 ps (10 frames per ps) for modes 7 to 100 with random

initial phases could be generated by:

WRIT TRAJ MODE 7 THRU 100 SUPE STEP 0.1 PHAS 3.6 NCYC 5 RAND TEMP 300.0

I/O For Normal modes

The VIBRAN section supports its own I/O commands. Commands to

read, write and print coordinates (

**»**corman .)and internal coordinates (

**»**intcor .) areidentical with those in the main program. This section can read and

write the Normal Mode data structure and write out the second

derivative matrix in several ways (for external use) and normal mode

trajectories (for the movie programs). Also, useful information about

normal modes may be printed using the PRINT NORM command.

READ { NORMal-modes [CARD] unit-spec [APPEnd] [mode-spec] }

WRITe { NORMal-modes [CARD] [mode-spec] } unit-spec

{ SECOnd-derivatives [RAISe] [MASS] -

[CARD [FINIt [STEP val] [TOL val] [atom-selection] ]] }

{ TRAJectory mode-spec magnitude-spec [PHAS real] [SHAKe] -

[SEQUential-files] [NCYC integer] [STEP real]

[SUPErpose] [RANDom] [ISEEd integer] }

PRINt NORMal-modes [mode-spec] [magnitude-spec] [INTDer [FINIt]] -

[VECTors] [DOTProducts] [DIPOles] [STATistics] -

[atom-selection]

By default, normal mode vectors are read and written in binary (FILE)

format, but ascii (CARD) can be specified. When writing, a unit must be

specified, and a contiguous subset of modes may be specified using the

mode-spec. When reading modes, all selected modes (from mode-spec) of the

modes in the normal mode file will be read (assuming there is enough space).

Note, when modes are selected on input, the selection is relative to the

ordering of modes in the input file and does NOT correspond to the destination

of these modes.

If the available space is exhausted, a warning is issued, and further

reading stops. Existing modes will be deleted when the READ NORM command

is executed unless the append option is used, in whichcase, the new

modes are added sequentially at the end. No modification of modes is

done upon reading (i.e. normalization, or orthogonalization).

When printing Normal Modes, a variety of options may be specified.

A contiguous subset of modes may be specified (the default is all modes), and

an appropriate magnitude may be specified ( modes:Normal Modes.).

For each specified mode, the frequency (cm**-1), eigenvalue (Kcal/gram/A**2),

force projection (Kcal/mole/A), % translation-rotation, and magnitude

information will be printed. In addition, internal derivatives (or optionally

by finite differences with the FINIte keyword) of the internal coordinate

data structure (INTD keyword), displacements in coordinate space (VECTors

keyword), dipole derivatives (DIPOles keyword), dotproducts with other modes

can be printed (DOTProducts keyword), and some vector statistics (STATistics

keywords).

The Second Derivative matrix may be written out in binary

or card format for input to other programs. In particular, there is a

program that extracts normal modes from a large secular equation (DIAGIT).

There is also a restartable diagonalization program for medium sized systems.

The RAISe keyword will shift the translation-rotation modes to high

frequency (currently 5000 cm-1). This option only work with the card output

format. The MASS keyword will calculate and write out M**(-1/2) * H * M**(-1/2)

which is the matrix used in the eigensolver with the DIAG command.

Finally, this command may be used to test the second derivative

energy surface determination by a comparison of finite derivatives and

analytic derivatives. This is done with the FINIte and CARD keywords.

Two values are also looked for, the finite difference step size (STEP,

def=0.005), and the difference tolerence for printing (TOL, def=0.0001).

Trajectory files may be written out for a set of modes with

a given magnitude factor. The modes for all specified modes may be

written out in one file, or in separate files for different modes

where sequential unit numbers are used starting with the specified

unit number. The SEQU keyword will cause sequential files to be written.

By default, one cycle of 12 frames will be written. The keywords

NCYC and PHASe can be specified to alter the number of cycles and the

phase angle between frames within a cycle. The PHASe keyword should be

an integer divisor of 360.0 ( a PHASe value of 7.2 will result in 50

frames per cycle). The total number of frames is given by NCYC * 360/PHASe.

If it is desired to specify a particular time step between frames,

the STEP keyword will specify this value in picoseconds. The total

number of frames will remain unchanged will remain unchanged.

If a movie of 10 modes and displaying one picosecond of each mode is

desired with 500 frames per picosecond (about 25 seconds of film time),

then the appropriate input could be:

WRIT TRAJ MODE 7 THRU 16 STEP 0.002 PHAS 3.6 NCYC 5 TEMP 2000.0

It is also possible to write out a trajectory that consists of a

superposition of a number of normal modes. The STEP parameter needs to be

specified, together with PHAS and NCYC, to set the length of the trajectory

in ps. By default, all normal modes in the trajectory have an initial phase

of 0. Random initial phases can be specified by using the keyword RANDom

and specifying a seed for the random number generator (default ISEED =

314159). A movie of 50 ps (10 frames per ps) for modes 7 to 100 with random

initial phases could be generated by:

WRIT TRAJ MODE 7 THRU 100 SUPE STEP 0.1 PHAS 3.6 NCYC 5 RAND TEMP 300.0

Top

Diagonalization of the second derivative matrix

The DIAGonalize command will generate the second derivative

matrix, mass weight this matrix, and then diagonalize to generate

normal modes. There are some needs and restrictions for this command.

They can be summarized;

1) SHAKE may not be used

2) ST2 waters may not be used

3) Periodic boundaries and images may not be used without FINIte (» crystl )

4) Group electrostatics and extended electrostatics may not be used without FINIte

5) All coordinates and energy lists (nonbond, hbond) must be set up

6) The number of atoms does not exceed the limit (300)

(unless BOMLEV is reduced)

Once normal modes have been generated, they may be saved (WRITE NORM...),

or analyzed directly.

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe]

[FINIte [STEP real] [DSCF] [NSDD integer] [REST]]

[ENTRopy [TEMPerature real] [SIGMa real]]

The RAISe keyword, will cause the normal modes corresponding to

translation-rotation to have a very high frequency (currently 5000 cm-1).

This option is intended for calculations where rotational coupling terms

are to be removed.

The NADD option will cause the the specified number of lowest

modes to be skipped in the evaluation. For example, if "NADD 100"

is specified, then the first mode of the result will correspond to mode

101 in the actual matrix. This option has been added, so that modes

of moderatly sized systems (200-400 atoms) can be found in groups

when the memory requrement for a full calculation are prohibitive.

The FINIte keywords causes the Hessian to be generated from the finite

differences of the forces. This option requires 6*N+2 energy determinations,

so it should be reserved for smaller systems. The step length for finite

difference may be specified with the STEP keyword (default 0.005 Angstroms).

A STEP value that is too large will cause errors due to anharmonicity.

A STEP value that is too small will result in inaccurate hessian elements

(force differences are divided by the step length).

The NSDD "x" option saves a restart file "dd1_save.dat" every x cycles.

When the REST option is set, the restart file "dd1_save.dat" (in the

parent directory of the calculation) is read in.

Regular vibrational analysis treats Drude particles as real atoms and

thereby shows extra peaks on the IR-spectrum due to Drude particles. This

complicates CHARMM IR-spectrum comparison with QM or experimental data.

The purpose of DSCF keyword is to allow vibrational spectrum analysis

for molecules in presence of Drude particles to be conducted in such

way that Drude particles will not be explicitly present in the IR-spectrum.

This regimen is called SCF Drudes where position of Drude particles is

instantenously adjusted to any rearrangement in position of real atoms.

In this mode CHARMM performs calculation of second derivatives by using

finite differences applied to real atoms and followed by Drude coordinate

relaxation after every change in coordinates of real atoms. This way

Drude degrees of freedom are projected onto second derivatives of real

atoms. This algorithm works via numerical differentiation only since

analytical solution is hardly possible. DSCF keyword can be invoked when

DIAG FINIte keywords are specified, otherwise it is ignored.

Entropy calculation

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe] [FINIte [STEP real]

[DSCF]] [ENTRopy [TEMPerature real] [SIGMa real]]

After second derivatives are calculated the vibrational entropy term

can be evaluated. Two other entropy terms, rotational and translational ones

are also calculated (» corman for details). Entropy calculation is

implemented as an extention to VIBRAN DIAG command, since entropy calculation

is based on vibrational frequencies.

Default value for TEMPerature is 298.15 K. Default SIGMa value is 1.0.

SIGMa is symmetry number which is 1 for non-symmetric molecule and some

low symmetry groups. For symmetric molecules one should enter a correct

value for sigma (see, for example, C.J.Cramer, "Essentials of Comp.Chem.",

2002,p.327).

EXAMPLE:

VIBRAN

DIAG ENTRopy

END

The units for entropy are cal/(mol*K). Rotational, translational and

vibrational entropy terms along with their sum can be accessed in

parameters after executing the entropy command.

Alternative implementation of entropy calculation is available under

keyword THERmo (see above). This is a kind of code duplication that should be

resolved sometime. The THERMo also includes questionable contribution from

trivial modes and calculates a vibrational entropy term only.

Diagonalization of the second derivative matrix

The DIAGonalize command will generate the second derivative

matrix, mass weight this matrix, and then diagonalize to generate

normal modes. There are some needs and restrictions for this command.

They can be summarized;

1) SHAKE may not be used

2) ST2 waters may not be used

3) Periodic boundaries and images may not be used without FINIte (» crystl )

4) Group electrostatics and extended electrostatics may not be used without FINIte

5) All coordinates and energy lists (nonbond, hbond) must be set up

6) The number of atoms does not exceed the limit (300)

(unless BOMLEV is reduced)

Once normal modes have been generated, they may be saved (WRITE NORM...),

or analyzed directly.

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe]

[FINIte [STEP real] [DSCF] [NSDD integer] [REST]]

[ENTRopy [TEMPerature real] [SIGMa real]]

The RAISe keyword, will cause the normal modes corresponding to

translation-rotation to have a very high frequency (currently 5000 cm-1).

This option is intended for calculations where rotational coupling terms

are to be removed.

The NADD option will cause the the specified number of lowest

modes to be skipped in the evaluation. For example, if "NADD 100"

is specified, then the first mode of the result will correspond to mode

101 in the actual matrix. This option has been added, so that modes

of moderatly sized systems (200-400 atoms) can be found in groups

when the memory requrement for a full calculation are prohibitive.

The FINIte keywords causes the Hessian to be generated from the finite

differences of the forces. This option requires 6*N+2 energy determinations,

so it should be reserved for smaller systems. The step length for finite

difference may be specified with the STEP keyword (default 0.005 Angstroms).

A STEP value that is too large will cause errors due to anharmonicity.

A STEP value that is too small will result in inaccurate hessian elements

(force differences are divided by the step length).

The NSDD "x" option saves a restart file "dd1_save.dat" every x cycles.

When the REST option is set, the restart file "dd1_save.dat" (in the

parent directory of the calculation) is read in.

Regular vibrational analysis treats Drude particles as real atoms and

thereby shows extra peaks on the IR-spectrum due to Drude particles. This

complicates CHARMM IR-spectrum comparison with QM or experimental data.

The purpose of DSCF keyword is to allow vibrational spectrum analysis

for molecules in presence of Drude particles to be conducted in such

way that Drude particles will not be explicitly present in the IR-spectrum.

This regimen is called SCF Drudes where position of Drude particles is

instantenously adjusted to any rearrangement in position of real atoms.

In this mode CHARMM performs calculation of second derivatives by using

finite differences applied to real atoms and followed by Drude coordinate

relaxation after every change in coordinates of real atoms. This way

Drude degrees of freedom are projected onto second derivatives of real

atoms. This algorithm works via numerical differentiation only since

analytical solution is hardly possible. DSCF keyword can be invoked when

DIAG FINIte keywords are specified, otherwise it is ignored.

Entropy calculation

DIAGonalize [NFREquencies integer] [NADD integer] [RAISe] [FINIte [STEP real]

[DSCF]] [ENTRopy [TEMPerature real] [SIGMa real]]

After second derivatives are calculated the vibrational entropy term

can be evaluated. Two other entropy terms, rotational and translational ones

are also calculated (» corman for details). Entropy calculation is

implemented as an extention to VIBRAN DIAG command, since entropy calculation

is based on vibrational frequencies.

Default value for TEMPerature is 298.15 K. Default SIGMa value is 1.0.

SIGMa is symmetry number which is 1 for non-symmetric molecule and some

low symmetry groups. For symmetric molecules one should enter a correct

value for sigma (see, for example, C.J.Cramer, "Essentials of Comp.Chem.",

2002,p.327).

EXAMPLE:

VIBRAN

DIAG ENTRopy

END

The units for entropy are cal/(mol*K). Rotational, translational and

vibrational entropy terms along with their sum can be accessed in

parameters after executing the entropy command.

Alternative implementation of entropy calculation is available under

keyword THERmo (see above). This is a kind of code duplication that should be

resolved sometime. The THERMo also includes questionable contribution from

trivial modes and calculates a vibrational entropy term only.

Top

Quasiharmonic dynamics from molecular dynamics

QUASIharmonics [NUNIts integer] FIRStunit integer [NSKIp integer]

atom-selection [FCUToff real]

[NFREquencies integer] [NADD integer]

<NOTP|TEMP real [THERmo [RESI]]> [<CORDiag|STPDiag|AUTOmatic>]

[NORMalize] [MEANasref]

For quasiharmonic dynamics, a dynamics trajectory file(s) is

read. During this read, atom position fluctuation tensors are generated for

the selected atoms (default: all). This module can also perform Principal

component analysis (see below).

The reference coordinates must be present in the main coordinate arrays.

The COOR DYNA command can preceed the QUASi command if the average coordinates

are to be used as a reference. You can also use the MEANasref keyword to

achieve this result. Another good choice is to use an energy minimized

coordinates set as the reference. The resulting fluctuation matrix is mass

weighted and diagonalized. The resulting modes are the quasiharmonic modes of

the system, and should roughly match those from a strightforward normal mode

calculation. The significant differences of these methods are that anharmonic

terms are included here. This method can yield misleading results when there

are long lived transitions, or when there is very slow interchange of energy

between degrees of freedom. The estimated frequency for a given mode will

strongly depend on the average energy in this mode. For the case of slow energy

transfer, this may be significantly different from kT. If internal motion is

to be studied, it is strongly recommended that translation and rotation be

removed from the dynamics trajectory. This is done with the MERGe command

using all atoms and mass weighting. Without mass weighting, the

translation-rotation motion is not projected out.

Important note: The quasiharmonic modes are reported in reverse order.

The lowest frequency global modes are at the end of the list. If you

want only the lowest 20 frequencies for a large system, then you should

use the NADD keyword with an integer value of 3*NATOM-20.

Important note: You cannot get more quaiharmonic modes than the number

of steps of dynamics used to create the fluctuation matrix. Keep this

in mind when testing with short simulations.

By default, the diagonalization is processed on the secular matrix

(of size 3*NATOM*3*NATOM) in coordinate space (CORDiag). For big systems with

few steps of dynamics this uses computational and memory resources, while the

number of non zero eigenvalues is at most the number of steps. In the latter

case, it is more efficient to perform the calculation in the space of MD steps

(STPDiag, using a matrix of size NSTEP*NSTEP). You can use either the CORDiag

or STPDiag keywords to force the diagonalization in each of these spaces, or

use the AUTOmatic keyword to let CHARMM decide in which space perform the

calculation.

Rationale: Secular matrix is given by M.(MT), where M is the trajectory

specified with coordinates in one dimension and MD step in the other.

MT is the transpose of M. (MT)M is the covariance matrix of the steps in the

trajectory. An eigenvalue, l, with an eigenvector, A, of the secular matrix

M.(MT).A=l.A, is also an eigenvalue of the second matrix:

(MT).M.[(MT).A]=l.[(MT).A]. Conversion between spaces is made with M.

Important note: in the dynamic step space, the THERmo keyword cannot be used

to calculate entropy, enthalpy and heat-capacity as the computed matrix does

not give access to these data.

In order for this method to estimate frequencies from fluctuations,

the average temperature (TEMP real) must be specified.

If you want to do a simple Principal Component Analysis (PCA) of the

trajectory, you need to specify the NOTPerature keyword without the TEMP

keyword. With PCA, eigenvalues give the variance along corresponding

eigenvectors. It is advised to normalize the eigenvectors after diagonaliation

with the NORMalize keyword. This is especially useful if you want to use the

PROJect command afterwards.

Keyword THERmo evaluates entropy [kcal/mol/K], enthalpy [kcal/mol]

and heat-capacity Cv [kcal/mol/K] at the specified temperature. RESI prints

out S, H and Cv using the fluctuations of the selected atoms in each residue.

Only frequencies > FCUToff are used in the sum (default value for FCUT=0.0001)

See also COOR COVA » corman . As stated above, this cannot be done if the

diagonalization has been computed in the dynamic step space.

The dynamics trajectory is read in the usual manner.

Specifications are;

NUNIts integer - number of I/O units

FIRStu integer - first I/O unit

NSKIP integer - integration step modulo to use

As with the DIAG command, this command will also accept the keywords;

NFREquencies integer, and NADD integer.

Reduced basis quasiharmonic calculations are also possible (RBQUas).

See the section for reduced basis normal mode analysis for information

on setting up a basis set. The method is exactly the same as above

except the fluctuation matrix is generated in the reduced basis instead

of the mass weighted cartesian basis.

RBQUasi IUNBas int [IUNTrans int] [NFREq integer] TEMP real

[NUNIts integer] FIRStunit integer [NSKIp integer]

Quasiharmonic dynamics from molecular dynamics

QUASIharmonics [NUNIts integer] FIRStunit integer [NSKIp integer]

atom-selection [FCUToff real]

[NFREquencies integer] [NADD integer]

<NOTP|TEMP real [THERmo [RESI]]> [<CORDiag|STPDiag|AUTOmatic>]

[NORMalize] [MEANasref]

For quasiharmonic dynamics, a dynamics trajectory file(s) is

read. During this read, atom position fluctuation tensors are generated for

the selected atoms (default: all). This module can also perform Principal

component analysis (see below).

The reference coordinates must be present in the main coordinate arrays.

The COOR DYNA command can preceed the QUASi command if the average coordinates

are to be used as a reference. You can also use the MEANasref keyword to

achieve this result. Another good choice is to use an energy minimized

coordinates set as the reference. The resulting fluctuation matrix is mass

weighted and diagonalized. The resulting modes are the quasiharmonic modes of

the system, and should roughly match those from a strightforward normal mode

calculation. The significant differences of these methods are that anharmonic

terms are included here. This method can yield misleading results when there

are long lived transitions, or when there is very slow interchange of energy

between degrees of freedom. The estimated frequency for a given mode will

strongly depend on the average energy in this mode. For the case of slow energy

transfer, this may be significantly different from kT. If internal motion is

to be studied, it is strongly recommended that translation and rotation be

removed from the dynamics trajectory. This is done with the MERGe command

using all atoms and mass weighting. Without mass weighting, the

translation-rotation motion is not projected out.

Important note: The quasiharmonic modes are reported in reverse order.

The lowest frequency global modes are at the end of the list. If you

want only the lowest 20 frequencies for a large system, then you should

use the NADD keyword with an integer value of 3*NATOM-20.

Important note: You cannot get more quaiharmonic modes than the number

of steps of dynamics used to create the fluctuation matrix. Keep this

in mind when testing with short simulations.

By default, the diagonalization is processed on the secular matrix

(of size 3*NATOM*3*NATOM) in coordinate space (CORDiag). For big systems with

few steps of dynamics this uses computational and memory resources, while the

number of non zero eigenvalues is at most the number of steps. In the latter

case, it is more efficient to perform the calculation in the space of MD steps

(STPDiag, using a matrix of size NSTEP*NSTEP). You can use either the CORDiag

or STPDiag keywords to force the diagonalization in each of these spaces, or

use the AUTOmatic keyword to let CHARMM decide in which space perform the

calculation.

Rationale: Secular matrix is given by M.(MT), where M is the trajectory

specified with coordinates in one dimension and MD step in the other.

MT is the transpose of M. (MT)M is the covariance matrix of the steps in the

trajectory. An eigenvalue, l, with an eigenvector, A, of the secular matrix

M.(MT).A=l.A, is also an eigenvalue of the second matrix:

(MT).M.[(MT).A]=l.[(MT).A]. Conversion between spaces is made with M.

Important note: in the dynamic step space, the THERmo keyword cannot be used

to calculate entropy, enthalpy and heat-capacity as the computed matrix does

not give access to these data.

In order for this method to estimate frequencies from fluctuations,

the average temperature (TEMP real) must be specified.

If you want to do a simple Principal Component Analysis (PCA) of the

trajectory, you need to specify the NOTPerature keyword without the TEMP

keyword. With PCA, eigenvalues give the variance along corresponding

eigenvectors. It is advised to normalize the eigenvectors after diagonaliation

with the NORMalize keyword. This is especially useful if you want to use the

PROJect command afterwards.

Keyword THERmo evaluates entropy [kcal/mol/K], enthalpy [kcal/mol]

and heat-capacity Cv [kcal/mol/K] at the specified temperature. RESI prints

out S, H and Cv using the fluctuations of the selected atoms in each residue.

Only frequencies > FCUToff are used in the sum (default value for FCUT=0.0001)

See also COOR COVA » corman . As stated above, this cannot be done if the

diagonalization has been computed in the dynamic step space.

The dynamics trajectory is read in the usual manner.

Specifications are;

NUNIts integer - number of I/O units

FIRStu integer - first I/O unit

NSKIP integer - integration step modulo to use

As with the DIAG command, this command will also accept the keywords;

NFREquencies integer, and NADD integer.

Reduced basis quasiharmonic calculations are also possible (RBQUas).

See the section for reduced basis normal mode analysis for information

on setting up a basis set. The method is exactly the same as above

except the fluctuation matrix is generated in the reduced basis instead

of the mass weighted cartesian basis.

RBQUasi IUNBas int [IUNTrans int] [NFREq integer] TEMP real

[NUNIts integer] FIRStunit integer [NSKIp integer]

Top

Reduced basis normal mode analysis

With the REDUce command, it is possible to do reduced basis

normal mode analysis. This can be affected to constrain certain degrees of

freedom (leave them out of the basis), or to reduce the size of a large

problem. I can also be used to remove translation and rotation from a

calculation. The same restrictions for a full normal mode calculation

apply here as well.

By defining the keyword CMPAct the initial second derivative matrix

in Cartesian coordinates will be stored in a compressed form. This

means that only non-zero elements are stored. This option is very

useful if you deal with very large molecules, where the initial

second derivative matrix may be too large to fit into memory. For

instance, in a system with 2000 atoms, the regular Cartesian Hessian

takes up about 144 Mbytes, whereas the compressed matrix takes up

an absolute maximum of 43 Mbytes (usually less, depending on nonbonded

cutoff distances). Currently, this option allows atoms to interact with

up to 300 other atoms, on average. This means that if large cutoff

distances (>15 A) are used, the command may exit with an error message.

This command requires an external basis set. The form of the basis

set is a CHARMM normal mode file of the correct dimension. The basis will

include all of the vectors in that file. The basis is expected to span an

orthonormal space. These basis sets may be made from the BASIS command

followed by the EDIT ORTHog command if appropriate.

The reduced basis may also be a subset of normal modes. For large

systems, this is the refinement step. By repeating the calculation in a

reduced basis, most roundoff effects from the tridiagonalization are removed.

This command removes all existing vectors and replaces them with

the result of the diagonalization in the original basis (i.e. the new vectors

are linear combinations of the basis vectors). The number of vectors to

compute may be specified with the NFREquencies keyword. The default is to

compute all frequencies (for the entire reduced basis).

REDUce IUNBas int [IUNTrans int] [BIG] [NFREquencies integer] [RAISe]

[FIX [[FINIte] [NSDD integer] [REST]]] [CMPAct]

The IUNBas keyword points to the basis vector file. If the

IUNTrans value is specified, the transformation matrix (NDIMxNFREQ)

relating the basis vectors and the final normal modes will be saved to

that unit. The number of frequencies to be computed may be specified.

The default is to compute all of them. The raise option raises the

translation/rotation degrees of freedom to a high frequency. This keyword

will have no affect if the net translation/rotation degrees of freedom

are not in the basis.

The BIG keyword signifies that the entire set of basis vectors

is not to be stored in memory. This is essential for large calculations

(i.e. when HEAP allocation errors occur without this option). In this

case, VIBRAN ... NMODE 1 ... should be specified to save space, since

no space is needed to store the basis vectors or the results.

The BIG option will cause the backtransformation step to be suppressed,

thus the IUNTrans unit should be specified (or all you will get is the

frequencies). The will be a special purpose support program to backtransform

this eigenvactors (normal modes) to the original basis.

If the BIG option is not specified, there must be enough

space allocated to store the entire basis in memory (VIBRAN NMODe int).

The keyword FIX should be used when part of the system is fixed by the

CONStraint FIX command. In the modes that are calculated, the fixed atoms

will not move, but their presence is taken into account for the motions

of the unfixed atoms. This option does not require a basis vector file,

i.e., the IUNBas parameter should not be specified. For large systems,

the use of a compressed second derivative matrix by specifying the

keyword CMPAct is recommended. The BIG option is not allowed.

The restart options NSDD and REST are the same as described for DIAG.

Reduced basis normal mode analysis

With the REDUce command, it is possible to do reduced basis

normal mode analysis. This can be affected to constrain certain degrees of

freedom (leave them out of the basis), or to reduce the size of a large

problem. I can also be used to remove translation and rotation from a

calculation. The same restrictions for a full normal mode calculation

apply here as well.

By defining the keyword CMPAct the initial second derivative matrix

in Cartesian coordinates will be stored in a compressed form. This

means that only non-zero elements are stored. This option is very

useful if you deal with very large molecules, where the initial

second derivative matrix may be too large to fit into memory. For

instance, in a system with 2000 atoms, the regular Cartesian Hessian

takes up about 144 Mbytes, whereas the compressed matrix takes up

an absolute maximum of 43 Mbytes (usually less, depending on nonbonded

cutoff distances). Currently, this option allows atoms to interact with

up to 300 other atoms, on average. This means that if large cutoff

distances (>15 A) are used, the command may exit with an error message.

This command requires an external basis set. The form of the basis

set is a CHARMM normal mode file of the correct dimension. The basis will

include all of the vectors in that file. The basis is expected to span an

orthonormal space. These basis sets may be made from the BASIS command

followed by the EDIT ORTHog command if appropriate.

The reduced basis may also be a subset of normal modes. For large

systems, this is the refinement step. By repeating the calculation in a

reduced basis, most roundoff effects from the tridiagonalization are removed.

This command removes all existing vectors and replaces them with

the result of the diagonalization in the original basis (i.e. the new vectors

are linear combinations of the basis vectors). The number of vectors to

compute may be specified with the NFREquencies keyword. The default is to

compute all frequencies (for the entire reduced basis).

REDUce IUNBas int [IUNTrans int] [BIG] [NFREquencies integer] [RAISe]

[FIX [[FINIte] [NSDD integer] [REST]]] [CMPAct]

The IUNBas keyword points to the basis vector file. If the

IUNTrans value is specified, the transformation matrix (NDIMxNFREQ)

relating the basis vectors and the final normal modes will be saved to

that unit. The number of frequencies to be computed may be specified.

The default is to compute all of them. The raise option raises the

translation/rotation degrees of freedom to a high frequency. This keyword

will have no affect if the net translation/rotation degrees of freedom

are not in the basis.

The BIG keyword signifies that the entire set of basis vectors

is not to be stored in memory. This is essential for large calculations

(i.e. when HEAP allocation errors occur without this option). In this

case, VIBRAN ... NMODE 1 ... should be specified to save space, since

no space is needed to store the basis vectors or the results.

The BIG option will cause the backtransformation step to be suppressed,

thus the IUNTrans unit should be specified (or all you will get is the

frequencies). The will be a special purpose support program to backtransform

this eigenvactors (normal modes) to the original basis.

If the BIG option is not specified, there must be enough

space allocated to store the entire basis in memory (VIBRAN NMODe int).

The keyword FIX should be used when part of the system is fixed by the

CONStraint FIX command. In the modes that are calculated, the fixed atoms

will not move, but their presence is taken into account for the motions

of the unfixed atoms. This option does not require a basis vector file,

i.e., the IUNBas parameter should not be specified. For large systems,

the use of a compressed second derivative matrix by specifying the

keyword CMPAct is recommended. The BIG option is not allowed.

The restart options NSDD and REST are the same as described for DIAG.

Top

Iterative Mixed-Basis Diagonalization

With the DIMB command, one can do an iterative diagonalization,

which will consume a lot less memory space than a regular (DIAG)

diagonalization, but will still result in exactly the same normal modes.

The method (see L.Mouawad and D.Perahia (1993), Biopolymers, 33, 599)

does repetitive reduced-basis diagonalizations. These reduced

bases are constructed partially from the not yet converged eigenvectors

and from regular Cartesian coordinates. A unit IUNMode for writing out

the eigenvectors has to be specified. For restarts from existing

eigenvector files, the unit IUNRead should be specified. The NFREq,

NADD, and RAISe keywords have the same effect as in the regular DIAG

command. The maximum size (in atoms) for a block to be diagonalized

is defined with the PARDim (default=200) keyword, and can be tailored to

the size of the available memory. This affects the

number of blocks the system will be divided into. Make sure that the

requested number of modes (lesser of NMODEs and NFREq) is smaller

than PARDim*3.

If no IUNRead unit is specified, initial basis vectors are calculated

by diagonalizing main diagonal blocks of the full matrix. This initial

calculation involves the use of residual (Lanczos) vectors, and will

result in only half the number of requested modes. The full number of

requested modes can be obtained by using the following sequence of

commands (in this example NMODes is set to 200 and PARDim to 100, but

these values can be changed):

Create the initial basis and write out on unit 20. This results

in (NMODes+6)/2 = 103 basis vectors. The usage of BIG reduces

memory requirements by writing intermediate vectors to disk

temporarily. Specification of ITERations 0 exits the routine

after the calculation of the basis vectors:

OPEN WRITe FILE UNIT 20 NAME initial.bas

VIBRan NMODes 200

DIMB ITERations 0 PARDim 100 IUNMode 20 BIG

END

Do the iterative diagonalization, using the precalculated initial

basis of 103 vectors. 103 converged modes will be written to unit 10:

OPEN READ FILE UNIT 20 NAME initial.bas

OPEN WRITe FILE UNIT 10 NAME modes.mod

VIBRan NMODes 103

DIMB ITERations 100 TOLErance 0.05 PARDim 100 -

IUNMode 10 IUNRead 20 DWIN

END

The usage of the keyword BIG is only allowed when ITERations 0 is specified.

It will use unit IUNMode to temporarily store intermediate

vectors. Make sure that there is enough available disk space. The size

of the intermediate file will be about (NMODes*NAT3*8) bytes,

where NAT3 = 3 * number of atoms.

A rough estimate of the required memory space is:

{ 4*(PARDim3*PARDim3) + (2*NMODes+10)*NAT3 } * 8 bytes (without BIG)

{ 4*(PARDim3*PARDim3) + (1*NMODes+10)*NAT3 } * 8 bytes (with BIG)

Usually convergence will be faster with larger PARDim and with

smaller number of modes. Too small a number of modes will slow

down converge due to a limited basis set of eigenvectors.

With CUTF1 (default=50.0) a cutoff frequency (cm-1) can be defined.

Only normal modes with frequencies below CUTF1 will be calculated.

The maximum number of iterations can be specified with the ITERations

(default=10) parameter, and the desired accuracy of the eigenvectors

with TOLErance (default=0.05). TOLErance values range between 0 and 1,

where 0 is the highest accuracy.

The standard DIMB algorithm uses a single "window" of Cartesian

coordinates that is added to the basis set. When the DWINdow keyword

is specified, two different "windows" are added. The DWINdow method

is more efficient, because it uses windows with strongly interacting

atoms more often than those with weakly interacting atoms. When the

DWINdow option is chosen, the parameter STREngth (default=0.0) defines

which atom sets are considered to be interacting at all. If the sum of

absolute values of the second derivatives between two particular

atom sets is lower than STREngth, those second derivatives will not be

considered.

SAVFreq (default=number of blocks) defines the frequency of saving

the eigenvectors to disk for the DWINdow option.

When DIMB calculations are carried out on a Cray vector computer,

it is advantageous to use the general EISPACK routines do

diagonalize the submatrices. This can be defined by adding the

keyword SCILib.

Iterative Mixed-Basis Diagonalization

With the DIMB command, one can do an iterative diagonalization,

which will consume a lot less memory space than a regular (DIAG)

diagonalization, but will still result in exactly the same normal modes.

The method (see L.Mouawad and D.Perahia (1993), Biopolymers, 33, 599)

does repetitive reduced-basis diagonalizations. These reduced

bases are constructed partially from the not yet converged eigenvectors

and from regular Cartesian coordinates. A unit IUNMode for writing out

the eigenvectors has to be specified. For restarts from existing

eigenvector files, the unit IUNRead should be specified. The NFREq,

NADD, and RAISe keywords have the same effect as in the regular DIAG

command. The maximum size (in atoms) for a block to be diagonalized

is defined with the PARDim (default=200) keyword, and can be tailored to

the size of the available memory. This affects the

number of blocks the system will be divided into. Make sure that the

requested number of modes (lesser of NMODEs and NFREq) is smaller

than PARDim*3.

If no IUNRead unit is specified, initial basis vectors are calculated

by diagonalizing main diagonal blocks of the full matrix. This initial

calculation involves the use of residual (Lanczos) vectors, and will

result in only half the number of requested modes. The full number of

requested modes can be obtained by using the following sequence of

commands (in this example NMODes is set to 200 and PARDim to 100, but

these values can be changed):

Create the initial basis and write out on unit 20. This results

in (NMODes+6)/2 = 103 basis vectors. The usage of BIG reduces

memory requirements by writing intermediate vectors to disk

temporarily. Specification of ITERations 0 exits the routine

after the calculation of the basis vectors:

OPEN WRITe FILE UNIT 20 NAME initial.bas

VIBRan NMODes 200

DIMB ITERations 0 PARDim 100 IUNMode 20 BIG

END

Do the iterative diagonalization, using the precalculated initial

basis of 103 vectors. 103 converged modes will be written to unit 10:

OPEN READ FILE UNIT 20 NAME initial.bas

OPEN WRITe FILE UNIT 10 NAME modes.mod

VIBRan NMODes 103

DIMB ITERations 100 TOLErance 0.05 PARDim 100 -

IUNMode 10 IUNRead 20 DWIN

END

The usage of the keyword BIG is only allowed when ITERations 0 is specified.

It will use unit IUNMode to temporarily store intermediate

vectors. Make sure that there is enough available disk space. The size

of the intermediate file will be about (NMODes*NAT3*8) bytes,

where NAT3 = 3 * number of atoms.

A rough estimate of the required memory space is:

{ 4*(PARDim3*PARDim3) + (2*NMODes+10)*NAT3 } * 8 bytes (without BIG)

{ 4*(PARDim3*PARDim3) + (1*NMODes+10)*NAT3 } * 8 bytes (with BIG)

Usually convergence will be faster with larger PARDim and with

smaller number of modes. Too small a number of modes will slow

down converge due to a limited basis set of eigenvectors.

With CUTF1 (default=50.0) a cutoff frequency (cm-1) can be defined.

Only normal modes with frequencies below CUTF1 will be calculated.

The maximum number of iterations can be specified with the ITERations

(default=10) parameter, and the desired accuracy of the eigenvectors

with TOLErance (default=0.05). TOLErance values range between 0 and 1,

where 0 is the highest accuracy.

The standard DIMB algorithm uses a single "window" of Cartesian

coordinates that is added to the basis set. When the DWINdow keyword

is specified, two different "windows" are added. The DWINdow method

is more efficient, because it uses windows with strongly interacting

atoms more often than those with weakly interacting atoms. When the

DWINdow option is chosen, the parameter STREngth (default=0.0) defines

which atom sets are considered to be interacting at all. If the sum of

absolute values of the second derivatives between two particular

atom sets is lower than STREngth, those second derivatives will not be

considered.

SAVFreq (default=number of blocks) defines the frequency of saving

the eigenvectors to disk for the DWINdow option.

When DIMB calculations are carried out on a Cray vector computer,

it is advantageous to use the general EISPACK routines do

diagonalize the submatrices. This can be defined by adding the

keyword SCILib.

Top

Exploring Energy Surfaces

The explore command is used to search along a particular mode and

to compute the energy at regular intervals. For now, this search is limited

to one dimension, but with the EXPL COMP (using the comparison coordinates)

option, a two dimensional search is possible. This is done by filling the

comparison coordinate set with a structure perturbed along one mode, and then

exploring along another.

EXPLore [mode-spec] [magnitude-spec] unit-spec -

[GRID int] [COMP] [SHAKe] -

[ [ADJUst] [BOLTzmann temp] [GAUSs factor] ]

For this command, a magnitude specification and grid selection

are read. The grid selection determines the number of energy evaluations.

An odd number will include the center point, and an even number will not.

The default value is 3, one energy evaluation at each extreem (determined

by the magnitude specification), and one at the center.

When the energies are computed, they are stored in a temporary

array which may be output (for plotting) by specifying a unit number.

They may also be used to adjust the eigenvalue of the particular mode

base on a least squares quardratic fit. This is done with the ADJUst

keyword. The weighting for this fitting is currently unity for every point.

The adjust feature is intended for relatively small displacements. Large

"rigid" dislacements will necessarily come up against bad close contacts.

Quadratic fittings for this type of interactions, will be misleading.

For this reason, two weighting options are available, an energy

Boltzman weighting (BOLTzmann keyword-value), and a gaussian displacment

weighting (GAUSs keyword-value) which weights nearby points with a

larger factor. When these keyword are used together, the overall weighting

is a product of individual weightings.

To avoid problems with excessive (quartic) bond stretching which

occurs with large displacements, SHAKE may be invoked with the SHAKe

keyword. In order to use this option, the SHAKe command in CHARMM must

fist be invoked specifying which bonds (and angles) are to be maintained.

A step value may be specified. By default, all shake comparisons

are done with respect to the center coordinates. This sometimes leads

to "DEVIATION IN SHAKE TOO LARGE" errors. The step option allows shake

to be invoked in small steps. The step value gives the relative step

for each intemediate SHAKE calculation. A value of 1.0 is the default, and

a value of 0.2 will cause the extreem points to be computed in 5 steps.

Exploring Energy Surfaces

The explore command is used to search along a particular mode and

to compute the energy at regular intervals. For now, this search is limited

to one dimension, but with the EXPL COMP (using the comparison coordinates)

option, a two dimensional search is possible. This is done by filling the

comparison coordinate set with a structure perturbed along one mode, and then

exploring along another.

EXPLore [mode-spec] [magnitude-spec] unit-spec -

[GRID int] [COMP] [SHAKe] -

[ [ADJUst] [BOLTzmann temp] [GAUSs factor] ]

For this command, a magnitude specification and grid selection

are read. The grid selection determines the number of energy evaluations.

An odd number will include the center point, and an even number will not.

The default value is 3, one energy evaluation at each extreem (determined

by the magnitude specification), and one at the center.

When the energies are computed, they are stored in a temporary

array which may be output (for plotting) by specifying a unit number.

They may also be used to adjust the eigenvalue of the particular mode

base on a least squares quardratic fit. This is done with the ADJUst

keyword. The weighting for this fitting is currently unity for every point.

The adjust feature is intended for relatively small displacements. Large

"rigid" dislacements will necessarily come up against bad close contacts.

Quadratic fittings for this type of interactions, will be misleading.

For this reason, two weighting options are available, an energy

Boltzman weighting (BOLTzmann keyword-value), and a gaussian displacment

weighting (GAUSs keyword-value) which weights nearby points with a

larger factor. When these keyword are used together, the overall weighting

is a product of individual weightings.

To avoid problems with excessive (quartic) bond stretching which

occurs with large displacements, SHAKE may be invoked with the SHAKe

keyword. In order to use this option, the SHAKe command in CHARMM must

fist be invoked specifying which bonds (and angles) are to be maintained.

A step value may be specified. By default, all shake comparisons

are done with respect to the center coordinates. This sometimes leads

to "DEVIATION IN SHAKE TOO LARGE" errors. The step option allows shake

to be invoked in small steps. The step value gives the relative step

for each intemediate SHAKE calculation. A value of 1.0 is the default, and

a value of 0.2 will cause the extreem points to be computed in 5 steps.

Top

Computing fluctuations from normal modes

The fluctuation command computes atom, internal coordinate, or

user specified fluctuations from normal modes. For atom fluctuations,

the magnitude of the components for the overall fluctuation is stored in

the comparison coordinate arrays. In addition, information giving the

contribution of each mode is printed. For the IC (internal coordinate) option,

the overall fluctuations are stored in the IC table. the "IC WRITE..."

command may be used to save this data.

FLUCtuations { ATOM [atom-selection] } [mode-spec] [magnitude-spec]

{ IC } [QUANtum] [VERBose]

{ USER [atom-selection] }

For the user specified option, the user may supply the subroutine

USEFLU which is call once for initialization (IMODE=0), once for each mode

(IMODE=n), and once for termination (IMODE=-1). In preparing this routine,

see the existing routine for interfacing requirements. If no USEFLU routine

is provided, the equal time cross-correlation matrix for all selected atoms

will be computed.

For this command, a selection of modes may be made (default all),

a selection of atoms may be made (default all), and a magnitude

specification may be made. For this application, a temperature factor

is usually used.

The QUANtum keyword may be used if a quantum scaling factor

is desired. For this option, higher frequency modes would have a diminished

amplitude for a given temperature.

The VERBose option causes the contribution for each selected

atom with each selected mode to be printed. This is useful when a power

spectrum is to be computed or prepared for plotting.

Computing fluctuations from normal modes

The fluctuation command computes atom, internal coordinate, or

user specified fluctuations from normal modes. For atom fluctuations,

the magnitude of the components for the overall fluctuation is stored in

the comparison coordinate arrays. In addition, information giving the

contribution of each mode is printed. For the IC (internal coordinate) option,

the overall fluctuations are stored in the IC table. the "IC WRITE..."

command may be used to save this data.

FLUCtuations { ATOM [atom-selection] } [mode-spec] [magnitude-spec]

{ IC } [QUANtum] [VERBose]

{ USER [atom-selection] }

For the user specified option, the user may supply the subroutine

USEFLU which is call once for initialization (IMODE=0), once for each mode

(IMODE=n), and once for termination (IMODE=-1). In preparing this routine,

see the existing routine for interfacing requirements. If no USEFLU routine

is provided, the equal time cross-correlation matrix for all selected atoms

will be computed.

For this command, a selection of modes may be made (default all),

a selection of atoms may be made (default all), and a magnitude

specification may be made. For this application, a temperature factor

is usually used.

The QUANtum keyword may be used if a quantum scaling factor

is desired. For this option, higher frequency modes would have a diminished

amplitude for a given temperature.

The VERBose option causes the contribution for each selected

atom with each selected mode to be printed. This is useful when a power

spectrum is to be computed or prepared for plotting.

Top

Calculation of anisotropic (and isotropic) fluctuations

from Normal Modes

The PAFL command sums over the current set of normal modes (default)

or some subset of this (given by the [mode-spec]) to create a fluctuation

matrix. The three-by-three fluctuation matrix for each atom may be

diagonalized (default) to produce the principal axis flucutions

given in terms of three mutually perpendicular unit principle axes. In

general, there will be a different set of principle axes for each atomic

center. Alternatively, the COORdinate option may be used, in which case

the fluctuation matricies are not diagonalized. Instead, the fluctuations

are given in term of the coordinate axes in which the normal modes were

calculated. Since the size of the fluctuations are temperature-dependent,

a [magnitude-spec] in terms of temperature (such as TEMP 300.0) should

be given.

PAFLuctuations { ATOM } [atom-selection] [mode-spec] [magnitude-spec]

{ GROUP [MASS] } [QUANtum] [VERBose] [COORdinate] [SAVE]

{ USER } [CONTinue]

The summation over modes which creates the fluctuation matrix may

be controlled in a number of ways. The easiest of these is to

specify a TFREquency. Normal modes of frequency

lower than TFREquency are simply ignored in the summation. By setting

TFREquency above the rotation-translation modes, but below the lowest

vibrational mode, one achieves what is the desired result (the fluctuations

due to internal modes of vibration) for most applications. For applications

requiring more specificty (such as calculating the fluctuations due to

modes 8,9,10,13,14, and 15 only) one may use a more detailed [mode-spec]

to select the desired modes over which the summation is to be performed).

The second way of controling the summation is necessary when

the normal modes for the desired system can not all be read into CHARMM

at one time due to space allocation limitations. In this case one uses

the SAVE and CONTinue options. SAVE tells the routine that you don't

want to manipulate the fluctuation matrix once it is created. CONTinue

indicates that you don't want to reset (zero) the fluctuation matrix

before the present summation. Therefore, if the normal modes are

stored on, let us say, four files, one reads in the first normal

mode file and gives the PAFL SAVE command. One then reads in the

second normal mode file (without the APPEnd option) and gives the

PAFL SAVE CONTinue command. One then reads in the third normal

mode file (without APPEnd) and gives the PAFL SAVE CONTinue command.

Finally, one reads in the fourth normal mode file (without APPEnd)

and gives the PAFL CONTinue command. Each of these four PAFL commands

should have the same options (such as GROUP, ATOM, USER; same TEMP;

same atom selection, MASS or not). Moreover, there should be no overlap

between modes in each of the four sets. If the four (or any n) files

have overlapping modes, then a selection must be made so that

no mode is counted twice in the summation (see the test case).

For the user specified option, the user may supply the subroutine

USPAFL which is call once for initialization (IMODE=0), once for each mode

(IMODE=n), and once for termination (IMODE=-1). In preparing this routine,

see the existing routine (and also USEFLU) for interfacing requirements.

The PAFL command is quite similar to the FLUCtuations command.

VERBose prints out lots of stuff and QUANtum uses quantum scaling in

calculating the contribution of each mode to the fluctuations.

When ATOM is specified, the fluctuations are calculated individually

for each atom currently selected. The fluctuations are given in angstroms,

and so mass-weighting would make no sense. When GROUp is specified, the

fluctuations for the movement of all specified atoms moving as a group are

calculated. When MASS is also specified, the fluctuation of the

center of gravity of that group of atoms is calculated. Otherwise, it is

the fluctuation of the center of geometry which is calculated. At present

USPAFL does nothing, and one would need to read the code to be able

to interface this routine properly with the surrounding code.

Calculation of anisotropic (and isotropic) fluctuations

from Normal Modes

The PAFL command sums over the current set of normal modes (default)

or some subset of this (given by the [mode-spec]) to create a fluctuation

matrix. The three-by-three fluctuation matrix for each atom may be

diagonalized (default) to produce the principal axis flucutions

given in terms of three mutually perpendicular unit principle axes. In

general, there will be a different set of principle axes for each atomic

center. Alternatively, the COORdinate option may be used, in which case

the fluctuation matricies are not diagonalized. Instead, the fluctuations

are given in term of the coordinate axes in which the normal modes were

calculated. Since the size of the fluctuations are temperature-dependent,

a [magnitude-spec] in terms of temperature (such as TEMP 300.0) should

be given.

PAFLuctuations { ATOM } [atom-selection] [mode-spec] [magnitude-spec]

{ GROUP [MASS] } [QUANtum] [VERBose] [COORdinate] [SAVE]

{ USER } [CONTinue]

The summation over modes which creates the fluctuation matrix may

be controlled in a number of ways. The easiest of these is to

specify a TFREquency. Normal modes of frequency

lower than TFREquency are simply ignored in the summation. By setting

TFREquency above the rotation-translation modes, but below the lowest

vibrational mode, one achieves what is the desired result (the fluctuations

due to internal modes of vibration) for most applications. For applications

requiring more specificty (such as calculating the fluctuations due to

modes 8,9,10,13,14, and 15 only) one may use a more detailed [mode-spec]

to select the desired modes over which the summation is to be performed).

The second way of controling the summation is necessary when

the normal modes for the desired system can not all be read into CHARMM

at one time due to space allocation limitations. In this case one uses

the SAVE and CONTinue options. SAVE tells the routine that you don't

want to manipulate the fluctuation matrix once it is created. CONTinue

indicates that you don't want to reset (zero) the fluctuation matrix

before the present summation. Therefore, if the normal modes are

stored on, let us say, four files, one reads in the first normal

mode file and gives the PAFL SAVE command. One then reads in the

second normal mode file (without the APPEnd option) and gives the

PAFL SAVE CONTinue command. One then reads in the third normal

mode file (without APPEnd) and gives the PAFL SAVE CONTinue command.

Finally, one reads in the fourth normal mode file (without APPEnd)

and gives the PAFL CONTinue command. Each of these four PAFL commands

should have the same options (such as GROUP, ATOM, USER; same TEMP;

same atom selection, MASS or not). Moreover, there should be no overlap

between modes in each of the four sets. If the four (or any n) files

have overlapping modes, then a selection must be made so that

no mode is counted twice in the summation (see the test case).

For the user specified option, the user may supply the subroutine

USPAFL which is call once for initialization (IMODE=0), once for each mode

(IMODE=n), and once for termination (IMODE=-1). In preparing this routine,

see the existing routine (and also USEFLU) for interfacing requirements.

The PAFL command is quite similar to the FLUCtuations command.

VERBose prints out lots of stuff and QUANtum uses quantum scaling in

calculating the contribution of each mode to the fluctuations.

When ATOM is specified, the fluctuations are calculated individually

for each atom currently selected. The fluctuations are given in angstroms,

and so mass-weighting would make no sense. When GROUp is specified, the

fluctuations for the movement of all specified atoms moving as a group are

calculated. When MASS is also specified, the fluctuation of the

center of gravity of that group of atoms is calculated. Otherwise, it is

the fluctuation of the center of geometry which is calculated. At present

USPAFL does nothing, and one would need to read the code to be able

to interface this routine properly with the surrounding code.

Top

Projection of normal modes onto vectors of interest

The PROJect command will project the selected modes onto one

of the definable vectors, or onto each step of a trajectory (using the

TRAJectory keyword).

PROJect { mode-definition [mode-spec] [magnitude-spec] }

{ TRAJectory [NUNIts integer] FIRStunit integer [NSKIp integer]

[BEGIn integer] [STOP integer] [mode-spec] [NOMAss]

[WRITe WUNIt integer coord-spec [SPIRal]] }

The information displayed is;

MODE integer - mode number

FREQUENCY - frequency of this mode (cm-1)

NORMAL DOTPR - actual dotproduct of normalized vectors

PROJECTION - ratio of guess vector projection to step length

APPROX DEL E - estimate of energy increase along this mode

TYPE - type of step (FACT, RMS, KCAL, TEMP)

STEP - step length for this step type

The NONOrm keyword may be used to prevent normalization of modes or structures

before projection.

The TRAJectory keyword can be used to project structures of a trajectory

(specified using the NUNIts, FIRStunit and NSKIp keywords) onto every stored

modes, or a subset specified with the mode-spec.

NOTE: The comparison set is substacted from each trajectory structure before dot

product calculation on the mode.

It is possible to write the projection of up to four modes in a

coordinate file using the WRITe keyword, for visualization with a third party

computer graphics program (e.g. VMD). Projections are written in the unit

specified by WUNIt and formatted using the coord-spec definition. For each step,

projections of the structure onto the modes are written as the coordinates of a

dummy atom. The "beta" or wmain column can be used to store the projection on

the fourth mode. The four modes with the highest eigenvalues are used for

projection (highest: X, 2nd highest: Y, 3rd highest: Z, 4th highest: beta/wmai).

Note that the sign of the projection is arbitrary for that of the mode is also

arbitrary.

The SPIRal keyword can be used to write coordinates respresenting a spiral in

which each atoms is distant from its sequential neighbours by less than 1.62 A

and is more than 2 A away from any other. The projections are written after.

This is to prompt molecular graphics program to render bonds between consecutive

dummy atoms creating a continuous line along the trajectory.

coord-spec ::= { FILE }

{ CARD }

{ PDB [OFFIcial] }

Projection of normal modes onto vectors of interest

The PROJect command will project the selected modes onto one

of the definable vectors, or onto each step of a trajectory (using the

TRAJectory keyword).

PROJect { mode-definition [mode-spec] [magnitude-spec] }

{ TRAJectory [NUNIts integer] FIRStunit integer [NSKIp integer]

[BEGIn integer] [STOP integer] [mode-spec] [NOMAss]

[WRITe WUNIt integer coord-spec [SPIRal]] }

The information displayed is;

MODE integer - mode number

FREQUENCY - frequency of this mode (cm-1)

NORMAL DOTPR - actual dotproduct of normalized vectors

PROJECTION - ratio of guess vector projection to step length

APPROX DEL E - estimate of energy increase along this mode

TYPE - type of step (FACT, RMS, KCAL, TEMP)

STEP - step length for this step type

The NONOrm keyword may be used to prevent normalization of modes or structures

before projection.

The TRAJectory keyword can be used to project structures of a trajectory

(specified using the NUNIts, FIRStunit and NSKIp keywords) onto every stored

modes, or a subset specified with the mode-spec.

NOTE: The comparison set is substacted from each trajectory structure before dot

product calculation on the mode.

It is possible to write the projection of up to four modes in a

coordinate file using the WRITe keyword, for visualization with a third party

computer graphics program (e.g. VMD). Projections are written in the unit

specified by WUNIt and formatted using the coord-spec definition. For each step,

projections of the structure onto the modes are written as the coordinates of a

dummy atom. The "beta" or wmain column can be used to store the projection on

the fourth mode. The four modes with the highest eigenvalues are used for

projection (highest: X, 2nd highest: Y, 3rd highest: Z, 4th highest: beta/wmai).

Note that the sign of the projection is arbitrary for that of the mode is also

arbitrary.

The SPIRal keyword can be used to write coordinates respresenting a spiral in

which each atoms is distant from its sequential neighbours by less than 1.62 A

and is more than 2 A away from any other. The projections are written after.

This is to prompt molecular graphics program to render bonds between consecutive

dummy atoms creating a continuous line along the trajectory.

coord-spec ::= { FILE }

{ CARD }

{ PDB [OFFIcial] }

Top

Optimize normal modes with a Newton-Raphson step

The OPTImize command will perform a one-step Newton-Raphson minimization on the selected modes.

OPTImize { mode-definition [mode-spec] [magnitude-spec] }

{[BEGIn integer] [STOP integer] [mode-spec] [ENERgy]

[PARAmeters] [CMPN] [TMPR real] [IUNO integer]}

The ENERgy keyword can be used to calculate the enthalpy change and vibrational entropy of the mode. For CBND and CANG mode types for constrained bonds and angles, also the change of the Jacobian contribution associated with the displacement is determined. This is useful for determining the the free energy costs of constraints. If the PARAmeter keyword is specified, OPTI will use Hessians derived from the force field parameters for the CBND and CANG modes instead of the eigenvalues. The CMPN command will use the coordinates in the comparison set. TMPR can be used to specify the temperature for the vibrational entropy. IUNOspecifies the unit to write the energy output of OPTI to (e.g., when analyzing trajectories).

The output contains -DG_CONS (the energy of releasing the constraint), ENERGY CHANGE (the energy difference to the energy minimum), VIBR. ENTROPY (the vibrational entropy of the mode) and JACOBIAN (the Jacobian free energy contribution associated with the displacement of the bond or angle).

Examples:

RAYLEIGH SAVE

OPTImize FORCE FACT 1.0

Uses the RAYLEIGH command to compute the Hessians and then employs the forces from the force array to perform a Newton Raphson minimization step for all nodes.

edit incl cbnd 1 A2 1 A1 orth

edit incl cbnd 1 A3 1 A4 orth

edit incl cang 1 a2 1 a3 1 a4 orth

edit incl cang 1 a3 1 a2 1 a1 orth

OPTImize FORCE FACT 1.0 ENERGY PARA

Defines two constrained bonds and two constrained angles and uses the forces in the force array together with Hessians derived from the force field parameters to approximate the free energy change of releasing the constraints.

Optimize normal modes with a Newton-Raphson step

The OPTImize command will perform a one-step Newton-Raphson minimization on the selected modes.

OPTImize { mode-definition [mode-spec] [magnitude-spec] }

{[BEGIn integer] [STOP integer] [mode-spec] [ENERgy]

[PARAmeters] [CMPN] [TMPR real] [IUNO integer]}

The ENERgy keyword can be used to calculate the enthalpy change and vibrational entropy of the mode. For CBND and CANG mode types for constrained bonds and angles, also the change of the Jacobian contribution associated with the displacement is determined. This is useful for determining the the free energy costs of constraints. If the PARAmeter keyword is specified, OPTI will use Hessians derived from the force field parameters for the CBND and CANG modes instead of the eigenvalues. The CMPN command will use the coordinates in the comparison set. TMPR can be used to specify the temperature for the vibrational entropy. IUNOspecifies the unit to write the energy output of OPTI to (e.g., when analyzing trajectories).

The output contains -DG_CONS (the energy of releasing the constraint), ENERGY CHANGE (the energy difference to the energy minimum), VIBR. ENTROPY (the vibrational entropy of the mode) and JACOBIAN (the Jacobian free energy contribution associated with the displacement of the bond or angle).

Examples:

RAYLEIGH SAVE

OPTImize FORCE FACT 1.0

Uses the RAYLEIGH command to compute the Hessians and then employs the forces from the force array to perform a Newton Raphson minimization step for all nodes.

edit incl cbnd 1 A2 1 A1 orth

edit incl cbnd 1 A3 1 A4 orth

edit incl cang 1 a2 1 a3 1 a4 orth

edit incl cang 1 a3 1 a2 1 a1 orth

OPTImize FORCE FACT 1.0 ENERGY PARA

Defines two constrained bonds and two constrained angles and uses the forces in the force array together with Hessians derived from the force field parameters to approximate the free energy change of releasing the constraints.

Top

Several commands use a mode_definition, which allows the

specification of a vector. There is a wide variety of possible vectors

which may be specified, and there is also a user supplied routine, USERNM,

which may be used to get any other desired motion (vector). These vectors

may be used for the analysis of normal modes, or as additions to the

basis of vectors (EDIT INCLude) for further analysis.

mode-definition ::=

{ { TRAN } { X } } [NONOrm] [NOTR]

{ { ROTA } { Y } }

{ { Z } }

{ }

{ SPHEre { X } [IX int] }

{ { Y } [IY int] }

{ { Z } [IZ int] }

{ { R } [IR int] }

{ { TX } }

{ { TY } }

{ { TZ } }

{ }

{ COMP }

{ DIFF }

{ FORC }

{ USER integer }

{ BOND atom atom }

{ ANGL atom atom atom }

{ DIHE atom atom atom atom }

{ CBND atom atom }

{ CANG atom atom atom }

atom::= residue-number atom-name

The NONOrm keyword supresses the automatic normalization of

the specified vector. This is desired for some applications, but is

not normally needed.

The NOTR keyword removes any new translation/rotation from the

specified mode. This may be needed when only internal motions are to

be analysed.

The vectors which may be defined are;

TRAN X - Translation along the X-axis

TRAN Y - Translation along the Y-axis

TRAN Z - Translation along the Z-axis

ROTA X - Rotation along the X-axis

ROTA Y - Rotation along the Y-axis

ROTA Z - Rotation along the Z-axis

COMP - Use the comparison coordinates (as a vector)

DIFF - Use the difference between the MAIN and COMP coordinates

FORC - Use the forces from the last energy evaluation

USER integer - Use a user specified vector (defined in USERNM)

BOND atom atom - Use vector which stretches the specified bond

ANGL 3X(atom) - Use vector which bends the specified angle

DIHE 4X(atom) - Use vector which twists the specified dihedral

SPHEre ... - Appropriate homogeneous motion (spherical harmonics)

CBND atom atom - Use vector which stretches the specified constrained bond

CANG 3X(atom) - Use vector which bends the specified constrained angle

For the TRANslate, ROTAte, COMP, DIFF, and FORCe options, an

atom selection may be specified. Any nonspecified atoms will have a zero

values in the vector.

For the BOND, ANGLe, and DIHEdral options, the atoms specified

don't have to be bonded together or have any special connectivity, but

the first atom specified must not close back through a loop to the last

atom specified. If this is a problem, then one of the bonds in the loop

must be deleted for this calculation to work properly.

For angle terms, the first two atoms specified (and anything

they are connected to) move as one unit, and the third atom and anything

its connected to will move as a second unit.

For dihedrals, the first 2 atoms specified define one block, and

the last 2 atoms defines the second block. The axis of rotation is about

the middle 2 atoms. For example if one specifies

PROJECT DIHE 1 N 1 CA 1 CB 1 CG1

for an isoleucine residue, the atom 1 CG2 will also rotate with CG1 because

it is connected to the third atom (CB) which is part of the second unit.

Several commands use a mode_definition, which allows the

specification of a vector. There is a wide variety of possible vectors

which may be specified, and there is also a user supplied routine, USERNM,

which may be used to get any other desired motion (vector). These vectors

may be used for the analysis of normal modes, or as additions to the

basis of vectors (EDIT INCLude) for further analysis.

mode-definition ::=

{ { TRAN } { X } } [NONOrm] [NOTR]

{ { ROTA } { Y } }

{ { Z } }

{ }

{ SPHEre { X } [IX int] }

{ { Y } [IY int] }

{ { Z } [IZ int] }

{ { R } [IR int] }

{ { TX } }

{ { TY } }

{ { TZ } }

{ }

{ COMP }

{ DIFF }

{ FORC }

{ USER integer }

{ BOND atom atom }

{ ANGL atom atom atom }

{ DIHE atom atom atom atom }

{ CBND atom atom }

{ CANG atom atom atom }

atom::= residue-number atom-name

The NONOrm keyword supresses the automatic normalization of

the specified vector. This is desired for some applications, but is

not normally needed.

The NOTR keyword removes any new translation/rotation from the

specified mode. This may be needed when only internal motions are to

be analysed.

The vectors which may be defined are;

TRAN X - Translation along the X-axis

TRAN Y - Translation along the Y-axis

TRAN Z - Translation along the Z-axis

ROTA X - Rotation along the X-axis

ROTA Y - Rotation along the Y-axis

ROTA Z - Rotation along the Z-axis

COMP - Use the comparison coordinates (as a vector)

DIFF - Use the difference between the MAIN and COMP coordinates

FORC - Use the forces from the last energy evaluation

USER integer - Use a user specified vector (defined in USERNM)

BOND atom atom - Use vector which stretches the specified bond

ANGL 3X(atom) - Use vector which bends the specified angle

DIHE 4X(atom) - Use vector which twists the specified dihedral

SPHEre ... - Appropriate homogeneous motion (spherical harmonics)

CBND atom atom - Use vector which stretches the specified constrained bond

CANG 3X(atom) - Use vector which bends the specified constrained angle

For the TRANslate, ROTAte, COMP, DIFF, and FORCe options, an

atom selection may be specified. Any nonspecified atoms will have a zero

values in the vector.

For the BOND, ANGLe, and DIHEdral options, the atoms specified

don't have to be bonded together or have any special connectivity, but

the first atom specified must not close back through a loop to the last

atom specified. If this is a problem, then one of the bonds in the loop

must be deleted for this calculation to work properly.

For angle terms, the first two atoms specified (and anything

they are connected to) move as one unit, and the third atom and anything

its connected to will move as a second unit.

For dihedrals, the first 2 atoms specified define one block, and

the last 2 atoms defines the second block. The axis of rotation is about

the middle 2 atoms. For example if one specifies

PROJECT DIHE 1 N 1 CA 1 CB 1 CG1

for an isoleucine residue, the atom 1 CG2 will also rotate with CG1 because

it is connected to the third atom (CB) which is part of the second unit.

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Rayleigh Quotients

The RAYLeigh command will compute the second derivative matrix,

and project all selected modes onto the second derivative matrix after

mass weighting. If the modes are eigenvectors, then the resulting quotients

will correspond to the eigenvalues. The quotient values are given by;

-1/2 -1/2

Q = < v | M H M | v >

RAYLeigh [mode-spec] [SAVE]

If the SAVE keyword is given, then the quotients and corresponding

frequencies are saved and become part of the data for the selected modes.

For example, a subsequent PRINT NORM command would then use these new values

in place of the original frequencies.

Rayleigh Quotients

The RAYLeigh command will compute the second derivative matrix,

and project all selected modes onto the second derivative matrix after

mass weighting. If the modes are eigenvectors, then the resulting quotients

will correspond to the eigenvalues. The quotient values are given by;

-1/2 -1/2

Q = < v | M H M | v >

RAYLeigh [mode-spec] [SAVE]

If the SAVE keyword is given, then the quotients and corresponding

frequencies are saved and become part of the data for the selected modes.

For example, a subsequent PRINT NORM command would then use these new values

in place of the original frequencies.

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Potential Energy Distribution

This command is designed to work with one mode at a time.

For a given magnitude specification, it computes the expectation

value for the energy contribution change for each internal coordinate

term (bond, angle, dihedral, and improper dihedral) and prints that

term if the fluctuation is greated than the tolerence (default TOL 0.0001).

PED [mode-spec] [magnitude-spec] [TOL real]

For this method, it assumes that the structure is at a stationary

point and that the potential is quadratic. In addition to printing out

the individual energy terms, it also prints out the total for each class

(bonds, angles...). These values can be used to determine the type of any

given mode.

Potential Energy Distribution

This command is designed to work with one mode at a time.

For a given magnitude specification, it computes the expectation

value for the energy contribution change for each internal coordinate

term (bond, angle, dihedral, and improper dihedral) and prints that

term if the fluctuation is greated than the tolerence (default TOL 0.0001).

PED [mode-spec] [magnitude-spec] [TOL real]

For this method, it assumes that the structure is at a stationary

point and that the potential is quadratic. In addition to printing out

the individual energy terms, it also prints out the total for each class

(bonds, angles...). These values can be used to determine the type of any

given mode.

Top

Editing the set of normal modes

There are several commands that can modify the normal mode

vector space. In addition to the obvious ones such as READ NORMal-modes

and DIAGonalize, there is also an EDIT command which can be used to

modify the normal mode data structure.

EDIT { INCL mode-definition [ORTHog] [TO mode] } [atom-selection]

{ REMOve [mode-spec] mode-definition [NONOrm] }

{ DELEte [mode-spec] }

{ ORTHogonalize [PURGe] [mode-spec] [TOL real] }

{ SHAKe mode-spec }

{ ZERO mode-spec }

{ MOVE MODE n [TO m] [SCALe real] [NONOrm] }

{ ADD MODE n [TO m] [SCALe real] [NONOrm] }

{ MULT MODE n SCALe real }

{ SET MODE n SCALe real [NONOrm] }

The EDIT DELETE command will delete specified modes from the

date structure.

The EDIT ORTHogonalize command is used to orthogononalize

and optionally normalize a particular subset of normal modes.

Additional modes can be added with the EDIT INCLude command.

This command will add on the defined mode to the end of the normal mode

vector, unless the destination is specified with TO n in which case it will

be placed as mode number n.

The translation and rotation options are important when setting

up guess vectors for the iterative diagonalization program, or when

individual coreolis coupling terms are needed. Single additional modes may

be added with the EDIT INCLude DIFF or the EDIT INCLude FORCe or the

EDIT INCLude USER or the EDIT INCL COMP commands. For the DIFF option,

the difference between the comparison and main coordinate sets will

be appended, for the FORCe option, the current values in the force

arrays (from the last energy evaluation) will be appended. The COMP

option will use the comparison coordinates as the appended mode. This

is option is intended for use in the case that the comparison coordinate

set is filled with displacements. There is also the ability to specify

a user vector. This is done by the inclusion of the subroutine USERNM

in your USERSB and using the USERLINK facility. For all of the EDIT

INCLude options, the defaults are to root mass weight, normalize, and

orthogonalize to the rest of the vector space. To skip any of these steps,

the NONO, and NOOR keywords must be specified.

See (*note define:Projections.) for a complete list of

definable modes.

The following commands (which all can take an optional atom-selection)

provide a simple means of manipulating, and reshuffling modes.

EDIT ZERO sets the specified modes to zero.

EDIT MOVE MODE n [TO m] [SCALe real] mode(m)=scale*mode(n)

EDIT ADD MODE n [TO m] [SCALe real] mode(m)=mode(m)+scale*mode(n)

EDIT SET MODE n SCALe real mode(n)=scale

EDIT MULT MODE n SCALe real mode(n)=scale*mode(n)

If the destination is not specified then the result will be appended

as a new mode after the existing ones. The default value for the SCALe factor

is 1.0.

Editing the set of normal modes

There are several commands that can modify the normal mode

vector space. In addition to the obvious ones such as READ NORMal-modes

and DIAGonalize, there is also an EDIT command which can be used to

modify the normal mode data structure.

EDIT { INCL mode-definition [ORTHog] [TO mode] } [atom-selection]

{ REMOve [mode-spec] mode-definition [NONOrm] }

{ DELEte [mode-spec] }

{ ORTHogonalize [PURGe] [mode-spec] [TOL real] }

{ SHAKe mode-spec }

{ ZERO mode-spec }

{ MOVE MODE n [TO m] [SCALe real] [NONOrm] }

{ ADD MODE n [TO m] [SCALe real] [NONOrm] }

{ MULT MODE n SCALe real }

{ SET MODE n SCALe real [NONOrm] }

The EDIT DELETE command will delete specified modes from the

date structure.

The EDIT ORTHogonalize command is used to orthogononalize

and optionally normalize a particular subset of normal modes.

Additional modes can be added with the EDIT INCLude command.

This command will add on the defined mode to the end of the normal mode

vector, unless the destination is specified with TO n in which case it will

be placed as mode number n.

The translation and rotation options are important when setting

up guess vectors for the iterative diagonalization program, or when

individual coreolis coupling terms are needed. Single additional modes may

be added with the EDIT INCLude DIFF or the EDIT INCLude FORCe or the

EDIT INCLude USER or the EDIT INCL COMP commands. For the DIFF option,

the difference between the comparison and main coordinate sets will

be appended, for the FORCe option, the current values in the force

arrays (from the last energy evaluation) will be appended. The COMP

option will use the comparison coordinates as the appended mode. This

is option is intended for use in the case that the comparison coordinate

set is filled with displacements. There is also the ability to specify

a user vector. This is done by the inclusion of the subroutine USERNM

in your USERSB and using the USERLINK facility. For all of the EDIT

INCLude options, the defaults are to root mass weight, normalize, and

orthogonalize to the rest of the vector space. To skip any of these steps,

the NONO, and NOOR keywords must be specified.

See (*note define:Projections.) for a complete list of

definable modes.

The following commands (which all can take an optional atom-selection)

provide a simple means of manipulating, and reshuffling modes.

EDIT ZERO sets the specified modes to zero.

EDIT MOVE MODE n [TO m] [SCALe real] mode(m)=scale*mode(n)

EDIT ADD MODE n [TO m] [SCALe real] mode(m)=mode(m)+scale*mode(n)

EDIT SET MODE n SCALe real mode(n)=scale

EDIT MULT MODE n SCALe real mode(n)=scale*mode(n)

If the destination is not specified then the result will be appended

as a new mode after the existing ones. The default value for the SCALe factor

is 1.0.

Top

Generate entire basis sets

The BASIs command will append requested basis vectors to an

existing (or null) set of orthonormal vectors. In this way, basis sets

for reduced diagonalizations, constrained normal modes, or other

calculations may be generated in a simple manner.

BASIS { IC { FIRSt BOND } } [NOORthonorm]

{ { FIRSt ANGLe } }

{ { DIHEdral } }

{ { SECOnd ANGLe } }

{ { SECOnd BOND } }

{ }

{ TR atom-selection [BALAnce] }

The BASIS command is similar to the EDIT INCLude ORTHog command,

except that many new vectors may be added. There are two modes for this

command. The IC mode will include a set of vectors based on the IC table.

The selection of which section of the table to use is required. The choices

are;

FIRSt BOND

FIRSt ANGLE

DIHEdral

SECOnd ANGLe

SECOnd BOND

All valid IC table entries (i.e. all atoms of specified set defined) will

result in the addition of one vector to the normal mode basis, provided that

this vector is not a linear combination of existing vectors. See the

description for IC mode specification (*note define:Projections.) for a

description of these vectors.

The second mode is the TR (translation/rotation) mode which will

usually add the 6 translation rotation degrees of freedom for the selected

set of atoms. If the selected set of atoms is linear, then only 5 vectors

will be added. If only one atom is selected, then just the 3 translation

vectors are added (for this case all numvers but one will contain a zero).

The BALAnce keyword is suggested, and its operation it to remove the

net (whole system) rotation/translation components from the added vectors.

If all atoms are selected, the BALAnce keyword will result in NO vectors

being added.

The purpose of this command is to facilitate setting a vector

basis for a reduced normal mode calculation. Another purpose is in setting

up translation/rotation modes as initial vectors for the iterative

diagonalization procedure (no BALAnce option).

This command does normalize the new basis vectors, but it will not

modify any existing vectors. Each added vector is then orthogonalized

from all exisiting vectors (unless the NOORthonormalize keyword is specified).

If the vector has a zero norm following orthogonalization, it is rejected.

This avoids any possibility of basis interdependancies (zero determinant).

The norm after orthogonalization is saved in the eigenvalue array.

Each added vector is then normalized to form an orthonormal basis.

NOTE: this method will not work unless all exisiting vectors form an

orthonormal subbasis (i.e. before the BASIS command is invoked, the PRINT

NORM DOTProducts should give the unit matrix). The EDIT ORTHog command may

be used to orthonormalize a set of vectors.

The user is expected to process these modes with the REDUce command

after saving them, or in an external program.

Generate entire basis sets

The BASIs command will append requested basis vectors to an

existing (or null) set of orthonormal vectors. In this way, basis sets

for reduced diagonalizations, constrained normal modes, or other

calculations may be generated in a simple manner.

BASIS { IC { FIRSt BOND } } [NOORthonorm]

{ { FIRSt ANGLe } }

{ { DIHEdral } }

{ { SECOnd ANGLe } }

{ { SECOnd BOND } }

{ }

{ TR atom-selection [BALAnce] }

The BASIS command is similar to the EDIT INCLude ORTHog command,

except that many new vectors may be added. There are two modes for this

command. The IC mode will include a set of vectors based on the IC table.

The selection of which section of the table to use is required. The choices

are;

FIRSt BOND

FIRSt ANGLE

DIHEdral

SECOnd ANGLe

SECOnd BOND

All valid IC table entries (i.e. all atoms of specified set defined) will

result in the addition of one vector to the normal mode basis, provided that

this vector is not a linear combination of existing vectors. See the

description for IC mode specification (*note define:Projections.) for a

description of these vectors.

The second mode is the TR (translation/rotation) mode which will

usually add the 6 translation rotation degrees of freedom for the selected

set of atoms. If the selected set of atoms is linear, then only 5 vectors

will be added. If only one atom is selected, then just the 3 translation

vectors are added (for this case all numvers but one will contain a zero).

The BALAnce keyword is suggested, and its operation it to remove the

net (whole system) rotation/translation components from the added vectors.

If all atoms are selected, the BALAnce keyword will result in NO vectors

being added.

The purpose of this command is to facilitate setting a vector

basis for a reduced normal mode calculation. Another purpose is in setting

up translation/rotation modes as initial vectors for the iterative

diagonalization procedure (no BALAnce option).

This command does normalize the new basis vectors, but it will not

modify any existing vectors. Each added vector is then orthogonalized

from all exisiting vectors (unless the NOORthonormalize keyword is specified).

If the vector has a zero norm following orthogonalization, it is rejected.

This avoids any possibility of basis interdependancies (zero determinant).

The norm after orthogonalization is saved in the eigenvalue array.

Each added vector is then normalized to form an orthonormal basis.

NOTE: this method will not work unless all exisiting vectors form an

orthonormal subbasis (i.e. before the BASIS command is invoked, the PRINT

NORM DOTProducts should give the unit matrix). The EDIT ORTHog command may

be used to orthonormalize a set of vectors.

The user is expected to process these modes with the REDUce command

after saving them, or in an external program.

Top

The Fill command

The comparison coordinates can be modified with the FILL DIFF

command. This command will copy the main coordinate set to the comparison

set, and then step along the specified mode by the specified magnitude.

When the append (APPE keyword) is used, the main coordinates are not first

copied.

FILL { DIFF } [mode-spec] [magnitude-spec] [APPE]

{ COMP }

The FILL COMP command will fill the comparison coordinate

displacement arrays with the specified vector. For this option,

the comparison coordinate are zeroed before the displacement is added.

The coordinates will then contain a displacement vector. The append option

will prevent the zeroing of these arrays before stepping along the mode.

The Fill command

The comparison coordinates can be modified with the FILL DIFF

command. This command will copy the main coordinate set to the comparison

set, and then step along the specified mode by the specified magnitude.

When the append (APPE keyword) is used, the main coordinates are not first

copied.

FILL { DIFF } [mode-spec] [magnitude-spec] [APPE]

{ COMP }

The FILL COMP command will fill the comparison coordinate

displacement arrays with the specified vector. For this option,

the comparison coordinate are zeroed before the displacement is added.

The coordinates will then contain a displacement vector. The append option

will prevent the zeroing of these arrays before stepping along the mode.

Top

Second Derivatives

The second derivatives are computed during energy

determination and they are stored in temporary arrays that are

allocated dynamically. Once obtained, they can be written out, or

diagonalized internally.

If 'QSECD=.TRUE.' the second derivatives of the energy

are returned in the array DD1. This array contains the

full upper half of the second derivative matrix, and

contains (NAT3*(NAT3+1)/2) REAL*8 elements (NAT3 = 3 * number

of atoms). Memory storage for the DD1 array may cause

memory overflows, especially for large systems.

If one wants to get the normal modes for large structures,

it is often advantageous to use the DIMB or REDU CMPAct option.

These options will fill a DD1CMP second derivative array with only

the non-zero elements. The size of this array depends heavily

on the non-bonded cutoff distance, since increasing that

distance increases the number of non-zero elements. At this

moment, the DD1CMP array will allow the average number of

interactions per atom to be as high as 300. This number will

allow non-bonded cutoffs up to 13A without problems, for all-

hydrogen systems.

A comparison between allocated memory space for DD1 versus

the maximum memory space for DD1CMP is given below:

Structure #atoms(explicit H) DD1 (MB) DD1CMP (MB)

Deca-alanine 66 0.2 1.4

BPTI 568 11.6 12.3

Lysozyme 1264 57.6 27.4

Hemoglobin 5600 1,129.2 121.2

Second Derivatives

The second derivatives are computed during energy

determination and they are stored in temporary arrays that are

allocated dynamically. Once obtained, they can be written out, or

diagonalized internally.

If 'QSECD=.TRUE.' the second derivatives of the energy

are returned in the array DD1. This array contains the

full upper half of the second derivative matrix, and

contains (NAT3*(NAT3+1)/2) REAL*8 elements (NAT3 = 3 * number

of atoms). Memory storage for the DD1 array may cause

memory overflows, especially for large systems.

If one wants to get the normal modes for large structures,

it is often advantageous to use the DIMB or REDU CMPAct option.

These options will fill a DD1CMP second derivative array with only

the non-zero elements. The size of this array depends heavily

on the non-bonded cutoff distance, since increasing that

distance increases the number of non-zero elements. At this

moment, the DD1CMP array will allow the average number of

interactions per atom to be as high as 300. This number will

allow non-bonded cutoffs up to 13A without problems, for all-

hydrogen systems.

A comparison between allocated memory space for DD1 versus

the maximum memory space for DD1CMP is given below:

Structure #atoms(explicit H) DD1 (MB) DD1CMP (MB)

Deca-alanine 66 0.2 1.4

BPTI 568 11.6 12.3

Lysozyme 1264 57.6 27.4

Hemoglobin 5600 1,129.2 121.2

Top

Block Normal Mode (BNM) Analysis

The Block normal mode method is based on the original work of

Tama and co-workers. BNM projects the full atomic hessian into a

subspace spanned by the eigenvectors of blocks, which reduces the size

of the eigenvalue problem dramatically. Each block can be defined by

the user in very flexible manners as an amino acid or a secondary

structural element. Currently only the T/R vectors of the blocks are

included as basis vectors, which therefore reduces the eigenvalue

problem from 3Nx3N to 6n*6n; N is the total number of atoms, and n is

the total number of blocks. In the future, it might be of interest

to include other low-frequency eigenvectors of the blocks into the

definition of the subspace, which would be more robust when the blocks

are large in size.

Compared to the original RTB work of Tama et al., the current

implementation has the following improvements:

1. The projected hessian was constructed in a direct manner;

i.e., the full atomic hessian was never stored, which is essential for

large systems.

2. A Lanczos algorithm was adapted for diagonalizing the

projected hessian, which can be very large but sparse for

super-molecular assemblies (e.g., ribosome).

3. BNM calculations can be carried out in parallel mode.

Keywords and options:

BHES {SERL} GENR [TMEM int MEMO int MEMA int]

{PARA} NNOD int

POST FLAG 1

SERL/PARA is the flag for serial or parallel computations.

GENR is the keyword for using one residue per block.

TMEM is the total memory (in MB) available to BNM calculations.

MEMO is the memory (in MB) allocated for other arrays (recommended value

is 20)

MEMA is the memory (in MB) allocated to contruct super blocks.

The most important variable is MEMA.

MEMA (in MegaB) can be estimated by the following expression

(nres is number of residues):

MEMA=6*nres*(6*nres+1)*8/2/10^6

In addition, it also depends on whether the P/ARPACK diagonalizer is

used or not. Without P/ARPACK, the standard diagonalizer in CHARMM

is used, which limits the size of the system that can be studied; only

MEMA is important.

With P/ARPACK, user can set TMEM and MEMA based on the available

resource and size of the system. It is possible to save the projected

matrix on the hard drive (if MEMA>TMEM+MEMO) for diagonalization.

Obviously the P/ARPACK library must be available for compiling the code

if one plans to use P/ARPACK.

For parallel calculations, NNOD needs to be specified,

which gives the number of nodes. The current version has only been

tested with the following copilation option:

./install.com gnu SIZE M mpich

In addition, the keyword "VIBPARA" has to be specified in pref.dat.

During BNM calculations, the following files will be generated

1. projected non-zero hessian matrix elements:hfinal-a-b.dat

where a is the index of nodes, b is the index of files on the ath node.

In these files, the first two columns are the Row and Column indeces of

the projected hessian matrix elements, the third value is the derivative

itself.

2. Normal mode eigenvectors:nmeigv-a-0.dat

where a is the index of normal modes.

These files can be used to perform analysis (e.g., fluctuations) with

other functions of VIBRAN using the POST keyword.

In the serial version, you can use BHES followed by "POST FLAG 1"

directly. In the parallel version, however, POST has to be done

separately.

3. The frequencies are reported in the file freq.out, which lists three

values for each mode: the first one is the eigenvalue itself, the

second one is the frequency that corresponds to the eigenvalue, and the

third one is SCALED frequency (by SCALe). As

discussed in the literature (see below), scaling is necessary because

the block approximation makes the vibrations more rigid; an appropriate

value is 0.5882 when one residue is treated as a block.

Finally, we note that in some systems, metal ions are present. Since a

single ion does not have rotational degrees of freedom, three redundent

vectors with zero eigenvalues are assigned. For example, for a system

with three metal ions, the BNM calculation would generate 15

zero-frequency modes - six of which correspond to the T/R of the entire

molecule, while nine (3*3) are redundent vectors.

References:

F. Tama et al., Proteins: Struct. Funct. Genet. 41: 1-7 (2000)

G. Li and Q. Cui, Biophys. J. 83, 2457-2474 (2002)

Block Normal Mode (BNM) Analysis

The Block normal mode method is based on the original work of

Tama and co-workers. BNM projects the full atomic hessian into a

subspace spanned by the eigenvectors of blocks, which reduces the size

of the eigenvalue problem dramatically. Each block can be defined by

the user in very flexible manners as an amino acid or a secondary

structural element. Currently only the T/R vectors of the blocks are

included as basis vectors, which therefore reduces the eigenvalue

problem from 3Nx3N to 6n*6n; N is the total number of atoms, and n is

the total number of blocks. In the future, it might be of interest

to include other low-frequency eigenvectors of the blocks into the

definition of the subspace, which would be more robust when the blocks

are large in size.

Compared to the original RTB work of Tama et al., the current

implementation has the following improvements:

1. The projected hessian was constructed in a direct manner;

i.e., the full atomic hessian was never stored, which is essential for

large systems.

2. A Lanczos algorithm was adapted for diagonalizing the

projected hessian, which can be very large but sparse for

super-molecular assemblies (e.g., ribosome).

3. BNM calculations can be carried out in parallel mode.

Keywords and options:

BHES {SERL} GENR [TMEM int MEMO int MEMA int]

{PARA} NNOD int

POST FLAG 1

SERL/PARA is the flag for serial or parallel computations.

GENR is the keyword for using one residue per block.

TMEM is the total memory (in MB) available to BNM calculations.

MEMO is the memory (in MB) allocated for other arrays (recommended value

is 20)

MEMA is the memory (in MB) allocated to contruct super blocks.

The most important variable is MEMA.

MEMA (in MegaB) can be estimated by the following expression

(nres is number of residues):

MEMA=6*nres*(6*nres+1)*8/2/10^6

In addition, it also depends on whether the P/ARPACK diagonalizer is

used or not. Without P/ARPACK, the standard diagonalizer in CHARMM

is used, which limits the size of the system that can be studied; only

MEMA is important.

With P/ARPACK, user can set TMEM and MEMA based on the available

resource and size of the system. It is possible to save the projected

matrix on the hard drive (if MEMA>TMEM+MEMO) for diagonalization.

Obviously the P/ARPACK library must be available for compiling the code

if one plans to use P/ARPACK.

For parallel calculations, NNOD needs to be specified,

which gives the number of nodes. The current version has only been

tested with the following copilation option:

./install.com gnu SIZE M mpich

In addition, the keyword "VIBPARA" has to be specified in pref.dat.

During BNM calculations, the following files will be generated

1. projected non-zero hessian matrix elements:hfinal-a-b.dat

where a is the index of nodes, b is the index of files on the ath node.

In these files, the first two columns are the Row and Column indeces of

the projected hessian matrix elements, the third value is the derivative

itself.

2. Normal mode eigenvectors:nmeigv-a-0.dat

where a is the index of normal modes.

These files can be used to perform analysis (e.g., fluctuations) with

other functions of VIBRAN using the POST keyword.

In the serial version, you can use BHES followed by "POST FLAG 1"

directly. In the parallel version, however, POST has to be done

separately.

3. The frequencies are reported in the file freq.out, which lists three

values for each mode: the first one is the eigenvalue itself, the

second one is the frequency that corresponds to the eigenvalue, and the

third one is SCALED frequency (by SCALe). As

discussed in the literature (see below), scaling is necessary because

the block approximation makes the vibrations more rigid; an appropriate

value is 0.5882 when one residue is treated as a block.

Finally, we note that in some systems, metal ions are present. Since a

single ion does not have rotational degrees of freedom, three redundent

vectors with zero eigenvalues are assigned. For example, for a system

with three metal ions, the BNM calculation would generate 15

zero-frequency modes - six of which correspond to the T/R of the entire

molecule, while nine (3*3) are redundent vectors.

References:

F. Tama et al., Proteins: Struct. Funct. Genet. 41: 1-7 (2000)

G. Li and Q. Cui, Biophys. J. 83, 2457-2474 (2002)

Top

MBH - Mobile Block Hessian approach

The Mobile Block Hessian approach is a normal mode analysis tool that

allows to calculate interesting frequencies for partially optimized structures.

The system is split up into groups of atoms (the blocks) and free atoms. The

internal geometry of the blocks does not need to be the equilibrium geometry.

In the vibrational analysis, the blocks move as a whole without changing their

internal geometry. The MBH approach was first discussed in J. Chem. Phys. 126,

224102 (2007) in which also guidelines for the block choice are formulated.

The corresponding MBH mass matrix and Hessian are corrected to account for the

gradients due to the partial optimization. Without these corrections, the

gradients would lead to unphysical imaginary frequencies.

The MBH approach has the advantage that by fixing the internal geometry of the

blocks, the MBH matrix and Hessian have a smaller dimension, which reduces the

computing time and memory requirements for the diagonalization. The total

number of resulting frequencies is 6K + 3n with K the number of blocks and

n the number of free atoms.

Commands for MBH

To initialize the list of blocks, use the command BLKS INIT. With the ADDB

command, blocks can be added by giving an atom selection:

BLKS ADDBlock atom-selection

The ADDB command can be repeated several times to add more then one block.

When all blocks are added, use the keyword MBH to perform the MBH analysis.

Thereafter commands such as PRINT NORM, PRINT DOTP, PRINT MODES, etcetera, can

be used in the same way as for a full Hessian normal mode analysis. The

BLKS INIT command can be reused to clear the information in the block list,

e.g. when one wants to restart over the MBH analysis with a different block

choice.

In the standard version of MBH, the global translational and rotational modes

are still present in the spectrum. These can be removed with the keyword

RAISe, which will bring the translational/rotational frequencies (in principle

these are zero) to an arteficially high value. This amounts to imposing

Eckart constraints on all other modes.

The keywords FINIte and ENTRopy work similarly with MBH as with DIAG (see DIAG).

Example of MBH

BLKS INIT

BLKS ADDB SELE bynumber 1:5 END

BLKS ADDB SELE bynumber 7:9 END

MBH

This input initializes the block list, adds two blocks and then performs

the MBH normal mode analysis.

Limitations of current implementation

At present the code for linear blocks is not implemented yet.

When a block consists of 2 atoms only, a warning will be issued.

An atom can belong to one block at the time only. In the future

the implementation might be extended in order to treat

linked blocks as well.

References

1. A. Ghysels, D. Van Neck, V. Van Speybroeck, T. Verstraelen, M. Waroquier,

J. Chem. Phys. 126, 224102 (2007)

2. A. Ghysels, D. Van Neck, M. Waroquier

J. Chem. Phys. 127, 164108 (2007)

MBH - Mobile Block Hessian approach

The Mobile Block Hessian approach is a normal mode analysis tool that

allows to calculate interesting frequencies for partially optimized structures.

The system is split up into groups of atoms (the blocks) and free atoms. The

internal geometry of the blocks does not need to be the equilibrium geometry.

In the vibrational analysis, the blocks move as a whole without changing their

internal geometry. The MBH approach was first discussed in J. Chem. Phys. 126,

224102 (2007) in which also guidelines for the block choice are formulated.

The corresponding MBH mass matrix and Hessian are corrected to account for the

gradients due to the partial optimization. Without these corrections, the

gradients would lead to unphysical imaginary frequencies.

The MBH approach has the advantage that by fixing the internal geometry of the

blocks, the MBH matrix and Hessian have a smaller dimension, which reduces the

computing time and memory requirements for the diagonalization. The total

number of resulting frequencies is 6K + 3n with K the number of blocks and

n the number of free atoms.

Commands for MBH

To initialize the list of blocks, use the command BLKS INIT. With the ADDB

command, blocks can be added by giving an atom selection:

BLKS ADDBlock atom-selection

The ADDB command can be repeated several times to add more then one block.

When all blocks are added, use the keyword MBH to perform the MBH analysis.

Thereafter commands such as PRINT NORM, PRINT DOTP, PRINT MODES, etcetera, can

be used in the same way as for a full Hessian normal mode analysis. The

BLKS INIT command can be reused to clear the information in the block list,

e.g. when one wants to restart over the MBH analysis with a different block

choice.

In the standard version of MBH, the global translational and rotational modes

are still present in the spectrum. These can be removed with the keyword

RAISe, which will bring the translational/rotational frequencies (in principle

these are zero) to an arteficially high value. This amounts to imposing

Eckart constraints on all other modes.

The keywords FINIte and ENTRopy work similarly with MBH as with DIAG (see DIAG).

Example of MBH

BLKS INIT

BLKS ADDB SELE bynumber 1:5 END

BLKS ADDB SELE bynumber 7:9 END

MBH

This input initializes the block list, adds two blocks and then performs

the MBH normal mode analysis.

Limitations of current implementation

At present the code for linear blocks is not implemented yet.

When a block consists of 2 atoms only, a warning will be issued.

An atom can belong to one block at the time only. In the future

the implementation might be extended in order to treat

linked blocks as well.

References

1. A. Ghysels, D. Van Neck, V. Van Speybroeck, T. Verstraelen, M. Waroquier,

J. Chem. Phys. 126, 224102 (2007)

2. A. Ghysels, D. Van Neck, M. Waroquier

J. Chem. Phys. 127, 164108 (2007)

Top

Gaussian (Anisotropic) Network Model

The implemented GANM is based on papers published by the Bahar

group; the ARPACK library also works with GANM with our implementation,

so that large systems can be studied efficiently.

The GANM calculation requires a user defined file named

CHAINS.DAT, which contains the definition of segments of a biomolecule.

Syntax:

GANM (atom selection) UNIT int {AISO} SERL int

UNIT: specifies the paramter file used in GANM calculation (stiffness,cutoff)

AISO: if specified, the Anisotropic Network Model will be used; otherwise, the

Gaussian Network model will be used.

SERL: can be 1 or 2; 1 uses the standard diagonalization method, and 2 uses

ARPACK.

atom selection: atoms included in GANM calcualtions.

Example of the parameter file (specified by UNIT):

1 1 : number of atom types, number of interaction types

CA : atom type(s) included in ANM

1 1 0.95 13.0 : index of atom type, index of atom type, force constant,

distance cutoff

Example of the file CHAINS.DAT:

2 148 : total number of segments, total number of residues

1 1 144 : the first segment , starting and ending residues

2 145 148 : the second segment , starting and ending residues

References:

1. GNM: Tirion, M. M. 1996, Phys. Rev. Lett. 77: 1905

2. ANM: Atilgan, A. R., Durell, S. R., Jernigan, R. L., Demirel, M. C.

Keskin, O., Bahar, I., 2001 Biophys. J. 80: 505

Doruker, P., Atligan, A. R., Bahar, I. 2000, Proteins, 40: 512

Gaussian (Anisotropic) Network Model

The implemented GANM is based on papers published by the Bahar

group; the ARPACK library also works with GANM with our implementation,

so that large systems can be studied efficiently.

The GANM calculation requires a user defined file named

CHAINS.DAT, which contains the definition of segments of a biomolecule.

Syntax:

GANM (atom selection) UNIT int {AISO} SERL int

UNIT: specifies the paramter file used in GANM calculation (stiffness,cutoff)

AISO: if specified, the Anisotropic Network Model will be used; otherwise, the

Gaussian Network model will be used.

SERL: can be 1 or 2; 1 uses the standard diagonalization method, and 2 uses

ARPACK.

atom selection: atoms included in GANM calcualtions.

Example of the parameter file (specified by UNIT):

1 1 : number of atom types, number of interaction types

CA : atom type(s) included in ANM

1 1 0.95 13.0 : index of atom type, index of atom type, force constant,

distance cutoff

Example of the file CHAINS.DAT:

2 148 : total number of segments, total number of residues

1 1 144 : the first segment , starting and ending residues

2 145 148 : the second segment , starting and ending residues

References:

1. GNM: Tirion, M. M. 1996, Phys. Rev. Lett. 77: 1905

2. ANM: Atilgan, A. R., Durell, S. R., Jernigan, R. L., Demirel, M. C.

Keskin, O., Bahar, I., 2001 Biophys. J. 80: 505

Doruker, P., Atligan, A. R., Bahar, I. 2000, Proteins, 40: 512

Top

Vibrational Subsystem Analysis (VSA) Method

(see test/c35test/VSA_Butane.inp)

If this method is used please cite...

Woodcock, HL; Zheng, W; Ghysels, A.; Shao, Y; Kong, J; Brooks, BR. Vibrational

Subsystem Analysis: A Method for Probing Free Energies and Correlations in the

Harmonic Limit. J. Chem. Phys. 129 (21) 214109 (2008).

The vibrational subsystem analysis (VSA) method is designed for coupling

global motion to a local subsystem. This method is a partitioning scheme that

separates (and integrates out) the motion of the environment from the user

defined subsystem (see Method Section) while still allowing the environmental

motion to perturb the local subsystem dynamics. It was originally developed

for EN models but is now extended for all-atom representations and hybrid

quantum mechanical / molecular mechanical (QM/MM) potentials. Below is a brief

list of possible uses:

1. examination of local-global motion

2. performing accurate NMA while eliminating unwanted degrees of freedom

3. eliminating excess noise from large NMA (i.e. QM/MM)

4. performing NMA while not at a stationary point with respect to all degrees

of freedom

5. integration of light particle during NMA (i.e. application to polarizable

models)

Vibrational Subsystem Analysis (VSA) Method

(see test/c35test/VSA_Butane.inp)

If this method is used please cite...

Woodcock, HL; Zheng, W; Ghysels, A.; Shao, Y; Kong, J; Brooks, BR. Vibrational

Subsystem Analysis: A Method for Probing Free Energies and Correlations in the

Harmonic Limit. J. Chem. Phys. 129 (21) 214109 (2008).

The vibrational subsystem analysis (VSA) method is designed for coupling

global motion to a local subsystem. This method is a partitioning scheme that

separates (and integrates out) the motion of the environment from the user

defined subsystem (see Method Section) while still allowing the environmental

motion to perturb the local subsystem dynamics. It was originally developed

for EN models but is now extended for all-atom representations and hybrid

quantum mechanical / molecular mechanical (QM/MM) potentials. Below is a brief

list of possible uses:

1. examination of local-global motion

2. performing accurate NMA while eliminating unwanted degrees of freedom

3. eliminating excess noise from large NMA (i.e. QM/MM)

4. performing NMA while not at a stationary point with respect to all degrees

of freedom

5. integration of light particle during NMA (i.e. application to polarizable

models)