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# pressure (c44b1)

Constant Pressure/Temperature (CPT) Dynamics

Two types of constant pressure/temperature dynamics are available

in CHARMM. The weak coupling method for temperature and pressure

control described in the paper by Berendsen et al. (JCP 81(8) p3684

1984) was the first constant pressure and temperature algortihm

implemented in CHARMM. Extended system constant pressure and

temperature algorithms have now been implemented based on the work

of Andersen (JCP 72(4) p2384 1980), Nose & Klein (Mol Physics 50(5)

p1055 1983), Hoover (Phys. Review A 31(3) p1695 1985). Additionally,

a variant on the extended system method which treats the control

variables by means of a Langevin equation is available (Feller, Zhang,

Pastor & Brooks, JCP, 103, 4613 (1995)).

Shape matrix propagation and coordinates scaling for triclinic

unit cell is done according to D. Brown and J.H.R. Clarke in

Computer Physics Comm. 62 (1991) 360-369.

A constant surface tension algorithm is included which is useful

for studying interfacial systems where one wishes to allow the area

to change dynamically during the simulation. The dynamical equations

and statistical ensemble are discussed in (Zhang, Feller, Brooks &

Pastor, JCP, 103, 10252 (1995)).

* Syntax | Syntax of the CPT dynamics command

* Description | Description of the keywords and options

* Notes | Other points to be noted

* Examples | Isotropic and interfacial systems; constant tensor

* Pressure | The pressure command

Two types of constant pressure/temperature dynamics are available

in CHARMM. The weak coupling method for temperature and pressure

control described in the paper by Berendsen et al. (JCP 81(8) p3684

1984) was the first constant pressure and temperature algortihm

implemented in CHARMM. Extended system constant pressure and

temperature algorithms have now been implemented based on the work

of Andersen (JCP 72(4) p2384 1980), Nose & Klein (Mol Physics 50(5)

p1055 1983), Hoover (Phys. Review A 31(3) p1695 1985). Additionally,

a variant on the extended system method which treats the control

variables by means of a Langevin equation is available (Feller, Zhang,

Pastor & Brooks, JCP, 103, 4613 (1995)).

Shape matrix propagation and coordinates scaling for triclinic

unit cell is done according to D. Brown and J.H.R. Clarke in

Computer Physics Comm. 62 (1991) 360-369.

A constant surface tension algorithm is included which is useful

for studying interfacial systems where one wishes to allow the area

to change dynamically during the simulation. The dynamical equations

and statistical ensemble are discussed in (Zhang, Feller, Brooks &

Pastor, JCP, 103, 10252 (1995)).

* Syntax | Syntax of the CPT dynamics command

* Description | Description of the keywords and options

* Notes | Other points to be noted

* Examples | Isotropic and interfacial systems; constant tensor

* Pressure | The pressure command

Top

[Syntax DYNAmics CPT]

DYNAmics CPT ... cpt-spec

cpt-spec::= [ pressure-spec ] [ temperature-spec ] [ surface-tension-spec ]

pressure-spec::= PCONST {[PINTernal]} {BEREndsen berensen-spec} ref-pressure-spec

{ PEXTernal } { langevin-piston-spec } [ IUPTEN int ]

temperature-spec::= { TCONst [TCOUpling real] [TREFerence real] } ! Berendsen

{ }

{ HOOVer [TMASs real] [ REFT real] } ! Hoover

berensen-spec::= [COMPressibility real] [PCOUpling real]

langevin-piston-spec::= piston-mass-spec [PGAMMA real] [TBATH real] [P21XCEN]

surface-tension-spec::= [SURFace] [TENSion real]

piston-mass-spec::= [PMASs real]

[PMXX real] [PMYY real] [PMZZ real] [PMXY real] [PMXZ real] [PMYZ real]

ref-pressure-spec::= [PREFerence real] [PREFInitial real] [PREFFinal real]

[PRXX real] [PRYY real] [PRZZ real] [PRXY real] [PRXZ real] [PRYZ real]

[PIXX real] [PIYY real] [PIZZ real] [PIXY real] [PIXZ real] [PIYZ real]

[PFXX real] [PFYY real] [PFZZ real] [PFXY real] [PFXZ real] [PFYZ real]

[VOLUME real]

[Syntax DYNAmics CPT]

DYNAmics CPT ... cpt-spec

cpt-spec::= [ pressure-spec ] [ temperature-spec ] [ surface-tension-spec ]

pressure-spec::= PCONST {[PINTernal]} {BEREndsen berensen-spec} ref-pressure-spec

{ PEXTernal } { langevin-piston-spec } [ IUPTEN int ]

temperature-spec::= { TCONst [TCOUpling real] [TREFerence real] } ! Berendsen

{ }

{ HOOVer [TMASs real] [ REFT real] } ! Hoover

berensen-spec::= [COMPressibility real] [PCOUpling real]

langevin-piston-spec::= piston-mass-spec [PGAMMA real] [TBATH real] [P21XCEN]

surface-tension-spec::= [SURFace] [TENSion real]

piston-mass-spec::= [PMASs real]

[PMXX real] [PMYY real] [PMZZ real] [PMXY real] [PMXZ real] [PMYZ real]

ref-pressure-spec::= [PREFerence real] [PREFInitial real] [PREFFinal real]

[PRXX real] [PRYY real] [PRZZ real] [PRXY real] [PRXZ real] [PRYZ real]

[PIXX real] [PIYY real] [PIZZ real] [PIXY real] [PIXZ real] [PIYZ real]

[PFXX real] [PFYY real] [PFZZ real] [PFXY real] [PFXZ real] [PFYZ real]

[VOLUME real]

Top

Description of CPT Dynamics Commands

Only a few changes are needed to a standard CHARMM dynamics input

file to run a CPT MD simulation. There are a few things to note :

a. The CPT algorithm is invoked by the CPT keyword.

b. It's not possible to use LANGEVIN dynamics with the constant

pressure or temperature algorithm.

c. All the non-Langevin dynamics keywords have the same meaning as

the in a standard dynamics input file. This includes the

keywords STRT and REST.

e. The CPT specific keywords (apart from CPT itself) are :

1. PCONstant - do a constant pressure calculation. Extended system

algorithm is the default, weak-coupling is available

with BEREndsen keyword.

2. TCONstant - do a constant temperature calculation with the weak-

coupling algorithm. HOOVer constant temperature is

only available with PCONstant simulations.

3a. To be used with Berendsen algorithm:

COMPressibility <real> - the isothermal compressibility

(atmospheres**-1).

PCOUple <real> - the pressure coupling constant

(picoseconds).

3b. To be used with extended system algorithm:

PMASs <real> - the mass of the pressure piston (amu)

PGAMma <real> - Langevin piston collision frequency (1/ps)

TBATh <real> - Langevin piston bath temperature

TENSion <real> - reference surface tension (dyne/cm)

IUPTEN <int> - unit number, P tensor at every step

P21XCEN - flag; enables dynamic XCEN for P21 TETRagonal

To be used with either constant pressure algorithm:

PREFerence <real> - the reference pressure (atmospheres).

(for isotropic pressure)

PREFInitial <real> - initial reference pressure tensor (atmospheres).

(for isotropic pressure)

PREFFnitial <real> - final reference pressure tensor (atmospheres).

(for isotropic pressure)

PRXX,PRYY,PRZZ <real> - the reference pressure tensor (atmospheres).

PRXY,PRXZ,PRYZ (for anisotropic pressure)

PIXX,PIYY,PIZZ <real> - initial reference pressure tensor (atmospheres).

PIXY,PIXZ,PIYZ (for anisotropic pressure)

PFXX,PFYY,PFZZ <real> - final reference pressure tensor (atmospheres).

PFXY,PFXZ,PFYZ (for anisotropic pressure)

PREFI,PREFF,PIXX...,PFXX... - are used for linear pressure ramping

4a. To be used with Berendsen algorithm

TCOUple <real> - the temperature coupling constant

(picoseconds).

TREFerence <real> - the berendsen reference temperature (K).

4b. To be used with extended system (HOOVer) algorithm

TMASs <real> - the mass of the thermal piston (kcal*mol^-1*ps^2).

REFT <real> - the hoover reference temperature (K).

Note : for full descriptions of these parameters and the suggested

values to use see the reference given above.

f. The CPT module is only available for use with the leap-frog integrator

Description of CPT Dynamics Commands

Only a few changes are needed to a standard CHARMM dynamics input

file to run a CPT MD simulation. There are a few things to note :

a. The CPT algorithm is invoked by the CPT keyword.

b. It's not possible to use LANGEVIN dynamics with the constant

pressure or temperature algorithm.

c. All the non-Langevin dynamics keywords have the same meaning as

the in a standard dynamics input file. This includes the

keywords STRT and REST.

e. The CPT specific keywords (apart from CPT itself) are :

1. PCONstant - do a constant pressure calculation. Extended system

algorithm is the default, weak-coupling is available

with BEREndsen keyword.

2. TCONstant - do a constant temperature calculation with the weak-

coupling algorithm. HOOVer constant temperature is

only available with PCONstant simulations.

3a. To be used with Berendsen algorithm:

COMPressibility <real> - the isothermal compressibility

(atmospheres**-1).

PCOUple <real> - the pressure coupling constant

(picoseconds).

3b. To be used with extended system algorithm:

PMASs <real> - the mass of the pressure piston (amu)

PGAMma <real> - Langevin piston collision frequency (1/ps)

TBATh <real> - Langevin piston bath temperature

TENSion <real> - reference surface tension (dyne/cm)

IUPTEN <int> - unit number, P tensor at every step

P21XCEN - flag; enables dynamic XCEN for P21 TETRagonal

To be used with either constant pressure algorithm:

PREFerence <real> - the reference pressure (atmospheres).

(for isotropic pressure)

PREFInitial <real> - initial reference pressure tensor (atmospheres).

(for isotropic pressure)

PREFFnitial <real> - final reference pressure tensor (atmospheres).

(for isotropic pressure)

PRXX,PRYY,PRZZ <real> - the reference pressure tensor (atmospheres).

PRXY,PRXZ,PRYZ (for anisotropic pressure)

PIXX,PIYY,PIZZ <real> - initial reference pressure tensor (atmospheres).

PIXY,PIXZ,PIYZ (for anisotropic pressure)

PFXX,PFYY,PFZZ <real> - final reference pressure tensor (atmospheres).

PFXY,PFXZ,PFYZ (for anisotropic pressure)

PREFI,PREFF,PIXX...,PFXX... - are used for linear pressure ramping

4a. To be used with Berendsen algorithm

TCOUple <real> - the temperature coupling constant

(picoseconds).

TREFerence <real> - the berendsen reference temperature (K).

4b. To be used with extended system (HOOVer) algorithm

TMASs <real> - the mass of the thermal piston (kcal*mol^-1*ps^2).

REFT <real> - the hoover reference temperature (K).

Note : for full descriptions of these parameters and the suggested

values to use see the reference given above.

f. The CPT module is only available for use with the leap-frog integrator

Top

Other Points

Suggested values for solvated systems:

COMPressibility (beta) = 4.63e-5 /atm (for proteins)

PCOUple = 5.0 ps (or more)

PREF = 1.0 atm (default)

PMASs = 500 amus (default is infinity)

TCOUPle = 5.0 ps (or more)

TREF = 298.0 K (default)

REFT = 298.0 K (default)

TBATh = 298.0 K (default)

TMASs = 1000.0 kcal ps^2 (default is infinity)

TENSion = 0.0 (default, results in regular constant pressure)

Other Points

------------

1. Although the heating and equilibration commands are the same as

for standard dynamics it is possible to use the CPT algorithm

to perform both without velocity modification (c.f. Langevin

dynamics).

2. The algorithm requires the use of the CHARMM CRYSTAL facility

for constant pressure dynamics. If only Berendsen constant temperature

is requested, then the crystal code need not be used.

3. For the Berendsen algorithm, when a reference pressure term

( PRXX,PRYY,PRZZ,PRXY,PRXZ,PRYZ is

set to a very large negative number (less than -9999.0), then this

component of the pressure will not be considered. For orthorhombic

simulations, the particular box length will not change (for example,

if the command says: PRXX 1.0 PRYY -10000. PRZZ -10000. then

only the box length in the x direction will change during dynamics).

If a cubic simulation is performed, then the pressure terms corresponding

to the large negative values are not considered in the calculation of

the instentaneous pressure.

4. For the extended system pressure algorithm, setting any component of the

piston mass array to zero will cause the corresponding simulation cell

length to remain constant. For example when using the orthormobic

cell, setting pmxx=pmyy=0 results in only the zdirection changing during

the dynamics (and it changes according to the z component of the pressure

tensor). This is the standard method for interfacial NPAT systems.

5. A discussion of Hoover temperature control can be found in the documentation

file nose.info. The temperature control implemented in the velocity verlet

integrator is very similar to the one used in the leapfrog integrator.

NOTE: Hoover temp control only works in conjunction with constant pressure

6. The Berendsen pressure/temperature control scheme may not be appropriate

for inhomegenous systems (protein in water, aqueous membrane, interfacial

systems). This is especially true if SHAKE constraints are used on one

component. A full discussion is given in the paper by Feller, Zhang, Pastor

and Brooks (JCP, 9/15/95).

7. The extended system pressure algorithm can be run with temperature control

(resulting in isothermal-isobaric ensemble) or without (resulting in

isoenthalpic ensemble). The Berendsen pressure method must be run with the

constant temperature control (the ensemble for these methods is unknown).

8. If PINTernal is used (default), then the pressure is determined by the

internal virial and the atoms in the box are instantaneously scaled in a

homogeneous response to the altered box dimensions. If PEXTernal is used,

then the external virial (related to the force required to maintain the

symmetry constraint) is used and the atom positions are not instantaneously

scaled by box size changes. The PEXTernal option is normally used for

minimization, but may be used with molecular dynamics. It is not recommended

for large systems.

9. The pressure tensor (extended system) on every integration step is saved

to the formatted file indicated by unit number specified by IUPTEN; this

allows calculation of viscosity using the Green-Kubo relationship. The

viscosity is computed from the integral of the autocorrelation function

of the off-diagonal elements of the P tensor, scaled by V/kT; see

J. Phys. Chem. 100:17011-17020 (1996). The column order of the data is:

Time PIXX PIXY PIXZ PIYX PIYY PIYZ PIZX PIZY PIZZ

10. For simulations using P21 symmetry with a tetragonal prism lattice, the

P21XCEN keyword enables dynamic updating of the XCEN value used for image

centering to be consistent with 0.25*A; for details on P21 symmetry, see

the example in » crystl

Other Points

Suggested values for solvated systems:

COMPressibility (beta) = 4.63e-5 /atm (for proteins)

PCOUple = 5.0 ps (or more)

PREF = 1.0 atm (default)

PMASs = 500 amus (default is infinity)

TCOUPle = 5.0 ps (or more)

TREF = 298.0 K (default)

REFT = 298.0 K (default)

TBATh = 298.0 K (default)

TMASs = 1000.0 kcal ps^2 (default is infinity)

TENSion = 0.0 (default, results in regular constant pressure)

Other Points

------------

1. Although the heating and equilibration commands are the same as

for standard dynamics it is possible to use the CPT algorithm

to perform both without velocity modification (c.f. Langevin

dynamics).

2. The algorithm requires the use of the CHARMM CRYSTAL facility

for constant pressure dynamics. If only Berendsen constant temperature

is requested, then the crystal code need not be used.

3. For the Berendsen algorithm, when a reference pressure term

( PRXX,PRYY,PRZZ,PRXY,PRXZ,PRYZ is

set to a very large negative number (less than -9999.0), then this

component of the pressure will not be considered. For orthorhombic

simulations, the particular box length will not change (for example,

if the command says: PRXX 1.0 PRYY -10000. PRZZ -10000. then

only the box length in the x direction will change during dynamics).

If a cubic simulation is performed, then the pressure terms corresponding

to the large negative values are not considered in the calculation of

the instentaneous pressure.

4. For the extended system pressure algorithm, setting any component of the

piston mass array to zero will cause the corresponding simulation cell

length to remain constant. For example when using the orthormobic

cell, setting pmxx=pmyy=0 results in only the zdirection changing during

the dynamics (and it changes according to the z component of the pressure

tensor). This is the standard method for interfacial NPAT systems.

5. A discussion of Hoover temperature control can be found in the documentation

file nose.info. The temperature control implemented in the velocity verlet

integrator is very similar to the one used in the leapfrog integrator.

NOTE: Hoover temp control only works in conjunction with constant pressure

6. The Berendsen pressure/temperature control scheme may not be appropriate

for inhomegenous systems (protein in water, aqueous membrane, interfacial

systems). This is especially true if SHAKE constraints are used on one

component. A full discussion is given in the paper by Feller, Zhang, Pastor

and Brooks (JCP, 9/15/95).

7. The extended system pressure algorithm can be run with temperature control

(resulting in isothermal-isobaric ensemble) or without (resulting in

isoenthalpic ensemble). The Berendsen pressure method must be run with the

constant temperature control (the ensemble for these methods is unknown).

8. If PINTernal is used (default), then the pressure is determined by the

internal virial and the atoms in the box are instantaneously scaled in a

homogeneous response to the altered box dimensions. If PEXTernal is used,

then the external virial (related to the force required to maintain the

symmetry constraint) is used and the atom positions are not instantaneously

scaled by box size changes. The PEXTernal option is normally used for

minimization, but may be used with molecular dynamics. It is not recommended

for large systems.

9. The pressure tensor (extended system) on every integration step is saved

to the formatted file indicated by unit number specified by IUPTEN; this

allows calculation of viscosity using the Green-Kubo relationship. The

viscosity is computed from the integral of the autocorrelation function

of the off-diagonal elements of the P tensor, scaled by V/kT; see

J. Phys. Chem. 100:17011-17020 (1996). The column order of the data is:

Time PIXX PIXY PIXZ PIYX PIYY PIYZ PIZX PIZY PIZZ

10. For simulations using P21 symmetry with a tetragonal prism lattice, the

P21XCEN keyword enables dynamic updating of the XCEN value used for image

centering to be consistent with 0.25*A; for details on P21 symmetry, see

the example in » crystl

Top

Examples of Constant Pressure Usage

1. Basic constant pressure, appropriate for a cubic simulation cell, box

length is coupled to the trace of the pressure tensor, using langevin on

pressure piston degree of freedom. This also works for a non cubic

cell, but in that case each length moves independently to maintain a

constant pressure tensor. Constant volume is the limit pmass -> infinity

(implementation in CHARMM: Set pmass = 0 for constant V).

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 400.0 pref 1.0 pgamma 20.0 -

tbath 300.0

2. Constant normal pressure, constant area. Appropriate for orthorombic

cell where only the z direction is allowed to change. The box

length in z direction is coupled to the z component of the pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmzz 225.0 pmxx 0.0 pmyy 0.0 pref 1.0

3. Constant pressure (stress) tensor. Each box length moves independently

to maintain the desired pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 225.0 przz 1.0 prxx 2.0 pryy 3.0

4. Constant pressure, constant surface tension. Z direction moves independently

of x and y and is coupled to the bulk pressure (z component of pressure

tensor). X and y box lengths move to maintain constant surface tension.

Note: this is only appropriate for interfacial systems where the interface

is perpendicular to the z axis.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 225.0 pref 1.0 surface tension 50.0

5. Constant pressure and temperature (NPT)

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 400.0 pref 1.0 pgamma 20.0 -

tbath 300.0 tcons hoover reft 300. tmass 1000.

Examples of Constant Temperature Usage

1. Basic constant temperature using the Hoover method

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

HOOVer TMASs 1000.0 REFT 298.0

2. Constant T with calculation of pressure data; this will also print

the surface tension in the output log, useful for studying

interfacial systems. The optional IUPTEN keyword will store the

pressure tensor data for every timestep.

open unit 29 card write name dyn.ptn

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pcons pmass 0.0 pint pref 1. iupten 29 -

hoover tmass 1000.0 reft 293.0

Examples of Constant Pressure Usage

1. Basic constant pressure, appropriate for a cubic simulation cell, box

length is coupled to the trace of the pressure tensor, using langevin on

pressure piston degree of freedom. This also works for a non cubic

cell, but in that case each length moves independently to maintain a

constant pressure tensor. Constant volume is the limit pmass -> infinity

(implementation in CHARMM: Set pmass = 0 for constant V).

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 400.0 pref 1.0 pgamma 20.0 -

tbath 300.0

2. Constant normal pressure, constant area. Appropriate for orthorombic

cell where only the z direction is allowed to change. The box

length in z direction is coupled to the z component of the pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmzz 225.0 pmxx 0.0 pmyy 0.0 pref 1.0

3. Constant pressure (stress) tensor. Each box length moves independently

to maintain the desired pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 225.0 przz 1.0 prxx 2.0 pryy 3.0

4. Constant pressure, constant surface tension. Z direction moves independently

of x and y and is coupled to the bulk pressure (z component of pressure

tensor). X and y box lengths move to maintain constant surface tension.

Note: this is only appropriate for interfacial systems where the interface

is perpendicular to the z axis.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 225.0 pref 1.0 surface tension 50.0

5. Constant pressure and temperature (NPT)

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pconstant pmass 400.0 pref 1.0 pgamma 20.0 -

tbath 300.0 tcons hoover reft 300. tmass 1000.

Examples of Constant Temperature Usage

1. Basic constant temperature using the Hoover method

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

HOOVer TMASs 1000.0 REFT 298.0

2. Constant T with calculation of pressure data; this will also print

the surface tension in the output log, useful for studying

interfacial systems. The optional IUPTEN keyword will store the

pressure tensor data for every timestep.

open unit 29 card write name dyn.ptn

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 -

pcons pmass 0.0 pint pref 1. iupten 29 -

hoover tmass 1000.0 reft 293.0

Top

The PRESsure command

Process the pressure commands for the system. There are three

modes :

Mode 1 : Initialise all pressure arrays.

Syntax:

PRESsure INITialise

Mode 2 : Calculate and print the instantaneous pressures for

a system.

Syntax:

PRESsure INSTantaneous TEMPerature <Real> VOLUme <Real> -

NDEGf <Integer> NOPRint

The external isotropic pressure and tensor are calculated

if a volume is present. The isotropic internal pressure is

calculated if a volume is present and a temperature has been

given. If no degrees of freedom are specified then a value

of 3*NATOM is taken be default. The virials are always printed.

NOPRint will suppress all printing.

Note: a previous call to energy is required so that the

virials (and volume if not specified) are available

in ENERGY.FCM. The command also accumulates the

average and the square of the pressure variables.

Mode 3 : Print the averages and fluctuations.

PRESsure STATistics

The PRESsure command

Process the pressure commands for the system. There are three

modes :

Mode 1 : Initialise all pressure arrays.

Syntax:

PRESsure INITialise

Mode 2 : Calculate and print the instantaneous pressures for

a system.

Syntax:

PRESsure INSTantaneous TEMPerature <Real> VOLUme <Real> -

NDEGf <Integer> NOPRint

The external isotropic pressure and tensor are calculated

if a volume is present. The isotropic internal pressure is

calculated if a volume is present and a temperature has been

given. If no degrees of freedom are specified then a value

of 3*NATOM is taken be default. The virials are always printed.

NOPRint will suppress all printing.

Note: a previous call to energy is required so that the

virials (and volume if not specified) are available

in ENERGY.FCM. The command also accumulates the

average and the square of the pressure variables.

Mode 3 : Print the averages and fluctuations.

PRESsure STATistics