cheq (c46b2)

The CHarge EQuilibration Method


The CHEQ and associated modules implement polarization via the
fluctuating charge method as based on the CHarge EQuilibration methods
outlined in the literature. While the current forcefield parameters are
valid for most small molecules and proteins, the force field is
constantly undergoing refinement and development.

The electrostatic model derives formally from the density functional
theory of atoms in molecules; polarization is effected as a result of
chemical potential equalization everywhere within a molecule, forcing
charge flow from regions of high to low chemical potential based on
atomic properties. These properties are the atomic hardness and
electronegativity. The parameters are treated as such and are
determined from fits to density functional calculations of charge
responses and mono- and dipole moments of small molecules in vacuum.

The method can be used to perform energy, minimization, and dynamics
calculations for the above-mentioned systems. For dynamics, the
charges are coupled to Nose-Hoover baths to maintain proper
adiabaticity. Several normalization schemes are allowed to maintain
charge constant over desired partitions. Several water models are
supported including the SPC-FQ and TIP4P-FQ models of Rick et al.


* Description | Description of the CHEQ Function
* Syntax | Syntax of the CHEQ commands
* Options | CHEQ Command Options
* Energy | Usage with Energy and Dynamics commands
* Scalar | Usage with the Scalar Command
* Examples | Usage Example Script
* Mixed Systems | Mixed Polarizable / Non-Polarizable Systems (FQ/MM)
* References | References for CHEQ Methods


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The CHarge EQuilibration routines implement the fluctuating charge
dynamics as described in recent literature (1-9). The method derives
from the density functional theory of atoms in molecules. The model
is a relatively simple approach to incorporate a means for electronic
density rearrangement (as reflected grossly in terms of some
partitioned 'charge' on an atom) due to changes in chemical
environment---polarizability. The mechanism for the redistribution is
the equalization of electronic chemical potential everywhere within a
molecule, a statement of Sanderson's principle of electronegativity
equalization ( since, in DFT, the chemical potential and
electronegativity are analogous). The electrostatic potential
adopted in this formalism is (for a system with M molecules with N_i
atoms in molecule 'i':
__ __
/ \
N N_i M M | N N |
E = sum sum CHI_ia(0) Q_ia + 1/2 sum sum | sum sum ETA_iajb Q_ia Q_jb |
i=1 a=1 i=1 j=1 | a=1 b=1 |
\__ __/


The ETA_iajb term comes from the hardness matrix whose elements are
determined via (Ref. 13):

1/2 ( ETA_i + ETA_j)
ETA_ij = ---------------------------------------------
sqrt( 1 + 0.25 (ETA_i + ETA_j)**2 R_ij**2)

Atoms involved in bonded interactions, angle interactions, and
dihedral interactions interact with each other via the combination
rule. Atoms in a molecule separated by more than three bonds interact
with the normal Coulomb 1/R interaction, as do charge sites on
different molecules.

The model requires parameterization of atomic electronegativities and
hardnesses. The hardness are determined via fitting the DFT charge
responses of small molecules containing the chemical functional groups
of interest in modelling proteins. The approach is hierarchical,
beginning with the fitting of aliphatic groups (methyl carbons,
hydrogens, for instance), and then carrying these over into the
determination of other groups. The electronegativities then are
determined by fitting to charge distributions and dipole moments of
isolated small molecules in vacuum.

A fictitious charge dynamics is performed in the spirit of
Car-Parrinello or 'ab initio' molecular dynamics simulations. The
charge sites are given masses (much smaller than the nuclei so as to
maintain the system on the Born-Oppenheimer (BO) surface) and the
entire system is propagated with an extened Lagrangian which enforces
the required charge normalization. The charges are thermostatted to
heat baths to maintain a relatively low temperature to ensure
adiabaticity. Currently this is done via coupling to Nose-Hoover heat
baths; groupings of charges can be separately coupled so as to avoid
'hot spots'.


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Syntax of the CHEQ commands

CHEQ [ON ]
[OFF ]
[RESEt]

[NORM ] {BYRE | BYAL | BYSE | BYGP | BYMO} atom_selection

[QMAS ] CGMA {charge-mass} TSTA {initial temperature} atom_selection

[TIP4p] atom_selection
[WATEr]
[SPC ]
[FLEX ]

CHEQ {WATE | SPC | FLEX} SELECT {selection} END


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CHEQ Command Options


ON sets QCG flag to .TRUE. (turns on fluctuating charges). This can
be issued anytime in order to switch between non-polarizable and
polarizable Hamiltonians

OFF sets QCG flag to .FALSE. (turns off fluctuating charges). This
can be issued anytime in order to switch between non-polarizable
and polarizable Hamiltonians.

RESE turns off CHEQ (QCG=.FALSE.) and resets some CHEQ arrays and
parameters as follows:

The variable 'QNPART' is set to zero (nullifies CHEQ
normalization units; the user will have to respecify these with
'CHEQ NORM norm-option atom-selection as discussed under the
'NORM' option command.

QCG is set to FALSE; thus, ENERGY, MINIMIZATION, and DYNAMICS
using the CHEQ method is no longer possible unless the CHEQ
option us used with the relevant commands.

All arrays associated with the partitions, partition counters,
and pointers to atoms of partitions are zeroed.

NORM sets up partitions for charge normalization. Implemented by
setting total charge force for a partition to zero. Format for
command:
CHEQ NORM {BYRE | BYAL | BYSE | BYGP | BYMO} SELECT {selection} END
description of options:
BYRE - charge constant within residues in the given selection
BYAL - charge constant within all atoms in the given selection
BYSE - charge constant within segments in the given selection
BYGR - charge constant within groups in the given selection
BYMO - charge constant within molecules in the given selection
NOFQ - turns off CHEQ for selected atoms


QMAS sets up mass and initial temperature for charges

QMAS CGMA {charge-mass} TSTA {initial temperature} {atom selection}


TIP4 selects the TIP4P-FQ water model of Rick and Berne
Note: Consult the LONEPAIR documentation for properly setting up the
constructs necessary to implement this 4-point water model and/or
check the testcases

WATE Rigid water, derivatives of intra-molecular hardness elements with
respect to coordinates are not computed.

SPC selects rigid 3-point water using special SPC parameters of Rick and Berne

FLEX generic CHEQ molecule type (flexible molecule; charge force on
nuclei computed). The above options (WATE, SPC and FLEX, TIP4)
are used similarly to the NORM command:

CHEQ {WATE | SPC | FLEX} SELECT {selection} END

PRIN Prints out several variables and arrays for CHEQ

WALP sets parameters for restraint potential to bound charges on
atoms; this is to prevent over-polarization in cases where the
charges sample regions further away from the minimum determined
by the quadratic form of the CHEQ potential. At this time, only
two forms of the restraint are supported. Can be extended in
the future.

For PTYP = 1 :

CHEQ WALP { PTYP integer} { QRQ1 real } { QRQ2 real } { QRK real } -
atom_selection

For PTYP = 2 :

CHEQ WALP { PTYP integer} { WALN integer } -
{ QRA1 real } { QRAB1 real } { QRA2 real } { QRB2 real } -
{ QRQ1 real } { QRQ2 real } { QRK real } atom_selection

PTYP sets the type of restraint potential; 1=harmonic, 2=Nth
order wall potential with switch. (Ref #)

QRQ1 the upper limit of the values a certain charge can take
QRQ2 the lower limit of the values a certain charge can take
QRK the force constant for harmonic restraint or the strength
for the wall potential (generally on the order of 10**2)

The following are further specifications needed for a
non-harmonic wall potential.

WALN integer value setting the hardness of the wall potential
QRA1 charge value below which switching function is zero
QRB1 charge value above which switching function is unity
** QRA1 < QRB1

QRA2 charge value above which switching function is zero
QRB2 charge value below which switching function is unity
** QRA2 < QRB2


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Energy and Dynamics


CHEQ can be used with ENERgy, MINImization, and DYNAmics commands.
Currently, minimization routines supporting CHEQ are the CONJugate
gradients and STEEPest descents. For DYNAmics, the leapfrog
integrator includes charge dymamics.

For these functions, the CHEQ flag must be specified so that the
appropriate subroutines are used:

ENERGY energy_options CHEQ CHEQ_options

DYNA dynamics_options CHEQ CHEQ_options

MINI minimization_options CHEQ CHEQ_options

where CHEQ_options are as in the following.

NOCO sets QNOCO flag to .TRUE. Freezes coordinates by zeroing DX,DY and DZ
resets to .FALSE. when exiting ENERgy, MINImization, or DYNAmics call.
Useful for minimizing charge for a fixed conformation. For a large
system this can be faster than CGIN since the charges tend to converge
rapidly.(<100 steps for 216 water system)

CGMD Used with ENERgy, MINIimization, and DYNAmics calls

int - 0 for normal Hamiltonian with exclusion in elec.interactions
(default)
1 using Hamiltonian without exclusions (Recommended for FLUQ)

CGIN Used with ENERgy call

charges will be calculated by matrix inversion whenever energy is
called. (WARNING: it is slow and memory intensive on big systems)
This option does not work with IMAGES.(but does work with BOUND)
This keyword must be specified every time it is wanted as the flag
CGINV is set to .FALSE. after the command is performed.


POLT Used with ENERgy call

calculates the components of the molecular polarizability tensor
based on the molecular geometry and hardness matrix
elements. Used in conjunction with the ENERGY call.

Use care when comparing to experimental data; usually need to
make sure that the same molecular orientations are being
compared (i.e, planar water case, depending on the orientation,
will get different results for the tensor component values).

FQPA Prints out the Eta matrix when doing matrix inversion. (i.e. only works
in conjunction with CGIN keyword) This is an NATOM by NATOM array so can
get very large. Flag resets to .FALSE. after command has executed.


FQINT used with DYNAmics call

sets the charge integration algorithm
1 = Nose-Hoover Temperature Control **
2 = No temperature control
required as input; default does not do charge dynamics

** Note: To use the Nose-Hoover algorithm for propagating the
charge dynamics with temperature control, one must specify the
degrees of freedom which are to be coupled to a given bath.
The method for specifying this is similar to the multi-heat
bath calls for the NOSE command to thermostat the nuclear
degrees of freedom. The following command must be issued
before the call to DYNAMICS:

FQBA I
CALL J atom-selection-option
COEF J QREF (0.005) TREF (1.0)
.
.
.
.
END

The integer 'I' indicates the number of baths for groupings of
charge degrees of freedom. For each bath, the 'CALL' and
'COEF' commands set the atoms coupled to that bath, the
Nose-Hoover fictitious mass, QREF, for that bath, and the
temperature, TREF, for that bath.

** CHEQ computation now turns on and off with SKIPE command. Tied
to ELEC keyword. If SKIPE ELEC command is given CHEQ energy and
derivatives are set to zero.



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SCALAR Command


The charge array has always been available from the scalar command, but
there are now additional arrays specific to Fluc-Q that are accessible,
namely the charge derivatives as well as both the eta and chi parameters.
The keynames that have been added are:

DCH - charge derivatives
EHA - hardness parameters for every atom
ECH - electronegativity parameters for every atom

See the description of the * scalar: for useage.

For information regarding variables used in conjunction with the CHEQ method,
consult the include files cheqdyn.fcm and derivq.fcm in the source/fcm
diretory.


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Examples


There are examples of many of the commands described above in the test
input script that is in the test/c30test directory. After the
structure has been generated the CHEQ options can be set up.
A typical sequence of commands might go something like:

{read RTF} ! read appropriate file to obtain CHEQ parameters;
! treated analogous to charges
{read standard parameters}

{read sequence}
GENErate

CHEQ norm byre select all end ! normalization over residues
CHEQ flex select all end ! Flexible molecules

energy cheq cgmd 1


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The CHEQ module currently allows one to simulate systems where some
segments are polarizable and others are not (non-polarizable ion in polarizable
solvent, see Example in this section). This set-up is referred to as FQ/MM by
analogy to QM/MM methods (since the polarizable region allows for electronic
response to local chemical environment). The algorithmically, the code checks
whether atoms are assigned to a charge normalization unit (required for CHEQ
minimization and dynamics); those charge on atoms which are not implicated in
a specified charge normalization scheme are not propagated dynamically nor are
they varied in minimization. In the case of mixed systems, the E14FAC
parameter is not required to be set explicitly in the operating input script.
The associated parameter file should use the default value of "1"; the code
automatically allows for inclusion of 1-4 electrostatic interactions within
the CHEQ formalism without any user input. The following is an example of
setting up a mixed system of polarizable solvent (TIP4P-FQ) solvating a
non-polarizable ion (sodium). The polarizability of the ion is effectively
turned off by not specifying a normalization scheme for the non-polarizable
solute (see also the test case /c32test/nawat.inp).

Example: box of 215 TIP4P-FQ water molecules solvation a single,
NON-POLARIZABLE SODIUM ION

# read rtf and paramater files as usual

read sequ tip4 215
generate wat first none last none setup noang nodihed

read sequence sod 1
generate ion first none last none setup noang nodihed

open read unit 1 form name @0tip4p_sod.crd
read coor card unit 1
close unit 1

coor copy comp

lonepair bisector dist 0.15 angle 0.0 dihe 0.0 -
sele atom wat * OM end -
sele atom wat * OH2 end -
sele atom wat * H1 end -
sele atom wat * H2 end

! *** To exclude the ion from having polarizability, note that it is assigned
! to no normalization unit. ***

CHEQ norm byres sele segid wat end
CHEQ tip4 sele segid wat end
CHEQ QMAS CGMA 0.000069 TSTA 0.01 sele segid wat end
CHEQ NORM NOFQ SELE SEGID ION END ! ******

The last line above signifies that the sodium ion (treated as a segment here)
will be treated as a fixed-charge entity.


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References


1. Parr, R. G., and W. Yang. Density-Functional Theory of Atoms and
Molecules. 1989. Oxford: Oxford University Press.

2. Sanderson, R. T. "Chemical Bonds and Bond Energy". 2nd. Edition,
1976, New York, Academic.

3. Sanderson, R. T. Science. 114. 1951, p.670.

4. Rick, S. W., S. J. Stuart, B. J. Berne. J. Chem. Phys. 101(7).
1994 pp.6141-6156.

5. Rick, S. W. and B. J. Berne. JACS. 118, 1996. pp672-679.

6. Mortier, W. J., S. K. Ghosh, S. Shankar. JACS. 108, 1986. pp.4315-4320.

7. Mortier, W. J., K. V. Genechten, and J. Gasteiger. JACS. 107,
1985. pp.829-835.

8. Rappe, A. K. and W. A. Goddard, III. J. Phys. Chem. 95, 1991. pp.3358-3363.

9. York, D. M. and W. Yang. J. Chem. Phys. 104(1), 1996. p.159.

10. Car. R, and M. Parrinello. Phys. Rev. Lett. 55, 1985. p.2471.

11. Blochl, P. E., and M. Parrinello. Phys. Rev. B. 45(16), 1992. p.9413.

12. Yoshii, N., R. Miyauchi, S. Miura, S. Okazaki. Chem. Phys. Lett. 317,
2000. pp.414-420.

13. Naleewajski, R. F., J. Korchowiec, and Z. Zhou. Int. J. Quant. Chem.
Quantum Chemistry Symposium 22, 1988. pp.349-366.

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