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flucq (c47b2)

Combined QM/MM Fluctuating Charge Potential for CHARMM

Ben Webb,, and Paul Lyne

The fluctuating charge potential (FlucQ or FQ) is based on the method
developed by Rick, Stuart and Berne (Rick et. al., J. Chem. Phys. 101
(7) 1994 p6141) for molecular dynamics, and extended for hybrid QM/MM
simulations (Bryce et. al., Chem. Phys. Lett. 279 1997, p367). It is
designed primarily for computationally efficient (approx. 10% overhead)
modelling of solvent polarisation in hybrid QM/MM systems, and as such
is implemented for QUANTUM, CADPAC and GAMESS codes, although the
current implementation is easily extensible to any atom type and bond.

* Syntax | Syntax of the FLUCQ command
* Activation | Starting FlucQ from a CHARMM input file
* Charge solution | Solving for exact charges
* Reference energy | Setting the ``zero'' for FlucQ polarisation
* Caveats | Changes to be aware of; known limitations
* Using FlucQ with QM:: Necessary changes for use with CADPAC or GAMESS
* Examples | Simple uses of the FLUCQ command
* Implementation | Mathematical and computational details


FLUCq { ON init-spec (atom selection) }
{ OFF }
{ PRINt }
{ EXACt exac-spec }
{ REFErence { GAS exac-spec } }
{ { SOLVent exac-spec } }
{ { CURRent } }
{ { ENERgy real } }

DYNAmics ... thermo-spec

init-spec::= [GROUp] [NOFIxed]

exac-spec::= [TIMEstep real] [ZETA real]
[TQDEsired real] [PRINt]

thermo-spec::= [FQTEmp real] [FQUNit integer]
{ FQTCoupling real } ! weak coupling
{ FQMAss real nose-spec } ! Nose-Hoover
{ FQSCale integer } ! velocity scaling

nose-spec::= [FQTOlerance real] [FQITerations integer]

FlucQ code is enabled within CHARMM by means of the FLUCQ ON
command. Future energy calculations will then include an extra energy
term - FQPO, the FlucQ polarisation energy, while dynamics simulations
involve a new energy property - FQKI, the FlucQ charge kinetic energy.
Once FlucQ is active, the selected atoms are treated as extra degrees
of freedom, free to fluctuate under the charge forces in the system,
and, by assigning each atom type a fictional charge "mass", these
charges can be accelerated in a conventional dynamics simulation, in a
completely analogous way to the Cartesian degrees of freedom.

If atoms are selected by the FLUCQ command which cannot be modelled
(i.e. they are QM atoms, or have no FlucQ parameters defined for them)
they will be automatically removed from the selection.

The FlucQ polarisation energy, FQPO, is an intramolecular
interaction; in full electronegativity equalisation, every atom
interacts through space, by means of a modified Coulomb-type
interaction, with every other atom in the molecule. In this
implementation, the only interactions calculated are those along
defined CHARMM bonds (even those with zero force constants).

[GROUp] conserves charge within groups, rather than the default
behaviour of conserving charge within residues; this prohibits charge
transfer between groups. Note that the FlucQ model makes no restriction
on the degree of charge transfer within each residue or group, or the
distance over which this transfer can occur.

[NOFIxed] instructs FlucQ that some or all of the bond lengths
between FlucQ-selected atoms are free to change during a simulation.
This forces the FlucQ code to recalculate the intramolecular
interaction at each step; since this is a costly calculation, the
default is to use interactions parameterised for equilibrium bond
lengths, with which it is strongly recommended to combine constraint
methods such as SHAKE BONH PARA.

The FLUCq PRINt command simply prints the current values of all
charges and charge forces (from the last energy calculation). A similar
effect can also be achieved with the standard SCALAR command (see for information on other FlucQ parameters available with the
SCALAR command).

The FLUCQ OFF command disables the FlucQ code. Further energy
calculations will not include FlucQ terms. Note, however, that if the
charges have been modified by FlucQ, they will remain at their altered

Default behaviour during dynamics is to allow the charge degrees of
freedom to fluctuate freely; however they can be thermostatted at a given
charge "temperature" by passing extra options to the DYNAmics command:-

[FQTEmp <real>] specifies the charge temperature (default 0).

[FQTCoupling <real>] (default 0) if set, uses the Berendsen weak
coupling algorithm to thermostat the charges. The coupling parameter
is given in 1/ps, and is analagous to the TCONS/TCOU dynamics options.

[FQMAss <real>] (default 0) if set, uses Nose-Hoover thermostatting,
with the given mass. The tolerance of the Nose-Hoover iterations can be
set with FQTOlerance (default 1.0d-7), and the maximum number of
iterations with FQITerations (default 100).

Thermostatting parameters (number of iterations, scale factor, etc.)
can be written out to a given unit number at every dynamics step by using
the FQUNit (default -1: no write) option.

[FQSCal <integer>] (default 0) if set, performs simple charge velocity
scaling every FQSCal dynamics steps.

The initialization process dimensions FlucQ with the current state
of the system. The QM region, if any, is detected, and the FlucQ atom
selection will then interact with the QM region. Thus, the FLUCQ
command should be placed after any QUANTUM, CADPAC, or GAMESS command,
and if the total number of atoms in the system is modified, FlucQ
should be disabled prior to this change and reinitialized afterwards.

To skip FlucQ energy calculations entirely, use the SKIP FQPOL FQKIN
command. The QM/MM FlucQ interaction is calculated in line with the
standard QM/MM electrostatic interaction, and as such is suppressed
with the SKIP QMEL command. Finally, the intermolecular contribution
to FlucQ is calculated in line with the standard electrostatic
interaction, and so is disabled with the SKIP ELEC command.

No FlucQ interaction energies are calculated between atoms
constrained with the CONS FIX command, as electrostatic energies are
not calculated for these atoms.

FlucQ parameters are specified in the parameter file, with the FLUCQ
keyword. The section should look like the following:-

atom chi zeta prin mass

Here, chi is an electronegativity measure (in Kcal/mol/e), zeta a
Slater orbital exponent (in 1/Angstrom), prin the Slater orbital
principal quantum number, and mass the charge mass (in (ps/e)**2
Kcal/mol) from the FlucQ model. For example, Rick's original
parameters for TIP4P hydrogen and M-site would be written as:-

HP 10.00 0.90 1 6.0d-5
MP 78.49 1.63 2 6.0d-5

The FlucQ model relies on keeping charge kinetic energy at a
temperature close to zero Kelvin, to maintain Born-Oppenheimer
separation between it and the other degrees of freedom. Thus, it is
best to acquire a minimum energy charge configuration for your system
before any dynamics simulation.

Two methods are available for such "charge solution". The first is
to use a standard CHARMM minimisation; FlucQ charges will be minimised
concurrently with the Cartesian coordinates. The second method is to
apply dissipative Langevin dynamics to the charges only, to achieve
minimum energy charges for fixed atomic coordinates; this is performed
by means of the FLUCq EXACt command. The code prints a running count
of the number of iterations required to quench the kinetic energy.

[TIMEstep real] sets the timestep to be used in Langevin dynamics,
by default 0.001ps.

[ZETA real] sets the frictional coefficient, by default 1600.

[TQDEsired real] sets the desired final temperature, by default
1.0d-6 K.

[PRINt] if set, prints the final charges.

By default, the charge polarisation energy FQPOL reported by FlucQ
is given relative to all atomic charges being zero. More generally, it
is useful to define this term relative to an arbitrary zero. This
reference energy can be set with the FLUCQ REFErence command.

FLUCQ REFE GAS disables all intermolecular interactions, solves for
exact charges, and then uses the resultant energy as the reference.
This essentially defines the polarisation energy relative to the energy
that the system would have in the gas phase, with all residues or
groups infinitely separated.

FLUCQ REFE SOLVENT merely disables the QM/MM interaction, and then
sets the reference energy similarly. This shows polarisation as a
function purely of the QM system.

FLUCQ REFE CURRent defines the current polarisation energy (from the
last energy calculation) to be zero - i.e. the reference energy is
increased by the current energy.

FLUCQ REFE ENERgy real sets the reference energy to a user-specified

Bear in mind that REFE GAS exac-spec is essentially identical to the
series of CHARMM commands:-

FLUCQ EXACT exac-spec

(The only difference is that any SKIP command in force before REFE
GAS will remain in force afterwards, whereas the above example will
re-include calculation of all energy terms at completion. Also, by
changing the second line in the above example to SKIP QMEL QMVDW, the
action of the REFE SOLVENT command can be reproduced.)

The fluctuating charge code alters the atomic charges during
dynamics runs. Thus, the charges cannot be treated as constant and
restart and trajectory files must include atomic charges. Files read or
written during FlucQ-enabled dynamics runs will be assumed to contain
charge information, and so will be a) somewhat larger and b)
incompatible with non-FQ files. (If FlucQ is compiled in but not
activated with FLUCQ ON, the restart and trajectory file formats are
unchanged from standard CHARMM.)

The FlucQ model is implemented primarily for the study of QM/MM
systems, with a fluctuating charge SHAKE-constrained MM solvent. Hence,
intramolecular interactions are restricted to those between FlucQ atoms
along bonds. This complicates the application of the model to large systems,
as for full electronegativity equalisation, every atom must interact with
every other atom in the group.

FlucQ is not implemented for all nonbond routines, in particular the
CFF, MMFF, CRAYVEC and PARVECT codes. FlucQ also works only with standard
Ewald, and not PME.

In order for the QM/MM calculation to be properly calculated, FlucQ
requires data to be passed back to it from the QM codes (in particular
the density matrix and one-electron integrals). Changes have been made
to the QUANTUM interface for this to be carried out correctly; however,
the GAMESS(US) and CADPAC codes, not being distributed with CHARMM, will
require modification. These modifications will not affect the
functioning of standard QM/MM calculations, when FlucQ is disabled.
GAMESS-UK (versions 6.3.1 and later) should incorporate the required

Patches for GAMESS(US), and CADPAC can be found in the
source/flucq/ directory in the main CHARMM distribution. They should be
applied in the top directory of the relevant QM code distributionm
i.e. gamess-us.patch and cadpac.patch should be applied in the
source/gamint/gamess/ and source/cadint/cadpac/ directories,
respectively. The patch files are standard unified diffs, and so should
be applied with a command similar to "patch -p1 < gamess-us.patch"

The following example initialises the FlucQ code for a system of SPC
waters, before calculating the gas phase energy, and then calculating
the self-polarisation of the solvent. Finally, the total energy,
including the self-polarisation relative to the gas phase, is printed,
and the charge forces from this energy calculation are displayed.


See the testcase test/c28test/fqam1.inp for an example of a FlucQ
dynamics simulation.

The standard CHARMM nonbond routines and QM codes have been modified
so as to sum the interaction electrostatic interaction energy between
charge "I" and all other nonbond pairs or QM atoms into index "I" of
the fluctuating charge array FQCFOR. The FlucQ model actually requires
the term dE/dQ, so these totals are divided by charge by the FlucQ
energy routine (as all such interactions are linear in charge). Note
that this gives erroneous results for FlucQ sites with exactly zero
charge; however, the CHARMM nonbond routines calculate no interactions
for such systems anyway.

Finally, the intramolecular terms, as contributions to dE/dQ, are
summed into the FQCFOR array, and charge forces are calculated from
these electronegativities by mass-weighted averaging over residues or
groups. These forces are then used by the standard minimisers, or by a
standard Verlet integrator during dynamics.

For further information, see the following:-
MM system; (Rick et. al., J. Chem. Phys. 101 (7) 1994 p6141)
QM/MM interaction; (Bryce et. al., Chem. Phys. Lett. 279 1997, p367)

Tag Table:
Node: Top103
Node: Syntax1371
Node: Activation2114
Node: Charge solution6634
Node: Reference energy7793
Node: Caveats9466
Node: Using FlucQ with QM10631
Node: Examples15843
Node: Implementation16424

End Tag Table