pipf (c47b1)

Polarizable Intermolecular Potential Functions (PIPF)

by Jingzhi Pu, Shuhua Ma, and Jiali Gao
(pu@comp.chem.chem.edu, gao@chem.umn.edu)

The PIPF module provides an implementation of the Polarizable
Inter and intra molecular Potential Functions based on a point
dipole interaction model. The force field for simulating proteins
is undergoing development.

* Description | Description of the PIPF Function
* Syntax | Syntax of the PIPF commands
* Options | PIPF Command Options
* Examples | Usage Example Script
* Installation | How to install PIPF in CHARMM environment.
* Status | Status of the PIPF code
* References | References for the PIPF Method

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Description of the PIPF method

In the point dipole interaction model used in PIPF, each interaction
site i is represented by an "atomic" polarizability (alpha_i), and the
induced dipoles (u_i) are created under the total electric field
experienced at the site i (E_i):

u_i = (alpha_i)(E_i)

where the total electric field at center i (E_i) is the sum of
the permanent electric field E_i^0 (caused by permanent charges)
and the induced electric field E_i^ind (caused by other induced
dipoles via an interaction tenser T_ij):

E_i = E_i^0 + sum[(T_ij)(u_j)]
j!=i

The induced dipoles can be obtained exactly by a direct matrix
inversion or solved through a self-consistent iterative procedure.
While the former scales as N^3 where N is the number of polarizable
sites, the latter is considered to be computationally efficient.
For a system with fully converged induced dipoles, the induction
energy (E_pol) can be evaluated by:

E_pol = -(1/2) sum[(u_i)(E_i^0)]
i

For a large-sized system, alternatively, the induced dipole
can be obtained approximately by employing the extended Lagrangian
approach without full convergence, where the dipoles become independent
variables of the extended system and are allowed to evolve as functions
of time during a molecular dynamics simulation. For this dynamical dipole
approach, the induced dipoles are coupled to a Nose-Hoover bath to yield
dipoles that fluctuate around their fully converged values.

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Syntax of the PIPF commands

PIPF [CONV real] [ITER int] [PFMD int]
[DAMP int] [AFAC real] [CTOF real] [EXCL]
[DYNA] [UMAS real] [TSTA real] [UINT int] [UFRS int]
[AVDP int] [ANGL]
[MINV] [MPOL] [VPOL]

PFBA I
CALL J {atom-selection}
COEF J [UREF real] [TREF real]
....
END

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PIPF Command Options

PIPF: turn on a PIPF calculation; specified before ENERGY is called to invoke
the polarizable force field option.

DYNA: turn on dynamical dipole piston.
Default: the iterative dipole procedure is adopted.

MINV: turn on matrix inverse procedure to calculate induced dipols,
only feasible for small systems

MPOL: calculate molecular polarizability for a single molecule, has to be used
MINV

VPOL: calculate second order derivative of energy (hessian),
has to be used with MINV

CTOF: polarization energy cut-off for both DYNA and iterative cases.

DAMP: = 0, no damping (default)
= 1, Thole's damping funtion roh2 (also used by Ren & Ponder)
= 2, Thole's damping function roh4
> 2, not defined, switch to no damping.

AFAC: is user controlled parameter related to the width of the
gaussian distribution of the charge in Thole's damping
functions. AFAC is set to 0.572 or 1.662 by default for
the case of DAMP=1 or DAMP=2, respectively.

EXCL: exclude the 1-4 intramolecular polarization.

Relevant to iterative dipole:
CONV: convergence criteria (in Deby/center);
Default value: 0.01 Debye/center. Note that this is a very good
convergence especially when the number atoms are large in the system.
ITER: max number of iterations
Default: 20. You don't want to use more than 20 iterations. If you
do, check near contacts and system set up.
PFMD: =0 iteration starts from 0 dipole (default)
=1 iteration starts from converged induced dipole from last dynacal step,
efficient in MD simulations

Relevant to DYNA:
UMAS: fictitious mass for dipole [(ps/e*A)^2*kcal/mol]
TSTA: initial dipole temperature (K)
UINT: = 1, nose-hoover constant temperature control
= 2, no temperature control

UFRS: = 1, starting from zero-valued dipoles
= 2, using the zero-ordered induced dipole as start point
u = alp.E^0
= 3, starting from the fully converged dipoles
(note: for system with image atoms present, currently ONLY primary
atoms are used to compute the zero-order induced dipole for
UFRS=2 and the fully converged initial dipoles are also
computed from the primary atom interactions for UFRS=3.
However, since this is only an initial guess for dynamics,
although they are not exact, they should be a better approximation
than starting from zero dipoles.)

ANGL: calculate the angle between dynamical dipole with total electric field

AVDP: specify the number of atoms per molecule to compute
average dipoles in pure liquid simulations. The average
total/permanent/induced dipole as well as the average
angle between the permanent and induced dipole will
be printed out if this option is used.

Relevant to dynamical dipole piston, a Nose-Hoover heat bath option
is added to specify the constant T control of dipole. The keyword is

PFBA I
CALL J atom-selection
COEF J UREF [real] TREF [real]
....
END

PFBA I: altogether there are I bath
CALL J: the Jth bath is applied to selected atoms
COEF J:
UREF: the mass associated with the heat bath coordinates in the
Nose-Hoover algorithm
TREF: temperature of the bath
(Note: the setup of the heat bath coupled to the dipole dynamics is
similar to the way used in CHEQ. One may refer cheq.info for
this part of the documentation.)

Misc. options:
For cases where the skip of the polarization energy in PIPF is desired,
one can use the energy skip command "SKIP EPOL".

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Examples of PIPF

Three examples are available in the test suite to demonstrate
the usage of the PIPF command.

cpipftest/pipf_test1:
Geometry optimization of a water dimer based on the polarizable
POL2 fwater model.

cpipftest/pipf_test2:
Constant pressure and temperature MD simulations of a small water
box containing 125 POL2 waters, where the induced dipoles in PIPF
calculations are obtained by the self-consistently iterative procedure.

cpipftest/pipf_test3:
Constant pressure and temperature MD simulations of a small water
box containing 125 POL2 waters, where the induced dipoles in PIPF
calculations are updated dynamically by using an extended Lagrangian
approach.

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Installation of PIPF

To compile the PIPF code under the CHARMM environment, the 'pipf'
argument needs to be specified when CHARMM is installed.
To compile using the CMake infrastructure, execute

./configure --with-pipf
make -C build/cmake install

The 'pipf' options invoke the compilation and installation
of the PIPF code.

The atomic polarizability parameters are read in from the second
column of the NONBOND section in the CHARMM parameter file.

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Status of the PIPF code

Analytical first order derivatives are available for both the self-consistently
converged dipole and the dynamical dipole approaches in the current
implementation. Analytical second order derivatives are available only for
matrix inverse approach. Matrix inverse approach is only available for systems
without image atoms. Energy minimization and molecular dynamics (MD) simulation
are allowed for PIPF with fully converged dipoles. Alternatively, the
induced dipoles can be dynamically updated with the extended Lagrangian
method in MD simulations, in which the dipole dynamics can be coupled to
a low temperature heat bath. Treatments of periodic boundary conditions in
PIPF have been incorporated to work with both BOUNd and CRYStal. Currently,
the CHARMM atom based non-bonded list is used to determine the interacting
centers in the polarization calculation, while the intramolecular 1-4
polarization can be optionally excluded. Two of Thole's damping schemes are
available to alleviate the over polarization between two atoms that are too
close. Additionally utilities have been added (1) to monitor the average angle
between the induced dipole (U_ind) and total electric field (E_tot) in
the dynamical dipole calculations (2) to compute the average dipole
properties, i.e., total/permanent/induced dipoles and the angle between
the permanent and induced dipoles in pure liquid simulations.

Several aspects of the code will be improved in the near future,
and new functionalities are under development:

1. Polarization calculations based on group-group non-bonded list.
2. The point-dipole interaction model based on a single dipole center
for each group.
3. Compatibility with the Monte Carlo code, where the complete
non-bonded list should be used instead of a miniature non-bonded
list since the many-body character of the polarization energy term.
4. Integration with quantum module to combine QM and a polarizable
MM based on PIPF, allowing the mutual polarization between both the
QM and the MM parts.

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References

1. Ponder, J.; Case, D. A. Adv. Prot. Chem. 2003, 66, 27.

2. Kaminski, G. A.; Stern, H. A.; Berne, B. J.; Friesner, R. A.
J. Phys. Chem. A 2004, 108, 621.

3. Lamoureux, G.; MacKerell, A. D., Jr.; Roux, B. J. Chem. Phys.
2003, 119, 5185.

4. Patel, S.; Brooks, C. L. III. J. Comput. Chem. 2004, 25, 1.

5. Silberstein, L. Phil. Mag. 1917, 33, 92, 215, 521.

6. Applequist, J.; Carl, J. R.; Fung, K.-K. J. Am. Chem. Soc.
1972, 94, 2952.

7. Birge, R. R. J. Chem. Phys. 1980, 72, 5312.

8. Thole, B. T. Chem. Phys. 1981, 59, 341.

9. Ahlstrom, P.; Wallqvist, A.; Engstrom, S. Mol. Phys. 1989, 68, 563.

10. Angyan, J. G.; Colonna-Cesari, F.; Tapia, O. Chem. Phys. Lett.
1990, 166, 180.

11. Bernardo, D. N.; Ding, Y.; Krogh-Jespersen, K.; Levy, R. M.
J. Phys. Chem. 1994, 98, 4180.

12. Gao, J.; Habibollazadeh, D.; Shao, L. J. Phys. Chem. 1995, 99, 16460.

13. Gao, J.; Pavelites, J. J.; Habibollazadeh, D. J. Phys. Chem.
1996, 100, 2689.

14. Thmopson, M. J. Phys. Chem. 1996, 100, 14492.

15. Gao, J. J. Comput. Chem. 1996, 18, 1061.

16. Ren, P.; Ponder, W. J. Phys. Chem. B 2003, 107, 5933.

17. Sprik, M.; Klein, M. L. J. Chem. Phys. 1988, 89, 7556.

18. Belle, D. V.; Froeyen, M.; Lippens, G.; Wodak, S. J. Mol. Phys.
1992, 77, 239.

19. Dang, L. X. J. Chem. Phys. 1992, 97, 2659.