# pipf (c45b1)

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

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

Top

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.

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.

Top

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

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

Top

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".

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".

Top

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.

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.

Top

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.

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.

Top

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.

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.

Top

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.

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.