# pbeq (c45b2)

Poisson-Bolztmann Equation Module

The PBEQ module allows the setting up and the numerical solution of

the Poisson-Boltzmann equation on a discretized grid for a solute molecule.

Attention: Problems should be reported to

. Benoit Roux at Benoit.Roux@med.cornell.edu, phone (212) 746-6018

. Wonpil Im at Wonpil.Im@cornell.edu

. Dmitrii Beglov at beglovd@moldyn.com

* Syntax | Syntax of the PBEQ commands

* Function | Purpose of each of the commands

* Examples | Usage examples of the PBEQ module

The PBEQ module allows the setting up and the numerical solution of

the Poisson-Boltzmann equation on a discretized grid for a solute molecule.

Attention: Problems should be reported to

. Benoit Roux at Benoit.Roux@med.cornell.edu, phone (212) 746-6018

. Wonpil Im at Wonpil.Im@cornell.edu

. Dmitrii Beglov at beglovd@moldyn.com

* Syntax | Syntax of the PBEQ commands

* Function | Purpose of each of the commands

* Examples | Usage examples of the PBEQ module

Top

Syntax

[SYNTAX PBEQ functions]

Syntax:

PBEQ enter the PBEQ module

END exit the PBEQ module

Subcommands:

SOLVe PB-theory-specifications

solver-specifications grid-specifications

iteration-specifications charge interpolation-spec.

boundary potential-spec. dielectric boundary-spec.

physical variable-spec. membrane-specifications

spherical droplet-spec. orthorhombic box-spec.

cylinder-specifications solvation force-spec.

atoms-selection

ITERate PB-theory-specifications solver-specifications

iteration-specifications

ENPB [INTE atoms-selection]

CAPAcitance

COUNTERION

WRITE property [[CARD] [write-range]] [UNIT integer]

READ [PHI] [PHIX] [FKAP] [MIJ] [UNIT integer]

COOR coordinate-manipulation-command

SCALar scalar-manipulation-command

PBAVerage [PHI] [ATOM atom-selection] [UPDATE] [units]

grid-specifications

HELP

RESET

PB-theory-specifications::= [NONLinear] [PARTlinear]

default : linear PB by default (no need to specify)

NONLin [.FALSE.] : non-linear PBEQ solver

PARTlin [.FALSE.] : partially linearized PBEQ solver

solver-specifications::=[OLDPB]

[OSOR] [UNDER] [[FMGR] [NCYC integer] [NPRE integer] [NPOS integer]]

default : SOR (Successive OverRelaxation) method for linearized PB

OLDPB [.FALSE.] : old PBEQ solver (used in c26a2)

OSOR [.FALSE.] : optimization of the over-relaxation parameter

UNDER [.FALSE.] : Under-relaxation for non-linear and partially linearized

PBEQ solvers with fixed LAMBda value

FMGR [.FALSE.] : full multigrid method

NCYC [100] : maximum number of cycles (in FMGR)

NPRE [2] : number of relaxation for PRE-smoothing (in FMGR)

NPOS [2] : number of relaxation for POST-smoothing (in FMGR)

grid-specifications::= [NCEL integer] [DCEL real]

[NCLX integer] [NCLY integer] [NCLZ integer]

[XBCEN real] [YBCEN real] [ZBCEN real]

NCEL [65] : number of grid point in 1D for a cubic

DCEL [0.1] : size of grid unit cell

NCLX [NCEL] : number of grid point in X for general parallelepiped

NCLY [NCEL] : number of grid point in Y for general parallelepiped

NCLZ [NCEL] : number of grid point in Z for general parallelepiped

XBCEN [0.0] : the center of a box in X

YBCEN [0.0] : the center of a box in Y

ZBCEN [0.0] : the center of a box in Z

iteration-specifications::=[MAXIter integer] [DEPS real]

[DOMEga real] [LAMBda real] [KEEPphi]

MAXIter [2000] : number of iterations

DEPS [0.000002] : parameter (tolerance) of convergence

DOMEga [1.0] : initial mixing factor

LAMBda [1.0] : initial mixing factor (LAMBda = DOMEga)

KEEPphi [.FALSE.] : Use the potential from previous calculation

as a initial guess for current calculation

charge interpolation-spec.::= [BSPLine]

default : the trilinear interpolation method

BSPLine [.FALSE.] : the Cardinal B-spline method is used?

boundary potential-specifications::= [ZERO] [INTBP] [FOCUS] [PBC] [NPBC]

[NIMGB integer]

default : use the Debye-Huckel approximation at each boundary point

use XY periodic boundary conditions in membrane

calculation

INTBP [.FALSE.] : INTerpolation of Boundary Potential is used?

ZERO [.FALSE.] : boundary potential is set to ZERO ?

(metallic conductor boundary conditions)

FOCUS [.FALSE.] : previous potential is used to set up boundary potential?

PBC [.FALSE.] : 3d periodic boundary condition

NPBC [.FALSE.] : supress XY periodic boundary conditions in membrane

calculations

NIMGB [0] : use the image atoms for boundary potential

in membrane calculation

(NIMGB=1 means the 8 nearest image cells)

(NIMGB=2 means the 24 nearest image cells, i.e.,

2 shells of images)

dielectric boundary-specifications::= [SMOOTH] [SWIN real] [REEN]

default : the vdW surface is used for the dielectric boundary

SMOOth [.FALSE.] : invoke smoothing dielectric boundary

SWIN [0.5] : solute-solvent dielectric boundary Smoothing WINdow

REEN [.FALSE.] : the molecular (contact+reentrant) surface is created

with WATRadius for the dielectric boundary

physical variable-specifications::= [EPSW real] [EPSP real]

[WATR real] [IONR real]

[CONC real] [TEMP real]

EPSW [80.0] : bulk solvent dielectric constant

EPSP [1.0] : protein interior dielectric constant

WATR [0.0] : solvent probe radius

IONR [0.0] : ion exclusion radius (Stern layer)

CONC [0.0] : salt concentration [moles/liter]

TEMP [300.0] : Temperature [K]

membrane-specifications:: [TMEMb real] [HTMEmb real] [ZMEMb real] [EPSM real]

[EPSH real] [VMEMB real]

TMEMB [0.0] : thickness of membrane (along Z)

HTMEMB [0.0] : thickness of headgroup region

ZMEMB [0.0] : membrane position (along Z)

EPSM [1.0] : membrane dielectric constant

EPSH [EPSM] : membrane headgroup dielectric constant (optional)

VMEMB [0.0] : potential difference across membrane (entered in [volts])

spherical droplet-spec.::= [DROPlet real] [EPSD real]

[XDROplet real] [YDROplet real] [ZDROplet real]

[DTOM] [DKAP]

DROPlet [0.0] : radius of spherical droplet

EPSD [1.0] : dielectric constant of spherical droplet

XDROp [0.0] : position of spherical droplet in X

YDROp [0.0] : position of spherical droplet in Y

ZDROp [0.0] : position of spherical droplet in Z

DTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

DKAP [.FALSE.] : the Debye-Huckel factor inside sphere is set to KAPPA ?

orthorhombic box-spec.::= [LXMAx real] [LYMAx real] [LZMAx real]

[LXMIn real] [LYMIn real] [LZMIn real]

[BTOM] [BKAP]

LXMAx [0.0] : maximum position of a box along X-axis

LYMAx [0.0] : maximum position of a box along Y-axis

LZMAx [0.0] : maximum position of a box along Z-axis

LXMIn [0.0] : minimum position of a box along X-axis

LYMIn [0.0] : minimum position of a box along Y-axis

LZMIn [0.0] : minimum position of a box along Z-axis

EPSB [1.0] : dielectric constant inside box

BTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

BKAP [.FALSE.] : the Debye-Huckel factor inside box is set to KAPPA?

cylinder-specifications::= [RCYLN real] [HCYLN real] [EPSC real]

[XCYLN real] [YCYLN real] [ZCYLN real]

[CTOM] [CKAP]

RCYLN [0.0] : radius of cylinder

HCYLN [0.0] : height of cylinder

EPSC [1.0] : dielectric constant inside cylinder

XCYLN [0.0] : position of cylinder in X

YCYLN [0.0] : position of cylinder in Y

ZCYLN [0.0] : position of cylinder in Z

CTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

CKAP [.FALSE.] : the Debye-Huckel factor inside cylinder is set to KAPPA?

solvation force-spec.::= [FORCE] [STEN real] [NPBEQ integer]

FORCe [.FALSE.] : invoke solvation force calculation

STEN [0.0] : surface tension coefficient (in kcal/mol/A^2)

NPBEQ [1] : the frequency for calculating solvation forces

during minimizations and MD simulations

EPSU [-1] : unit to read given epsilon grid from

xval yval zval epsx epsy epsz

...

EPSG [-1] : unit to read given epsilon grid from

nx ny nz

xmin ymin zmin

dx dy dz

epsx epsy epsz

...

write-range::= [XFIRST real] [YFIRST real] [ZFIRST real]

[XLAST real] [YLAST real] [ZLAST real]

property::= [[PHI] [KCAL] [VOLTS]] [[PHIX] [KCAL] [VOLTS]]

[FKAPPA2]

[CHRG]

[EPSX] [EPSY] [EPSZ]

[MIJ]

[TITLE]

PHI : electrostatic potential [ KCAL/MOL ] [ VOLTS ]

(default [UNIT CHARGE]/[ANGS])

PHIX : external static electrostatic Potential [ KCAL/MOL ] [ VOLTS ]

(default [UNIT CHARGE]/[ANGS])

FKAPPA2 : Debye screening factor

CHRG : charges on the lattice

EPSX : X sets of dielectric constant

EPSY : Y sets of dielectric constant

EPSZ : Z sets of dielectric constant

MIJ : MIJ matrix

TITLE : formatted title line

atoms-selection::= a selection of a group of atoms

Syntax

[SYNTAX PBEQ functions]

Syntax:

PBEQ enter the PBEQ module

END exit the PBEQ module

Subcommands:

SOLVe PB-theory-specifications

solver-specifications grid-specifications

iteration-specifications charge interpolation-spec.

boundary potential-spec. dielectric boundary-spec.

physical variable-spec. membrane-specifications

spherical droplet-spec. orthorhombic box-spec.

cylinder-specifications solvation force-spec.

atoms-selection

ITERate PB-theory-specifications solver-specifications

iteration-specifications

ENPB [INTE atoms-selection]

CAPAcitance

COUNTERION

WRITE property [[CARD] [write-range]] [UNIT integer]

READ [PHI] [PHIX] [FKAP] [MIJ] [UNIT integer]

COOR coordinate-manipulation-command

SCALar scalar-manipulation-command

PBAVerage [PHI] [ATOM atom-selection] [UPDATE] [units]

grid-specifications

HELP

RESET

PB-theory-specifications::= [NONLinear] [PARTlinear]

default : linear PB by default (no need to specify)

NONLin [.FALSE.] : non-linear PBEQ solver

PARTlin [.FALSE.] : partially linearized PBEQ solver

solver-specifications::=[OLDPB]

[OSOR] [UNDER] [[FMGR] [NCYC integer] [NPRE integer] [NPOS integer]]

default : SOR (Successive OverRelaxation) method for linearized PB

OLDPB [.FALSE.] : old PBEQ solver (used in c26a2)

OSOR [.FALSE.] : optimization of the over-relaxation parameter

UNDER [.FALSE.] : Under-relaxation for non-linear and partially linearized

PBEQ solvers with fixed LAMBda value

FMGR [.FALSE.] : full multigrid method

NCYC [100] : maximum number of cycles (in FMGR)

NPRE [2] : number of relaxation for PRE-smoothing (in FMGR)

NPOS [2] : number of relaxation for POST-smoothing (in FMGR)

grid-specifications::= [NCEL integer] [DCEL real]

[NCLX integer] [NCLY integer] [NCLZ integer]

[XBCEN real] [YBCEN real] [ZBCEN real]

NCEL [65] : number of grid point in 1D for a cubic

DCEL [0.1] : size of grid unit cell

NCLX [NCEL] : number of grid point in X for general parallelepiped

NCLY [NCEL] : number of grid point in Y for general parallelepiped

NCLZ [NCEL] : number of grid point in Z for general parallelepiped

XBCEN [0.0] : the center of a box in X

YBCEN [0.0] : the center of a box in Y

ZBCEN [0.0] : the center of a box in Z

iteration-specifications::=[MAXIter integer] [DEPS real]

[DOMEga real] [LAMBda real] [KEEPphi]

MAXIter [2000] : number of iterations

DEPS [0.000002] : parameter (tolerance) of convergence

DOMEga [1.0] : initial mixing factor

LAMBda [1.0] : initial mixing factor (LAMBda = DOMEga)

KEEPphi [.FALSE.] : Use the potential from previous calculation

as a initial guess for current calculation

charge interpolation-spec.::= [BSPLine]

default : the trilinear interpolation method

BSPLine [.FALSE.] : the Cardinal B-spline method is used?

boundary potential-specifications::= [ZERO] [INTBP] [FOCUS] [PBC] [NPBC]

[NIMGB integer]

default : use the Debye-Huckel approximation at each boundary point

use XY periodic boundary conditions in membrane

calculation

INTBP [.FALSE.] : INTerpolation of Boundary Potential is used?

ZERO [.FALSE.] : boundary potential is set to ZERO ?

(metallic conductor boundary conditions)

FOCUS [.FALSE.] : previous potential is used to set up boundary potential?

PBC [.FALSE.] : 3d periodic boundary condition

NPBC [.FALSE.] : supress XY periodic boundary conditions in membrane

calculations

NIMGB [0] : use the image atoms for boundary potential

in membrane calculation

(NIMGB=1 means the 8 nearest image cells)

(NIMGB=2 means the 24 nearest image cells, i.e.,

2 shells of images)

dielectric boundary-specifications::= [SMOOTH] [SWIN real] [REEN]

default : the vdW surface is used for the dielectric boundary

SMOOth [.FALSE.] : invoke smoothing dielectric boundary

SWIN [0.5] : solute-solvent dielectric boundary Smoothing WINdow

REEN [.FALSE.] : the molecular (contact+reentrant) surface is created

with WATRadius for the dielectric boundary

physical variable-specifications::= [EPSW real] [EPSP real]

[WATR real] [IONR real]

[CONC real] [TEMP real]

EPSW [80.0] : bulk solvent dielectric constant

EPSP [1.0] : protein interior dielectric constant

WATR [0.0] : solvent probe radius

IONR [0.0] : ion exclusion radius (Stern layer)

CONC [0.0] : salt concentration [moles/liter]

TEMP [300.0] : Temperature [K]

membrane-specifications:: [TMEMb real] [HTMEmb real] [ZMEMb real] [EPSM real]

[EPSH real] [VMEMB real]

TMEMB [0.0] : thickness of membrane (along Z)

HTMEMB [0.0] : thickness of headgroup region

ZMEMB [0.0] : membrane position (along Z)

EPSM [1.0] : membrane dielectric constant

EPSH [EPSM] : membrane headgroup dielectric constant (optional)

VMEMB [0.0] : potential difference across membrane (entered in [volts])

spherical droplet-spec.::= [DROPlet real] [EPSD real]

[XDROplet real] [YDROplet real] [ZDROplet real]

[DTOM] [DKAP]

DROPlet [0.0] : radius of spherical droplet

EPSD [1.0] : dielectric constant of spherical droplet

XDROp [0.0] : position of spherical droplet in X

YDROp [0.0] : position of spherical droplet in Y

ZDROp [0.0] : position of spherical droplet in Z

DTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

DKAP [.FALSE.] : the Debye-Huckel factor inside sphere is set to KAPPA ?

orthorhombic box-spec.::= [LXMAx real] [LYMAx real] [LZMAx real]

[LXMIn real] [LYMIn real] [LZMIn real]

[BTOM] [BKAP]

LXMAx [0.0] : maximum position of a box along X-axis

LYMAx [0.0] : maximum position of a box along Y-axis

LZMAx [0.0] : maximum position of a box along Z-axis

LXMIn [0.0] : minimum position of a box along X-axis

LYMIn [0.0] : minimum position of a box along Y-axis

LZMIn [0.0] : minimum position of a box along Z-axis

EPSB [1.0] : dielectric constant inside box

BTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

BKAP [.FALSE.] : the Debye-Huckel factor inside box is set to KAPPA?

cylinder-specifications::= [RCYLN real] [HCYLN real] [EPSC real]

[XCYLN real] [YCYLN real] [ZCYLN real]

[CTOM] [CKAP]

RCYLN [0.0] : radius of cylinder

HCYLN [0.0] : height of cylinder

EPSC [1.0] : dielectric constant inside cylinder

XCYLN [0.0] : position of cylinder in X

YCYLN [0.0] : position of cylinder in Y

ZCYLN [0.0] : position of cylinder in Z

CTOM [.FALSE.] : the dielectric constant of the overlapped region

with membrane is set to EPSM ?

CKAP [.FALSE.] : the Debye-Huckel factor inside cylinder is set to KAPPA?

solvation force-spec.::= [FORCE] [STEN real] [NPBEQ integer]

FORCe [.FALSE.] : invoke solvation force calculation

STEN [0.0] : surface tension coefficient (in kcal/mol/A^2)

NPBEQ [1] : the frequency for calculating solvation forces

during minimizations and MD simulations

EPSU [-1] : unit to read given epsilon grid from

xval yval zval epsx epsy epsz

...

EPSG [-1] : unit to read given epsilon grid from

nx ny nz

xmin ymin zmin

dx dy dz

epsx epsy epsz

...

write-range::= [XFIRST real] [YFIRST real] [ZFIRST real]

[XLAST real] [YLAST real] [ZLAST real]

property::= [[PHI] [KCAL] [VOLTS]] [[PHIX] [KCAL] [VOLTS]]

[FKAPPA2]

[CHRG]

[EPSX] [EPSY] [EPSZ]

[MIJ]

[TITLE]

PHI : electrostatic potential [ KCAL/MOL ] [ VOLTS ]

(default [UNIT CHARGE]/[ANGS])

PHIX : external static electrostatic Potential [ KCAL/MOL ] [ VOLTS ]

(default [UNIT CHARGE]/[ANGS])

FKAPPA2 : Debye screening factor

CHRG : charges on the lattice

EPSX : X sets of dielectric constant

EPSY : Y sets of dielectric constant

EPSZ : Z sets of dielectric constant

MIJ : MIJ matrix

TITLE : formatted title line

atoms-selection::= a selection of a group of atoms

Top

General discussion regarding the PBEQ module

1. SOLVE

Prepare grids and solve PB equation for the selected atoms and return the

electrostatic free energy in ?enpb = (1/2)*Sum Q_i PHI_i over the lattice.

The factor of 1/2 is there for the linear response free energy of charging.

The atomic contributions are returned in WMAIN (destroying the radii).

NOTE: At the first stage of PBEQ or after "RESET", WMAIN should be set to

the atomic radii for the calculation. After a call to SOLVE the atomic

radii are saved in a special array. The atomic contribution to the

electrostatic free energy are returned in WMAIN (destroying the radii).

To modify the value of the radii, the keyword RESET must be issued.

1) PB SOLVERs

(Reference: Klapper et al. Proteins 1, 47 (1986)

A. Nicholls et al; J. Comput. Chem, 12(4),435-445 (1991))

Currently, PBEQ module supports various PB equation solvers.

The default solver uses the SOR (Successive OverRelaxation) method for

the linearized PB equation.

This is much faster than the old PBEQ solver which was used in c26a2.

With OSOR keyword, the relaxation parameter will be optimized. This is

especially useful when the system contains a salt concentration.

Solvers for non-linear and partially linearized PB equations for

1:1 charge-paired salt are now available. Both use the SOR method as a

default. In many cases, the direct use of both solvers may cause some

convergence problems. So, it is the best way to use the potential from

the linearized PB equation as a initial guess. Though, you may want to

use the under-relaxation by adjusting the mixing factor (LAMBda).

The partially linearized PB equation means that the linearized form of

one of two exponential function is used like

phi > 0 --> exp(phi) = 1 + phi

phi < 0 --> exp(-phi) = 1 - phi

Full multigrid (FMG) method is efficient for the uniform dielectric

medium. When there is a discontinuity in the dielectric function,

the method could be slower than the SOR method. You can improve the

calculation speed using the smoothing dielectric boundary. Cubic grid

should be used and number of grid points should be 2**(n+1) where n is

a integer upto 9. Currently, FMG does not support MEMBRANE and PBC.

(see ~chmtest/c28/pbeqtest5.inp and pbeqtest6.inp)

2) Grid

The number of grid points in X, Y, and Z (NCEL,NCLX,NCLY,NCLZ) must

be odd. Otherwise, the number of grid points will be increased by ONE

without any WARNING message.

3) Iteration

The maximum number of iterations (MAXIter) can be specified.

The convergence parameters DEPS should not be modified.

One could use the potential from previous calculation as a initial

guess for current calculation using KEEPphi keyword. This is useful for

the nonlinear (or partially linearized) PB equation. See also ITERate.

4) Charge Distribution Method

The default is the trilinear method to distribute a charge over

nearest 8 grid points. BSPLINE keyword will invoke the 3rd-order

B-splines interpolation over nearest 27 grid points.

B-splines method removes discontinuities in the reaction field forces.

5) Boundary Potential

By default, boundary potential is calculated using the Debye-Huckel

approximation for every boundary point. However, the computational

time increases prohibitively as the number of grid points and of atoms

in the system increases.

INTBP keyword uses the bilinear interpolation to construct

boundary potential in a box with DCEL and (NCLx,NCLy,NCLz) from those

in the same box with 2*DCEL and (NCLx/2+1,NCLy/2+1,NCLz/2+1).

ZERO keyword sets boundary potential at the edge of the grid to zero.

FOCUS keyword uses previously calculated potentials to set up boundary

potential.

(Reference: M.K. Gilson et al; J. Comput. Chem. 9(4),327-335 (1987))

(see also an example below)

PBC keyword invokes the full 3d periodic boundary condition so that

no boundary potential is calculated directly using the Debye-Huckel

approximation.

(Reference: P.H. Hunenberger and J.A. McCammon JCP v.110(4) p.1856 (1999))

(alos, see ~chmtest/c28/pbeqtest4.inp)

NPBC keyword surpress XY periodic boundary conditions in membrane

calculations.

Boundary potential of XY plane in membrane calculations can be constructed

using the image atoms. When NIMGB=1, boundary potential includes the

influence of the 8 nearest image cells.

6) Dielectric boundary

SMOOTH and REEN change the attribute of the solute-solvent boundary.

By default (NO SMOOTH), the boundary is defined by the van der Waals

surface or the molecular surface (with WATR). SMOOTH keyword changes

the boundary as a region having +/- SWIN (Smoothing WINdow) from the

surface of the solute. Within the solute-solvent boundary,

the dielectric constant and the Debye screening factor will be changed

continuously from EPSP and zero to EPSW and the screening factor

at bulk solvent.

REEN keyword with WATR creates the molecular (contact+reentrant) surface

as the dielectric boundary.

NOTE: WATR without REEN just increases the atomic radii by it.

7) Various geometric objects

PBEQ module supports three geometric objects with various options

(see spherical droplet-, orthorhombic box-, and cylinder-spec. above)

When using more than one geometry at the same time, the order of creating

geometries is as follows: first is a droplet, second is a cylinder, and

the last is a box.

4) Solvation force

This keyword invokes the calculation of the solvation free energy and

forces and must be followed by SMOOTH keyword. The solvation energy is

taken as a sum of electrostatic and nonpolar solvation energy.

The former is calculated from the PB equation and the latter by using

the surface tension coefficient (STEN) that relates free energy with

surface area. Note that the calculated surface is approximately the

van der Waals surface. If membrane is considered, the surface of the

membrane is also approximately included. The corresponding forces are

also calculated and will be used in minimizations and MD simulations

where NPBEQ can be used to specify the frequency for calculating the

solvation forces. Note that SWIN must be equal or greater to DCEL to

get correct solvation free energy and forces.

(Reference: W. Im, D. Beglov and B. Roux

Continuum Solvation Model: computation of electrostatic

forces from numerical solutions to the PB equation,

Comput. Phys. Commun. 109,1-17 (1998))

NOTE:To print out the force of each atom, PRNLEV should be greater

than 6.

2. ITERATE

Pursue the iteration on the grid. SOLVE must have been called first.

The main difference with the keyword KEEPphi (see above) is that the

physical specifications (e.g., dielectric interface, membrane, etc...)

must remain the same with ITERate. However, it is possible to change

from linear to non-linear PB using ITERate. (see pbeqtest5.inp)

3. ENPB

Compute the electrostatic PB energy Sum Q_i PHI_i over the lattice.

Notice that the electrostatic energy is twice as much as the electrostatic

free energy (see above). The value of the electrostatic energy is passed

through the substitution parameter enpb. With INTE keyword, you can specify

the atoms of interest.

4. CAPACITANCE

Compute the capacitance based on the net induced charge in the double

layer. The induced charge beyond the limits of the box are estimated based on

the analytical solution to a planar membrane.

5. COUNTERION

Compute the counter-ion (1:1 salt) distribution along Z-axis.

6. WRITE

The WRITE command is used to write out the grid properties. By default,

a binary file of the property will be written for the whole grid. The keyword

CARD implies that a formatted output will be produced. In that case, the

spatial range can be specified for the output. By default, the electrostatic

potential PHI is given in [UNIT CHARGE]/[ANGS]. If specified, the PHI can be

given in [VOLTS] or in [KCAL/MOL].

7. READ

The READ command is used to read the electrostatic potential PHI or PHIX

in [UNIT CHARGE]/[ANGS], Debye screening factor FKAPPA2, and

the generalized reaction field MIJ matrix written in a binary file.

8. RESET

Resets all assignments of the PBEQ module and free the HEAP array.

Destroys all lists and grids. By default, the grids and arrays remain assigned

when exiting and re-entering the PBEQ module. This is to allow multiple call

to PBEQ without having to free the HEAP and other arrays if they are going

to be used again. The RESET keyword must be used to re-assign new values for

the atomic radii.

9. Miscellaneous command manipulations

allowing opening and closing of files, streaming of files, label assignments

(e.g., LABEL), and repeated loops (e.g., GOTO), parameter substitutions

(e.g., @1,@2, etc...) control (e.g., IF 1 eq 10.0 GOTO LOOP) and CALC

(e.g., CALC energy = ?enpb).

NOTE: TIMER 2 gives the times of various components in PBEQ module;

the grid parameter preparation (subroutine MAYER),

iterative solution (subroutine PBEQ1), and,

force calculation (subroutine RFORCE and BFORCE).

10. COORMAN and SCALAR commands

the PBEQ module, allowing the easy manipulation of charges, radii, rotation

and translations of molecules, etc...

11. A set of "ATOMIC BORN RADII"

Atomic radii derived from solvent electrostatic charge distribution may be

used. (test/data/radius.str) These radii were tested with free energy

perturbation with explicit solvent.

(Reference: M. Nina, D. Beglov and B. Roux.

Atomic Radii for Continuum Electrostatics Calculations based on

Molecular Dynamics Free Energy Simulations.

J. Phys. Chem. 101(26),5239-5248,1997).

NOTE: A typo for residue HSD was present in the original set of radii.

Check with M. Nina for new updated file.

To get the set of appropriate radii when using SWIN,

the commands are as follows;

STREAM RADIUS.STR

SCALAR WMAIN ADD {SWIN}

SCALAR WMAIN MULT {FACTOR}

SCALAR WMAIN SET 0.0 SELE TYPE H* END

The factor has a linear relationship with SWIN.

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

SWIN 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FACTOR 0.979 0.965 0.952 0.939 0.927 0.914 0.901 0.888 0.875 0.861

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

** FACTOR = -0.1296 x SWIN + 0.9914 (a least-square fit)

12. PBAVerage subcommand

This subcommand allows for the averaging of the (precalculated) electrostatic

potential (PHI values) over specified regions of the grid. The region is

specified as a rectangular box, with or without an atom selection. The units

may be specified as KCAL (kcal/mol), VOLT (volts), or not at all, in which

case the default units (charge/angs) are used. The calculated average may

be assigned to a CHARMM parameter through the symbol ?AVPH. The PBAV PHI

subcommand does not calculate the PHI values themselves; hence the electro-

static potential should have already been calculated before this subcommand

is given.

The following calculates the average PHI value over a rectangular-box region

of the grid:

PBAV PHI KCAL xfirst [real] xlast [real] -

yfirst [real] ylast [real] -

zfirst [real] zlast [real]

The grid limits must be specified the first time the PBAV PHI subcommand is

invoked. For subsequent invocations, the command will use the stored limits

unless the limits are respecified.

The following calculates the average PHI values over the grid points that are

both within the grid limits and within the van der Waals radii of the selected

atoms:

PBAV PHI KCAL UPDAte xfirst [real] xlast [real] -

yfirst [real] ylast [real] -

zfirst [real] zlast [real] -

ATOM SELE [selection] END

The UPDAte keyword updates the atom-based grid, so that when the

PBAV PHI ATOM subcommand is given for the first time, the UPDATE keyword

must be used and an atom selection given. For subsequent invocations,

the atom selection (for defining the set of atoms over which the

calculation is to be done) and the UPDATE command (for updating the

grid, based on the position of the selected atoms) are optional.

If UPDATE is specified but the atom selection (or grid limits) are not,

the algorithm will use the atom selection (or grid limits) that were

last specified. If the PBAV PHI subcommand has not been

previously given, the grid limits must be specified.

General discussion regarding the PBEQ module

1. SOLVE

Prepare grids and solve PB equation for the selected atoms and return the

electrostatic free energy in ?enpb = (1/2)*Sum Q_i PHI_i over the lattice.

The factor of 1/2 is there for the linear response free energy of charging.

The atomic contributions are returned in WMAIN (destroying the radii).

NOTE: At the first stage of PBEQ or after "RESET", WMAIN should be set to

the atomic radii for the calculation. After a call to SOLVE the atomic

radii are saved in a special array. The atomic contribution to the

electrostatic free energy are returned in WMAIN (destroying the radii).

To modify the value of the radii, the keyword RESET must be issued.

1) PB SOLVERs

(Reference: Klapper et al. Proteins 1, 47 (1986)

A. Nicholls et al; J. Comput. Chem, 12(4),435-445 (1991))

Currently, PBEQ module supports various PB equation solvers.

The default solver uses the SOR (Successive OverRelaxation) method for

the linearized PB equation.

This is much faster than the old PBEQ solver which was used in c26a2.

With OSOR keyword, the relaxation parameter will be optimized. This is

especially useful when the system contains a salt concentration.

Solvers for non-linear and partially linearized PB equations for

1:1 charge-paired salt are now available. Both use the SOR method as a

default. In many cases, the direct use of both solvers may cause some

convergence problems. So, it is the best way to use the potential from

the linearized PB equation as a initial guess. Though, you may want to

use the under-relaxation by adjusting the mixing factor (LAMBda).

The partially linearized PB equation means that the linearized form of

one of two exponential function is used like

phi > 0 --> exp(phi) = 1 + phi

phi < 0 --> exp(-phi) = 1 - phi

Full multigrid (FMG) method is efficient for the uniform dielectric

medium. When there is a discontinuity in the dielectric function,

the method could be slower than the SOR method. You can improve the

calculation speed using the smoothing dielectric boundary. Cubic grid

should be used and number of grid points should be 2**(n+1) where n is

a integer upto 9. Currently, FMG does not support MEMBRANE and PBC.

(see ~chmtest/c28/pbeqtest5.inp and pbeqtest6.inp)

2) Grid

The number of grid points in X, Y, and Z (NCEL,NCLX,NCLY,NCLZ) must

be odd. Otherwise, the number of grid points will be increased by ONE

without any WARNING message.

3) Iteration

The maximum number of iterations (MAXIter) can be specified.

The convergence parameters DEPS should not be modified.

One could use the potential from previous calculation as a initial

guess for current calculation using KEEPphi keyword. This is useful for

the nonlinear (or partially linearized) PB equation. See also ITERate.

4) Charge Distribution Method

The default is the trilinear method to distribute a charge over

nearest 8 grid points. BSPLINE keyword will invoke the 3rd-order

B-splines interpolation over nearest 27 grid points.

B-splines method removes discontinuities in the reaction field forces.

5) Boundary Potential

By default, boundary potential is calculated using the Debye-Huckel

approximation for every boundary point. However, the computational

time increases prohibitively as the number of grid points and of atoms

in the system increases.

INTBP keyword uses the bilinear interpolation to construct

boundary potential in a box with DCEL and (NCLx,NCLy,NCLz) from those

in the same box with 2*DCEL and (NCLx/2+1,NCLy/2+1,NCLz/2+1).

ZERO keyword sets boundary potential at the edge of the grid to zero.

FOCUS keyword uses previously calculated potentials to set up boundary

potential.

(Reference: M.K. Gilson et al; J. Comput. Chem. 9(4),327-335 (1987))

(see also an example below)

PBC keyword invokes the full 3d periodic boundary condition so that

no boundary potential is calculated directly using the Debye-Huckel

approximation.

(Reference: P.H. Hunenberger and J.A. McCammon JCP v.110(4) p.1856 (1999))

(alos, see ~chmtest/c28/pbeqtest4.inp)

NPBC keyword surpress XY periodic boundary conditions in membrane

calculations.

Boundary potential of XY plane in membrane calculations can be constructed

using the image atoms. When NIMGB=1, boundary potential includes the

influence of the 8 nearest image cells.

6) Dielectric boundary

SMOOTH and REEN change the attribute of the solute-solvent boundary.

By default (NO SMOOTH), the boundary is defined by the van der Waals

surface or the molecular surface (with WATR). SMOOTH keyword changes

the boundary as a region having +/- SWIN (Smoothing WINdow) from the

surface of the solute. Within the solute-solvent boundary,

the dielectric constant and the Debye screening factor will be changed

continuously from EPSP and zero to EPSW and the screening factor

at bulk solvent.

REEN keyword with WATR creates the molecular (contact+reentrant) surface

as the dielectric boundary.

NOTE: WATR without REEN just increases the atomic radii by it.

7) Various geometric objects

PBEQ module supports three geometric objects with various options

(see spherical droplet-, orthorhombic box-, and cylinder-spec. above)

When using more than one geometry at the same time, the order of creating

geometries is as follows: first is a droplet, second is a cylinder, and

the last is a box.

4) Solvation force

This keyword invokes the calculation of the solvation free energy and

forces and must be followed by SMOOTH keyword. The solvation energy is

taken as a sum of electrostatic and nonpolar solvation energy.

The former is calculated from the PB equation and the latter by using

the surface tension coefficient (STEN) that relates free energy with

surface area. Note that the calculated surface is approximately the

van der Waals surface. If membrane is considered, the surface of the

membrane is also approximately included. The corresponding forces are

also calculated and will be used in minimizations and MD simulations

where NPBEQ can be used to specify the frequency for calculating the

solvation forces. Note that SWIN must be equal or greater to DCEL to

get correct solvation free energy and forces.

(Reference: W. Im, D. Beglov and B. Roux

Continuum Solvation Model: computation of electrostatic

forces from numerical solutions to the PB equation,

Comput. Phys. Commun. 109,1-17 (1998))

NOTE:To print out the force of each atom, PRNLEV should be greater

than 6.

2. ITERATE

Pursue the iteration on the grid. SOLVE must have been called first.

The main difference with the keyword KEEPphi (see above) is that the

physical specifications (e.g., dielectric interface, membrane, etc...)

must remain the same with ITERate. However, it is possible to change

from linear to non-linear PB using ITERate. (see pbeqtest5.inp)

3. ENPB

Compute the electrostatic PB energy Sum Q_i PHI_i over the lattice.

Notice that the electrostatic energy is twice as much as the electrostatic

free energy (see above). The value of the electrostatic energy is passed

through the substitution parameter enpb. With INTE keyword, you can specify

the atoms of interest.

4. CAPACITANCE

Compute the capacitance based on the net induced charge in the double

layer. The induced charge beyond the limits of the box are estimated based on

the analytical solution to a planar membrane.

5. COUNTERION

Compute the counter-ion (1:1 salt) distribution along Z-axis.

6. WRITE

The WRITE command is used to write out the grid properties. By default,

a binary file of the property will be written for the whole grid. The keyword

CARD implies that a formatted output will be produced. In that case, the

spatial range can be specified for the output. By default, the electrostatic

potential PHI is given in [UNIT CHARGE]/[ANGS]. If specified, the PHI can be

given in [VOLTS] or in [KCAL/MOL].

7. READ

The READ command is used to read the electrostatic potential PHI or PHIX

in [UNIT CHARGE]/[ANGS], Debye screening factor FKAPPA2, and

the generalized reaction field MIJ matrix written in a binary file.

8. RESET

Resets all assignments of the PBEQ module and free the HEAP array.

Destroys all lists and grids. By default, the grids and arrays remain assigned

when exiting and re-entering the PBEQ module. This is to allow multiple call

to PBEQ without having to free the HEAP and other arrays if they are going

to be used again. The RESET keyword must be used to re-assign new values for

the atomic radii.

9. Miscellaneous command manipulations

**»**miscom are supported within the PBEQ module,allowing opening and closing of files, streaming of files, label assignments

(e.g., LABEL), and repeated loops (e.g., GOTO), parameter substitutions

(e.g., @1,@2, etc...) control (e.g., IF 1 eq 10.0 GOTO LOOP) and CALC

(e.g., CALC energy = ?enpb).

NOTE: TIMER 2 gives the times of various components in PBEQ module;

the grid parameter preparation (subroutine MAYER),

iterative solution (subroutine PBEQ1), and,

force calculation (subroutine RFORCE and BFORCE).

10. COORMAN and SCALAR commands

**»**corman and » scalar are supported withinthe PBEQ module, allowing the easy manipulation of charges, radii, rotation

and translations of molecules, etc...

11. A set of "ATOMIC BORN RADII"

Atomic radii derived from solvent electrostatic charge distribution may be

used. (test/data/radius.str) These radii were tested with free energy

perturbation with explicit solvent.

(Reference: M. Nina, D. Beglov and B. Roux.

Atomic Radii for Continuum Electrostatics Calculations based on

Molecular Dynamics Free Energy Simulations.

J. Phys. Chem. 101(26),5239-5248,1997).

NOTE: A typo for residue HSD was present in the original set of radii.

Check with M. Nina for new updated file.

To get the set of appropriate radii when using SWIN,

the commands are as follows;

STREAM RADIUS.STR

SCALAR WMAIN ADD {SWIN}

SCALAR WMAIN MULT {FACTOR}

SCALAR WMAIN SET 0.0 SELE TYPE H* END

The factor has a linear relationship with SWIN.

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

SWIN 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FACTOR 0.979 0.965 0.952 0.939 0.927 0.914 0.901 0.888 0.875 0.861

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

** FACTOR = -0.1296 x SWIN + 0.9914 (a least-square fit)

12. PBAVerage subcommand

This subcommand allows for the averaging of the (precalculated) electrostatic

potential (PHI values) over specified regions of the grid. The region is

specified as a rectangular box, with or without an atom selection. The units

may be specified as KCAL (kcal/mol), VOLT (volts), or not at all, in which

case the default units (charge/angs) are used. The calculated average may

be assigned to a CHARMM parameter through the symbol ?AVPH. The PBAV PHI

subcommand does not calculate the PHI values themselves; hence the electro-

static potential should have already been calculated before this subcommand

is given.

The following calculates the average PHI value over a rectangular-box region

of the grid:

PBAV PHI KCAL xfirst [real] xlast [real] -

yfirst [real] ylast [real] -

zfirst [real] zlast [real]

The grid limits must be specified the first time the PBAV PHI subcommand is

invoked. For subsequent invocations, the command will use the stored limits

unless the limits are respecified.

The following calculates the average PHI values over the grid points that are

both within the grid limits and within the van der Waals radii of the selected

atoms:

PBAV PHI KCAL UPDAte xfirst [real] xlast [real] -

yfirst [real] ylast [real] -

zfirst [real] zlast [real] -

ATOM SELE [selection] END

The UPDAte keyword updates the atom-based grid, so that when the

PBAV PHI ATOM subcommand is given for the first time, the UPDATE keyword

must be used and an atom selection given. For subsequent invocations,

the atom selection (for defining the set of atoms over which the

calculation is to be done) and the UPDATE command (for updating the

grid, based on the position of the selected atoms) are optional.

If UPDATE is specified but the atom selection (or grid limits) are not,

the algorithm will use the atom selection (or grid limits) that were

last specified. If the PBAV PHI subcommand has not been

previously given, the grid limits must be specified.

Top

Generalized Solvent Boundary Potential (GSBP)

GSBP is a boundary potential for simulating a reduced system while

incorporating implicitly the dominant electrostatic forces of the surrounding

atoms. It has been developed in the same spirit as the SBOUND and the SSBP,

see

The current implementation of the method is described in W. IM, S. Berneche,

and B. Roux. J. Chem. Phys. (2000, in preparation). Briefly, the system is

partitioned in two regions: an inner region of interest and an outer region.

The inner region includes all atom explicitly.

GSBP represents the electrostatic forces from the outer region as the sum of

two components. One is the static external field (PHIX) which arises from

the charge distribution in the outer region (taking into consideration the

solvent as a featureless dielectric medium). The second contribution is

the reaction field which is created by the charge distribution inside the

inner region considering the whole molecular configuration and the dielectric

solvent. In the GSBP, the reaction field is calculated through a generalized

multipolar expansion of the instantaneous charge density in the inner system

coupled with a generalized reaction field matrix MIJ.

The numerical implementation of the GSBP can be divided into two parts;

SETUP and UPDATE parts. In the SETUP part, the static external field and the

MIJ matrix are calculated once and stored before a simulation. The SETUP part

mostly uses the PBEQ module. In UPDATE part, the energy and forces are

updated using the stored external field and the MIJ matrix in each step of

the molecular dynamics.

1. GSBP Syntax

GSBP is a subcommand inside PBEQ module like SOLVe and uses all options

(except solvation force-spec.) in SOLVe.

GSBP decomposition-spec. inner region-specifications

basis functions-spec. large box-specifications

cavity potential-spec. all options in SOLVE

decomposition-spec.::= [GTOT] [G_oo] [G_io] [G_ii]

GTOT [.FALSE.] : total electrostatic solvation free energy

G_oo [.FALSE.] : electrostatic solvation free energy in outer region

G_io [.FALSE.] : electrostatic free energy due to the interactions

between inner and outer regions

G_ii [.FALSE.] : electrostatic solvation free energy in inner region

inner region-specifications:: [ [RECTbox]

[XMAX real] [YMAX real] [YMAX real]

[XMIN real] [YMIN real] [YMIN real] ]

[ [SPHEre]

[SRDIst real]

[RRXCen real] [RRYCen real] [RRZCen real] ]

RECTbox [.FALSE.] : rectangular (box) inner region

XMAX [0.0] : maximum position of inner region along X-axis

YMAX [0.0] : maximum position of inner region along Y-axis

ZMAX [0.0] : maximum position of inner region along Z-axis

XMIN [0.0] : minimum position of inner region along X-axis

YMIN [0.0] : minimum position of inner region along Y-axis

ZMIN [0.0] : minimum position of inner region along Z-axis

SPHEre [.FALSE.] : spherical inner region

SRDIst [0.0] : radius of spherical inner region

RRXCen [0.0] : X position of spherical inner region

RRYCen [0.0] : Y position of spherical inner region

RRZCen [0.0] : Z position of spherical inner region

basis function-spec.:: [ [XNPOl integer] [YNPOl integer] [ZNPOl integer] ]

[NMPOl integer]

[MAXNpol integer] [NLISt integer] [NOSOrt]

[CGSCal real]

XNPOl [0] : number of Legendre polynomials in X direction

YNPOl [0] : number of Legendre polynomials in Y direction

ZNPOl [0] : number of Legendre polynomials in Z direction

NMPOl [0] : number of multipoles with spherical harmonics

MAXNpol [NTPOL] : maximum number of basis functions which are used in

the energy and forces calculations

NLISt [1] : updating frequency for the ordered list of basis

functions during molecular dynamics

NOSOrt [.FALSE.] : surpress the ordering of basis functions

CGSCale [1.0] : charge scaling factor for the monopole basis

function

large box-specifications:: [LBOX] [LDCEl real] [LNCEl integer] [FOCUS]

[LXBCen real] [LYBCen real] [LZBCen real]

LBOX [.FALSE.] : invoke large box calculation (see below)

LDCEL [4*DCEL] : grid spacing of large box

LNCEL [33] : number of grid point in 1D for a cubic large box

: this should be smaller than or equal to NCEL

LXBCEN [0.0] : the center of a large box in X

LYBCEN [0.0] : the center of a large box in Y

LZBCEN [0.0] : the center of a large box in Z

FOCUS [.FALSE.] : use the potential from a large box calculation for

the boundary potential in finer calculation

cavity potential spec ::= CAVI atom-selection [DRDI real] [DRCA real]

2. Free energy decomposition

The total electrostatic solvation energy is decomposed into G_oo, G_io, and

G_ii. All decomposition calculations are performed using the PB solver.

With G_io keyword we can calculate the static external field and save it using

WRITE PHIX. G_ii gives the exact reaction field energy with which we can

compare the basis-set reaction field energy.

3. Inner region & Basis functions

Currently, GSBP supports two shapes for the inner regions: an orthorhombic

rectangular box and a sphere. For the rectangular box, Legendre polynomials

are used as a basis-set. The number of function along each cartesian axis can

be specified using XNPOL, YNPOL, and ZNPOL. The resulting total number of

basis functions (NTPOL) is XNPOL*YNPOL*ZNPOL. For the spherical inner region,

spherical harmonics are used. The number of electric multipoles is specified

as NMPOL, and the resulting total number of basis functions (NTPOL) is

NMPOL*NMPOL (e.g., with NMPOL = 2 one is including the reaction field for the

monopole and dipole of the inner system).

The calculation of the MIJ matrix can be done in a single job but can also

be restarted. This is convenient since one does not always know how many basis

functions would yield accurate results. For example, one could calculate the

MIJ matrix with NMPOL=11 spherical harmonics. After comparing the result with

exact PB reaction field, one may decide to increase the number of multipoles

in NMPOL. This procedure is illustrated in the test case gsbptest1.inp.

The list of basis functions can be ordered and sorted such that the number of

multipole basis function used for the energy and force (MAXNpol) calculations

is reduced.

The focussing method with a large initial box and interpolating boundary

condition (INTBP) is a necessary procedure for computing the MIJ matrix

because the charge distribution corresponding to a given basis function

involves a large number of lattice point charges. All grid points inside the

inner region contain a partial charge assigned by a basis function.

Therefore, it would take a long time to set the boundary potential directly.

In practice, the charges density from a basis function are interpolated onto

a large (coarse) grid to reduce the number of grid-point charges which

increase the computational cost of setting up the boundary conditions.

In this case, the focussing method is much more useful because the boundary

potential can be obtained from the coarse grid calculation.

4. Cavity Potential

The GSBP cavity potential is a restrictive potential that keeps

water molecules from escaping the simulation region. Usually it is

applied only on the oxgen atom of the water molecules. The DRDI option

specifies the offset where the restrictive potential is placed

from the dielectic boundary for the spherical geometry.

The DRCA option gives the offset of the quartic potential (same form

as the one in MMFP module) for the orthorombic geometry.

Generalized Solvent Boundary Potential (GSBP)

GSBP is a boundary potential for simulating a reduced system while

incorporating implicitly the dominant electrostatic forces of the surrounding

atoms. It has been developed in the same spirit as the SBOUND and the SSBP,

see

**»**sbound and » mmfpThe current implementation of the method is described in W. IM, S. Berneche,

and B. Roux. J. Chem. Phys. (2000, in preparation). Briefly, the system is

partitioned in two regions: an inner region of interest and an outer region.

The inner region includes all atom explicitly.

GSBP represents the electrostatic forces from the outer region as the sum of

two components. One is the static external field (PHIX) which arises from

the charge distribution in the outer region (taking into consideration the

solvent as a featureless dielectric medium). The second contribution is

the reaction field which is created by the charge distribution inside the

inner region considering the whole molecular configuration and the dielectric

solvent. In the GSBP, the reaction field is calculated through a generalized

multipolar expansion of the instantaneous charge density in the inner system

coupled with a generalized reaction field matrix MIJ.

The numerical implementation of the GSBP can be divided into two parts;

SETUP and UPDATE parts. In the SETUP part, the static external field and the

MIJ matrix are calculated once and stored before a simulation. The SETUP part

mostly uses the PBEQ module. In UPDATE part, the energy and forces are

updated using the stored external field and the MIJ matrix in each step of

the molecular dynamics.

1. GSBP Syntax

GSBP is a subcommand inside PBEQ module like SOLVe and uses all options

(except solvation force-spec.) in SOLVe.

GSBP decomposition-spec. inner region-specifications

basis functions-spec. large box-specifications

cavity potential-spec. all options in SOLVE

decomposition-spec.::= [GTOT] [G_oo] [G_io] [G_ii]

GTOT [.FALSE.] : total electrostatic solvation free energy

G_oo [.FALSE.] : electrostatic solvation free energy in outer region

G_io [.FALSE.] : electrostatic free energy due to the interactions

between inner and outer regions

G_ii [.FALSE.] : electrostatic solvation free energy in inner region

inner region-specifications:: [ [RECTbox]

[XMAX real] [YMAX real] [YMAX real]

[XMIN real] [YMIN real] [YMIN real] ]

[ [SPHEre]

[SRDIst real]

[RRXCen real] [RRYCen real] [RRZCen real] ]

RECTbox [.FALSE.] : rectangular (box) inner region

XMAX [0.0] : maximum position of inner region along X-axis

YMAX [0.0] : maximum position of inner region along Y-axis

ZMAX [0.0] : maximum position of inner region along Z-axis

XMIN [0.0] : minimum position of inner region along X-axis

YMIN [0.0] : minimum position of inner region along Y-axis

ZMIN [0.0] : minimum position of inner region along Z-axis

SPHEre [.FALSE.] : spherical inner region

SRDIst [0.0] : radius of spherical inner region

RRXCen [0.0] : X position of spherical inner region

RRYCen [0.0] : Y position of spherical inner region

RRZCen [0.0] : Z position of spherical inner region

basis function-spec.:: [ [XNPOl integer] [YNPOl integer] [ZNPOl integer] ]

[NMPOl integer]

[MAXNpol integer] [NLISt integer] [NOSOrt]

[CGSCal real]

XNPOl [0] : number of Legendre polynomials in X direction

YNPOl [0] : number of Legendre polynomials in Y direction

ZNPOl [0] : number of Legendre polynomials in Z direction

NMPOl [0] : number of multipoles with spherical harmonics

MAXNpol [NTPOL] : maximum number of basis functions which are used in

the energy and forces calculations

NLISt [1] : updating frequency for the ordered list of basis

functions during molecular dynamics

NOSOrt [.FALSE.] : surpress the ordering of basis functions

CGSCale [1.0] : charge scaling factor for the monopole basis

function

large box-specifications:: [LBOX] [LDCEl real] [LNCEl integer] [FOCUS]

[LXBCen real] [LYBCen real] [LZBCen real]

LBOX [.FALSE.] : invoke large box calculation (see below)

LDCEL [4*DCEL] : grid spacing of large box

LNCEL [33] : number of grid point in 1D for a cubic large box

: this should be smaller than or equal to NCEL

LXBCEN [0.0] : the center of a large box in X

LYBCEN [0.0] : the center of a large box in Y

LZBCEN [0.0] : the center of a large box in Z

FOCUS [.FALSE.] : use the potential from a large box calculation for

the boundary potential in finer calculation

cavity potential spec ::= CAVI atom-selection [DRDI real] [DRCA real]

2. Free energy decomposition

The total electrostatic solvation energy is decomposed into G_oo, G_io, and

G_ii. All decomposition calculations are performed using the PB solver.

With G_io keyword we can calculate the static external field and save it using

WRITE PHIX. G_ii gives the exact reaction field energy with which we can

compare the basis-set reaction field energy.

3. Inner region & Basis functions

Currently, GSBP supports two shapes for the inner regions: an orthorhombic

rectangular box and a sphere. For the rectangular box, Legendre polynomials

are used as a basis-set. The number of function along each cartesian axis can

be specified using XNPOL, YNPOL, and ZNPOL. The resulting total number of

basis functions (NTPOL) is XNPOL*YNPOL*ZNPOL. For the spherical inner region,

spherical harmonics are used. The number of electric multipoles is specified

as NMPOL, and the resulting total number of basis functions (NTPOL) is

NMPOL*NMPOL (e.g., with NMPOL = 2 one is including the reaction field for the

monopole and dipole of the inner system).

The calculation of the MIJ matrix can be done in a single job but can also

be restarted. This is convenient since one does not always know how many basis

functions would yield accurate results. For example, one could calculate the

MIJ matrix with NMPOL=11 spherical harmonics. After comparing the result with

exact PB reaction field, one may decide to increase the number of multipoles

in NMPOL. This procedure is illustrated in the test case gsbptest1.inp.

The list of basis functions can be ordered and sorted such that the number of

multipole basis function used for the energy and force (MAXNpol) calculations

is reduced.

The focussing method with a large initial box and interpolating boundary

condition (INTBP) is a necessary procedure for computing the MIJ matrix

because the charge distribution corresponding to a given basis function

involves a large number of lattice point charges. All grid points inside the

inner region contain a partial charge assigned by a basis function.

Therefore, it would take a long time to set the boundary potential directly.

In practice, the charges density from a basis function are interpolated onto

a large (coarse) grid to reduce the number of grid-point charges which

increase the computational cost of setting up the boundary conditions.

In this case, the focussing method is much more useful because the boundary

potential can be obtained from the coarse grid calculation.

4. Cavity Potential

The GSBP cavity potential is a restrictive potential that keeps

water molecules from escaping the simulation region. Usually it is

applied only on the oxgen atom of the water molecules. The DRDI option

specifies the offset where the restrictive potential is placed

from the dielectic boundary for the spherical geometry.

The DRCA option gives the offset of the quartic potential (same form

as the one in MMFP module) for the orthorombic geometry.

Top

Solvent Macromolecule Boundary Potential (SMBP)

The SMBP is a boundary potential that is analogous to the GSBP, yet

can be used in conjunction with ab-initio QM/MM setups. As, in contrast

to the GSBP, the PB equations have to be solved for every step, it is

targeted for use in geometry optimizations. The SMBP is especially useful

for higher-level QM/MM optimizations of MD snapshots obtained with the

GSBP using a lower-level QM/MM or pure MM setup. The original method is

described in T. Benighaus and W. Thiel, J. Chem. Theory Comput. 5, 3114 (2009).

The current implementation of the method is described in J. Zienau and

and Q. Cui (2012, in preparation). In the SMBP, the electrostatic

interactions between the QM part and all other entities (except for the

inner region MM charges) are handled via a surface charge projection approach,

where the virtual surface charges are situated on the boundary between

the inner and outer regions. As no GSBP type basis set is used, the SMBP

can be viewed as the basis set limit of the GSBP, although divergence

effects when atoms are close at the boundary can still occur even for very

large GSBP basis sets.

As in the GSBP the numerical implementation is divided into SETUP and

UPDATE parts; in the SETUP part, however, only the static external field is

calculated. The UPDATE part is fully analogous to the GSBP.

The SMBP has been interfaced with the Gaussian 09 and Q-Chem codes,

although the Q-Chem interface is currently NOT functional due to problems with

the ESP charge approach implemented in Q-Chem. Therefore, only Gaussian 09

can be used as ab-initio QM method with the SMBP at the present stage.

For benchmark purposes, an interface with the semi-empirical SCC-DFTB method

is provided as well.

IMPORTANT:

(i) It is necessary to source a radius file in the PBEQ module

for BOTH SETUP and UPDATE parts!

(ii) For SMBP/Q-Chem geometry optimizations (future implementation),

the jobtype in the qchem.inp file must be set to "SP" (single point)!

1. SMBP Syntax

SMBP is a subcommand inside PBEQ module like SOLVe and uses all options

(except solvation force-spec.) in SOLVe. It supports all inner region and

large box options of the GSBP. Special or additional options are described below.

SMBP decomposition-spec. inner region-specifications (GSBP and additional)

large box-specifications (GSBP) all options in SOLVE

decomposition-spec.::= [PHIX]

PHIX [.FALSE.] : calculate static outer potential

inner region-specifications:: [ RECTbox (all GSBP options)

[INCX real] [INCY real] [INCZ real] ]

[ SPHEre (all GSBP options)

[NSPT integer] [SPAL integer] ]

[ [IGUE integer] [QCCH integer]

[CGTH real] [CGMX integer] [SCTH real] [SCMX integer] ]

INCX [1.0] : Spacing of surface charges along X for RECTbox

INCY [1.0] : Spacing of surface charges along Y for RECTbox

INCZ [1.0] : Spacing of surface charges along Z for RECTbox

NSPT [90] : Number of surface charges for SPHEre

SPAL [2] : Algorithm for placing surface charges on SPHEre

"1" uses a distribution along circles

"2" uses a distribution along spirals (recommended)

IGUEss [1] : Initial guess for QM atomic charges

"1" uses charges from the previous step if possible

"2" uses zero guess charges always (not recommended)

QCCH [1] : atomic charge representation from QM calculation

(ab-initio only)

"1" uses ESP charges

(default for Gaussian09: Merz-Kollmann)

"2" uses "charges.dat" file from Q-Chem. By default

these are Mulliken, but both ESP and ChelpG charges

are available in Q-Chem using the $rem variables

"esp_charges = true" or "chelpg = true".

CGTH [1.e-6] : Numerical threshold for Conjugate Gradient (CG)

optimizer of the surface charges

CGMX [2000] : Maximum number of iterations for the CG optimizer

SCTH [5.e-4] : Numerical threshold for the Self Consistent

Reaction Field (SCRF) calculation

SCMX [50] : Maximum number of SCRF iterations

2. Free energy decomposition

This part is analogous to the GSBP G_io option, as only the static outer

field is calculated. The option is renamed to PHIX in the SMBP.

3. Inner region

The same geometric shapes as for the GSBP (sphere and box) are currently

supported. As a "perfectly even" distribution of points on a sphere does not

exist, two approximate surface charge distributions are implemented for the

spherical boundary. With a reasonable large number of charges (about 30 and

more), the difference between both algorithms was found to be negligible,

so that the default setting is recommended, as it allows for an arbitrary

number of charges to be specified. The default setting for the number of

charges NSPT (90) should be sufficient for most cases. For the rectangular

box shaped boundary, the NSPT and SPAL options are ignored, as the surface

charges are arranged on a rectangular grid on the box surface and their number

is calculated from the INCX, INCY, and INCZ values. The default settings are

recommended for the other options. If the SCRF calculation does not converge,

the SCRF threshold SCTH can be set to a (slightly) larger value.

Concerning the focussing method with interpolating boundary potential

condition, the same remarks as mentioned for the GSBP apply for the SMBP.

No cavity potential has been implemented for the SMBP, but, e.g., MMFP

constraints can be used.

Solvent Macromolecule Boundary Potential (SMBP)

The SMBP is a boundary potential that is analogous to the GSBP, yet

can be used in conjunction with ab-initio QM/MM setups. As, in contrast

to the GSBP, the PB equations have to be solved for every step, it is

targeted for use in geometry optimizations. The SMBP is especially useful

for higher-level QM/MM optimizations of MD snapshots obtained with the

GSBP using a lower-level QM/MM or pure MM setup. The original method is

described in T. Benighaus and W. Thiel, J. Chem. Theory Comput. 5, 3114 (2009).

The current implementation of the method is described in J. Zienau and

and Q. Cui (2012, in preparation). In the SMBP, the electrostatic

interactions between the QM part and all other entities (except for the

inner region MM charges) are handled via a surface charge projection approach,

where the virtual surface charges are situated on the boundary between

the inner and outer regions. As no GSBP type basis set is used, the SMBP

can be viewed as the basis set limit of the GSBP, although divergence

effects when atoms are close at the boundary can still occur even for very

large GSBP basis sets.

As in the GSBP the numerical implementation is divided into SETUP and

UPDATE parts; in the SETUP part, however, only the static external field is

calculated. The UPDATE part is fully analogous to the GSBP.

The SMBP has been interfaced with the Gaussian 09 and Q-Chem codes,

although the Q-Chem interface is currently NOT functional due to problems with

the ESP charge approach implemented in Q-Chem. Therefore, only Gaussian 09

can be used as ab-initio QM method with the SMBP at the present stage.

For benchmark purposes, an interface with the semi-empirical SCC-DFTB method

is provided as well.

IMPORTANT:

(i) It is necessary to source a radius file in the PBEQ module

for BOTH SETUP and UPDATE parts!

(ii) For SMBP/Q-Chem geometry optimizations (future implementation),

the jobtype in the qchem.inp file must be set to "SP" (single point)!

1. SMBP Syntax

SMBP is a subcommand inside PBEQ module like SOLVe and uses all options

(except solvation force-spec.) in SOLVe. It supports all inner region and

large box options of the GSBP. Special or additional options are described below.

SMBP decomposition-spec. inner region-specifications (GSBP and additional)

large box-specifications (GSBP) all options in SOLVE

decomposition-spec.::= [PHIX]

PHIX [.FALSE.] : calculate static outer potential

inner region-specifications:: [ RECTbox (all GSBP options)

[INCX real] [INCY real] [INCZ real] ]

[ SPHEre (all GSBP options)

[NSPT integer] [SPAL integer] ]

[ [IGUE integer] [QCCH integer]

[CGTH real] [CGMX integer] [SCTH real] [SCMX integer] ]

INCX [1.0] : Spacing of surface charges along X for RECTbox

INCY [1.0] : Spacing of surface charges along Y for RECTbox

INCZ [1.0] : Spacing of surface charges along Z for RECTbox

NSPT [90] : Number of surface charges for SPHEre

SPAL [2] : Algorithm for placing surface charges on SPHEre

"1" uses a distribution along circles

"2" uses a distribution along spirals (recommended)

IGUEss [1] : Initial guess for QM atomic charges

"1" uses charges from the previous step if possible

"2" uses zero guess charges always (not recommended)

QCCH [1] : atomic charge representation from QM calculation

(ab-initio only)

"1" uses ESP charges

(default for Gaussian09: Merz-Kollmann)

"2" uses "charges.dat" file from Q-Chem. By default

these are Mulliken, but both ESP and ChelpG charges

are available in Q-Chem using the $rem variables

"esp_charges = true" or "chelpg = true".

CGTH [1.e-6] : Numerical threshold for Conjugate Gradient (CG)

optimizer of the surface charges

CGMX [2000] : Maximum number of iterations for the CG optimizer

SCTH [5.e-4] : Numerical threshold for the Self Consistent

Reaction Field (SCRF) calculation

SCMX [50] : Maximum number of SCRF iterations

2. Free energy decomposition

This part is analogous to the GSBP G_io option, as only the static outer

field is calculated. The option is renamed to PHIX in the SMBP.

3. Inner region

The same geometric shapes as for the GSBP (sphere and box) are currently

supported. As a "perfectly even" distribution of points on a sphere does not

exist, two approximate surface charge distributions are implemented for the

spherical boundary. With a reasonable large number of charges (about 30 and

more), the difference between both algorithms was found to be negligible,

so that the default setting is recommended, as it allows for an arbitrary

number of charges to be specified. The default setting for the number of

charges NSPT (90) should be sufficient for most cases. For the rectangular

box shaped boundary, the NSPT and SPAL options are ignored, as the surface

charges are arranged on a rectangular grid on the box surface and their number

is calculated from the INCX, INCY, and INCZ values. The default settings are

recommended for the other options. If the SCRF calculation does not converge,

the SCRF threshold SCTH can be set to a (slightly) larger value.

Concerning the focussing method with interpolating boundary potential

condition, the same remarks as mentioned for the GSBP apply for the SMBP.

No cavity potential has been implemented for the SMBP, but, e.g., MMFP

constraints can be used.

Top

Examples

This examples are meant to be a partial guide in setting up

an input file for PBEQ. There are two test files, pbeqtest1.inp,

pbeqtest2.inp, pbeqtest3.inp, and pbeqtest7.inp.

Example (1)

-----------

This example shows how to perform two PB calculations, one for a surrounding

dielectric of 80 (water) and one for a surrounding of 1.0 (vacuum). The

difference between the two energies then corresponds to the electrostatic

contribution to the solvation free energy. The salt concentration was zero

in this calculation.

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 conc 0.0 ncel 30 dcel 0.4

set ener80 = ?ENPB

SOLVE epsw 1.0

set ener1 = ?ENPB

CALC total = @ener80 - @ener1

RESET

END

Example(2)

----------

This example shows how to use a set of atomic Born radii with a smoothing

window.

set sw 0.4

set factor 0.939

PBEQ

stream radius.str

scalar wmain add @sw

scalar wmain mult @factor

scalar wmain set 0.0 sele type H* end

scalar wmain show

SOLVE epsw 80.0 ncel 100 dcel 0.3 -

smooth swin @sw force sten 0.03 npbeq 1

RESET !! If you consider a minimization or dynamics with PB forces,

!! don't use RESET here.

END

Example(3)

----------

This example shows how to set up a membrane potential and how to get

the electrostatic contribution to the solvation free energy in the membrane

environment. Note that a non-zero concentration is required for a sensible

system with a membrane potential.

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 ncel 150 dcel 0.5 conc 0.150 -

Tmemb 25.0 Zmemb 0.0 epsm 2.0 vmemb 0.100

set ener80 = ?ENPB

SOLVE epsw 1.0 conc 0.000 -

Tmemb 25.0 Zmemb 0.0 epsm 1.0 vmemb 0.000

set ener1 = ?ENPB

CALC total = @ener80 - @ener1

RESET

END

Example(4)

----------

This example shows how to set up boundary potentials using FOCUS keyword,

how to read the saved potential, and how to calculate the electrostatic

contribution to the solvation free energy using FOCUS.

PBEQ

scalar wmain = radius

SOLVE epsw 1.0 ncel 60 dcel 0.4

open write file unit 40 name phi.dat

write phi unit 40

SOLVE epsw 1.0 dcel 0.2 focus ! boundary potentials from DCEL 0.4 potentials

! NOTE: YOU CAN CHANGE NCEL IN THE FOCUSSED SYSTEM AS FOLLOWS;

! SOLVE epsw 1.0 ncel 80 dcel 0.2 focus

SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.2 potentials

open read file unit 41 name phi.dat

read phi unit 41

SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.4 potentials

RESET

END

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 ncel 60 dcel 0.4

set ener81 = ?ENPB

SOLVE epsw 80.0 dcel 0.2 focus

set ener82 = ?ENPB

SOLVE epsw 80.0 dcel 0.1 focus

set ener83 = ?ENPB

SOLVE epsw 80.0 dcel 0.05 focus

set ener84 = ?ENPB

SOLVE epsw 1.0 dcel 0.4

set ener11 = ?ENPB

SOLVE epsw 1.0 dcel 0.2 focus

set ener12 = ?ENPB

SOLVE epsw 1.0 dcel 0.1 focus

set ener13 = ?ENPB

SOLVE epsw 1.0 dcel 0.05 focus

set ener14 = ?ENPB

calc total = @ener81 - @ener11

calc total = @ener82 - @ener12

calc total = @ener83 - @ener13

calc total = @ener84 - @ener14

SOLVE epsw 80.0 ncel 120 dcel 0.2

set ener80 = ?ENPB

SOLVE epsw 1.0

set ener1 = ?ENPB

calc total = @ener80 - @ener1

RESET

END

Example(5)

----------

This example shows pKa Poisson-Bolztmann calculations which

deals with explicit charge distribution on the ionizable site.

(see also ~chmtest/c28/pbeqtest7.inp)

! set residue for pKa calculation and the patch for the ionizable sidechain

set segid = syst

set resid = 2

set patch = GLUP

!Miscelaneous variables

set Dcel = 0.5 ! initial value for the mesh size in the finite-difference

set Ncel = 65 ! maximum number of grid points

set EpsP = 1.0 ! dielectric constant for the protein interior

set EpsW = 80.0 ! solvent dielectric constant

set Conc = 0.0 ! salt concentration

set Focus = Yes

!Note that the resid must be set before streaming into this file

scalar wcomp = charge

patch @patch @Segid @resid setup

hbuild !build any missing hydrogens

scalar wcomp store 1

scalar charge store 2

define SITE select .bygroup. ( resid @resid ) show end

define REST select .not. site end

! Charges of the unprotonated state

scalar wmain recall 1

scalar wmain show

scalar wmain stat select SITE end

! Charges of the protonated state

scalar wmain recall 2

scalar wmain show

scalar wmain stat select SITE end

! Estimate the grid dimensions

format (f15.5)

coor orient norotate

coor stat select all end

calc DcelX = ( ?Xmax - ?Xmin ) / @Ncel

calc DcelY = ( ?Ymax - ?Ymin ) / @Ncel

calc DcelZ = ( ?Zmax - ?Zmin ) / @Ncel

if @DcelX gt @Dcel set Dcel = @DcelX

if @DcelY gt @Dcel set Dcel = @DcelY

if @DcelZ gt @Dcel set Dcel = @DcelZ

coor stat select SITE end

set Xcen = ?xave

set Ycen = ?yave

set Zcen = ?zave

PBEQ

stream @0radii.str

scalar charge recall 2 ! Protonated charge distribution

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen

set EnerPs = ?enpb ! Protonated side chain in structure

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end

set EnerPi = ?enpb ! Protonated side chain isolated

scalar charge recall 1 ! Unprotonated charge distribution

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen

set EnerUs = ?enpb ! Unprotonated side chain in structure

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end

if Focus eq yes

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end

set EnerUi = ?enpb ! Unprotonated side chain isolated

calc Energy = ( @EnerPs - @EnerUs ) - ( @EnerPi - @EnerUi )

calc pKa = -@Energy/( ?KBLZ * 300.0 ) * log10(exp(1)) != log10(exp(-@Energy/(?KBLZ*300)))

END

Examples

This examples are meant to be a partial guide in setting up

an input file for PBEQ. There are two test files, pbeqtest1.inp,

pbeqtest2.inp, pbeqtest3.inp, and pbeqtest7.inp.

Example (1)

-----------

This example shows how to perform two PB calculations, one for a surrounding

dielectric of 80 (water) and one for a surrounding of 1.0 (vacuum). The

difference between the two energies then corresponds to the electrostatic

contribution to the solvation free energy. The salt concentration was zero

in this calculation.

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 conc 0.0 ncel 30 dcel 0.4

set ener80 = ?ENPB

SOLVE epsw 1.0

set ener1 = ?ENPB

CALC total = @ener80 - @ener1

RESET

END

Example(2)

----------

This example shows how to use a set of atomic Born radii with a smoothing

window.

set sw 0.4

set factor 0.939

PBEQ

stream radius.str

scalar wmain add @sw

scalar wmain mult @factor

scalar wmain set 0.0 sele type H* end

scalar wmain show

SOLVE epsw 80.0 ncel 100 dcel 0.3 -

smooth swin @sw force sten 0.03 npbeq 1

RESET !! If you consider a minimization or dynamics with PB forces,

!! don't use RESET here.

END

Example(3)

----------

This example shows how to set up a membrane potential and how to get

the electrostatic contribution to the solvation free energy in the membrane

environment. Note that a non-zero concentration is required for a sensible

system with a membrane potential.

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 ncel 150 dcel 0.5 conc 0.150 -

Tmemb 25.0 Zmemb 0.0 epsm 2.0 vmemb 0.100

set ener80 = ?ENPB

SOLVE epsw 1.0 conc 0.000 -

Tmemb 25.0 Zmemb 0.0 epsm 1.0 vmemb 0.000

set ener1 = ?ENPB

CALC total = @ener80 - @ener1

RESET

END

Example(4)

----------

This example shows how to set up boundary potentials using FOCUS keyword,

how to read the saved potential, and how to calculate the electrostatic

contribution to the solvation free energy using FOCUS.

PBEQ

scalar wmain = radius

SOLVE epsw 1.0 ncel 60 dcel 0.4

open write file unit 40 name phi.dat

write phi unit 40

SOLVE epsw 1.0 dcel 0.2 focus ! boundary potentials from DCEL 0.4 potentials

! NOTE: YOU CAN CHANGE NCEL IN THE FOCUSSED SYSTEM AS FOLLOWS;

! SOLVE epsw 1.0 ncel 80 dcel 0.2 focus

SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.2 potentials

open read file unit 41 name phi.dat

read phi unit 41

SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.4 potentials

RESET

END

PBEQ

scalar wmain = radius

SOLVE epsw 80.0 ncel 60 dcel 0.4

set ener81 = ?ENPB

SOLVE epsw 80.0 dcel 0.2 focus

set ener82 = ?ENPB

SOLVE epsw 80.0 dcel 0.1 focus

set ener83 = ?ENPB

SOLVE epsw 80.0 dcel 0.05 focus

set ener84 = ?ENPB

SOLVE epsw 1.0 dcel 0.4

set ener11 = ?ENPB

SOLVE epsw 1.0 dcel 0.2 focus

set ener12 = ?ENPB

SOLVE epsw 1.0 dcel 0.1 focus

set ener13 = ?ENPB

SOLVE epsw 1.0 dcel 0.05 focus

set ener14 = ?ENPB

calc total = @ener81 - @ener11

calc total = @ener82 - @ener12

calc total = @ener83 - @ener13

calc total = @ener84 - @ener14

SOLVE epsw 80.0 ncel 120 dcel 0.2

set ener80 = ?ENPB

SOLVE epsw 1.0

set ener1 = ?ENPB

calc total = @ener80 - @ener1

RESET

END

Example(5)

----------

This example shows pKa Poisson-Bolztmann calculations which

deals with explicit charge distribution on the ionizable site.

(see also ~chmtest/c28/pbeqtest7.inp)

! set residue for pKa calculation and the patch for the ionizable sidechain

set segid = syst

set resid = 2

set patch = GLUP

!Miscelaneous variables

set Dcel = 0.5 ! initial value for the mesh size in the finite-difference

set Ncel = 65 ! maximum number of grid points

set EpsP = 1.0 ! dielectric constant for the protein interior

set EpsW = 80.0 ! solvent dielectric constant

set Conc = 0.0 ! salt concentration

set Focus = Yes

!Note that the resid must be set before streaming into this file

scalar wcomp = charge

patch @patch @Segid @resid setup

hbuild !build any missing hydrogens

scalar wcomp store 1

scalar charge store 2

define SITE select .bygroup. ( resid @resid ) show end

define REST select .not. site end

! Charges of the unprotonated state

scalar wmain recall 1

scalar wmain show

scalar wmain stat select SITE end

! Charges of the protonated state

scalar wmain recall 2

scalar wmain show

scalar wmain stat select SITE end

! Estimate the grid dimensions

format (f15.5)

coor orient norotate

coor stat select all end

calc DcelX = ( ?Xmax - ?Xmin ) / @Ncel

calc DcelY = ( ?Ymax - ?Ymin ) / @Ncel

calc DcelZ = ( ?Zmax - ?Zmin ) / @Ncel

if @DcelX gt @Dcel set Dcel = @DcelX

if @DcelY gt @Dcel set Dcel = @DcelY

if @DcelZ gt @Dcel set Dcel = @DcelZ

coor stat select SITE end

set Xcen = ?xave

set Ycen = ?yave

set Zcen = ?zave

PBEQ

stream @0radii.str

scalar charge recall 2 ! Protonated charge distribution

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen

set EnerPs = ?enpb ! Protonated side chain in structure

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end

set EnerPi = ?enpb ! Protonated side chain isolated

scalar charge recall 1 ! Unprotonated charge distribution

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW

if Focus eq yes -

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen

set EnerUs = ?enpb ! Unprotonated side chain in structure

SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end

if Focus eq yes

SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -

XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end

set EnerUi = ?enpb ! Unprotonated side chain isolated

calc Energy = ( @EnerPs - @EnerUs ) - ( @EnerPi - @EnerUi )

calc pKa = -@Energy/( ?KBLZ * 300.0 ) * log10(exp(1)) != log10(exp(-@Energy/(?KBLZ*300)))

END