12.2 Chemical Solvent Models

12.2.10 Poisson Boundary Conditions

Each of the implicit solvation models described above is designed for isotropic, bulk solvation—conditions that can be qualitatively described using a scalar dielectric constant, ε. For an anisotropic environment, such as a liquid/vapor interface, a more general approach is to solve Poisson’s equation with a spatially-varying dielectric function, ε(𝐫). Such an approach can be used, for example, to model the air/water interface by describing certain regions of space using ε=1 (air) and other regions using ε=78 (water).188, 187 The atomistic region is described at the SCF level. Construction of the dielectric function ε(𝐫) is based on a solute cavity, somewhat analogous to the solute cavity in a PCM calculation but where the dielectric changes smoothly (rather than abruptly) from ε=1 inside the cavity (in the atomistic QM region) to ε=εsolvent outside, in the continuum solvent. Options for modeling a liquid/vapor interface are also available; see Section 12.2.10.3. In contrast to PCMs, which must approximate the “volume polarization” due to penetration of the tails of the QM charge density beyond the solute cavity, this effect is described exactly under Poisson boundary conditions. The price to be paid for lifting this approximation is that charge densities must be discretized and integrated over three-dimensional space rather than simply a two-dimensional solute cavity surface.

Q-Chem’s implementation of Poisson boundary conditions was introduced in Ref. 188 and refined in Ref. 187. Users of this methodology are asked to cite at least Ref. 187.

12.2.10.1 Theory

The most general formulation of Poisson’s equation, for a dielectric function rather than a dielectric constant, is

^[ε(𝐫)^φtot(𝐫)]=-4πρsol(𝐫). (12.13)

The solute’s charge density will be separated into nuclear and electronic components,

ρsol(𝐫)=ρnuc(𝐫)+ρelec(𝐫). (12.14)

The total electrostatic potential φtot is comprised of the solute’s electrostatic potential φelec+φnuc, which is obtained from the density in Eq. (12.14), plus the polarization potential induced in the medium:

φtot(𝐫)=φelec(𝐫)+φnuc(𝐫)+φpol(𝐫). (12.15)

To compute ρelec, the electronic contribution to the electrostatic potential in vacuum is first evaluated on a Cartesian grid,

φelec(𝐫i)=μνNbasisPμνgμ(𝐫)|1|𝐫-𝐫i||gν(𝐫). (12.16)

Here P is the one-electron density matrix, gμ and gν are atom-centered Gaussian basis functions, and the integration is over 𝐫. The electronic part of the solute’s charge density is then obtained from

ρelec(𝐫)=-14π^2φelec(𝐫), (12.17)

where in practice the Laplacian of φelec is evaluated using an eighth-order finite difference scheme.187 The nuclear charge density ρnuc is described classically,

ρnuc(𝐫)=-ANatomsZAδ(𝐫-𝐑A), (12.18)

but to avoid numerical problems the nuclear charges are smeared out over one Cartesian grid voxel in practice. Operationally, this is achieved by adding ZA/dV to the grid point nearest 𝐑A, where dV is the volume of a Cartesian voxel. The exact nuclear electrostatic potential in vacuum is computed according to

φnuc(𝐫)=-14πANatomsZA|𝐫-𝐑A|. (12.19)

The Dirac delta function in Eq. (12.18) has dimensions of (volume)-1 and therefore incorporates the aforementioned factor of dV-1

Having computed the electronic and nuclear charge densities and the electrostatic potentials in vacuum, one has in hand an exact solution of Eq. (12.13) for the case where ε(𝐫)=1. The induced polarization charge density and corresponding electrostatic potential are then obtained iteratively, following closely the procedure outlined in Refs. 262 and 36. Equation (12.13) is rewritten to appear as Poisson’s equation in vacuum with an additional source charge density:

^2φtot(𝐫)=-4π[ρsol(𝐫)ε(𝐫)+^lnε(𝐫)^φtot(𝐫)4π]=-4π[ρsol(𝐫)+ρpol(𝐫)], (12.20)

where the polarization charge density is

ρpol(𝐫)=ρiter(𝐫)+(1-ε(𝐫)ε(𝐫))ρsol(𝐫). (12.21)

The iterative charge density ρiter(𝐫) takes the form

ρiter(k+1)(𝐫)=^lnε(𝐫)^φtot(k)(𝐫)4π (12.22)

at iteration k+1. This function is nonzero only in transition regions where the dielectric is being interpolated from vacuum to solvent. Note also that the second term in Eq. (12.21) vanishes wherever ε(𝐫)=1. The quantity ρiter(𝐫) is iterated to convergence by performing updates ρiter(k)(𝐫)ρiter(k+1)(𝐫) using Eq. (12.22), taking φtot(0)(𝐫) to be the solute’s electrostatic potential in vacuum. Each time ρiter(𝐫) is updated, a new polarization charge density is generated and Eq. (12.20) is solved to obtain a new total electrostatic potential. To stabilize the iterative updates of ρiter(𝐫), we use a damping procedure

ρiter(k+1)(𝐫)=η4π[^lnε(𝐫)^φtot(k)(𝐫)]+(1-η)ρiter(k)(𝐫)=ηρiter(k+1)+(1-η)ρiter(k)(𝐫) (12.23)

rather than using Eq. (12.22) as written. Following Refs. 262 and 36, we use η=0.6.

Once the total charge density and electrostatic potential are iterated to self-consistency, the free energy of solvation,

Gpol=12𝑑𝐫φpol(𝐫)ρsol(𝐫), (12.24)

is computed, where

φpol(𝐫)=φtot(𝐫)-φsol(𝐫). (12.25)

Since φtot and ρtot are computed self-consistently at each SCF iteration, the polarization effects must be incorporated into the Fock matrix. This is accomplished by adding the correction term ΔF^=δGpol/δρelec. The matrix form of this correction in the atomic orbital basis is

ΔFμν=𝑑𝐫φpol(𝐫)gμ(𝐫)gν(𝐫). (12.26)

For additional details and a full description of the algorithm, see Ref. 187.

12.2.10.2 Nonequilibrium Solvation for Vertical Ionization

Nonequilibrium solvation within the framework of PCMs is discussed in Section 12.2.2.3, and that methodology630, 1028 has been adapted for vertical ionization processes in conjunction with Poisson boundary conditions.188, 187 A state-specific approach has been implemented that requires solution of a nonlinear Schrödinger equation, Eq. (12.6). For the reference state, corresponding to i=0 in Eq. (12.6), this is equivalent to solving Eq. (12.13) for the induced polarization potential and computing the solvation free energy and Fock matrix correction according to Eqs. (12.24) and (12.26), respectively. For the ionized state, denoted by a subscript i, the solvent polarization is partitioned into fast and slow components. Within the Marcus partitioning scheme,1028 Eq. (12.20) becomes187

-14π^2φtot,i(𝐫)=ρsol,i(𝐫)+ρpol,0slow(𝐫)+ρpol,ifast(𝐫), (12.27)

where the fast polarization charge density of the ionized state, ρpol,ifast, is given by

ρpol,ifast(𝐫)=ρiter,i(𝐫)+(1-εopt(𝐫)εopt(𝐫))[ρsol,i(𝐫)+ρpol,0slow(𝐫)] (12.28)

and the fast polarization potential, φpol,ifast, is

φpol,ifast(𝐫)=φtot,i(𝐫)-φsol,i(𝐫)-φpol,0slow(𝐫). (12.29)

Subscripts i and 0 refer to the ionized state and the reference state, respectively. The quantity εopt in Eq. (12.28) is the solvent’s optical dielectric constant, and ρiter,i is computed using Eq. (12.23) but with a dielectric function constructed using εopt and with φtot,ifast substituted in place of φtot. For the Marcus partitioning scheme, the slow component of the induced solvent polarization charge density is computed as the three-dimensional (volume charge rather than surface charge) analogue of Eq. (12.8).

12.2.10.3 Job Control for the Poisson Equation Solver

A calculation using Poisson boundary conditions is requested by setting SOLVE_PEQ = TRUE in the $rem section. For computational efficiency, solvent effects from the Poisson equation solver are not incorporated until the error in the vacuum SCF calculation falls below a specified threshold, taken to be 10-3 a.u. by default and controllable using the $rem variable PEQ_SWITCH.

Note:  When SOLVE_PEQ = TRUE, the keywords SYM_IGNORE and NO_REORIENT are also set to TRUE. Poisson’s equation is discretized on a three-dimensional grid and the energy need not be rotationally invariant unless the grid spacing is sufficiently small.

SOLVE_PEQ
       Perform a solvation free energy calculation on a Cartesian grid using Poisson equation boundary conditions.
TYPE:
       STRING
DEFAULT:
       False
OPTIONS:
       TRUE/FALSE
RECOMMENDATION:
       None.

PEQ_SWITCH
       Inclusion of solvent effects begins when the SCF error falls below 10-PEQ_SWITCH.
TYPE:
       INTEGER
DEFAULT:
       3
OPTIONS:
       n Corresponding to 10-n
RECOMMENDATION:
       Use the default unless solvent effects need to be incorporated earlier in the SCF procedure.

Further job control for the Poisson equation solver (PEqS) routines is set up in two sections: $peqs_grid and $peqs. The former is used to define the Cartesian discretization grid, as follows:

$peqs_grid
   DimX <Nx> <Xmin> <Xmax>
   DimY <Ny> <Ymin> <Ymax>
   DimZ <Nz> <Zmin> <Zmax>
$end

The Cartesian grid must be orthorhombic and Nx, Ny, and Nz refer to the number of grid points for the x, y, and z axes.

Note:  A fourth-order multigrid algorithm is used to accelerate convergence of the conjugate gradient PEqS routine that solves Eq. (12.20).187 This requires that the number of grid points be odd, with the additional constraint that the quantities Nx-1, Ny-1, and Nz-1 must all be divisible by 8.

Values in the last two columns of the $peqs_grid section specify the minimum and maximum values of x, y, and z, in units of Ångstroms. The length of the grid in the x direction is Lx=xmax-xmin and the grid spacing is Δx=Lx/(Nx-1). The volume element discussed in the context of Eq. (12.18) is dV=ΔxΔyΔz.

The $peqs section controls other aspects of a PEqS calculation, including construction of the solute cavity and other required parameters for interfacial or nonequilibrium solvation. The format is:

$peqs
   <Keyword>  <parameter/option>
$end

Available keywords are described below.

PEQMaxIter
       Sets the maximum number of iterations used in the conjugate gradient solver.
INPUT SECTION: $peqs
TYPE:
       INTEGER
DEFAULT:
       500
OPTIONS:
       User-defined.
RECOMMENDATION:
       Use the default unless the calculation fails to converge.

PEQSolverThresh
       The electrostatic potential is considered converged when the error falls below 10-PEQSolverThresh.
INPUT SECTION: $peqs
TYPE:
       INTEGER
DEFAULT:
       5
OPTIONS:
       n Corresponding to 10-n
RECOMMENDATION:
       Use the default unless a tighter convergence criterion is desired, at greater computational cost.

PolarIterScale
       Specifies the mixing parameter η that is used in Eq. (12.23) to stabilize iterative solution for the polarization charge density.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       0.6
OPTIONS:
       η Desired value of the mixing parameter (unit-less).
RECOMMENDATION:
       Use the default, which was tested in Refs. 262 and 36, unless the calculation proves difficult to converge.

BatchSize
       Evaluate electrostatic potential integrals in batches over small parts of the Cartesian grid, rather than computing all integrals in a single batch.
INPUT SECTION: $peqs
TYPE:
       INTEGER
DEFAULT:
       5000
OPTIONS:
       n Corresponding to a batch size of n grid points.
RECOMMENDATION:
       For large grids (106 grid points), a batch size nNxNyNz/5 is recommended.

SolventDielectric
       Sets the dielectric value for the solvent.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       78.39
OPTIONS:
       ε Desired value of ε (dimensionless).
RECOMMENDATION:
       The default value corresponds to water at 25C.

OpticalDielectric
       Sets the optical dielectric value of the solvent.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       1.7778
OPTIONS:
       εopt Desired value of εopt (dimensionless).
RECOMMENDATION:
       The optical dielectric is equal to the square of the index of refraction. The default value corresponds to water at 25C.

SoluteCavity
       Specifies the type of solute cavity, which determines the form of the dielectric function ε(𝐫).
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       Vacuum
OPTIONS:
       Vacuum Perform calculation in vacuum, ε(𝐫)1. RigidVDW Create a cavity using spherically symmetric error functions. Spherical Create a single spherical cavity around the solute.
RECOMMENDATION:
       None.

In conventional PCMs the solute cavity is a rigid two-dimensional surface constructed from a union of atomic spheres, the radii of which are generally take to be equal to the van der Waals radius (rvdW) scaled by a factor of 1.2; see Section 12.2.3.370 This cavity is rigid in the sense that once the atomic coordinates are specified, it remains unchanged during the SCF cycles. (The isodensity cavity discussed in Section 12.2.5 is an exception, but is not available for the PEqS method.) Furthermore, there is an abrupt and discontinuous change in the dielectric constant at the solute/continuum boundary. A three-dimensional analogue of this cavity, using continuous and differentiable spherically-symmetric error functions, has been implemented for PEqS calculations, following the procedure in Ref. 262. The dielectric function, which depends parametrically on the nuclear positions 𝐑A, is

ε(𝐫;{𝐑A})=(εsolvent-1){ANatomsh(dA,Δ;|𝐫-𝐑A|)}, (12.30)

where

h(dA,Δ;|𝐫-𝐑A|)=12[1+erf(|𝐫-𝐑A|-dAΔ)]. (12.31)

Equation (12.30) smoothly interpolates between ε=1 and ε=εsolvent, over a length scale of 4Δ. The value of Δ is specified using the RigidScale keyword. The quantity dA in Eqs. (12.30) and (12.31) sets radius of the atomic sphere for atom A. By default, dA=1.2rvdW but this can be controlled as described below.

RigidScale
       Sets the length scale on which the error function employed in the rigid vdW cavity construction interpolates the dielectric value from vacuum to solvent.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       0.265 Å
OPTIONS:
       Δ Specifies the desired value (in Å); see Eq. (12.31).
RECOMMENDATION:
       Use the default value, which was tuned in Ref. 262 so that errors in small-molecule solvation energies were 1 kcal/mol.

VDWType
       Specifies details for the rigid vdW cavity construction.
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       Scaled
OPTIONS:
       Unscaled dA=rvdW Scaled dA=rvdW×scale Shifted dA=(rvdW+shift)×scale
RECOMMENDATION:
       None. The values of scale and shift are set with the VDWScale and VDWShift keywords.

VDWScale
       Sets the empirical scale factor applied to the atomic van der Waals radius.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       1.2
OPTIONS:
       scale Specifies the desired dimensionless scaling factor for the atomic vdW radii.
RECOMMENDATION:
       Use the default value.

VDWShift
       Adjusts the center of the spherically-symmetric error functions when constructing the rigid vdW cavity.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       0.0 Ångstroms
OPTIONS:
       shift Specifies the desired shift (in Å).
RECOMMENDATION:
       None. If VDWType is set to Shifted, the vdW scale factor is set to 1.0 by default. This can be adjusted using the VDWScale keyword.

Setting the SoluteCavity keyword to Spherical requests the construction of a spherical cavity around the solute, and the dielectric is smoothly interpolated from vacuum to solvent using a hyperbolic tangent function:188

ε(r)=12{(εsolvent+1)+(εsolvent-1)tanh[α(r-rmid)]}. (12.32)

Here, rmid is the distance where the dielectric assumes the value ε(rmid)=(εsolvent+1)/2. The value of rmid is taken to be the sum of the sphere radius, R, and half of the interpolation length, L: rmid=R+L/2. The sphere radius and interpolation length are controlled with the SphereRadius and InterpolLength keywords described below. The parameter α controls the sharpness of the switching process, with α=4/L by default.

SphereRadius
       Sets the radius of the spherical solute cavity.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       No default.
OPTIONS:
       R Desired spherical cavity radius (in Å).
RECOMMENDATION:
       None. See the Supporting Information of Ref. 188 for more information.

InterpolLength
       Sets the length scale on which the dielectric is smoothly interpolated from vacuum to solvent.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       No default.
OPTIONS:
       L Desired interpolation length (in Å).
RECOMMENDATION:
       None.

InterpolScale
       For a given interpolation length (L), InterpolScale (α) sets the sharpness of the dielectric transition from vacuum to solvent.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       α = 4/L
OPTIONS:
       α Desired interpolation scale factor (in Å-1).
RECOMMENDATION:
       Use the default unless a broader (smaller α) or narrower (larger α) transition region is desired.

Interface
       Perform a solvation calculation at a solvent/vacuum interface.
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       False
OPTIONS:
       True Modify the dielectric function to simulate an interface between solvent and vacuum. False Perform a solvation calculation in bulk solvent.
RECOMMENDATION:
       The user will also need to specify the length scale on which the dielectric is smoothly interpolated from the bulk solvent value to vacuum, and the location of the Gibbs dividing surface (see below).

By setting Interface = True, the dielectric function on the Cartesian grid is further modified to mimic a solvent/vacuum interface. First, the solute cavity is constructed as specified by the SoluteCavity keyword as discussed above. Then, the dielectric function is smoothly interpolated in the z direction across the Gibbs dividing surface (zzGDS) using the following hyperbolic tangent switching function:188, 187

ε(z)=12{(εsolvent+1)+(1-εsolvent)tanh[β(z-zGDS)]}. (12.33)

This interpolates the dielectric function over the interface length Linterface, centered at the Gibbs dividing surface, zzGDS. Both of these values are controlled by the keywords InterfaceLength and GibbsDS, respectively. Similar to the parameter α used in the spherical cavity construction, the parameter β=4/Linterface controls the sharpness of the interpolation across the Gibbs dividing surface.

InterfaceLength
       Sets the length scale over which the dielectric function is smoothly transitioned from bulk solvent to vacuum in the z direction
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       None
OPTIONS:
       Linterface Desired interface length (in Å).
RECOMMENDATION:
       This sets the value β=4/Linterface in Eq. (12.33). See the Supporting Information of Ref. 188 for a full description of the solvent/vacuum interface construction.

GibbsDS
       Sets the location of the Gibbs dividing surface, in the z direction.
INPUT SECTION: $peqs
TYPE:
       FLOAT
DEFAULT:
       None
OPTIONS:
       zGDS Desired location of the Gibbs dividing surface (in Å).
RECOMMENDATION:
       Consult the literature. One such way to determine this value is to compute a density profile of the solvent as a function of z and set this location to be where the solvent density has decreased to 50% of the bulk value. Usually zGDSLinterface/2.

NonequilJob
       Obtain the nonequilibrium free energy of solvation for a vertical ionization process.
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       False
OPTIONS:
       True Compute the nonequilibrium free energy for a vertical ionization process. False Compute the equilibrium solvation free energy.
RECOMMENDATION:
       None.

NonequilPartition
       Specifies the manner in which the solvent response is partitioned into fast and slow components.
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       Marcus
OPTIONS:
       Marcus Employ the Marcus partitioning scheme. Pekar Employ the Pekar partitioning scheme.
RECOMMENDATION:
       Use the default. Although the fast and slow solvation responses are different between the two approaches, the total solvation free energy is the same,1028 but the Pekar scheme is computationally more expensive than the Marcus scheme.

NonequilState
       Specifies the state of interest for a nonequilibrium vertical ionization.
INPUT SECTION: $peqs
TYPE:
       STRING
DEFAULT:
       Reference
OPTIONS:
       Reference The reference (initial) state, from which an electron will be removed. Ionized The final (ionized) state.
RECOMMENDATION:
       None. Both values will be needed in a compound input job, in order to compute the non-equilibrium response to vertical ionization; see Example 12.2.10.4.

12.2.10.4 Examples

The following example computes the solvation free energy of a water molecule immersed in water. The Cartesian grid is cubic with a side length of 15.0 Å and 73 grid points in each direction. A rigid vdW cavity is used based on scaled vdW radii for the atomic spheres. The dielectric is not set, so takes the default value of 78.39.

Example 12.15  Free energy of solvation of water in water.

$molecule
   0 1
   O     0.053004    -0.020947    -0.034784
   H     0.003424     0.185855     0.910594
   H    -0.844842     0.146674    -0.358413
$end

$rem
   SCF_CONVERGENCE   5
   THRESH            14
   EXCHANGE          wB97X-V
   BASIS             6-31+G*
   SOLVE_PEQ         TRUE
   PEQ_SWITCH        0
$end

$peqs
   SOLUTECAVITY RIGIDVDW
$end

$peqs_grid
   DimX 73 -7.50 7.50
   DimY 73 -7.50 7.50
   DimZ 73 -7.50 7.50
$end

The next example illustrates calculation of the solvation free energy of a water molecule at a water/vacuum interface, with the Gibbs dividing surface placed at z=0.50 Å. The length of the interface is set to Linterface=2.75 Å  and the dielectric is interpolated from bulk solvent to vacuum in the positive z direction across the Gibbs dividing surface. The Cartesian grid, solute cavity, and solvent dielectric are the same as in the previous example.

Example 12.16  Free energy of solvation of water at a water/vacuum interface.

$rem
   SCF_CONVERGENCE   5
   THRESH            14
   EXCHANGE          wB97X-V
   BASIS             6-31+G*
   SOLVE_PEQ         TRUE
   PEQ_SWITCH        0
$end

$molecule
   0 1
   O     0.053004    -0.020947    -0.034784
   H     0.003424     0.185855     0.910594
   H    -0.844842     0.146674    -0.358413
$end

$peqs
   SOLUTECAVITY RIGIDVDW
   INTERFACE TRUE
   INTERFACELENGTH 2.75
   GIBBSDS 0.50
   INTERFACEDIRECTION POSITIVE
$end

$peqs_grid
   DimX 73 -7.50 7.50
   DimY 73 -7.50 7.50
   DimZ 73 -7.50 7.50
$end

The final example illustrates a nonequilibrium (NonEquilJob = True) solvation calculation for the vertical ionization of H2O- in bulk water. This is a compound job that first calculates the equilibrium solvation free energy of the anionic state (NonEquilState = Reference), then computes the nonequilibrium energy correction for the ionized state (NonEquilState = Ionized). The two jobs are separated by “@@@”. The Cartesian grid and solvent dielectric are the same as the previous examples, but the solute cavity is chosen to be spherical with a radius of 2.0 Å. The Marcus scheme (NonEquilPartition = Marcus) is used to partition the solvent response into fast and slow components. Since this is the default method, the NonEquilPartition keyword is omitted.

Example 12.17  Nonequilibrium free energy of solvation for the vertical ionization of H2O-

$molecule
   -1 2
   O     0.053004    -0.020947    -0.034784
   H     0.003424     0.185855     0.910594
   H    -0.844842     0.146674    -0.358413
$end

$rem
   SCF_CONVERGENCE   5
   THRESH            14
   EXCHANGE          HF
   BASIS             6-31++G*
   SOLVE_PEQ         TRUE
   PEQ_SWITCH        0
$end

$peqs
   SOLUTECAVITY   SPHERICAL
   SPHERERADIUS   2.00
   NONEQUILJOB    TRUE
   NONEQUILSTATE  REFERENCE
$end

$peqs_grid
   DimX 73 -7.50 7.50
   DimY 73 -7.50 7.50
   DimZ 73 -7.50 7.50
$end

@@@

$molecule
   0 1
   O     0.053004    -0.020947    -0.034784
   H     0.003424     0.185855     0.910594
   H    -0.844842     0.146674    -0.358413
$end

$rem
   SCF_CONVERGENCE   5
   THRESH            14
   EXCHANGE          HF
   BASIS             6-31++G*
   SOLVE_PEQ         TRUE
   PEQ_SWITCH        0
$end

$peqs
   SOLUTECAVITY   SPHERICAL
   SPHERERADIUS   2.00
   NONEQUILJOB    TRUE
   NONEQUILSTATE  IONIZED
$end

$peqs_grid
   DimX 73 -7.50 7.50
   DimY 73 -7.50 7.50
   DimZ 73 -7.50 7.50
$end