11.2 Chemical Solvent Models 11.2.5 Linear-Scaling QM/MM/PCM Calculations 11.2.7 Composite Method for Implicit Representation of Solvent (CMIRS)

11.2.6 Isodensity Implementation of SS(V)PE

(July 14, 2022)

11.2.6.1 Basic Job Control

As discussed above, results obtained various types of PCMs are quite sensitive to the details of the cavity construction. Q-Chem’s implementation of PCMs, using Lebedev grids, simplifies this construction somewhat, but leaves the radii of the atomic spheres as empirical parameters (albeit ones for which widely-used default values are provided). An alternative implementation of the SS(V)PE solvation model is also available, ²⁰⁸ Chipman D. M., Dupuis M.
Theor. Chem. Acc.
(2002), 107, pp. 90. Link which attempts to further eliminate empiricism associated with cavity construction by taking the cavity surface to be a specified iso-contour of the solute’s electron density. [We call this the isodensity implementation of SS(V)PE in Table 11.3, and it is based on Chipman’s “symmetrized” form of the $\mathbf{K}$ matrix, ²⁰⁸ Chipman D. M., Dupuis M.
Theor. Chem. Acc.
(2002), 107, pp. 90. Link ^, ⁶⁶⁴ Lange A. W., Herbert J. M.
Chem. Phys. Lett.
(2011), 509, pp. 77. Link although the difference between symmetric and asymmetric forms is essentially negligible when an isodensity cavity construction is used. ²⁰⁸ Chipman D. M., Dupuis M.
Theor. Chem. Acc.
(2002), 107, pp. 90. Link ] In this case, the cavity surface is discretized by projecting a single-center Lebedev grid onto the iso-contour surface. Unlike the PCM implementation discussed in Section 11.2.3, for which point-group symmetry is disabled, this implementation of SS(V)PE supports full symmetry for all Abelian point groups. The larger and/or the less spherical the solute molecule is, the more points are needed to get satisfactory precision in the results. Further experience will be required to develop detailed recommendations for this parameter. Values as small as 110 points are usually sufficient for diatomic or triatomic molecules. The default value of 1202 points is adequate to converge the energy within 0.1 kcal/mol for solutes the size of mono-substituted benzenes.

Energy gradients are also not available for this implementation of SS(V)PE, although they are available for the implementation described in Section 11.2.3 in which the cavity is constructed from atom-centered spheres. As with the PCMs discussed in that section, the solute may be described using Hartree-Fock theory or DFT; post-Hartree–Fock correlated wave functions can also take advantage of molecular orbitals that are polarized using SS(V)PE. Researchers who use the isodensity SS(V)PE feature are asked to cite Ref. 211 Chipman D. M.
J. Chem. Phys.
(2000), 112, pp. 5558. Link .

In related work, Pomogaeva and Chipman ⁹⁶⁷ Pomogaeva A., Chipman D. M.
J. Chem. Theory Comput.
(2011), 7, pp. 3952. Link ^, ⁹⁶⁸ Pomogaeva A., Chipman D. M.
J. Phys. Chem. A
(2013), 117, pp. 5812. Link ^, ⁹⁶⁹ Pomogaeva A., Chipman D. M.
J. Chem. Theory Comput.
(2014), 10, pp. 211. Link ^, ⁹⁷⁰ Pomogaeva A., Chipman D. M.
J. Phys. Chem. A
(2015), 119, pp. 5173. Link recently introduced a “composite method for implicit representation of solvent” (CMIRS) that is based on SS(V)PE electrostatics but adds non-electrostatic terms. This model is available in Q-Chem ¹³²⁷ You Z.-Q., Herbert J. M.
J. Chem. Theory Comput.
(2016), 12, pp. 4338. Link and is discussed in Section 11.2.7. In its current implementation, CMIRS requires an isodensity SS(V)PE calculation, However, the current implementation computes the non-electrostatic interactions using the cavity and the solute’s charge density generated from the isodensity SS(V)PE. To use the CMIRS model, an isodensity SS(V)PE calculation must be requested (as described below), and the IDEFESR keyword must be set to 1 in the $svp input section. The CMIRS model is further described in Section 11.2.6.2.

An isodensity SS(V)PE calculation is requested by setting SOLVENT_METHOD = ISOSVP in the $rem section, in addition to normal job control variables for a single-point energy calculation. Whereas the other solvation models described in this chapter use specialized input sections (e.g., $pcm) in lieu of a slew of $rem variables, the isodensity SS(V)PE code is an interface between Q-Chem and a code written by Chipman, ²⁰⁸ Chipman D. M., Dupuis M.
Theor. Chem. Acc.
(2002), 107, pp. 90. Link so some $rem variables are used for job control of isodensity SS(V)PE calculations. These are listed below.

SVP_MEMORY

SVP_MEMORY
       Specifies the amount of memory for use by the solvation module.
TYPE:
       INTEGER
DEFAULT:
       125
OPTIONS:
       $n$ corresponds to the amount of memory in MB.
RECOMMENDATION:
       The default should be fine for medium size molecules with the default Lebedev grid, only increase if needed.

SVP_PATH

SVP_PATH
       Specifies whether to run a gas phase computation prior to performing the solvation procedure.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 runs a gas-phase calculation and after convergence runs the SS(V)PE computation. 1 does not run a gas-phase calculation.
RECOMMENDATION:
       Running the gas-phase calculation provides a good guess to start the solvation stage and provides a more complete set of solvated properties.

SVP_CHARGE_CONV

SVP_CHARGE_CONV
       Determines the convergence value for the charges on the cavity. When the change in charges fall below this value, if the electron density is converged, then the calculation is considered converged.
TYPE:
       INTEGER
DEFAULT:
       7
OPTIONS:
       $n$ Convergence threshold set to $10^{-n}$ .
RECOMMENDATION:
       The default value unless convergence problems arise.

SVP_CAVITY_CONV

SVP_CAVITY_CONV
       Determines the convergence value of the iterative isodensity cavity procedure.
TYPE:
       INTEGER
DEFAULT:
       10
OPTIONS:
       $n$ Convergence threshold set to $10^{-n}$ .
RECOMMENDATION:
       The default value unless convergence problems arise.

SVP_GUESS

SVP_GUESS
       Specifies how and if the solvation module will use a given guess for the charges and cavity points.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 No guessing. 1 Read a guess from a previous Q-Chem solvation computation. 2 Use a guess specified by the $svpirf section from the input
RECOMMENDATION:
       It is helpful to also set SCF_GUESS to READ when using a guess from a previous Q-Chem run.

This last $rem variable requires specification of a $svpirf input section, the format for which is the following:

$svpirf
   <# point> <x point>  <y point>  <z point>  <charge> <grid weight>
   <# point> <x normal> <y normal> <z normal>
$end

11.2.6.2 The $svp Input Section

More refined control over SS(V)PE jobs is obtained using a $svp input section. These are read directly by Chipman’s SS(V)PE solvation module and therefore must be specified in the context of a FORTRAN namelist. The format is as follows:

$svp
   <KEYWORD>=<VALUE>, <KEYWORD>=<VALUE>,...
   <KEYWORD>=<VALUE>
$end

For example, the section may look like this:

$svp
   RHOISO=0.001, DIELST=78.39, NPTLEB=110
$end

The following keywords are supported in the $svp section:

DielSt
       The static dielectric constant.
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       78.39
OPTIONS:
       real number specifying the constant.
RECOMMENDATION:
       The default value 78.39 is appropriate for water solvent.

IDEFESR
       Specifies whether to request a CMIRS calculation.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 do not invoke a CMIRS calculation. 1 do invoke a CMIRS calculation.
RECOMMENDATION:

IShape
       A flag to set the shape of the cavity surface.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 use the electronic isodensity surface. 1 use a spherical cavity surface.
RECOMMENDATION:
       Use the default surface.

RhoIso
       Value of the electronic isodensity contour used to specify the cavity surface. (Only relevant for IShape = 0.)
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       0.001
OPTIONS:
       Real number specifying the density in electrons/bohr ${}^{3}$ .
RECOMMENDATION:
       The default value is optimal for most situations. Increasing the value produces a smaller cavity which ordinarily increases the magnitude of the solvation energy.

RadSph
       Sphere radius used to specify the cavity surface (Only relevant for IShape=1.)
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       Half the distance between the outermost atoms plus 1.4 Å.
OPTIONS:
       Real number specifying the radius in Bohr (if positive) or in Å(if negative).
RECOMMENDATION:
       Make sure that the cavity radius is larger than the length of the molecule.

IntCav
       A flag to select the surface integration method.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Single center Lebedev integration. 1 Single center spherical polar integration.
RECOMMENDATION:
       The Lebedev integration is by far the more efficient.

NPtLeb
       The number of points used in the Lebedev grid for the single-center surface integration. (Only relevant if IntCav = 0.)
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       1202
OPTIONS:
       Valid choices are: 6, 18, 26, 38, 50, 86, 110, 146, 170, 194, 302, 350, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074, 3470, 3890, 4334, 4802, or 5294.
RECOMMENDATION:
       The default value has been found adequate to obtain the energy to within 0.1 kcal/mol for solutes the size of mono-substituted benzenes.

NPtThe, NPtPhi
       The number of ( $\theta$ , $\phi$ ) points used for single-centered surface integration (relevant only if IntCav = 1.)
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       8,16
OPTIONS:
       $\theta$ , $\phi$ specifying the number of points.
RECOMMENDATION:
       These should be multiples of 2 and 4 respectively, to provide symmetry sufficient for all Abelian point groups. Defaults are too small for all but the tiniest and simplest solutes.

LinEq
       Flag to select the method for solving the linear equations that determine the apparent point charges on the cavity surface.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       0 use LU decomposition in memory if space permits, else switch to LinEq = 2 1 use conjugate gradient iterations in memory if space permits, else use LinEq = 2 2 use conjugate gradient iterations with the system matrix stored externally on disk.
RECOMMENDATION:
       The default should be sufficient in most cases.

CvgLin
       Convergence criterion for solving linear equations by the conjugate gradient iterative method (relevant if LinEq = 1 or 2.)
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       1.0E-7
OPTIONS:
       Real number specifying the actual criterion.
RECOMMENDATION:
       The default value should be used unless convergence problems arise.

Note that the single-center surface integration approach that is used to find the isodensity surface may fail for certain very non-spherical solute molecules. The program will automatically check for this, aborting with a warning message if necessary. The single-center approach succeeds only for what is called a “star surface”, meaning that an observer sitting at the center has an unobstructed view of the entire surface. Said another way, for a star surface any ray emanating out from the center will pass through the surface only once. Some cases of failure may be fixed by simply moving to a new center with the ITrnGr parameter described below. But some surfaces are inherently non-star surfaces and cannot be treated with this program until more sophisticated surface integration approaches are developed and implemented.

ITrnGr
       Translation of the cavity surface integration grid.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       2
OPTIONS:
       0 No translation (i.e., center of the cavity at the origin of the atomic coordinate system) 1 Translate to the center of nuclear mass. 2 Translate to the center of nuclear charge. 3 Translate to the midpoint of the outermost atoms. 4 Translate to midpoint of the outermost non-hydrogen atoms. 5 Translate to user-specified coordinates in Bohr. 6 Translate to user-specified coordinates in Ångstroms.
RECOMMENDATION:
       The default value is recommended unless the single-center integrations procedure fails. If cavity construction fails for a small, high-symmetry system, consider setting ITrnGr = 0.

TranX, TranY, TranZ
       $x$ , $y$ , and $z$ value of user-specified translation (only relevant if ITrnGr is set to 5 or 6).
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       0, 0, 0
OPTIONS:
       $x$ , $y$ , and $z$ relative to the origin in the appropriate units.
RECOMMENDATION:
       None.

IRotGr
       Rotation of the cavity surface integration grid.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       2
OPTIONS:
       0 No rotation. 1 Rotate initial $x y z$ axes of the integration grid to coincide with principal moments of nuclear inertia (relevant if ITrnGr = 1) 2 Rotate initial $x y z$ axes of integration grid to coincide with principal moments of nuclear charge (relevant if ITrnGr = 2) 3 Rotate initial $x y z$ axes of the integration grid through user-specified Euler angles as defined by Wilson, Decius, and Cross.
RECOMMENDATION:
       The default is recommended unless the knowledgeable user has good reason otherwise. If cavity construction fails for a small, high-symmetry system, consider setting IRotGr = 0.

RotThe RotPhi RotChi
       Euler angles ( $\theta$ , $\phi$ , $\chi$ ) in degrees for user-specified rotation of the cavity surface (relevant if IRotGr = 3).
INPUT SECTION: $svp
TYPE:
       FLOAT
DEFAULT:
       0,0,0
OPTIONS:
       $\theta$ , $\phi$ , $\chi$ in degrees
RECOMMENDATION:
       None.

IOpPrd
       Specifies the choice of system operator-product form.
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Symmetric form. 1 Non-symmetric form.
RECOMMENDATION:
       The default uses more memory but is generally more efficient, we recommend its use unless there is shortage of memory available.

By default, Q-Chem will check the validity of the single-center expansion by searching for the isodensity surface in two different ways: first, working inwards from a large distance, and next by working outwards from the origin. If the same result is obtained (within tolerances) using both procedures, then the cavity is accepted. If the two results do not agree, then the program exits with an error message indicating that the inner isodensity surface is found to be too far from the outer isodensity surface.

Note: For some small molecules (such as atoms and diatomics), construction of the isodensity cavity may fail with the default parameters. In such cases, we recommend setting ITrnGr = 0 and also IRotGr = 0, with the molecule centered at the origin of the grid (i.e., in the standard nuclear orientation).

Some molecules, for example C ${}_{60}$ , can have a hole in the middle. Such molecules have two different “legal” isodensity surfaces, a small inner one inside the “hole”, and a large outer one that is the desired surface for solvation. In such cases, the cavity check described in the preceding paragraph causes the program to exit. To avoid this, one can consider turning off the cavity check that works out from the origin, leaving only the outer cavity determined by working in from large distances.

ICvICk
       Specifies whether to perform cavity check
INPUT SECTION: $svp
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       0 no cavity check, use only the outer cavity 1 cavity check, generating both the inner and outer cavities and compare.
RECOMMENDATION:
       Consider turning off cavity check only if the molecule has a hole and if a star (outer) surface is expected.

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11.2.6 Isodensity Implementation of SS(V)PE

11.2.6.1 Basic Job Control

11.2.6.2 The $svp Input Section