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,171 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 12.3, and it is based on Chipman’s “symmetrized” form of the matrix.171, 521] 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 12.2.2, 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 12.2.2 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. 173.
In related work, Pomogaeva and Chipman734, 735, 736, 737 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-Chem1025 and is discussed in Section 12.2.6. 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 must be set to 1 in the $svp input section (see Section 18.104.22.168).
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,171 so some $rem variables are used for job control of isodensity SS(V)PE calculations. These are listed below.
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
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:
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.
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.
Some molecules, for example C, 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.