12.2.7 COSMO

According to Table 12.3, COSMO and C-PCM appear to differ only in the dielectric screening factor, $f_{\epsilon }$ in Eq. (12.3). Indeed, surface charges in either model are computed according to

and as discussed in Section 12.2.3 the user has the option to choose either the original value suggested by Klamt,^{477, 475} $f_{\epsilon }=(\epsilon -1)/(\epsilon +1/2)$, or else $f_{\epsilon }=(\epsilon -1)/\epsilon$ as in, e.g., Refs. 934, 195, 525. More importantly, however, COSMO differs from C-PCM in that the former includes a correction for outlying charge that goes beyond Eq. (12.12), whereas C-PCM consists of nothing more than induced surface charges computed (self-consistently) according to Eq. (12.12)

Upon solution of Eq. (12.12), the outlying charge correction in COSMO^{475, 51} is obtained by first defining a larger cavity that is likely to contain essentially all of the solute’s electron density; in practice, this typically means using atomic radii of 1.95 $R$, where $R$ denotes the original atomic van der Waals radius that was used to compute $𝐪$. (Note that unlike the PCMs described in Sections 12.2.2 and 12.2.3, where the atomic radii have default values but a high degree of user-controllability is allowed, the COSMO atomic radii are parameterized for this model and are fixed.) A new set of charges, ${𝐪}^{\prime }=-f_{\epsilon }{({𝐒}^{\prime })}^{-1}{𝐯}^{\prime }$, is then computed on this larger cavity surface, and the charges on the original cavity surface are adjusted to new values, ${𝐪}^{\prime \prime }=𝐪+{𝐪}^{\prime }$. Finally, a corrected electrostatic potential on the original surface is computed according to ${𝐯}^{\prime \prime }=-f_{\epsilon }{\mathrm{𝐒𝐪}}^{\prime \prime }$. It is this potential that is used to compute the solute–continuum electrostatic interaction (polarization energy), $G_{\mathrm{pol}}=\frac{1}{2}{\sum }_i{q}_i^{\prime \prime }{v}_i^{\prime \prime }$. (For comparison, when the C-PCM approach described in Section 12.2.2 is used, the electrostatic polarization energy is $G_{\mathrm{pol}}=\frac{1}{2}{\sum }_i{q}_i{v}_i$, computed using the original surface charges $𝐪$ and surface electrostatic potential $𝐯$.) With this outlying charge correction, Q-Chem’s implementation of COSMO resembles the one in Turbomole.⁸¹³

A COSMO calculation is requested by setting SOLVENT_METHOD = COSMO in the $rem section, in addition to normal job control variables. The keyword Dielectric in the $solvent section is used to set the solvent’s static dielectric constant, as described above for other solvation models. COSMO calculations can also be used as a starting point for COSMO-RS calculations,^{474, 473} where “RS” stands for “real solvent”. The COSMO-RS approach is not included in Q-Chem and requires the COSMOtherm program, which is licensed separately through COSMOlogic.¹² Q-Chem users who are interested in COSMOtherm can request special versions of Q-Chem for the generation of $\sigma$-surface files that are needed by COSMOtherm.