# 12.2.7 COSMO

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

 $\mathbf{q}=-f_{\varepsilon}\mathbf{S}^{-1}\mathbf{v}\;,$ (12.12)

and as discussed in Section 12.2.3 the user has the option to choose either the original value suggested by Klamt,474, 472 $f_{\varepsilon}=(\varepsilon-1)/(\varepsilon+1/2)$, or else $f_{\varepsilon}=(\varepsilon-1)/\varepsilon$ as in, e.g., Refs. 924, 194, 521. 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 COSMO472, 50 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 $\mathbf{q}$. (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, $\mathbf{q}^{\prime}=-f_{\varepsilon}(\mathbf{S}^{\prime})^{-1}\mathbf{v}^{\prime}$, is then computed on this larger cavity surface, and the charges on the original cavity surface are adjusted to new values, $\mathbf{q}^{\prime\prime}=\mathbf{q}+\mathbf{q}^{\prime}$. Finally, a corrected electrostatic potential on the original surface is computed according to $\mathbf{v}^{\prime\prime}=-f_{\varepsilon}\mathbf{S}\mathbf{q}^{\prime\prime}$. It is this potential that is used to compute the solute–continuum electrostatic interaction (polarization energy), $G_{\rm pol}=\tfrac{1}{2}\sum_{i}q_{i}^{\prime\prime}v_{i}^{\prime\prime}$. (For comparison, when the C-PCM approach described in Section 12.2.2 is used, the electrostatic polarization energy is $G_{\rm pol}=\tfrac{1}{2}\sum_{i}q_{i}v_{i}$, computed using the original surface charges $\mathbf{q}$ and surface electrostatic potential $\mathbf{v}$.) With this outlying charge correction, Q-Chem’s implementation of COSMO resembles the one in Turbomole.805

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,471, 470 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.