According to Table 11.3, COSMO and C-PCM appear to differ only in the dielectric screening factor, ${f}_{\epsilon}$ in Eq. (11.3). Indeed, surface charges in either model are computed according to

$$\mathbf{q}=-{f}_{\epsilon}{\mathbf{S}}^{-1}\mathbf{v},$$ | (11.12) |

and as discussed in Section 11.2.3 the user has the
option to choose either the original value suggested by
Klamt,^{Klamt:1993, Klamt:1996}
${f}_{\epsilon}=(\epsilon -1)/(\epsilon +1/2)$,
or else ${f}_{\epsilon}=(\epsilon -1)/\epsilon $ as in, *e.g.*,
Refs. Truong:1995, Cossi:2003, Lange:2011b. More importantly,
however, COSMO differs from C-PCM in that the former includes a correction for
outlying charge that goes beyond Eq. (11.12), whereas C-PCM consists
of nothing more than induced surface charges computed (self-consistently)
according to Eq. (11.12)

Upon solution of Eq. (11.12), the outlying charge correction in
COSMO^{Klamt:1996, Baldridge:1997} 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 11.2.2 and 11.2.3, 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, ${\mathbf{q}}^{\prime}=-{f}_{\epsilon}{({\mathbf{S}}^{\prime})}^{-1}{\mathbf{v}}^{\prime}$, 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 ${\mathbf{v}}^{\prime \prime}=-{f}_{\epsilon}{\mathrm{\mathbf{S}\mathbf{q}}}^{\prime \prime}$. 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 11.2.2 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 $\mathbf{q}$ and surface
electrostatic potential $\mathbf{v}$.) With this outlying charge correction,
Q-Chem’s implementation of COSMO resembles the one in
Turbomole.^{Schafer:2000}

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,^{Klamt:2001, Klamt:2010} 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.^{COSMOlogic} 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.