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(June 30, 2021)

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

$$\mathbf{q}=-{f}_{\epsilon}{\mathbf{S}}^{-1}\mathbf{v}.$$ | (11.25) |

As discussed in Section 11.2.3, the user can choose between various values of
${f}_{\epsilon}$, including the original value
${f}_{\epsilon}=(\epsilon -1)/(\epsilon +1/2)$ that was suggested by Klamt and co-workers,
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J. Chem. Phys.

(1996),
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or else ${f}_{\epsilon}=(\epsilon -1)/\epsilon $ as is typically used in C-PCM
calculations.
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. More importantly,
however, COSMO differs from C-PCM in that the former includes an ad hoc correction for
outlying charge that goes beyond Eq. (11.25), whereas C-PCM consists
of nothing more than induced surface charges computed (self-consistently)
according to Eq. (11.25). This correction, which is common to many implementations of
COSMO,
involves the use of two separate solute cavities. It is worth noting that
Eq. (11.25) was later shown to *implicitly* include an outlying charge correction,
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J. Chem. Phys.

(1999),
110,
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by virtue of the fact that it is derivable from the SS(V)PE model,
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(2011),
134,
pp. 204110.
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and
the latter was developed specifically with an eye towards the treatment of outlying charge. As such, there is little
theoretical justification for the additional *explicit* correction for outlying charge, despite its success in
practice.
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J. Chem. Theory Comput.

(2015),
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pp. 4220.
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See Ref. Herbert:2021b for a discussion of these issues.

In any case, the nature of the *a posteriori* correction for the outlying charge proceeds as follows.
Upon solution of Eq. (11.25), the outlying charge correction in
COSMO
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(1996),
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pp. 9972.
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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 $1.95R$,
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.
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(2000),
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pp. 2187.
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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.