11.2 Chemical Solvent Models

11.2.7 COSMO

According to Table 11.3, COSMO and C-PCM appear to differ only in the dielectric screening factor, fε in Eq. (11.3). Indeed, surface charges in either model are computed according to

𝐪=-fε𝐒-1𝐯, (11.12)

and as discussed in Section 11.2.3 the user has the option to choose either the original value suggested by Klamt,484, 482 fε=(ε-1)/(ε+1/2), or else fε=(ε-1)/ε as in, e.g., Refs. 974, 186, 533. 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 COSMO482, 36 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 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, 𝐪=-fε(𝐒)-1𝐯, is then computed on this larger cavity surface, and the charges on the original cavity surface are adjusted to new values, 𝐪′′=𝐪+𝐪. Finally, a corrected electrostatic potential on the original surface is computed according to 𝐯′′=-fε𝐒𝐪′′. It is this potential that is used to compute the solute–continuum electrostatic interaction (polarization energy), Gpol=12iqi′′vi′′. (For comparison, when the C-PCM approach described in Section 11.2.2 is used, the electrostatic polarization energy is Gpol=12iqivi, 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.844

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,481, 480 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 σ-surface files that are needed by COSMOtherm.