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(June 30, 2021)

Whereas PCMs, including sophisticated ones like SS(V)PE and IEF-PCM, account for long-range solute–solvent interactions, an accurate model for free energies of solvation must also include a treatment of short-range, non-electrostatic interactions. Various models decompose these interactions in different ways, but usually the non-electrostatic terms attempt to model all or most of the following: solute–solvent dispersion (van der Waals) interactions, Pauli (exchange) repulsion between solute and solvent, the work associated with forming the solute cavity within the dielectric medium (the so-called “cavitation energy”), hydrogen-bonding and other specific interactions due to the molecular structure of the solvent, and changes in the structure (and therefore the entropy) of the neat solvent upon introduction of the solute

Pomogaeva and
Chipman
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have
introduced an implicit solvation model that attempts to model these
non-electrostatic interactions alongside a PCM-style treatment of the bulk
electrostatics. They call this approach the “composite method for implicit
representation of solvent” (CMIRS), and it consists first of a self-consistent
treatment of solute–continuum electrostatics using the SS(V)PE model
(Section 11.2.5). To this electrostatics calculation, CMIRS adds
a solute–solvent dispersion term that is modeled upon the non-local VV09 van
der Waals dispersion density functional,
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Phys. Rev. Lett.

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a Pauli repulsion
contribution that depends upon the tail of the solute’s electron density that
extends beyond the solute cavity, and a hydrogen-bonding correction based on
the maximum and minimum values of the normal component of the electric field
generated by the solute at the cavity surface. The Gibbs free energy of
solvation is thus modeled as

$$\begin{array}{cc}\hfill \mathrm{\Delta}{G}_{\text{CMIRS}}({\rho}_{s})=& \mathrm{\Delta}{G}_{\text{SS(V)PE}}({\rho}_{s})+\mathrm{\Delta}{G}_{\text{DEFESR}}({\rho}_{s}),\hfill \end{array}$$ | (11.23) |

where $\mathrm{\Delta}{G}_{\text{SS(V)PE}}$ is the continuum electrostatics contribution from the SS(V)PE model, which is based on a solute cavity defined as an isocontour ${\rho}_{s}$ of the solute’s charge density. The second term contains the short-range dispersion, exchange, and "field-extremum short-range" (DEFESR) interactions:

$$\begin{array}{cc}\hfill \mathrm{\Delta}{G}_{\text{DEFESR}}=& \mathrm{\Delta}{G}_{\text{disp}}+\mathrm{\Delta}{G}_{\text{exch}}+\mathrm{\Delta}{G}_{\text{FESR}}.\hfill \end{array}$$ | (11.24) |

These terms are evaluated only once, using a converged charge density for the solute from a SS(V)PE calculation.

The CMIRS approach was implemented in Q-Chem by Zhi-Qiang You and John
Herbert.
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J. Chem. Theory Comput.

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In the course of this work, a serious error was
discovered in the the original implementation of $\mathrm{\Delta}{G}_{\text{disp}}$ by
Pomogaeva and Chipman, in the gamess program. Although reparameterization
of a corrected version of the model leads to only small changes in the overall
error statistics across a large database of experimental free energies of
solvation, the apportionment between energy components in
Eq. (11.24) changes significantly.
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By
request of Dan Chipman, the Q-Chem implementation is termed “CMIRS v. 1.1",
reserving v. 1.0 for the original gamess implementation of Pomogaeva and Chipman.

The CMIRS model is independently parametrized for each solvent of interest, but
uses no more than five empirical parameters per solvent. It is presently
available in Q-Chem for water, acetonitrile, dimethyl sulfoxide, benzene, and
cyclohexane. Error statistics for $\mathrm{\Delta}G$ compare very favorably to those
of the SM$x$ models that are described in Section 11.2.8, *e.g.*, mean
unsigned errors $$ kcal/mol in benzene and cyclohexane and $$ kcal/mol
in water. The latter statistic includes challenging ionic solutes; errors for
charge-neutral aqueous solutes are smaller still.
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Solvent | SolvRho | A | B | C | D | Gamma |
---|---|---|---|---|---|---|

Benzene | $0.0421$ | $-0.00522$ | $0.01294$ | |||

Cyclohexane | $0.0396$ | $-0.00938$ | $0.03184$ | |||

DMSO | $0.05279$ | $-0.00951$ | $0.044791$ | $-162.07$ | $4.1$ | |

${\mathrm{CH}}_{3}\mathrm{CN}$ | $0.03764$ | $-0.008178$ | $0.045278$ | $-0.33914$ | $1.3$ | |

Water | $0.05$ | $-0.006736$ | $0.032698$ | $-1249.6$ | $-21.405$ | $3.7$ |

Solvent | SolvRho | A | B | C | D | Gamma |
---|---|---|---|---|---|---|

Benzene | $0.0421$ | $-0.00572$ | $0.01116$ | |||

Cyclohexane | $0.0396$ | $-0.00721$ | $0.05618$ | |||

DMSO | $0.05279$ | $-0.002523$ | $0.011757$ | $-817.93$ | $4.3$ | |

${\mathrm{CH}}_{3}\mathrm{CN}$ | $0.03764$ | $-0.003805$ | $0.03223$ | $-0.44492$ | $1.2$ | |

Water | $0.05$ | $-0.006496$ | $0.050833$ | $-566.7$ | $-30.503$ | $3.2$ |

The current implementation of CMIRS in Q-Chem computes the electrostatic
energy using Chipman’s isodensity SS(V)PE module. The resulting isodensity
cavity and the solute charge density are then employed in the calculation of
the DEFESR interactions. To request a CMIRS calculation, users must set
IDEFESR = 1 in an isodensity SS(V)PE calculation (see
Section 11.2.5.2). The solvent-dependent empirical parameters
A, B, C, D, Gamma in the CMIRS
model need to be specified in the *$pcm_nonels* section. Three additional
parameters are also required. One is the damping parameter Delta in
the dispersion equation. We recommend the parameter fixed at $\delta =7$ a.u. (about 3.7 Å), an optimized value that only considers dispersion at
intermolecular distances larger than van der Waals contact distance. The
second is solvent’s average electron density SolvRho.
The last one is the number of Gauss–Laguerre points GauLag_N for the
integration over the solvent region in the exchange equation. We recommend $40$
grid points for efficient integration with accuracy. Optimized parameters for
the supported solvents are listed in Tables 11.4
and 11.5 for two different values of
${\rho}_{s}$.
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$molecule 0 1 C 0.000000 0.000005 0.000000 H 0.748558 0.801458 0.000000 H 0.506094 -0.972902 0.000000 H -0.627326 0.085706 0.895425 H -0.627326 0.085706 -0.895425 $end $rem EXCHANGE = b3lyp5 BASIS = 6-31+g* SCF_CONVERGENCE = 8 MEM_TOTAL = 4000 MEM_STATIC = 400 SYM_IGNORE = true XC_GRID = 000096000974 $end @@@ $rem EXCHANGE = b3lyp5 BASIS = 6-31+g* SCF_CONVERGENCE = 8 MAX_SCF_CYCLES = 100 SOLVENT_METHOD = isosvp SCF_GUESS = read PCM_PRINT = 1 MEM_TOTAL = 4000 MEM_STATIC = 400 SVP_MEMORY = 1000 SYM_IGNORE = true XC_GRID = 000096000974 $end $molecule read $end $svp RHOISO=0.001, DIELST=78.36, NPTLEB=974,ITRNGR=2, IROTGR=2, IPNRF=1, IDEFESR=1 $end $pcm_nonels A -0.006736 B 0.032698 C -1249.6 D -21.405 Delta 7.0 Gamma 3.7 SolvRho 0.05 GauLag_N 40 $end