Density-Functional and Hybrid-DFT SM5.43R Continuum Solvation Models for Aqueous and Organic Solvents

Thompson, J. D.; Cramer, C. J.; Truhlar, D. G.

* Theor. Chem. Acc.*
**2005**, *113*, 107.

Hybrid density functional theory, which is a combined Hartree-Fock and
density functional method, provides a simple but effective way to
incorporate nonlocal exchange effects and dynamical correlation energy into
an orbital-based theory with affordable computational cost for many
important problems of gas-phase chemistry. The inclusion of a reaction
field representing an implicit solvent in a self-consistent hybrid density
functional calculation provides an effective and efficient way to extend
this approach to problems of liquid-phase chemistry. In previous work, we
have parameterized several models based on this approach, and in the
present article, we present several new parameterizations based on implicit
solvation models SM5.43 and SM5.43R. In particular, we extend the
applicability of these solvation models to several combinations of the
MPW*X* hybrid-density functional with various one-electron basis sets,
where MPWX denotes combining Barone and Adamo's modified version of Perdew
and Wang's exchange functional, Perdew and Wang's correlation functional,
and a percentage *X* of exact Hartree-Fock (HF) exchange. SM5.43R
parameter optimizations are presented for the MPW*X*/MIDI!,
MPW*X*/MIDI!6D, and MPW*X*/6-31+G(d,p) combinations with *X*
= 0 (i.e., pure DFT), 25, 42.8, and 60.6, and for MPW*X*/6-31G(d) and
MPW*X*/6-31+G(d), with X = 0, 42.8, and 60.6; this constitutes a total
of 18 new parameter sets. (Note that parameter optimizations using
MPW25/6-31G(d) and MPW25/6-31+G(d) were carried out in a previous SM5.43R
parameterization.) For each of the five basis sets, we found no
significant loss in the accuracy of the model when parameters averaged over
the four values of *X* are used instead of the parameters optimized
for a specific value of *X*. Therefore for each of the five basis
sets used here, the SM5.43R model is defined to have a single parameter set
that can be used for any value of *X* between 0 and 60.6. The new
models yield accurate free energies of solvation for a broad range of
solutes in both water and organic solvents. On the average, the
mean-unsigned errors, as compared to experiment, of the free energies of
solvation of neutral solutes range from 0.50 to 0.55 kcal/mol and those for
ions range from 4.5 to 4.9 kcal/mol. Since the SM5.43R model computes the
free energy of solvation as a sum of bulk-electrostatic and
non-bulk-electrostatic contributions, it lends itself useful for detailed
analysis of the physical effects underlying a calculation of the free
energy of solvation. Several calculations illustrating the partitioning of
these contributions for a variety of solutes in *n*-hexadecane,
1-octanol, and water are presented.

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