Solvent Dependence of ^{14}N Nuclear Magnetic Resonance Chemical
Shielding
Constants as a Test of the Accuracy of the Computed Polarization of Solute
Electron Densities by the Solvent

Ribeiro, R. F.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G.

* J. Chem. Theor. Comput.*
**2009**, *5*, 2284.

Although continuum solvation models have now been shown to provide good
quantitative accuracy for calculating free energies of solvation, questions
remain about the accuracy of the perturbed solute electron densities and
properties computed from them. Here we examine those questions by applying
the SM8, SM8AD, SMD, and IEF-PCM continuum solvation models in combination
with the M06-L density functional to compute the ^{14}N magnetic resonance
nuclear shieldings of CH_{3}CN, CH_{3}NO_{2},
CH_{3}NCS, and CH_{3}ONO_{2} in multiple
solvents, and we analyze the dependence of the chemical shifts on solvent
dielectric constant. We examine the dependence of the computed chemical
shifts on the definition of the molecular cavity (both united-atom models
and models based on superposed individual atomic spheres) and three kinds
of treatments of the electrostatics, namely the generalized Born
approximation with the Coulomb field approximation, the generalized Born
model with asymmetric descreening, and models based on approximate
numerical solution schemes for the nonhomogeneous Poisson equation. Our
most systematic analyses are based on the computation of relative
^{14}N
chemical shifts in a series of solvents, and we compare calculated
shielding constants relative to those in CCl_{4} for various solvation models
and density functionals. While differences in the overall results are found
to be reasonably small for different solvation models and functionals, the
SMx models SM8, and SM8AD, using the same cavity definitions (which for
these models means the same atomic radii) as those employed for the
calculation of free energies of solvation, exhibit the best agreement with
experiment for every functional tested. This suggests that in addition to
predicting accurate free energies of solvation, the SM8 and SM8AD
generalized Born models also describe the solute polarization in a manner
reasonably consistent with experimental ^{14}N nuclear magnetic resonance
spectroscopy. Models based on the nonhomogeneous Poisson equation show
slightly reduced accuracy. Scaling the intrinsic Coulomb radii to larger
values (as has sometimes been suggested in the past) does not uniformly
improve the results for any kind of solvent model; furthermore it uniformly
degrades the results for generalized Born models. Use of a basis set that
increases the outlying charge diminishes the accuracy of continuum models
that solve the nonhomogeneous Poisson equation, which we ascribe to the
inability of the numerical schemes for approximately solving the
nonhomogeneous Poisson equation to fully account for the effects of
electronic charge outside the solute cavity.