Aleksandr V. Marenich

Use of solution-phase vibrational frequencies in continuum models for the free energy of solvation.

We find that vibrational contributions to a solutes free energy are in general insensitive to whether the solute vibrational frequencies are computed in the gas phase or in solution. In most cases, the difference is smaller than the intrinsic error in solvation free energies associated with the continuum approximation to solvation modeling, although care must be taken to avoid spurious results associated with limitations in the quantum-mechanical harmonic-oscillator approximation for very low-frequency molecular vibrations. We compute solute vibrational partition functions in aqueous and carbon tetrachloride solution and compare them to gas-phase molecular partition functions computed with the same level of theory and the same quasiharmonic approximation for the diverse and extensive set of molecules and ions included in the training set of the SMD continuum solvation model, and we find mean unsigned differences in vibrational contributions to the solute free energy of only about 0.2 kcal/mol. On the basis of these results and a review of the theory, we conclude, in contrast to previous work (Ho, J.; Klamt, H.; Coote, M. L. J. Phys. Chem. A 2010, 114, 13442), that using partition functions computed for molecules optimized in solution is a correct and useful approach for averaging over solute degrees of freedom when computing free energies of solutes in solution, and it is moreover recommended for cases where liquid and gas-phase solute structures differ appreciably or when stationary points present in liquid solution do not exist in the gas phase, for which we provide some examples. When gas-phase and solution-phase geometries and frequencies are similar, the use of gas-phase geometries and frequencies is a useful approximation.

Charge Model 5: An Extension of Hirshfeld Population Analysis for the Accurate Description of Molecular Interactions in Gaseous and Condensed Phases

We propose a novel approach to deriving partial atomic charges from population analysis. The new model, called Charge Model 5 (CM5), yields class IV partial atomic charges by mapping from those obtained by Hirshfeld population analysis of density functional electronic charge distributions. The CM5 model utilizes a single set of parameters derived by fitting to reference values of the gas-phase dipole moments of 614 molecular structures. An additional test set (not included in the CM5 parametrization) contained 107 singly charged ions with nonzero dipole moments, calculated from the accurate electronic charge density, with respect to the center of nuclear charges. The CM5 model is applicable to any charged or uncharged molecule composed of any element of the periodic table in the gas phase or in solution. The CM5 model predicts dipole moments for the tested molecules that are more accurate on average than those from the original Hirshfeld method or from many other popular schemes including atomic polar tensor and Löwdin, Mulliken, and natural population analyses. In addition, the CM5 charge model is essentially independent of a basis set. It can be used with larger basis sets, and thereby this model significantly improves on our previous charge models CMx (x = 1-4 or 4M) and other methods that are prone to basis set sensitivity. CM5 partial atomic charges are less conformationally dependent than those derived from electrostatic potentials. The CM5 model does not suffer from ill conditioning for buried atoms in larger molecules, as electrostatic fitting schemes sometimes do. The CM5 model can be used with any level of electronic structure theory (Hartree-Fock, post-Hartree-Fock, and other wave function correlated methods or density functional theory) as long as an accurate electronic charge distribution and a Hirshfeld analysis can be computed for that level of theory.

Performance of SM6, SM8, and SMD on the SAMPL1 Test Set for the Prediction of Small-Molecule Solvation Free Energies †

The SM6, SM8, and SMD quantum mechanical aqueous continuum solvation models are applied to predict free energies of aqueous solvation for 61 molecules in the SAMPL1 test set described elsewhere (Guthrie. J. Phys. Chem. B 2009, 113, 4501-4507). For direct comparison to other models, frozen geometries, provided by Guthrie, were used together with the M06-2X density functional and the 6-31G(d) basis set. For the bulk electrostatic component of the solvation free energy, SM6 and SM8 employ a generalized Born model that uses polarized discrete partial atomic charges to model the electron density, with these charges being calculated by the CM4 and CM4M class IV charge models, respectively; SMD uses the polarized continuous quantum mechanical charge density. If five sulfonylureas are removed from the SAMPL1 set, the root-mean-square deviations (RMSDs) of SM6, SM8, and SMD on the remaining 56 molecules are 2.4, 2.6, and 2.5 kcal mol(-1), respectively. The SM6, SM8, and SMD RMSDs on the five sulfonylureas are 14.2, 12.6, and 11.1 kcal mol(-1), respectively; however, we suggest that the uncertainty in the target solvation free energies for these molecules may be quite large.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Practical computation of electronic excitation in solution: vertical excitation model

We present a unified treatment of solvatochromic shifts in liquid-phase absorption spectra, and we develop a self-consistent state-specific vertical excitation model (called VEM) for electronic excitation in solution. We discuss several other approaches to calculate vertical excitations in solution as an approximation to VEM. We illustrate these methods by presenting calculations of the solvatochromic shifts of the lowest excited states of several solutes (acetone, acrolein, coumarin 153, indolinedimethine-malononitrile, julolidine-malononitrile, methanal, methylenecyclopropene, and pyridine) in polar and nonpolar solvents (acetonitrile, cyclohexane, dimethyl sulfoxide, methanol, n-hexane, n-pentane, and water) using implicit solvation models combined with configuration interaction based on single excitations and with time-dependent density functional theory.

Generalized Born Solvation Model SM12.

We present a new self-consistent reaction-field implicit solvation model that employs the generalized Born approximation for the bulk electrostatic contribution to the free energy of solvation. The new solvation model (SM) is called SM12 (where ″12″ stands for 2012), and it is available with two sets of parameters, SM12CM5 and SM12ESP. The SM12CM5 parametrization is based on CM5 partial atomic charges, and the SM12ESP parametrization is based on charges derived from a quantum-mechanically calculated electrostatic potential (ESP) (in particular, we consider ChElPG and Merz-Kollman-Singh charges). The model was parametrized over 10 combinations of theoretical levels including the 6-31G(d) and MG3S basis sets and the B3LYP, mPW1PW, M06-L, M06, and M06-2X density functionals against 2979 reference experimental data. The reference data include 2503 solvation free energies and 144 transfer free energies of neutral solutes composed of H, C, N, O, F, Si, P, S, Cl, Br, and I in water and in 90 organic solvents as well as 332 solvation free energies of singly charged anions and cations in acetonitrile, dimethyl sulfoxide, methanol, and water. The advantages of the new solvation model over our previous generalized Born model (SM8) and all other previous generalized Born solvation models are (i) like the SMD model based on electron density distributions, it may be applied with a single set of parameters with arbitrary extended basis sets, whereas the SM8 model involves CM4 or CM4M charges that become unstable for extended basis sets, (ii) it is parametrized against a more diverse training sets than any previous solvation model, and (iii) it is defined for the entire periodic table.

Universal Solvation Model Based on the Generalized Born Approximation with Asymmetric Descreening

We present a new self-consistent reaction field continuum solvation model based on the generalized Born (GB) approximation for the bulk electrostatic contribution to the free energy of solvation. The new model improves on the earlier SM8 model by using the asymmetric descreening algorithm of Grycuk to treat dielectric descreening effects rather than the Coulomb field approximation; it will be called Solvation Model 8 with asymmetric descreening (SM8AD). The SM8AD model is applicable to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known, in particular dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters. It does not require the user to assign molecular mechanics types to an atom or a group; all parameters are unique and continuous functions of geometry. This model employs a single set of parameters (solvent acidity-dependent intrinsic Coulomb radii for the treatment of bulk electrostatics and solvent description-dependent atomic surface tensions coefficients for the treatment of nonelectrostatic and short-range electrostatic effects). The SM8AD model was optimized over 26 combinations of theoretical levels including various basis sets (MIDI!, 6-31G*, 6-31+G*, 6-31+G**, 6-31G**, cc-pVDZ, DZVP, 6-31B*) and electronic structure methods (M05-2X, M05, M06-2X, M06, M06-HF, M06-L, mPW1PW, mPWPW, B3LYP, HF). It may be used with confidence with any level of electronic structure theory as long as self-consistently polarized Charge Model 4 or other self-consistently polarized charges compatible with CM4 charges are used, for example, CM4M charges can be used. With M05-2X/6-31G*, the SM8AD model achieves a mean unsigned error of 0.6 kcal/mol on average over 2 560 solvation free energies of tested aqueous and nonaqueous neutral solutes and a mean unsigned error of 3.9 kcal/mol on average over 332 solvation free energies of aqueous and nonaqueous ions.

Quantum Mechanical Continuum Solvation Models for Ionic Liquids

The quantum mechanical SMD continuum universal solvation model can be applied to predict the free energy of solvation of any solute in any solvent following specification of various macroscopic solvent parameters. For three ionic liquids where these descriptors are readily available, the SMD solvation model exhibits a mean unsigned error of 0.48 kcal/mol for 93 solvation free energies of neutral solutes and a mean unsigned error of 1.10 kcal/mol for 148 water-to-IL transfer free energies. Because the necessary solvent parameters are not always available for a given ionic liquid, we determine average values for a set of ionic liquids over which measurements have been made in order to define a generic ionic liquid solvation model, SMD-GIL. Considering 11 different ionic liquids, the SMD-GIL solvation model exhibits a mean unsigned error of 0.43 kcal/mol for 344 solvation free energies of neutral solutes and a mean unsigned error of 0.61 kcal/mol for 431 water-to-IL transfer free energies. As these errors are similar in magnitude to those typically observed when applying continuum solvation models to ordinary liquids, we conclude that the SMD universal solvation model may be applied to ionic liquids as well as ordinary liquids.

Resolution of a challenge for solvation modeling: Calculation of dicarboxylic acid dissociation constants using mixed discrete-continuum solvation models

First and second dissociation constants (pKa values) of oxalic acid, malonic acid, and adipic acid were computed by using a number of theoretical protocols based on density functional theory and using both continuum solvation models and mixed discrete-continuum solvation models. We show that fully implicit solvation models (in which the entire solvent is represented by a dielectric continuum) fail badly for dicarboxylic acids with mean unsigned errors (averaged over six pKa values) of 2.4-9.0 log units, depending on the particular implicit model used. The use of water-solute clusters and accounting for multiple conformations in solution significantly improve the performance of both generalized Born solvation models and models that solve the nonhomogeneous dielectric Poisson equation for bulk electrostatics. The four most successful models have mean unsigned errors of only 0.6-0.8 log units.

Charge Model 4 and Intramolecular Charge Polarization.

Partial atomic charges provide the most widely used model for molecular charge polarization, and Charge Model 4 (CM4) is designed to provide partial atomic charges that correspond to an accurate charge distribution, even though they may be calculated with polarized double-ζ basis sets with any density functional. Here we extend CM4 to six additional basis sets, and we present a model (CM4M) that is individually optimized for the M06 suite of density functionals for ten basis sets. These charge models yield class IV partial atomic charges by mapping from those obtained with Löwdin or redistributed Löwdin population analyses of density functional electronic charge distributions. CM4M/M06-2X/6-31G(d)//M06-2X/6-31+G(d,p) partial atomic charges are calculated for ethylene, CHnCl4-n (n = 0-4), benzene, nitrobenzene, phenol, and fluoromethanol and used to discuss gas-phase polarization effects.