Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation

Abstract

We find that vibrational contributions to a solute's 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.

Chemical synthesis of lactic acid from cellulose catalysed by lead(II) ions in water

“…Natural bond orbital analyses at the B3LYP/6-311 þ þ G(d,p) level were performed to determine the atomic charge populations. For estimation of the Gibbs free energy, direct calculations in combination with frequency analysis in solution were performed, which has been verified to be a correct and practical approach 39 especially when liquid-phase and gas-phase structures differed significantly or when the stationary points present in the liquid solution could not survive in the gas phase. The B3LYP method was compared with several other popular density functional theoretical methods, including B3PW91, B97-D, M06, X3LYP and M06-2X, for the isomerization of glucose to its enol form, and B3LYP was found to be adequate for the present mechanistic study.…”

Hydrophosphination of Styrene and Polymerization of Vinylpyridine: A Computational Investigation of Calcium-Catalyzed Reactions and the Role of Fluxional Noncovalent Interactions

“…[44][45][46] Large structures such as the bulky spectator ligands, as well as methyl-containing substituent groups, can result in low frequency modes due to small internal rotations. These soft rotations are approximated as simple harmonic vibrations, which can introduce significant errors particularly when calculating entropy.…”

“…These soft rotations are approximated as simple harmonic vibrations, which can introduce significant errors particularly when calculating entropy. 46 Dispersion and solvent models can have a strong influence on low frequency modes and increase their occurrence. In particular, translation and rotation motions of a molecular system, which contribute significantly to entropy are hindered in solution.…”

“…In particular, translation and rotation motions of a molecular system, which contribute significantly to entropy are hindered in solution. 44,46,48,49 Consequently, solvent corrected entropy and subsequently Gibbs free energy of a system in solution can be overestimated. Therefore, enthalpies, as well as Gibbs free energies are often employed for comparison, and we report both throughout this article.…”

Comparison of DFT Methods for the Investigation of the Reduction Mechanisms of Aromatic Nitro- and Nitroso Compounds

“…[29] To minimize the negative influence of small frequencies to thermodynamic data, molecular partition functions were calculated using the quasiharmonic oscillator approximation. [30] All calculations were performed using Gaussian09, Revision D.01. [31] Theoretical standard reaction Gibbs energies for the reduction reactions relative to the SHE were calculated by the formula…”