Effects of hydration on scale factors for ab initio force constants III: supermolecules

Abstract

Experimentally measured vibrational frequencies from the polar groups of peptides in aqueous solutions do not agree with frequencies calculated from scaled quantum mechanical force fields (SQMFF) using differential scale factors developed for molecules in the vapor phase. Measured frequencies often differ by more than 50 wavenumbers from calculated values. In order to obtain a more reliable interpretation of our measurements, we need a force field that incorporates the effects of solvation on peptides. Calculations on such systems require the use of small basis sets because of current limitations on computational resources. The primary focus of this work is the use of supermolecule calculations, using a relatively small basis set, 4–31G, as a simulation of the effects of hydration on force constants and corresponding vibrational frequencies. In the context of the SQMFF methodology, it appears that supermolecule calculations provide a better model for the effect of solvation on force constants than do calculations on isolated molecules. We present here an analysis of the effects of basis set superposition error (BSSE), of basis set quality, and of electron correlation at the MP2 level on the vibrational frequencies and force constants obtained from ab initio supermolecule calculations. Our goal is to test the usefulness of the relatively small 4–31G basis set in this context. We show here the results of our calculations on formic acid hydrogen-bonded to water. The simplicity of this system allows comparisons with calculations using much larger basis sets, and with correlation effects at the MP2 level of theory. We make the following observations. Scaled force matrices obtained using different basis sets, and using MP2 calculations, are similar. Supermolecule calculations using different basis sets, and at the MP2 level, produce similar shifts in diagonal force constants (from values obtained from isolated molecules). The BSSE does not significantly affect the calculation of frequencies. Supermolecule calculations, and scaling of force constants obtained using small basis sets are useful strategies for simulating the effects of hydration.