Entropy plays a major role in reaction free energies, but calculating entropy accurately has been a challenging task for computational chemists over the years. The standard ab initio codes calculate the thermodynamic properties of molecules using the harmonic oscillator (HO) approximation and microscopic partition functions. However, it has long been recognized that vibrational entropic contributions computed using HO vibrational frequencies are fundamentally inaccurate for low frequency modes such as internal rotations. Treating internal rotations (torsions) as hindered rotors is a better approximation. The hindered rotor potential can be approximated by a finite Fourier series, and the relevant coefficients can be determined by fitting to a calculated potential energy surface. However, such a method is difficult and time consuming. Here we present a simple method to calculate the torsional entropy by approximating the torsional potential by a single cosine function.  The key feature of this method is that the barrier height is expressed in terms of the HO frequency, the local periodicity, and the reduced moment of inertia of the rotation. Thus, the 1D Schr�dinger equation for the internal rotation can be solved without finding the torsional potential, transition states, or barrier heights. Torsional entropy, HO frequency, moment of inertia, and periodicity are interrelated, and these variations will be discussed. Further simplification to this approached, achieved through a simple mathematical formula, which extrapolates the hindered rotor entropy between the free rotor and harmonic oscillator limits, will also be presented. Using this approximate function, the hindered rotor entropy can be calculated at effectively zero computational cost. The proposed methods have been implemented in an experimental version of the Q-Chem electronic structure program.

Simple approach to accurately determine the entropy of low frequency internal rotations

248th National Meeting (2014)

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