Approximate calculation of anharmonic densities of vibrational states for very large molecules

A fast linear-scaling method for calculating the density of vibrational states for a system of coupled anharmonic oscillators, applicable to very large molecules, is presented. Instead of discrete counting of molecular eigenstates, convolution of one-dimensional densities of states is performed in order to obtain the numbers and densities of states as a function of total internal energy. An efficient numerical integration scheme over an n-simplex is used. The density of states is given as the harmonic density multiplied by a correction factor that exclusively depends on dissociation energies and the bonding topology of the molecule. While the harmonic contribution to the density of states relies on the usual normal-mode picture, local modes are employed to account for anharmonicity and intermode coupling. Mode assignment problems encountered in previous models are absent due to permutational invariance of the integrand in the numerical integration. One-dimensional densities of states for coupled systems are defined as partial derivatives. Stretch-bend coupling is accounted for through the empirical model proposed by Troe [J. Troe, Chem. Phys. 90 (1995) 381]. The proposed method reproduces very well the results obtained from discrete counting for triatomic molecules. Extension to energies beyond the first dissociation limit is possible. Calculations on very large alkanes indicate anharmonic corrections to the number and density of states in the order of 2 at the lowest dissociation limit, while explicit consideration of hindered rotations increases this value to about 4. These large corrections have far-reaching consequences for all processes that directly depend on the density of vibrational states.