Anharmonic force fields and thermodynamic functions using density functional theory

Abstract

The very good performance of modern density functional theory for molecular geometries and harmonic vibrational frequencies has been well established. We investigate the performance of density functional theory (DFT) for quartic force fields, vibrational anharmonicity and rotation–vibration coupling constants, and thermodynamic functions beyond the RRHO (rigid rotor–harmonic oscillator) approximation of a number of small polyatomic molecules. Convergence in terms of basis set, integration grid and the numerical step size for determining the quartic force field by using central differences of analytical second derivatives has been investigated, as well as the performance of various exchange-correlation functionals. DFT is found to offer a cost-effective approach with manageable scalability for obtaining anharmonic molecular properties, and particularly as a source for anharmonic zero-point and thermal corrections for use in conjunction with benchmark ab initio thermochemistry methods.

Acknowledgements

ADB acknowledges a postdoctoral fellowship from the Feinberg Graduate School (Weizmann Institute). Research at Weizmann was supported by the Minerva Foundation, Munich, Germany, by the Lise Meitner-Minerva Center for Computational Quantum Chemistry (of which JMLM is a member), and by the Helen and Martin Kimmel Center for Molecular Design. This work is related to Project 2003-024-1-100, ‘Selected Free Radicals and Critical Intermediates: Thermodynamic Properties from Theory and Experiment', of the International Union of Pure and Applied Chemistry (IUPAC).

Note

A reader of a preprint of this paper wondered whether, considering the cost imposed by the large grids required for DFT anharmonic force fields, it would not be preferable to carry out MP2 calculations instead. We carried out MP2/TZ2P calculations for the molecules in table 2. While this basis set is obviously still further from convergence for MP2 than it is for DFT, the results are somewhat indicative. We obtain the following mean(RMS) errors in cm⁻¹: harmonic frequencies +16(+57), fundamental frequencies +19(+61), anharmonic corrections −3.5(+9.8) cm⁻¹. This performance compares unfavorably with the hybrid DFT functionals in table 2. We intend to address this point more fully in a future paper.