  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 {\it ab initio}
thermochemistry methods.
