Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Molecular Modeling

Background:

• Harmonic approximations often fail to provide quantitative accuracy for molecular energies and thermodynamic functions.
• Anharmonic corrections are essential for precise calculations, especially for small to medium-sized molecules.
• Previous methods for anharmonic corrections were computationally intensive or less accurate.

Purpose of the Study:

• To compare harmonic and anharmonic zero-point energies and thermodynamic functions.
• To develop and validate an efficient perturbative method for calculating anharmonic corrections.
• To automate the calculation of anharmonic corrections within a widely used computational chemistry package.

Main Methods:

• A perturbative approach incorporating cubic force constants to the second order and semidiagonal quartic constants to the first order.
• Utilizing simple finite difference equations requiring at most 6N-11 Hessian evaluations (N = number of atoms).
• Employing the Becke three-parameter Lee-Yang-Parr (B3LYP) functional with medium-sized basis sets and accounting for internal rotations.

Main Results:

• Anharmonic corrections significantly impact quantitative studies of molecular energies and thermodynamics.
• The proposed perturbative method effectively calculates anharmonic corrections.
• The method demonstrates accuracy when combined with B3LYP, appropriate basis sets, and internal rotation treatment.

Conclusions:

• Anharmonic corrections are indispensable for accurate molecular property predictions.
• The developed perturbative method offers an efficient and accurate route to these corrections.
• The automation of this model in the Gaussian package facilitates its application in computational chemistry research.