Analytic cubic and quartic force fields using density-functional theory.

Area of Science:

• Computational chemistry
• Theoretical chemistry
• Quantum chemistry

Background:

• Accurate calculation of molecular vibrational frequencies is crucial for understanding chemical properties and reactions.
• Previous methods for calculating anharmonic corrections were computationally intensive.
• Density-functional theory (DFT) offers a balance of accuracy and efficiency for electronic structure calculations.

Purpose of the Study:

• To present the first analytic implementation of cubic and quartic force constants within Kohn-Sham DFT.
• To enable more efficient and accurate calculations of molecular vibrational frequencies.
• To investigate the necessity of electron correlation for computing force constants.

Main Methods:

• Developed an open-ended formalism for evaluating energy derivatives in an atomic-orbital basis.
• Utilized open-ended codes for differentiated one- and two-electron integrals.
• Employed automatic differentiation for exchange-correlation kernels.
• Applied generalized second-order vibrational perturbation theory (GVPT2) for frequency calculations.

Main Results:

• Successfully implemented analytic cubic and quartic force constants in Kohn-Sham DFT.
• Calculated fundamental vibrational frequencies for methane, ethane, benzene, and aniline.
• Observed good agreement between Hartree-Fock and B3LYP anharmonic corrections.
• Demonstrated that electron correlation is not essential for reliable force constant calculations.

Conclusions:

• The developed analytic implementation provides an efficient route to anharmonic vibrational frequencies.
• Hartree-Fock calculations can yield reliable cubic and quartic force constants, reducing the need for computationally expensive electron correlation.
• This work advances the capability of computational chemistry for predicting molecular vibrational properties.