Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Density Functional Theory

Background:

• Kohn-Sham (KS) methods are central to modern computational chemistry.
• New correlation functionals, termed σ-functionals, have emerged, closely related to the random phase approximation (RPA).
• σ-functionals are rooted in perturbation theory along the adiabatic connection.

Purpose of the Study:

• To develop and implement methods for calculating first derivatives of total energy for σ-functional methods.
• To perform geometry optimizations and vibrational frequency calculations using σ-functionals.
• To assess the accuracy of σ-functionals for various chemical systems.

Main Methods:

• Post-self-consistent field calculations using σ-functionals within a Gaussian basis set framework.
• Calculation of first derivatives of total energy with respect to nuclear coordinates.
• Geometry optimization and vibrational frequency analysis for diverse molecular systems.

Main Results:

• σ-functional methods demonstrate high accuracy and computational efficiency for main group chemistry, comparable to high-level wave-function methods.
• Achieved chemical accuracy of ~1 kcal/mol for reaction and transition state energies.
• σ-functionals yield highly accurate geometries and vibrational frequencies for main group molecules, outperforming conventional KS and RPA methods.
• For transition metal compounds, RPA methods provide superior geometries, while σ-functionals offer good, though less accurate, results.
• For non-covalently bonded systems, σ-functionals provide geometries comparable to RPA or KS methods with dispersion corrections.

Conclusions:

• σ-functional methods represent a computationally efficient and accurate approach, particularly for main group chemistry.
• These methods show promise for accurate predictions of molecular geometries and vibrational frequencies.
• Further development may be needed to optimize σ-functionals for transition metal systems due to data limitations.