Computation of molecular vibrational frequencies using anomalous harmoniclike potentials

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Quantum Chemistry

Background:

• Hartree-Fock (HF) instabilities at equilibrium geometries indicate lower-energy broken-symmetry solutions.
• These instabilities distort nuclear frameworks, causing anomalous behavior in potential energy surfaces (PES).
• Anomalies propagate to post-HF methods, hindering reliable vibrational frequency determination via PES differentiation.

Purpose of the Study:

• To present an alternative method for accurately determining vibrational frequencies in systems with anomalous PES behavior.
• To overcome the limitations of traditional PES differentiation methods when HF instabilities are present.

Main Methods:

• Introduction of the integral averaging method (IAM) as a novel approach.
• IAM significantly reduces the number of required PES calculations compared to solving the nuclear motion Schrodinger equation.
• Application of IAM to ABA-type triatomics and the allyl radical.

Main Results:

• IAM yields results of comparable accuracy to solving the Schrodinger equation.
• The method effectively addresses anomalies in PES due to spin-preserving instabilities in restricted open-shell HF solutions.
• Demonstrated applicability to systems with problematic asymmetric stretching modes, such as the allyl radical.

Conclusions:

• The integral averaging method (IAM) provides an efficient and accurate alternative for calculating vibrational frequencies in challenging molecular systems.
• IAM circumvents the need for extensive PES computations, simplifying the analysis of systems with inherent HF instabilities.
• This method facilitates reliable determination of vibrational frequencies, even when standard differentiation techniques fail.