Pitfalls in the n-mode representation of vibrational potentials

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Molecular Dynamics

Background:

• Accurate potential energy surfaces are crucial for simulating anharmonic vibrational motion.
• The n-mode representation (n-MR) is an efficient many-body expansion for molecular vibrations, widely used in vibrational self-consistent field (VSCF) calculations.
• Convergence issues in VSCF calculations have been observed, particularly with strong anharmonic coupling.

Purpose of the Study:

• To identify the origin of non-convergence in VSCF calculations using the n-MR.
• To propose a method for correcting negative and unbound potentials encountered in truncated n-MR expansions.
• To demonstrate the effectiveness of the proposed correction method on challenging molecular systems.

Main Methods:

• Analysis of potential energy surfaces generated by truncated n-mode representations (n-MR).
• Identification of negative and unbound potentials arising from strong anharmonic coupling.
• Development and application of a "painting in" method to correct problematic n-MR potentials.
• Testing the correction method on VSCF calculations for water dimer, water trimer, and protonated tropine.

Main Results:

• Non-convergence in VSCF calculations is linked to negative potentials at truncated n-MR orders.
• Strong anharmonic coupling can cause n-MR to dip below the global minimum and create unbound single-mode potentials.
• The proposed "painting in" method effectively corrects these issues with minimal additional computational cost.
• The correction method restores SCF convergence and approximates results from higher-order n-MR expansions.

Conclusions:

• The study provides a detailed pathology of VSCF non-convergence related to n-MR.
• A practical and computationally inexpensive method is presented to resolve these convergence issues.
• The approach successfully identifies and corrects problematic mode couplings in complex molecular systems.