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Semi-quartic force fields retrieved from multi-mode expansions: Accuracy, scaling behavior, and approximations.

Raghunathan Ramakrishnan1, Guntram Rauhut2

  • 1Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.

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|April 24, 2015
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Summary

This study explores multi-mode expansions for calculating semi-quartic force fields (QFF) and anharmonic vibrational frequencies. It compares computational costs with Taylor expansions and introduces a generalized Duschinsky transformation for efficient isotopologue frequency calculations.

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Area of Science:

  • Computational chemistry
  • Theoretical chemistry
  • Quantum chemistry

Background:

  • Semi-quartic force fields (QFF) are crucial for calculating anharmonic vibrational frequencies using 2nd order vibrational perturbation theory (VPT2).
  • Traditionally, QFFs are derived from Taylor expansions of the potential energy surface (PES) via differentiation of electronic energy.
  • Alternative methods like multi-mode expansions offer derivative-free approaches to PES representation.

Purpose of the Study:

  • To investigate the computational efficiency of retrieving QFFs from size-reduced multi-mode expansions compared to standard Taylor expansions.
  • To explore the advantages of multi-mode expansions, including the introduction of approximations.
  • To assess the applicability of a generalized Duschinsky transformation for calculating VPT2 frequencies of isotopologues.

Main Methods:

  • Taylor expansion of the multi-dimensional Born-Oppenheimer potential energy surface (PES).
  • Size-reduced multi-mode expansions for PES representation.
  • Computational cost analysis comparing multi-mode and Taylor expansions.
  • Application of a generalized Duschinsky transformation for isotopologue frequency calculations.

Main Results:

  • The study analyzes the computational effort required for QFF retrieval using multi-mode expansions versus Taylor expansions.
  • Subtle approximations enabled by multi-mode expansions are discussed.
  • A preliminary investigation into the generalized Duschinsky transformation for QFFs is presented.

Conclusions:

  • Multi-mode expansions offer a computationally viable alternative for generating QFFs, potentially reducing computational cost.
  • The generalized Duschinsky transformation shows promise for efficiently calculating isotopologue frequencies without recalculating PESs.
  • These advancements can streamline the computation of anharmonic vibrational frequencies for various molecular systems.