Diagrammatic theories of anharmonic molecular vibrations

Matthew R Hermes, So Hirata

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this review, we summarise recent developments in our laboratory in the field of many-body quantum-mechanical calculations of the anharmonic vibrational structure of molecules. Our size-extensive vibrational self-consistent field (XVSCF) and size-extensive second-order many-body perturbation (XVMP2) methods are, unlike their parent methods (VSCF and VMP2), defined in diagrammatic formulations of the energies and Dyson self-energies, leading to manifestly size-consistent expressions for zero-point energies and anharmonic vibrational frequencies calculable with much greater efficiency. The effective one-mode potentials of XVSCF are quadratic and hence the Schrödinger equation for each mode can be solved analytically, unlike VSCF, where a basis-set expansion of wave functions on more complex one-mode potentials need to be performed; VSCF potentials and their minima (anharmonic geometry) are shown to reduce to the quadratic potentials and their minima (also given analytically) of XVSCF in the thermodynamic limit. By self-consistently solving the Dyson equation with frequency-dependent self-energies, XVMP2 has the ability to calculate anharmonic frequencies of fundamentals as well as combinations and overtones in the presence of strong anharmonic resonance without a multireference or quasi-degenerate formulation, which tends to be non-size-consistent.To eliminate the computational bottleneck of XVSCF and XVMP2, which is the high-rank force-constant evaluation, we have developed alternative algorithms in which the diagrammatic equations are recast as a small number of high-dimensional integrals and then evaluated stochastically using a Metropolis Monte Carlo (MC) method. These MC-XVSCF and MC-XVMP2 methods not only remove the need for force-constant evaluation or storage, but also take into account force constants of up to infinite order according to their importance. They are a new branch of quantum Monte Carlo which can calculate frequencies (excitation energies) directly without fixed-node errors.

Original languageEnglish (US)
Pages (from-to)71-97
Number of pages27
JournalInternational Reviews in Physical Chemistry
Volume34
Issue number1
DOIs
StatePublished - Jan 1 2015

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Molecular vibrations
Monte Carlo methods
vibration
Excitation energy
Vibrational spectra
Wave functions
Monte Carlo method
Thermodynamics
formulations
Molecules
Geometry
energy
evaluation
zero point energy
self consistent fields
wave functions
harmonics
perturbation
thermodynamics
expansion

Keywords

  • Anharmonic vibrations
  • Diagrams
  • Dyson equation
  • Monte Carlo

Cite this

Diagrammatic theories of anharmonic molecular vibrations. / Hermes, Matthew R; Hirata, So.

In: International Reviews in Physical Chemistry, Vol. 34, No. 1, 01.01.2015, p. 71-97.

Research output: Contribution to journalArticle

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