Impact of complex-valued energy function singularities on the behaviour of Rayleigh-Schrödinger perturbation series. H2CO molecule vibrational energy spectrum.

Duchko, Andrey

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https://hdl.handle.net/2142/79117 Copy

Description

Title

Impact of complex-valued energy function singularities on the behaviour of Rayleigh-Schrödinger perturbation series. H2CO molecule vibrational energy spectrum.

Author(s)

Duchko, Andrey

Contributor(s)

Bykov, Alexandr

Issue Date

25-Jun-15

Keyword(s)

Vibrational structure/frequencies

Abstract

"Nowadays the task of spectra processing is as relevant as ever in molecular spectroscopy. Nevertheless, existing techniques of vibrational energy levels and wave functions computation often come to a dead-lock. Application of standard quantum-mechanical approaches often faces inextricable difficulties. Variational method requires unimaginable computational performance. On the other hand perturbational approaches beat against divergent series. That�s why this problem faces an urgent need in application of specific resummation techniques. In this research Rayleigh�Schr�dinger perturbation theory is applied to vibrational energy levels calculation of excited vibrational states of chem{H_2CO}. It is known that perturbation series diverge in the case of anharmonic resonance coupling between vibrational states [1]. Nevertheless, application of advanced divergent series summation techniques makes it possible to calculate the value of energy with high precision (more than 10 true digits) even for highly excited states of the molecule [2]. For this purposes we have applied several summation techniques based on high-order Pade-Hermite approximations. Our research shows that series behaviour completely depends on the singularities of complex energy function inside unit circle. That's why choosing an approximation function modelling this singularities allows to calculate the sum of divergent series. Our calculations for formaldehyde molecule show that the efficiency of each summation technique depends on the resonant type. \ REFERENCES\ 1. J. Cizek, V. Spirko, and O. Bludsky, ON THE USE OF DIVERGENT SERIES IN VIBRATIONAL SPECTROSCOPY. TWO- AND THREE-DIMENSIONAL OSCILLATORS, J. Chem. Phys. 99, 7331 (1993).\ 2. A. V. Sergeev and D. Z. Goodson, SINGULARITY ANALYSIS OF FOURTH-ORDER M\""{O}LLER-PLESSET PERTURBATION THEORY, J. Chem. Phys. 124, 4111 (2006)."

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

text

Language

English

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http://hdl.handle.net/2142/79117

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