Application of Advanced Divergent Series Summation Techniques forMolecule Vibrational Energy Spectrum Calculations. Analytical Properties of Complex-valued Energy Function of Different Molecules

Application of Advanced Divergent Series Summation Techniques forMolecule Vibrational Energy Spectrum Calculations. Analytical Properties of Complex-valued Energy Function of Different Molecules

Bibliographic Details
Parent link:8th International Congress on Industrial and Applied Mathematics, China, August 10-14, 2015: Program and Abstracts. [CP-Th-E-62-5].— , 2015
Main Author: Duchko A. N. Andrey Nikolaevich
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Институт международного образования и языковой коммуникации (ИМОЯК) Кафедра междисциплинарная (МД)
Summary:Title screen
The Rayleigh-Schrödinger perturbation theory is applied to energy levels calculation of excited vibrational states for different molecules. The calculations are carried out for the vibrational states that correspond to three- to seven-fold vibrational excitations. Perturbation series diverge in the case of strong resonance interactions. Nevertheless, considering vibrational energy of each excited state not as a real number, but as a complex function and applying corresponding analytical functions theory, we were able not only to get the exact value of energy, but to find the reason of divergence, and to choose the best summation technique. Our summation technique is based on high-order Pade-Hermite approximations. Further research shows that series behavior completely depends on the singularities of complex energy function inside unit circle. This analysis helped us to make the first exact definition of resonance interaction and to develop a unique technique for vibrational energy spectrum calculations avoiding resonances.
Language:English
Published: 2015
Subjects:
электронный ресурс
труды учёных ТПУ
Online Access:http://www.iciam2015.cn/Program%20&%20Abstracts.pdf#page=285
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=647407

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