On boundedness of isomerization paths for non- and semirelativistic molecules

Ioannis Anapolitanos*, Marco Olivieri, Sylvain Zalczer

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Abstract

This article focuses on isomerizations of molecules, i.e. chemical reactions during which a molecule is transformed into another one with atoms in a different spatial configuration. We consider the special case in which the system breaks into two submolecules whose internal geometry is solid during the whole procedure. We prove, under some conditions, that the distance between the two submolecules stays bounded during the reaction. This paper extends [Anapolitanos-Lewin, 2020] in two directions. The first one is that we relax assumptions that the ground state eigenspaces of the submolecules have to fulfill. The second one is that we allow semirelativistic kinetic energy as well. We provide an asymptotic expansion of the interaction energy between two molecules, including multipolar interactions and the van der Waals attraction. In addition to this static result, we proceed to a quasistatic analysis to investigate the variation of the energy when the nuclei move.

OriginalsprogEngelsk
Artikelnummer110713
TidsskriftJournal of Functional Analysis
Vol/bind288
Udgave nummer3
Antal sider81
ISSN0022-1236
DOI
StatusUdgivet - 2025

Bibliografisk note

Funding Information:
The research of all authors was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 258734477 - SFB 1173. The one of S.Z. was also supported by the Basque Government through the BERC 2022-2025 program and by the Ministry of Science and Innovation: BCAM Severo Ochoa accreditation SEV-2017-0718 and PID2020-112948GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by \u201CERDF A way of making Europe\u201D. The research of M.O. was partially supported by the grant 0135-00166B from the Independent Research Fund Denmark. I.A. is grateful to Mathieu Lewin for numerous inspiring discussions on the problem of isomerizations. He also acknowledges discussions with Roland Schnaubelt, which improved the presentation of the Introduction and of Section 1 . We thank Semjon Vugalter and Jean-Marie Barbaroux for suggesting to us the problem of extending the results of [6] in the semirelativistic case. All authors are grateful to Dirk Hundertmark for communicating that the results of [11] work if the irreducibility assumption is replaced by the assumption that all ground states of all atoms are spherically symmetric and for discussing the importance of this. This was an inspiration for us to relax the irreducibility assumption, as well.

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