Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

Jonathan I. Rawlinson; Csaba Fábri; Attila G. Császár

doi:10.1039/d1cc01214b

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

Jonathan I. Rawlinson
, Csaba Fábri
, Attila G. Császár

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH ₅ ⁺based on the motion of an effective particle confined to a 60-vertex graphΓ ₆₀with a single edge length parameter. Within this model, the quantum states of CH ₅ ⁺are obtained in analytic form and are related to combinatorial properties ofΓ ₆₀. The bipartite structure ofΓ ₆₀gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH ₅ ⁺

Original language	English
Pages (from-to)	4827-4830
Number of pages	4
Journal	Chemical Communications
Volume	57
Issue number	39
Early online date	12 Apr 2021
DOIs	https://doi.org/10.1039/d1cc01214b
Publication status	Published - 14 May 2021

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title = "Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane",

abstract = "A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH 5 +based on the motion of an effective particle confined to a 60-vertex graphΓ 60with a single edge length parameter. Within this model, the quantum states of CH 5 +are obtained in analytic form and are related to combinatorial properties ofΓ 60. The bipartite structure ofΓ 60gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 + ",

author = "Rawlinson, \{Jonathan I.\} and Csaba F{\'a}bri and Cs{\'a}sz{\'a}r, \{Attila G.\}",

note = "Funding Information: The work of JIR was supported by the EPSRC grant CHAMPS EP/P021123/1. The work performed in Budapest received Funding Information: support from NKFIH (grant no. K119658) and from the ELTE Institutional Excellence Program (TKP2020-IKA-05) financed by the Hungarian Ministry of Human Capacities. Publisher Copyright: {\textcopyright} The Royal Society of Chemistry 2021.",

year = "2021",

month = may,

day = "14",

doi = "10.1039/d1cc01214b",

language = "English",

volume = "57",

pages = "4827--4830",

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publisher = "Royal Society of Chemistry",

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T1 - Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

AU - Rawlinson, Jonathan I.

AU - Fábri, Csaba

AU - Császár, Attila G.

N1 - Funding Information: The work of JIR was supported by the EPSRC grant CHAMPS EP/P021123/1. The work performed in Budapest received Funding Information: support from NKFIH (grant no. K119658) and from the ELTE Institutional Excellence Program (TKP2020-IKA-05) financed by the Hungarian Ministry of Human Capacities. Publisher Copyright: © The Royal Society of Chemistry 2021.

PY - 2021/5/14

Y1 - 2021/5/14

N2 - A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH 5 +based on the motion of an effective particle confined to a 60-vertex graphΓ 60with a single edge length parameter. Within this model, the quantum states of CH 5 +are obtained in analytic form and are related to combinatorial properties ofΓ 60. The bipartite structure ofΓ 60gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 +

AB - A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH 5 +based on the motion of an effective particle confined to a 60-vertex graphΓ 60with a single edge length parameter. Within this model, the quantum states of CH 5 +are obtained in analytic form and are related to combinatorial properties ofΓ 60. The bipartite structure ofΓ 60gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 +

UR - https://doi.org/10.1039/D1CC01214B

U2 - 10.1039/d1cc01214b

DO - 10.1039/d1cc01214b

M3 - Article

SN - 1359-7345

VL - 57

SP - 4827

EP - 4830

JO - Chemical Communications

JF - Chemical Communications

IS - 39

ER -

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

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