Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane
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 graph Γ 60 with a single edge length parameter. Within this model, the quantum states of CH 5 + are obtained in analytic form and are...
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| Veröffentlicht in: | Chemical communications (Cambridge, England) England), 2021-05, Vol.57 (39), p.4827-483 |
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| creator | Rawlinson, Jonathan I Fábri, Csaba Császár, Attila G |
| description | 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 graph
Γ
60
with 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 of
Γ
60
. The bipartite structure of
Γ
60
gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH
5
+
.
We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH
5
+
. |
| doi_str_mv | 10.1039/d1cc01214b |
| format | Article |
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5
+
based on the motion of an effective particle confined to a 60-vertex graph
Γ
60
with 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 of
Γ
60
. The bipartite structure of
Γ
60
gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH
5
+
.
We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH
5
+
.</description><identifier>ISSN: 1359-7345</identifier><identifier>EISSN: 1364-548X</identifier><identifier>DOI: 10.1039/d1cc01214b</identifier><identifier>PMID: 33861262</identifier><language>eng</language><publisher>England: Royal Society of Chemistry</publisher><subject>Combinatorial analysis ; Energy levels ; One dimensional models</subject><ispartof>Chemical communications (Cambridge, England), 2021-05, Vol.57 (39), p.4827-483</ispartof><rights>Copyright Royal Society of Chemistry 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c373t-be924a63c440f9920a6897eedc188533b5241be9f901971a6995763f9bc8ded43</citedby><cites>FETCH-LOGICAL-c373t-be924a63c440f9920a6897eedc188533b5241be9f901971a6995763f9bc8ded43</cites><orcidid>0000-0001-9746-1548 ; 0000-0001-5640-191X ; 0000-0001-9681-3775</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/33861262$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Rawlinson, Jonathan I</creatorcontrib><creatorcontrib>Fábri, Csaba</creatorcontrib><creatorcontrib>Császár, Attila G</creatorcontrib><title>Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane</title><title>Chemical communications (Cambridge, England)</title><addtitle>Chem Commun (Camb)</addtitle><description>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 graph
Γ
60
with 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 of
Γ
60
. The bipartite structure of
Γ
60
gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH
5
+
.
We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH
5
+
.</description><subject>Combinatorial analysis</subject><subject>Energy levels</subject><subject>One dimensional models</subject><issn>1359-7345</issn><issn>1364-548X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNpd0c9LHDEUB_BQlGrVS--WQC9FGM3Lj5nJ0a5ahYVeWvA2ZDJvdCSz2SaZ1f3vzXa3Fswlgffh8d43hHwGdg5M6IsOrGXAQbYfyCGIUhZK1vd7m7fSRSWkOiCfYnxi-YCqP5IDIeoSeMkPib1-MTa5NY3erUzrkMIVHX2HjuLL0plhEWl6ROr8c4ELDA9ruhraYNLgF8ZRh6ssYwqTTVNA6nu6DD7lWsKOjpgezQKPyX5vXMST3X1Eft9c_5rdFvOfP-5ml_PCikqkokXNpSmFlZL1WnNmylpXiJ2FulZCtIpLyKjXDHQFptRaVaXodWvrDjspjsi3bd88wp8JY2rGIVp0Ls_gp9hwBVJpxThk-vUdffJTyBttFC-ZqGqmsjrbKht8jAH7ZhmG0YR1A6zZRN9cwWz2N_rvGX_ZtZzaEbs3-i_rDE63IET7Vv3_d-IVXj6H_w</recordid><startdate>20210513</startdate><enddate>20210513</enddate><creator>Rawlinson, Jonathan I</creator><creator>Fábri, Csaba</creator><creator>Császár, Attila G</creator><general>Royal Society of Chemistry</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-9746-1548</orcidid><orcidid>https://orcid.org/0000-0001-5640-191X</orcidid><orcidid>https://orcid.org/0000-0001-9681-3775</orcidid></search><sort><creationdate>20210513</creationdate><title>Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane</title><author>Rawlinson, Jonathan I ; Fábri, Csaba ; Császár, Attila G</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-be924a63c440f9920a6897eedc188533b5241be9f901971a6995763f9bc8ded43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Combinatorial analysis</topic><topic>Energy levels</topic><topic>One dimensional models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rawlinson, Jonathan I</creatorcontrib><creatorcontrib>Fábri, Csaba</creatorcontrib><creatorcontrib>Császár, Attila G</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Chemical communications (Cambridge, England)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rawlinson, Jonathan I</au><au>Fábri, Csaba</au><au>Császár, Attila G</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane</atitle><jtitle>Chemical communications (Cambridge, England)</jtitle><addtitle>Chem Commun (Camb)</addtitle><date>2021-05-13</date><risdate>2021</risdate><volume>57</volume><issue>39</issue><spage>4827</spage><epage>483</epage><pages>4827-483</pages><issn>1359-7345</issn><eissn>1364-548X</eissn><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 graph
Γ
60
with 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 of
Γ
60
. The bipartite structure of
Γ
60
gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH
5
+
.
We present a simple, one-dimensional, exactly solvable model which explains not one but the first 60 vibrational eigenstates of the 6-atom molecule CH
5
+
.</abstract><cop>England</cop><pub>Royal Society of Chemistry</pub><pmid>33861262</pmid><doi>10.1039/d1cc01214b</doi><tpages>4</tpages><orcidid>https://orcid.org/0000-0001-9746-1548</orcidid><orcidid>https://orcid.org/0000-0001-5640-191X</orcidid><orcidid>https://orcid.org/0000-0001-9681-3775</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Chemical communications (Cambridge, England), 2021-05, Vol.57 (39), p.4827-483 |
| issn | 1359-7345 1364-548X |
| language | eng |
| recordid | cdi_proquest_journals_2526037805 |
| source | Royal Society Of Chemistry Journals 2008-; Alma/SFX Local Collection |
| subjects | Combinatorial analysis Energy levels One dimensional models |
| title | Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane |
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