Quantum theory of vibrational, rotational, and translational energy exchange in collisions of polyatomic molecules. Application to methyl halides
We derive a quantum theory of inter- and intramolecular transfer of vibrational, rotational, and translational energy in collisions of polyatomic molecules, in the case that short range forces between the collision partners are of prevailing importance. For this purpose, we first transform the Hamil...
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Veröffentlicht in: | J. Chem. Phys.; (United States) 1983-04, Vol.78 (7), p.4502-4514 |
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creator | Miklavc, Adolf |
description | We derive a quantum theory of inter- and intramolecular transfer of vibrational, rotational, and translational energy in collisions of polyatomic molecules, in the case that short range forces between the collision partners are of prevailing importance. For this purpose, we first transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of six rotational and three translational coordinates, we are then left with one single relevant generalized coordinate. The corresponding mass can easily be calculated; it depends on the usual reduced mass of the colliding molecules, on their moments of inertia, and on the geometry of the potential surface. The motion of the only relevant generalized coordinate is then quantized. To calculate the probabilities for the collision induced vibrational-rotational transitions, one can make use of any of a large number of the approximation schemes which have been developed in scattering theory. In the present work, we use the distorted wave expansion, for its simplicity and also because it leads, in the corresponding limit, directly to the results obtained recently by the semiclassical theory. As an application, we study vibrational deactivation probabilities of methyl halides colliding with inert gases: He, Ne, Ar, Kr, and Xe. Calculations are performed for two intermolecular potentials: exponential repulsive and Morse potential. The results obtained by the two potentials are very similar and agree well with the measured vibrational transition probabilities. |
doi_str_mv | 10.1063/1.445343 |
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Application to methyl halides</title><source>AIP Digital Archive</source><creator>Miklavc, Adolf</creator><creatorcontrib>Miklavc, Adolf ; Boris Kidric Institute of Chemistry, 61000 Ljubljana, Yugoslavia</creatorcontrib><description>We derive a quantum theory of inter- and intramolecular transfer of vibrational, rotational, and translational energy in collisions of polyatomic molecules, in the case that short range forces between the collision partners are of prevailing importance. For this purpose, we first transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of six rotational and three translational coordinates, we are then left with one single relevant generalized coordinate. The corresponding mass can easily be calculated; it depends on the usual reduced mass of the colliding molecules, on their moments of inertia, and on the geometry of the potential surface. The motion of the only relevant generalized coordinate is then quantized. To calculate the probabilities for the collision induced vibrational-rotational transitions, one can make use of any of a large number of the approximation schemes which have been developed in scattering theory. In the present work, we use the distorted wave expansion, for its simplicity and also because it leads, in the corresponding limit, directly to the results obtained recently by the semiclassical theory. As an application, we study vibrational deactivation probabilities of methyl halides colliding with inert gases: He, Ne, Ar, Kr, and Xe. Calculations are performed for two intermolecular potentials: exponential repulsive and Morse potential. The results obtained by the two potentials are very similar and agree well with the measured vibrational transition probabilities.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.445343</identifier><language>eng</language><publisher>United States</publisher><subject>640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena ; ATOMIC AND MOLECULAR PHYSICS ; COLLISIONS ; ENERGY LEVELS ; ENERGY TRANSFER ; EXCITED STATES ; HALOGENATED ALIPHATIC HYDROCARBONS ; MECHANICS ; MOLECULE COLLISIONS ; MOLECULE-MOLECULE COLLISIONS ; MOLECULES ; ORGANIC COMPOUNDS ; ORGANIC HALOGEN COMPOUNDS ; POLYATOMIC MOLECULES ; QUANTUM MECHANICS ; ROTATIONAL STATES ; VIBRATIONAL STATES</subject><ispartof>J. Chem. Phys.; (United States), 1983-04, Vol.78 (7), p.4502-4514</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c252t-c24b0c5f1c896635f0dd0ec022516129dc3db9eb846b9be246133cb4c929bc93</citedby><cites>FETCH-LOGICAL-c252t-c24b0c5f1c896635f0dd0ec022516129dc3db9eb846b9be246133cb4c929bc93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/5704189$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Miklavc, Adolf</creatorcontrib><creatorcontrib>Boris Kidric Institute of Chemistry, 61000 Ljubljana, Yugoslavia</creatorcontrib><title>Quantum theory of vibrational, rotational, and translational energy exchange in collisions of polyatomic molecules. Application to methyl halides</title><title>J. Chem. Phys.; (United States)</title><description>We derive a quantum theory of inter- and intramolecular transfer of vibrational, rotational, and translational energy in collisions of polyatomic molecules, in the case that short range forces between the collision partners are of prevailing importance. For this purpose, we first transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of six rotational and three translational coordinates, we are then left with one single relevant generalized coordinate. The corresponding mass can easily be calculated; it depends on the usual reduced mass of the colliding molecules, on their moments of inertia, and on the geometry of the potential surface. The motion of the only relevant generalized coordinate is then quantized. To calculate the probabilities for the collision induced vibrational-rotational transitions, one can make use of any of a large number of the approximation schemes which have been developed in scattering theory. In the present work, we use the distorted wave expansion, for its simplicity and also because it leads, in the corresponding limit, directly to the results obtained recently by the semiclassical theory. As an application, we study vibrational deactivation probabilities of methyl halides colliding with inert gases: He, Ne, Ar, Kr, and Xe. Calculations are performed for two intermolecular potentials: exponential repulsive and Morse potential. The results obtained by the two potentials are very similar and agree well with the measured vibrational transition probabilities.</description><subject>640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena</subject><subject>ATOMIC AND MOLECULAR PHYSICS</subject><subject>COLLISIONS</subject><subject>ENERGY LEVELS</subject><subject>ENERGY TRANSFER</subject><subject>EXCITED STATES</subject><subject>HALOGENATED ALIPHATIC HYDROCARBONS</subject><subject>MECHANICS</subject><subject>MOLECULE COLLISIONS</subject><subject>MOLECULE-MOLECULE COLLISIONS</subject><subject>MOLECULES</subject><subject>ORGANIC COMPOUNDS</subject><subject>ORGANIC HALOGEN COMPOUNDS</subject><subject>POLYATOMIC MOLECULES</subject><subject>QUANTUM MECHANICS</subject><subject>ROTATIONAL STATES</subject><subject>VIBRATIONAL STATES</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1983</creationdate><recordtype>article</recordtype><recordid>eNo9kM1KAzEUhYMoWKvgIwRXLpyav0mbZSn-QUGE7ofMnUwnkkmGJBXnMXxjW1vc3HM55_AtDkK3lMwokfyRzoQoueBnaELJQhVzqcg5mhDCaKEkkZfoKqVPQgidMzFBPx877fOux7kzIY44tPjL1lFnG7x2DziG_P9r3-ActU_uZGHjTdyO2HxDp_3WYOsxBOds2sfpwBqCG3UOvQXcB2dg50ya4eUwOAt_EJwD7k3uRoc77Wxj0jW6aLVL5uakU7R5ftqsXov1-8vbarkugJUs76-oCZQthYWSkpctaRpigDBWUkmZaoA3tTL1Qsha1YYJSTmHWoBiqgbFp-juiA0p2yqBzQY6CN4byFU5J4IuDqX7YwliSCmathqi7XUcK0qqw9wVrY5z819HLHVC</recordid><startdate>19830401</startdate><enddate>19830401</enddate><creator>Miklavc, Adolf</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>19830401</creationdate><title>Quantum theory of vibrational, rotational, and translational energy exchange in collisions of polyatomic molecules. Application to methyl halides</title><author>Miklavc, Adolf</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c252t-c24b0c5f1c896635f0dd0ec022516129dc3db9eb846b9be246133cb4c929bc93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1983</creationdate><topic>640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena</topic><topic>ATOMIC AND MOLECULAR PHYSICS</topic><topic>COLLISIONS</topic><topic>ENERGY LEVELS</topic><topic>ENERGY TRANSFER</topic><topic>EXCITED STATES</topic><topic>HALOGENATED ALIPHATIC HYDROCARBONS</topic><topic>MECHANICS</topic><topic>MOLECULE COLLISIONS</topic><topic>MOLECULE-MOLECULE COLLISIONS</topic><topic>MOLECULES</topic><topic>ORGANIC COMPOUNDS</topic><topic>ORGANIC HALOGEN COMPOUNDS</topic><topic>POLYATOMIC MOLECULES</topic><topic>QUANTUM MECHANICS</topic><topic>ROTATIONAL STATES</topic><topic>VIBRATIONAL STATES</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Miklavc, Adolf</creatorcontrib><creatorcontrib>Boris Kidric Institute of Chemistry, 61000 Ljubljana, Yugoslavia</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>J. Chem. Phys.; (United States)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Miklavc, Adolf</au><aucorp>Boris Kidric Institute of Chemistry, 61000 Ljubljana, Yugoslavia</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum theory of vibrational, rotational, and translational energy exchange in collisions of polyatomic molecules. Application to methyl halides</atitle><jtitle>J. Chem. Phys.; (United States)</jtitle><date>1983-04-01</date><risdate>1983</risdate><volume>78</volume><issue>7</issue><spage>4502</spage><epage>4514</epage><pages>4502-4514</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><abstract>We derive a quantum theory of inter- and intramolecular transfer of vibrational, rotational, and translational energy in collisions of polyatomic molecules, in the case that short range forces between the collision partners are of prevailing importance. For this purpose, we first transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of six rotational and three translational coordinates, we are then left with one single relevant generalized coordinate. The corresponding mass can easily be calculated; it depends on the usual reduced mass of the colliding molecules, on their moments of inertia, and on the geometry of the potential surface. The motion of the only relevant generalized coordinate is then quantized. To calculate the probabilities for the collision induced vibrational-rotational transitions, one can make use of any of a large number of the approximation schemes which have been developed in scattering theory. In the present work, we use the distorted wave expansion, for its simplicity and also because it leads, in the corresponding limit, directly to the results obtained recently by the semiclassical theory. As an application, we study vibrational deactivation probabilities of methyl halides colliding with inert gases: He, Ne, Ar, Kr, and Xe. Calculations are performed for two intermolecular potentials: exponential repulsive and Morse potential. The results obtained by the two potentials are very similar and agree well with the measured vibrational transition probabilities.</abstract><cop>United States</cop><doi>10.1063/1.445343</doi><tpages>13</tpages></addata></record> |
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subjects | 640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena ATOMIC AND MOLECULAR PHYSICS COLLISIONS ENERGY LEVELS ENERGY TRANSFER EXCITED STATES HALOGENATED ALIPHATIC HYDROCARBONS MECHANICS MOLECULE COLLISIONS MOLECULE-MOLECULE COLLISIONS MOLECULES ORGANIC COMPOUNDS ORGANIC HALOGEN COMPOUNDS POLYATOMIC MOLECULES QUANTUM MECHANICS ROTATIONAL STATES VIBRATIONAL STATES |
title | Quantum theory of vibrational, rotational, and translational energy exchange in collisions of polyatomic molecules. Application to methyl halides |
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