Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei m...
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Veröffentlicht in: | The Journal of chemical physics 2013-12, Vol.139 (21), p.214107-214107 |
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description | In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly. |
doi_str_mv | 10.1063/1.4829856 |
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We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. 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Almost, but only with decoherence</title><title>The Journal of chemical physics</title><addtitle>J Chem Phys</addtitle><description>In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.</description><subject>Adiabatic flow</subject><subject>ALGORITHMS</subject><subject>BOLTZMANN-VLASOV EQUATION</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Couplings</subject><subject>Liouville equations</subject><subject>LIOUVILLE THEOREM</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>MATRIX ELEMENTS</subject><subject>SEMICLASSICAL APPROXIMATION</subject><subject>Switches</subject><subject>Trajectories</subject><subject>Wave packets</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqF0U-L1DAYBvAiijuuHvwCEvCwKnZ9k7ZJepJl8B8MeFnPIU3fbrOkTTdJZ5m7H9yOM84eBL0kEH48b5Iny15SuKTAiw_0spSslhV_lK0oyDoXvIbH2QqA0bzmwM-yZzHeAgAVrHyanbGyYFDwcpX9XOuR3CNpMdgtkuvZud1FJHEOnTaY936a7HhDtLvxwaZ-IF3wA0k9koiDNU7HaI125G7WY5oHsrF-3lrnkOBylKwfP5IrN_iY3pNmTsSPbkful6RlovE9BhwNPs-edNpFfHHcz7Mfnz9dr7_mm-9fvq2vNrmpaJnyrqbIuGx0UbStYQCSt5JpwWoQoqhRQ1dILZelBQOsYg0i1E3JaqRtUVbFefb6kLtcx6pobELTGz-OaJJijFWUyb16c1BT8HczxqQGGw06p0f0c1S0Wv6cC07l_2nJBXAmSv4w-0Rv_RzG5bmKUSYElwLoot4elAk-xoCdmoIddNgpCmrftaLq2PViXx0T52bA9iT_lLuAdwewf-nvLk5m68NDkpra7l_479G_AN4evzw</recordid><startdate>20131207</startdate><enddate>20131207</enddate><creator>Subotnik, Joseph E.</creator><creator>Ouyang, Wenjun</creator><creator>Landry, Brian R.</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><scope>7U5</scope><scope>OTOTI</scope></search><sort><creationdate>20131207</creationdate><title>Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? 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Almost, but only with decoherence</atitle><jtitle>The Journal of chemical physics</jtitle><addtitle>J Chem Phys</addtitle><date>2013-12-07</date><risdate>2013</risdate><volume>139</volume><issue>21</issue><spage>214107</spage><epage>214107</epage><pages>214107-214107</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied – some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). 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subjects | Adiabatic flow ALGORITHMS BOLTZMANN-VLASOV EQUATION CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Couplings Liouville equations LIOUVILLE THEOREM MATHEMATICAL METHODS AND COMPUTING MATRIX ELEMENTS SEMICLASSICAL APPROXIMATION Switches Trajectories Wave packets |
title | Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence |
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