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The mixed quantum-classical (MQC) molecular dynamics (MD) approaches are extremely important in practice since, with the increase of atomic degrees of freedom, a full quantum mechanical evaluation for molecular dynamics would quickly become intractable. Moreover, in some cases, the nonadiabatic effects are of crucial importance in the proximity of conical intersection of potential energy surfaces (PESs), where the energy separation between different PESs becomes comparable to the nonadiabatic coupling. In the past decades, there has been great interest in developing and improving various nonadiabatic MQC-MD protocols. The widely known nonadiabatic MD proposals include the so-called Ehrenfest or time-dependent-Hartree mean-field approach, the trajectory surface-hopping method, and their mixed scheme. Among the trajectory-based surface hopping methods, the most popular one is Tully's fewest switches surface hopping approach. In this approach, the nonadiabatic dynamics is treated by allowing hops from one PES to another, with the hopping probability determined by a certain artificial hopping algorithm. In our present work, we extend the study of a recent work on the nonadiabatic MQC-MD scheme, which is based on a view that the nonadiabatic MQC-MD actually implies an effective quantum measurement on the electronic states by the classical motion of atoms. The new protocol, say, the quantum trajectory (QT) approach, provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also connects two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. In our present study, we implement further the QT approach to simulate several typical potential-surface models, i.e., including the single avoided crossing, dual avoided crossing, extended coupling, dumbbell and double arch potentials. In particular, we simulate and compare three decoherence rates, which are from different physical considerations, i.e., the frozen Gaussian approximation, energy discrimination and force discrimination. We also design simulation algorithms to properly account for the energy conservation and force direction change associated with the surface hopping. In most cases, we find that the QT results are in good agreement with those from the full quantum dynamics, which is insensitive to the specific form of the decoherence rate. But for the model involving strong quantum interference, like other nonadiabatic MQC-MD schemes, the QT approach cannot give desirable results. Developing better method should be useful for future investigations in this research area.
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[2] Micha D A 1983 J. Chem. Phys. 78 7138
[3] Li X S, Tully J C, Schlegel H B, Frisch M J 2005 J. Chem. Phys. 123 084106
[4] Tully J C, Preston P K 1971 J. Chem. Phys. 55 562
[5] Miller W H, George T F 1972 J. Chem. Phys. 56 5637
[6] Kuntz P J, Kendrick J, Whitton W N 1979 Chem. Phys. 38 147
[7] Blais N C, Truhlar D G 1983 J. Chem. Phys. 79 1334
[8] Ali D P, Miller W H 1983 J. Chem. Phys. 78 6640
[9] Tully J C 1990 J. Chem. Phys. 93 1061
[10] Kuntz P J 1991 J. Chem. Phys. 95 141
[11] Webster F, Wang E T, Rossky P J, Friesner R A 1994 J. Chem. Phys. 100 4835
[12] Prezhdo O V, Rossky P J 1997 J. Chem. Phys. 107 825
[13] Zhu C Y, Jasper A W, Truhlar D G 2004 J. Chem. Phys. 120 5543
[14] Zhu C Y, Nangia S, Jasper A W, Truhlar D G 2004 J. Chem. Phys. 121 7658
[15] Feng W, Xu L T, Li X Q, Fang W H, Yan Y J 2014 AIP Adv. 4 077131
[16] Li B, Han K L 2009 J. Phys. Chem. A 113 10189
[17] Li B, Chu T S, Han K L 2010 J. Comput. Chem. 31 362
[18] Yang M H, Huo C Y, Li A Y, Lei Y B, Yu L, Zhu C Y 2017 Phys. Chem. Chem. Phys. 19 12185
[19] Lu J F, Zhou Z N 2016 J. Chem. Phys. 145 124109
[20] Schubert A, Falvo C, Meier C 2016 J. Chem. Phys. 145 054108
[21] Wang L J, Prezhdo O V, Beljonne D 2015 Phys. Chem. Chem. Phys. 17 12395
[22] Kosloff R 1988 J. Phys. Chem. 92 2087
[23] Schatz G C 1996 J. Phys. Chem. 100 12839
[24] Zhang J Z H, Dai J, Zhu W 1997 J. Phys. Chem. A 101 2746
[25] Guo H, Yarkony D R 2016 Phys. Chem. Chem. Phys. 18 26335
[26] Chu T S, Zhang Y, Han K L 2006 Int. Rev. Phys. Chem. 25 201
[27] Chu T S, Han K L 2008 Phys. Chem. Chem. Phys. 10 2431
[28] Zhang S B, Wu Y, Wang J G 2016 J. Chem. Phys. 145 224306
[29] Jacobs K, Steck D A 2006 Contemp. Phys. 47 279
[30] Xie B B, Liu L H, Cui G L, Fang W H, Cao J, Feng W, Li X Q 2015 J. Chem. Phys. 143 194107
[31] Akimov A V, Long R, Prezhdo O V 2014 J. Chem. Phys. 140 194107
[32] Zhu C Y, Jasper A W, Truhlar D G 2005 J. Chem. Theory Comput. 1 527
[33] Bedard-Hearn M J, Larsen R E, Schwartz B J 2005 J. Chem. Phys. 123 234106
[34] Prezhdo O V 1999 J. Chem. Phys. 111 8366
[35] Granucci G, Persico M 2007 J. Chem. Phys. 126 134114
[36] Thachuk M, Ivanov M Y, Wardlaw D M 1998 J. Chem. Phys. 109 5747
[37] Heller E J 1981 J. Chem. Phys. 75 2923
[38] Schwartz B J, Bittner E R, Prezhdo O V, Rossky P J 1996 J. Chem. Phys. 104 5942
[39] Lan Z G, Shao J S 2012 Prog. Chem. 24 1105 (in Chinese) [兰峥岗, 邵久书 2012 化学进展 24 1105]
[40] Hammes-Schiffer S, Tully J C 1994 J. Chem. Phys. 101 4657
[41] Subotnik J E 2010 J. Chem. Phys. 132 134112
[42] Subotnik J E, Shenvi N 2011 J. Chem. Phys. 134 024105
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[1] Gerber R B, Buch V, Ratner M A 1982 J. Chem. Phys. 77 3022
[2] Micha D A 1983 J. Chem. Phys. 78 7138
[3] Li X S, Tully J C, Schlegel H B, Frisch M J 2005 J. Chem. Phys. 123 084106
[4] Tully J C, Preston P K 1971 J. Chem. Phys. 55 562
[5] Miller W H, George T F 1972 J. Chem. Phys. 56 5637
[6] Kuntz P J, Kendrick J, Whitton W N 1979 Chem. Phys. 38 147
[7] Blais N C, Truhlar D G 1983 J. Chem. Phys. 79 1334
[8] Ali D P, Miller W H 1983 J. Chem. Phys. 78 6640
[9] Tully J C 1990 J. Chem. Phys. 93 1061
[10] Kuntz P J 1991 J. Chem. Phys. 95 141
[11] Webster F, Wang E T, Rossky P J, Friesner R A 1994 J. Chem. Phys. 100 4835
[12] Prezhdo O V, Rossky P J 1997 J. Chem. Phys. 107 825
[13] Zhu C Y, Jasper A W, Truhlar D G 2004 J. Chem. Phys. 120 5543
[14] Zhu C Y, Nangia S, Jasper A W, Truhlar D G 2004 J. Chem. Phys. 121 7658
[15] Feng W, Xu L T, Li X Q, Fang W H, Yan Y J 2014 AIP Adv. 4 077131
[16] Li B, Han K L 2009 J. Phys. Chem. A 113 10189
[17] Li B, Chu T S, Han K L 2010 J. Comput. Chem. 31 362
[18] Yang M H, Huo C Y, Li A Y, Lei Y B, Yu L, Zhu C Y 2017 Phys. Chem. Chem. Phys. 19 12185
[19] Lu J F, Zhou Z N 2016 J. Chem. Phys. 145 124109
[20] Schubert A, Falvo C, Meier C 2016 J. Chem. Phys. 145 054108
[21] Wang L J, Prezhdo O V, Beljonne D 2015 Phys. Chem. Chem. Phys. 17 12395
[22] Kosloff R 1988 J. Phys. Chem. 92 2087
[23] Schatz G C 1996 J. Phys. Chem. 100 12839
[24] Zhang J Z H, Dai J, Zhu W 1997 J. Phys. Chem. A 101 2746
[25] Guo H, Yarkony D R 2016 Phys. Chem. Chem. Phys. 18 26335
[26] Chu T S, Zhang Y, Han K L 2006 Int. Rev. Phys. Chem. 25 201
[27] Chu T S, Han K L 2008 Phys. Chem. Chem. Phys. 10 2431
[28] Zhang S B, Wu Y, Wang J G 2016 J. Chem. Phys. 145 224306
[29] Jacobs K, Steck D A 2006 Contemp. Phys. 47 279
[30] Xie B B, Liu L H, Cui G L, Fang W H, Cao J, Feng W, Li X Q 2015 J. Chem. Phys. 143 194107
[31] Akimov A V, Long R, Prezhdo O V 2014 J. Chem. Phys. 140 194107
[32] Zhu C Y, Jasper A W, Truhlar D G 2005 J. Chem. Theory Comput. 1 527
[33] Bedard-Hearn M J, Larsen R E, Schwartz B J 2005 J. Chem. Phys. 123 234106
[34] Prezhdo O V 1999 J. Chem. Phys. 111 8366
[35] Granucci G, Persico M 2007 J. Chem. Phys. 126 134114
[36] Thachuk M, Ivanov M Y, Wardlaw D M 1998 J. Chem. Phys. 109 5747
[37] Heller E J 1981 J. Chem. Phys. 75 2923
[38] Schwartz B J, Bittner E R, Prezhdo O V, Rossky P J 1996 J. Chem. Phys. 104 5942
[39] Lan Z G, Shao J S 2012 Prog. Chem. 24 1105 (in Chinese) [兰峥岗, 邵久书 2012 化学进展 24 1105]
[40] Hammes-Schiffer S, Tully J C 1994 J. Chem. Phys. 101 4657
[41] Subotnik J E 2010 J. Chem. Phys. 132 134112
[42] Subotnik J E, Shenvi N 2011 J. Chem. Phys. 134 024105
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