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基于近期发展的经典-量子混合模拟非绝热分子动力学的量子路径方案，本文对5个典型势能面模型进行了模拟，包括单交叉模型、双交叉模型、拓展耦合模型、哑铃模型以及双弓模型.由于难以在严格意义上得到退相干速率，数值模拟中，我们比较了三个不同的退相干速率公式，包括冻结高斯波包近似退相干速率、能量分辨速率以及力分辨速率.在模拟过程中，我们恰当地处理了势能面跳跃时的能量守恒和力的反向问题.通过与全量子动力学模拟的精确结果进行对比发现，对于结构较简单的势能面模型，三种退相干速率都能得到较好的结果；然而对于较复杂的势能面模型，由于复杂量子干涉的原因，与其他混合经典-量子动力学方案类似，量子路径方案仍然难以得到较准确的结果.如何发展更加有效的混合经典-量子模拟方案，是未来研究的重要课题.
[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
-
[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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