-
3
-
-
63849197095
-
-
Miller, W. H. Adv. Chem. Phys. 1974, 25, 69; 1975, 30, 77.
-
(c) Miller, W. H. Adv. Chem. Phys. 1974, 25, 69; 1975, 30, 77.
-
-
-
-
5
-
-
84869269603
-
-
Interestingly, the motivation for using SC methods now is essentially the same as it was in the 1960s and 1970s. The 1960s saw the first use of numerically computed classical trajectories to describe inelastic and reactive collisions of small molecular systems e.g, A, BC → AB, C, and they played a very important role because it was not possible at that time to carry out the corresponding fully quantum calculations. Similarly, today, one would be happy to solve the Schrödinger equation for large molecular systems if it were possible. Numerically computed classical trajectory calculations are possible, though, and are immensely useful. The SC idea, now and then, is to take these numerically computed classical trajectories and use them as input to an SC description, thereby having all of the classical mechanics correct and an approximation description of the quantum effects
-
Interestingly, the motivation for using SC methods now is essentially the same as it was in the 1960s and 1970s. The 1960s saw the first use of numerically computed classical trajectories to describe inelastic and reactive collisions of small molecular systems (e.g., A + BC → AB + C), and they played a very important role because it was not possible at that time to carry out the corresponding fully quantum calculations. Similarly, today, one would be happy to solve the Schrödinger equation for large molecular systems if it were possible. Numerically computed classical trajectory calculations are possible, though, and are immensely useful. The SC idea, now and then, is to take these numerically computed classical trajectories and use them as input to an SC description, thereby having all of the classical mechanics correct and an approximation description of the quantum effects.
-
-
-
-
7
-
-
36449004965
-
-
(b) Kay, K. G. J. Chem. Phys. 1994, 100, 4377-1432.
-
(1994)
J. Chem. Phys
, vol.100
, pp. 4377-1432
-
-
Kay, K.G.1
-
15
-
-
0001321007
-
-
I do not know who first used this approach for treating electronically nonadiabatic processes. It is also sometimes used on one PES to treat a vibrational DOF quantum mechanically, and all the other nuclear DOF classically. An early example is: (a) Billing, G. D. Chem. Phys. Lett. 1975, 30, 391. and a very recent one is:
-
I do not know who first used this approach for treating electronically nonadiabatic processes. It is also sometimes used on one PES to treat a vibrational DOF quantum mechanically, and all the other nuclear DOF classically. An early example is: (a) Billing, G. D. Chem. Phys. Lett. 1975, 30, 391. and a very recent one is:
-
-
-
-
16
-
-
54849404745
-
-
(b) Bastida, A.; Zuniga, J.; Requena, A.; Miquiel, B. J. Chem. Phys. 2008, 129, 154501.
-
(2008)
J. Chem. Phys
, vol.129
, pp. 154501
-
-
Bastida, A.1
Zuniga, J.2
Requena, A.3
Miquiel, B.4
-
17
-
-
63849110588
-
-
One can equally well use the adiabatic representation for the N electronic states-see eq 2.17a below-but it is simpler to discuss the development using a diabatic representation.
-
One can equally well use the adiabatic representation for the N electronic states-see eq 2.17a below-but it is simpler to discuss the development using a diabatic representation.
-
-
-
-
22
-
-
0345882268
-
-
Bergmann, K.; Leone, S. R.; Moore, C. B. J. Chem. Phys. 1975, 63, 4161.
-
(1975)
J. Chem. Phys
, vol.63
, pp. 4161
-
-
Bergmann, K.1
Leone, S.R.2
Moore, C.B.3
-
30
-
-
0000897620
-
-
McCurdy, C. W.; Meyer, H. D.; Miller, W. H. J. Chem. Phys. 1979, 70, 3177-3187.
-
(1979)
J. Chem. Phys
, vol.70
, pp. 3177-3187
-
-
McCurdy, C.W.1
Meyer, H.D.2
Miller, W.H.3
-
33
-
-
0003767850
-
-
See, for example, Baer, M, Ed, CRC Press: Boca Raton, FL
-
See, for example, Raff, L. M. and Thompson, D. L. In The Theory of Reaction Dynamics: Baer, M., Ed.; CRC Press: Boca Raton, FL, 1985; Vol. 3, p 1.
-
(1985)
The Theory of Reaction Dynamics
, vol.3
, pp. 1
-
-
Raff, L.M.1
Thompson, D.L.2
-
34
-
-
0001174256
-
-
See, for example
-
See, for example: Porter, R. N.; Raff, L. M.; Miller, W. H. J. Chem. Phys. 1975, 63, 2214-2218.
-
(1975)
J. Chem. Phys
, vol.63
, pp. 2214-2218
-
-
Porter, R.N.1
Raff, L.M.2
Miller, W.H.3
-
43
-
-
0032094712
-
-
(a) Wang, H.; Sun, X.; Miller, W. H. J. Chem. Phys. 1998, 108, 9726-9736.
-
(1998)
J. Chem. Phys
, vol.108
, pp. 9726-9736
-
-
Wang, H.1
Sun, X.2
Miller, W.H.3
-
44
-
-
0000543438
-
-
(b) Sun, X.; Wang, H.; Miller, W. H. J. Chem. Phys. 1998, 109, 4190-4200.
-
(1998)
J. Chem. Phys
, vol.109
, pp. 4190-4200
-
-
Sun, X.1
Wang, H.2
Miller, W.H.3
-
45
-
-
33749481524
-
-
For example: a
-
For example: (a) Imne, K.; Ozizmir, E.; Rosenbaum, M.; Zweifel, P. F. J. Math Phys. 1967, 8, 10907.
-
(1967)
J. Math Phys
, vol.8
, pp. 10907
-
-
Imne, K.1
Ozizmir, E.2
Rosenbaum, M.3
Zweifel, P.F.4
-
50
-
-
0346058194
-
-
(f) Poulsen, J. A.; Nyman, G.; Rossky, P. J. J. Chem. Phys. 2003, 119, 12179.
-
(2003)
J. Chem. Phys
, vol.119
, pp. 12179
-
-
Poulsen, J.A.1
Nyman, G.2
Rossky, P.J.3
-
51
-
-
63849169739
-
-
The two trajectories in eq 3.6 can both be considered to start at t = 0, with the IVR expression of one being complex-conjugated, or equivalently, one can think of one propagating forward in time from 0 to t, and the other propagating backward in time from t to 0.
-
The two trajectories in eq 3.6 can both be considered to start at t = 0, with the IVR expression of one being complex-conjugated, or equivalently, one can think of one propagating forward in time from 0 to t, and the other propagating backward in time from t to 0.
-
-
-
-
59
-
-
0001036887
-
-
(b) Sun, X.; Wang, H.; Miller, W. H. J. Chem. Phys. 1998,109, 7064-7074.
-
(1998)
J. Chem. Phys
, vol.109
, pp. 7064-7074
-
-
Sun, X.1
Wang, H.2
Miller, W.H.3
-
60
-
-
0000132034
-
-
(c) Wang, H.; Song, X.; Chandler, D.; Miller, W. H. J. Chem. Phys. 1999, 110, 4828-1840.
-
(1999)
J. Chem. Phys
, vol.110
, pp. 4828-1840
-
-
Wang, H.1
Song, X.2
Chandler, D.3
Miller, W.H.4
-
62
-
-
0012969142
-
-
(e) Rabani, E.; Egorov, S. A.; Berne, B. J. J. Phys. Chem. A 1999, 103, 9539.
-
(1999)
J. Phys. Chem. A
, vol.103
, pp. 9539
-
-
Rabani, E.1
Egorov, S.A.2
Berne, B.J.3
-
63
-
-
0033699907
-
-
(f) Thoss, M.; Miller, W. H.; Stock, G. J. Chem. Phys. 2000, 112, 10282-10292.
-
(2000)
J. Chem. Phys
, vol.112
, pp. 10282-10292
-
-
Thoss, M.1
Miller, W.H.2
Stock, G.3
-
68
-
-
1042290529
-
-
(k) Novikov, A.; Kleinkathoefer, U.; Schreiber, M. Chem. Phys. 2004, 296, 149.
-
(2004)
Chem. Phys
, vol.296
, pp. 149
-
-
Novikov, A.1
Kleinkathoefer, U.2
Schreiber, M.3
-
70
-
-
50849119690
-
-
(m) Kim, H.; Nassimi, A.; Kapral, R. J. Chem. Phys. 2008, 129, 084102.
-
(2008)
J. Chem. Phys
, vol.129
, pp. 084102
-
-
Kim, H.1
Nassimi, A.2
Kapral, R.3
-
75
-
-
1942535102
-
-
Zhu, C.; Jasper, A. W.; Truhlar, D. G. J. Chem. Phys. 2004, 120, 5543.
-
(2004)
J. Chem. Phys
, vol.120
, pp. 5543
-
-
Zhu, C.1
Jasper, A.W.2
Truhlar, D.G.3
|