Quasi-classical trajectory computations

Figure 3.11 Orientation dependence of the cross-section for the reaction H + D2(v= /= 0) HD + D at the two indicated values of the collision energy Ej- The ordinate is dff R/dcos y = 2ctr(cos y). The solid curves were calculated from the angle-dependent line-of-centers model, Eq. (3.34), and the (open and filled) points represent dynamical computations (these are quasi-classical trajectory results that have statistical error bars as discussed in Chapter 5) on the ab initio potential surface referred to in Figure 3.10 [adapted from N. C. Blais, R. B. Bernstein, and R. D. Levine, J. Phys. Chem. 89, 20 (1985)].

In the early 1930 s, Eyring and his co-workers made some preliminary studies of the trajectories of systems on potential-energy surfaces, but not much progress could be made until the development of high-speed computers. There has recently been a revival of interest in this field, now known as molecular dynamics. In particular, Karplus, Porter, and Sharma have carried out calculations on the H -b Hg system, using what appears to be a very reliable potential-energy surface. The calculations are quasi-classical in nature the vibrational and rotational states in the Hg molecule are quantized, but the course of the collision is treated classically. 

Figure 2.25 Variation in the three in-plane CO-Cr-CO angles along the entire CrlCOlg and Cr(CO)5 trajectory computed at the CASSCF/6-31G quasi-classical/TSH level. In the first phase a symmetric bend is excited and the angles a and y increase. The second phase corresponds to vibrational energy transfer from symmetric to antisymmetric bending coordinates. In the final phase, the molecule oscillates in a square planar minimum energy well with a frequency of 98 cm 1. (Adapted from Paterson, M.J., Hunt, P.A. and Robb, M.A., J. Phys. Chem. A, 106, 10494-10504, 2002.)...

Figure 2.30 Instantaneous average values of the lifetime (t) and cis—>trans isomerization ratio (p) of the model chromophores 1 and Im (computed by quasi-classical CASSCF/3-21G trajectory calculations) for three t5rpes of sampling.

Figure 2.31 Distribution of the energy at the hop geometry of the model chromophore Im (computed by combined quasi-classical CASSCF/3-21G trajectory calculations) for the three series of calculations presented in Figure 2.30.

Force-field methods form the basis of molecular dynamics. They use a parameterised quasi-classical description of interatomic forces to model the trajectory of systems typically composed of hundreds or even thousands of atoms. One good feature of these types of calculations is that with large systems the computational effort increases linearly with the size of the problem. This means that increased computational power allows considerably larger systems to be studied. Further gains can also be made by using parallel processors since energy calculations in molecular dynamics simulations are inherently parallel. 

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