Trajectory studies anharmonicity

The first classical trajectory study of unimolecular decomposition and intramolecular motion for realistic anharmonic molecular Hamiltonians was performed by Bunker [12,13]. Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,17,30,M,65,66 and 62] from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3.12.7. Chaotic vibrational motion is not regular as predicted by the normal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9]. For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is formed and the probability of decomposition becomes that of RRKM theory. 

Hase and co-workers (136-140) have reported an extensive series of trajectory studies on overtone relaxation in benzene. Comparisons between our quantum studies for the five- and nine-mode benzene fragments of C,H and C3H, and the trajectory results were presented in Benzene I (103). Further comparisons for 16-mode and 21-mode benzene were presented in Benzene II and III (104,105). Clarke and Collins (141) also used classical trajectories to study overtone relaxation in benzene. Finally, Thompson et al. have also used trajectory methods to study energy flow from excited CH overtones (142,143) and from various excited CC stretch, CCH wag, and CCC bend normal modes. Several potential surfaces with varying degrees of anharmonicity were used. 

The enharmonic RRKM unimolecular rate constant for each of the eleven potential energy surfaces was determined at 50.0 kcal/mol from the t = 0 intercept of the trajectory lifetime distribution, equation (15). Time intervals of 1.0 x 10" and 0.5 x 10 s were used in trajectory P(t) histograms, and the resulting rate constants are given in Table 3. Within statistical uncertainties these time intervals give identical rate constants, which means that a At of 1.0 X 10 s is sufficiently small for establishing the intercepts. Bunker found the same result.A comparison between the enharmonic and harmonic RRKM rate constants in Table 3 shows that the enharmonic ones are all approximately a factor of two smaller. A similar enharmonic correction factor was found by Bunker and Pattengill in their triatomic trajectory studies.The enharmonic rate constants are expected to be smaller than the harmonic ones, since anharmonicity increases the HCC density of states and, thus, decreases the dissociation probability. 

In the fourth part, we study the effect of Cl on IC. It was applied to study the TtTt ->nTT transition of the pyrazine molecule. In this nonadiabatic process, the Cl of the TCK and nir PESs is believed to play a major role in the nonadiabatic fs transition. In fact, the Cl has been widely proposed to play the key factor in an IC, and quantum trajectory calculations have been used to calculate the IC rates [45]. However, this method cannot properly take into account of the initial conditions of the population and coherence of the system created by the fs pumping laser. In this chapter, we propose to develop a method to calculate the IC with conical intersections. It should be known that for the IC between Si and So in most molecules (in these cases, the energy gap between and So is of several eV), the surface crossings do not take place due to the anharmonic effect in the two PESs. Thus, the Cl should not play any role in these cases. We have proposed one method to calculate the IC rate of mt of the pyrazine molecule. The... 

The application of normal mode analysis to macromolecules such as proteins and nucleic acids has only recently become more common. Normal modes can be calculated either using harmonic analysis, where the second derivative matrix of the potential energy is calculated for a minimized structure, or using quasi-harmonic analysis, where the matrix of correlations of atomic displacements is calculated from a molecular dynamics (MD) trajectory. At temperatures below about 200 K, protein dynamics are primarily harmonic. Above this temperature there is appreciable non-harmonic motion which can be studied using quasi-elastic scattering techniques. There is evidence that such anharmonic motions are also important for protein function and quasi-harmonic analysis allows them to be incorporated implicitly to some extent within a harmonic model. 

At the present time, we only have a qualitative understanding of the features that lead to intrinsic non-RRKM behavior for the A and B surfaces. In studying the potential energy contour maps in the r,R plane (Fig. 2), one sees that the C and D surfaces become strongly enharmonic with negative curvature as the HC bond is extended. This anharmonicity is expected to make trajectories which sample this part of the surface separate exponentially in time instead of linearly.Exponential separation of trajectories results in stochastic behavior which should give rise to RRKM dissociation probabilities. The absence of this anharmonicity on the A and B surfaces is an explanation for their intrinsic non-RRKM lifetime distributions. 

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