Microcanonical effects

Song K and Hase W L 1999 Fitting classical microcanonical unimolecular rate constants to a modified RRK expression anharmonic and variational effects J. Chem. Phys. 110 6198-207... 

Temperature effects are included explicitly in molecular dynamics simulations by including kinetic energy terms - the balls representing the atoms are now on the move The principles are simple. In the microcanonical ensemble (NVE) ... 

To conclude our brief overview of ab initio MD, we note that the dynamics defined by Eq. (9.16) define a microcanonical ensemble. That is, trajectories defined by this Lagrangian will conserve the total energy of the system. Similar to the situation for classical MD simulations, it is often more useful to calculate trajectories associated with dynamics at a constant temperature. One common and effective way to do this is to add additional terms to the Lagrangian so that calculations can be done in the canonical ensemble (constant N, V, and T) using the Nose-Hoover thermostat introduced in Section 9.1.2. 

How thermal activation can take place following the Lindemann and the Lindemann-Hinshelwood mechanisms. An effective rate constant is found that shows the interplay between collision activation and unimolecular reaction. In the high-pressure limit, the effective rate constant approaches the microcanonical rate... 

Comment Experiments point to a gap in the existing theory, namely, the need for a microcanonical theory which takes some account of the solvent frictional effects. What is desirable next is a detailed comparison of theory and experiment. 

The first applications (230-234) concerned a study of the dependence of the tunneling effect on the curvature of the reaction path, of an energy transfer among different vibrational modes in the course of a reaction, and of the evaluation of microcanonical rate constants for study-case reactions, HCN - CNH, H2CO -> H2 + CO, H2CC -> HC=CH, and proton transfer in malonaldehyde. 

Equation (2.30) can be solved analytically only for a few simple systems, for most other cases numerical solution is required. Solution is usually effected by using the graining technique whereby the energy is partitioned into a series of contiguous intervals or grains, each of which is characterized by a number of states, a mean energy and a mean microcanonical rate coefficient. Equation (2.30) is thus approximated by. 

Like Eq. (27.2), Eqs. (27.11) and (27.12) are also hybrid quantized expressions in which the bound modes are treated quantum mechanically but the reaction coordinate motion is treated classically. Whereas it is difficult to see how quantum mechanical effects on reaction coordinate motion can be included in VTST, the path forward is straightforward in the adiabatic theory, since the one-dimensional scattering problem can be treated quantum mechanically. Since Eq. (27.12) is equivalent to the expression for the rate constant obtained from microcanonical variational theory [7, 15], the quantum correction factor obtained for the adiabatic theory of reactions can also be used in VTST. 

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