Chemical direct dynamics trajectory

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the information from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using direct dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic information about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

One of the most attractive features of AIMD simulations is the possibility to directly follow the course of chemical reactions, as they occur spontaneously during a molecular dynamics trajectory. 

In atomic scale simulations, there is often a clear separation of timescales. The rate of rare events, e.g., chemical reactions, in a system coupled to a heat bath can be estimated by evaluating the free energy barriers for the transitions. Transition State Theory (TST) [9] is the foundation for this approach. Due to the large difference in time scale between atomic vibrations and typical thermally induced processes such as chemical reactions or diffusion, this would require immense computational power to directly simulate dynamical trajectories for a sufficient period of time to include these rare events. Identification of transition states is often the critical step in assessing rates of chemical reactions and path techniques like the nudged elastic band method is often used to identify these states [10-12,109]. 

Density functional theory (DPT) offers the opportunity to calculate the energies of nuclear configurations of polyatomic systems with an increasing efficiency. Direct dynamics , where the energies of the nuclear configurations are calculated as they are reached by a trajectory, promise to bypass the need for a PES in rate calculations. However, chemists need more general and structure-motivated methods to interpret and predict reactivity. Semi-anpirical methods may play a significant role in this respect, because they offer a simple, accurate and structure-related approach to chemical reactivity. 

The remainder of this chapter is organized as follows. Born-Oppen-heimer direct dynamics is reviewed in the next (second major) section. Approaches for integrating the classical equations of motion are outlined in the third major section (on integrating classical equations of motion). Algorithms for choosing initial conditions for ensembles of trajectories representing unimolecular and bimolecular reactions are reviewed in the fourth major section. The adequacy of classical mechanics for describing the dynamics of chemical processes, and the possible importance of quantum effects, is reviewed in the fifth major section. The final section surveys several applications of direct dynamics. 

With the current development of quantum chemistry, it is routine to evaluate Eq. [17] for the QM + MM model and the application of QM + MM direct dynamics is described in the section on trajectory initial conditions. However, in many situations the QM/MM boundary must cut through a chemical bond in a molecule. In such a case, the total electronic Hamiltonian cannot be divided as for the QM + MM model. Different approaches have been developed to treat QM/MM interactions when the boundary cuts through a chemical bond. Gao et al. identified a criterion for treating a covalent bond at the QM/MM boundary. In general, a reasonable boundary method should be able to mimic the real physical properties of the model system as closely as possible. The obtained properties such as vibrational frequencies, energies, and electronegativities, etc. should be comparable to experiment or accurate ab initio calculations. 

It was commented that In most reactions of complex molecules the intermediate has many more degrees of freedom and so the tendency will be to spend more time near the intermediate potential minimum and, thereby, to lose the directional information in the trajectory , but the model simulation certainly displays a possible role of dynamics effect on chemical reaction. 

The modified spectator stripping model (polarization model) thus appears to be a satisfactory one which explains the experimental velocity distribution from very low to moderately high energies. The model emphasizes that the long-range polarization force has the dominant effect on the dynamics of some ion—molecule reactions. However, a quite different direct mechanism based on short-range chemical forces has been shown to explain the experimental results equally satisfactorily [107, 108]. This model is named direct interaction with product repulsion model (DIPR model) and was originally introduced by Kuntz et al. [109] in the classical mechanical trajectory study of the neutral reaction of the type... 

Assigning in advance a dynamics of the chemical system composition to the pre-quasistationary state of its evolution can be done in two ways. First is the indirect or experimental way due to determination of the concentrations of reacting substances in time. The second is the direct or theoretical way via determination of the rate of an elementary reaction. Both methods assign in advance a phase trajectory a - a(t) and x = x(t) only at well-known starting concentrations of the reacting substances. 

Three novel approaches to the simulation of NA dynamics of large chemical systems have been presented [20-22]. The approaches extend the standard quantum-classical NA MD to incorporate quantum effects of the solvent subsystem that have been traditionally treated by classical mechanics. These effects include quantum trajectory branching (wave packet splitting), loss of quantum coherence directly related to the Franck-Condon overlap contribution to the NA transition probability, and ZPE of nuclear motion that contributes to the NA coupling and must be preserved during the equilibration of the energy released by the NA transition. 

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