Polyatomic systems method

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

New Methods in Quantum Molecular Dynamics of Large Polyatomic Systems... 

Gerber, R. B., Ratner, M. A. Self-consistent field methods for vibrational excitations in polyatomic systems. Adv. Chem. Phys. 70 (1988) 97-132... 

P. Jungwirth and R. B. Gerber. Quantum dynamics of large polyatomic systems using a classically based separable potential method. J. Chem. Phys., 102 6046-6056, 1995. 

The elementary empirical tool for the molecular modelling of polyatomic systems is the method of molecular mechanics (MM) [2,3]. It explicitly employs intuitively transparent features of molecular electronic structure like localization of chemical bonds and groups. The basic assumption of the MM is the possibility to directly parameterize molecular PES in the form of a sum of contributions (force fields) relevant to bonds, their interactions, and to interactions of non-bonded atoms ... 

So far we have considered a system with two reservoirs separated by one bottleneck in general a polyatomic system wil1 have many reservoirs in its configuration space, and the location of the critical bottleneck or bottlenecks will be unknown. Here we will first distinguish critical and rate-limiting bottlenecks from less important ones, and then discuss several more or less heuristic methods for for finding bottlenecks. 

The calculation of a point on a potential-energy hypersurface is equivalent to calculating the energy of a diatomic or polyatomic system for a specified nuclear configuration and thus presents considerable practical computational difficulty. For certain problems or nuclear configurations, the maximum possible accuracy is needed, and under these conditions relatively elaborate ab initio methods are indicated. For other problems, the description to a uniform accuracy of many electronically excited states of a given system is required. Such is the situation for the atmospheric systems described here, and thus most of our final potential curves are based on the analysis of VCI wave functions constructed to uniform quality for representation of the excited states. 

The necessary starting positions r (0)of the atoms are in the given case usually obtained from methods of chain-packing procedures (see below). The starting velocities v (0) of all atoms are assigned via a suited application of the well-known relation between the average kinetic fc ipolyatomic system and its temperature T ... 

Finally, application of the time-dependent density functional theory (TD-DFT) to the dynamics of the electrons and nucleus of a simple molecule has been realized recently. Although this method is only limited to quite small size of polyatomic systems at present, the approach is promising and has plenty rooms to be improved and extended. Thus, it may be wise to consider an effective combination of TD-DFT and the GME. 

This method should find its most challenging developments in large polyatomic systems, as well as larger systems (cluster) where the selective approaches in organic photochemistry could be mimicked through the formation and excitation of the equivalent isomers, nucleophilic substitution, etc. 

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