Numerical Applications to Polyatomic Molecules

It is quite straightforward to perform quasiclassical trajectory computations (QCT) on the reactions of polyatomic molecules providing a smooth global potential energy surface is available from which derivatives can be obtained with respect to the atomic coordinates. This method is described in detail in Classical Trajectory Simulations Final Conditions. Hamilton s equations are solved to follow the motion of the individual atoms as a function of time and the reactant and product vibrational and rotational states can be set or boxed to quantum mechanical energies. The method does not treat purely quantum mechanical effects such as tunneling, resonances. or interference but it can treat the full state-to-state, eneigy-resolved dynamics of a reaction and also produces rate constants. Numerous applications to polyatomic reactions have been reported. ... 

In this chapter, the diverse coupling constants and MEC components identified in the combined electronic-nuclear approach to equilibrium states in molecules and reactants are explored. The reactivity implications of these derivative descriptors of the interaction between the electronic and geometric aspects of the molecular structure will be commented upon within both the EP and EF perspectives. We begin this analysis with a brief survey of the basic concepts and relations of the generalized compliant description of molecular systems, which simultaneously involves the electronic and nuclear degrees-of-freedom. Illustrative numerical data of these derivative properties for selected polyatomic molecules, taken from the recent computational analysis (Nalewajski et al., 2008), will also be discussed from the point of view of their possible applications as reactivity criteria and interpreted as manifestations of the LeChatelier-Braun principle of thermodynamics (Callen, 1962). 

Applications based on the even-tempered prescription (1) have shown that it can lead to atomic and diatomic Hartree-Fock ground state energies of an accuracy approaching that achieved in numerical Hartree-Fock calculations [4] It is conjectured that a comparable accuracy can be achieved for small polyatomic molecules [12], [13] by constructing basis sets according to the prescription established for diatomic molecules. Similar procedures can... 

Thebook reviews low-dimensional theories and clarifies their insufficiency conceptually and numerically. It also examines the phenomenon of nonadiabatic tunneling, which is common in molecular systems. The book describes applications to real polyatomic molecules, such as vinyl radicals and malonaldehyde, demonstrating the high efficiency and accuracy of the method. It discusses tunneling in chemical reactions, including theories for direct evaluation of reaction rate constants for both electronically adiabatic and nonadiabatic chemical reactions. In the final chapter, the authors touch on future perspectives. 

Applications of relativistic quantum mechanical techniques to chemical problems have been numerous in the last several years. These techniques have been applied to both diatomics and polyatomics containing very heavy atoms. The author has written several reviews " which have dealt with the applications of these techniques to main group hydrides, halides and chalconides, main group dimers and trimers, and actinide and lanthanide containing molecules. In this section we shall give very selected applications to some very heavy molecules to demonstrate the power of these techniques. The readers are referred to these extensive reviews on the topic for further details. 

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