Quantum mechanics methods potential energy surface based

Chapter 1 outlined the tools that computational chemists have at their disposal, Chapter 2 set the stage for the application of these tools to the exploration of potential energy surfaces, and Chapter 3 introduced one of these tools, molecular mechanics. In this chapter you will be introduced to quantum mechanics, and to quantum chemistry, the application of quantum mechanics to chemistry. Molecular mechanics is based on classical physics, physics before modern physics one of the cornerstones of modem physics is quantum mechanics, and ab initio (Chapter 5), semiempirical (Chapter 6), and density functional (Chapter 7) methods belong to quantum chemistry. This chapter is designed to ease the way to an understanding of... 

In order to obtain the potential energy surfaces associated with chemical reactions we, typically, need the lowest eigenvalue of the electronic Hamiltonian. Unlike systems such as a harmonic oscillator and the hydrogen atom, most problems in quantum mechanics cannot be solved exactly. There are, however, approximate methods that can be used to obtain solutions to almost any degree of accuracy. One such method is the variational method. This method is based on the variational principle, which says... 

A wide variety of dynamical approximations have been applied to cluster dynamics and kinetics. Most calculations to date are based on simplified potentials and classical mechanics or statistical methods. In the near future, we can expect to see more work with detailed potential energy surfaces (both analytic and implicitly defined by electronic structure calculations) and progress in sorting out quantum effects and treating them more accurately. 

What then, can organic chemistry as a science draw out from quantum chemistry In the search for the answer it is useful to look at the already accumulated experience of the interactions in these closely related areas of chemical science. In the last decades there have evolved various methods for the non-empirical and semi-empirical calculations of structure and reactivity of organic molecules based on quantum mechanics. In numerous cases these calculations turned out to be of extreme usefulness in obtaining quantitative information such as the charge distribution in a molecule, the reaction indices of alternate reaction centers, the energy of stabilization for various structures, the plausible shape of potential energy surfaces for chemical transformations, etc. This list seems to include almost all parameters that are needed for the explanation and prediction of the reactivity of a compound, that is, for solving the main chemical task. Yet there are several intrinsic defaults that impose rather severe limitations on the scope of the reliability of this approach. 

Two methods are in common use for simulating molecular liquids the Monte Carlo method (MC) and molecular dynamics calculations (MD). Both depend on the availability of reasonably accurate potential energy surfaces and both are based on statistical classical mechanics, taking no account of quantum effects. In the past 10-15 years quantum Monte Carlo methods (QMC) have been developed that allow intramolecular degrees of freedom to be studied, but because of the computational complexity of this approach results have only been reported for water clusters. 

A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

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