Potential energy surface Quantum-mechanical system

An attempt in this direction has, in fact, been made by Preuss >, who recognized the importance of the above problem and developed methods for the treatment of the "incomplete associations of atoms which contain the FIEM (see Section A.) as subsets. The complexity of the Preuss approach limits its application to systems which contain much fewer nuclei and electrons than those involved in complicated chemical problems, such as synthetic design. For the latter, a different type of theory is needed, a theory that affords insights into the relations between complex chemical systems, without the sometimes formidable effort of solving the pertinent quantum mechanical problems. It is, however, conceivable that the potential energy surfaces of polyatomic systems will be the basis of future computer programs for the solution of chemical problems. 

In this chapter, quantum mechanical methods developed for enzyme kinetics modeling in our group have been presented, including the treatment of the potential energy surface for reactive system and the incorporation of nuclear quantum effects in dynamics simulations. Two aspects are emphasized ... 

Several ab initio quantum mechanical calculations have been done to determine the PES and a large number of analytical surfaces have been constructed. Classical trajectories have been computed on PESs that range from semiempirical to accurate fits of ab initio results. A partial list of the potential energy surfaces for this system is given in Table 1. (Some of the earlier formulations of the potential have proven inaccurate.) The history of the studies of this system is illustrative of the evolution in the accuracy of theoretical treatments which is typical in chemical dynamics, particularly the continuous improvements in the description of the PES (see Table 1) as ab initio results and experimental data became available. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. 

Potential energy surfaces are also central to our quantum-mechanical studies, and we are going to meet them again and again in subsequent chapters. Let s start then with Figure 3.1, which shows H2+. We are not going to be concerned with the overall translational motion of the molecule. For simphcity, I have drawn a local axis system with the centre of mass as the origin. By convention, we label the intemuclear axis the z-axis. 

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