Strategies, studying quantum mechanics

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

M. Pavanello, B. Mennucci and A. Ferrarini, Quantum-mechanical studies of NMR properties of solutes in liquid crystals A new strategy to determine orientational order parameters, J. Chem. Phys., 122 (2005) 064906. 

New Computational Strategies for the Quantum Mechanical Study of Biological Systems in Condensed Phases... 

This chapter describes computational strategies for investigating the species in the catalytic cycle of the enzyme cjdochrome P450, and the mechanisms of its main processes alkane hydroxylation, alkene epoxidation, arene hydroxylation, and sulfoxidation. The methods reviewed are molecular mechanical (MM)-based approaches (used e.g., to study substrate docking), quantum mechanical (QM) and QM/MM calculations (used to study electronic structure and mechanism). 

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