On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions

: Quantum mechanics (QM) is physics based theory which explains the physical properties of nature at the level of atoms and sub-atoms. Molecular mechanics (MM) construct molecular systems through the use of classical mechanics. So, hybrid quantum mechanics and molecular mechanics (QM/MM) when combined together can act as computer-based methods which can be used to calculate structure and property data of molecular structures. Hybrid QM/MM combines the strengths of QM with accuracy and MM with speed. QM/MM simulation can also be applied for the study of chemical process in solutions as well as in the proteins, and has a great scope in structure-based drug design (CADD) and discovery. Hybrid QM/MM also applied to HTS, to derive QSAR models and due to availability of many protein crystal structures; it has a great role in computational chemistry, especially in structure- and fragment-based drug design. Fused QM/MM simulations have been developed as a widespread method to explore chemical reactions in condensed phases. In QM/MM simulations, the quantum chemistry theory is used to treat the space in which the chemical reactions occur; however the rest is defined through molecular mechanics force field (MMFF). In this review, we have extensively reviewed recent literature pertaining to the use and applications of hybrid QM/MM simulations for ligand and structure-based computational methods for the design and discovery of therapeutic agents.

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Chemical Reactions In Condensed Phases

Chemical Dynamics in Condensed Phases ◽

10.1093/oso/9780198529798.003.0021 ◽

2006 ◽

Author(s):

Abraham Nitzan

Keyword(s):

Chemical Reactions ◽

Condensed Phase ◽

Chemical Change ◽

Classical Mechanics ◽

Chemical System ◽

Condensed Phases ◽

Molecular Configuration ◽

Middle Stage ◽

Condensed Phase Reactions ◽

Energy Surfaces

Understanding chemical reactions in condensed phases is essentially the understanding of solvent effects on chemical processes. Such effects appear in many ways. Some stem from equilibrium properties, for example, solvation energies and free energy surfaces. Others result from dynamical phenomena: solvent effect on diffusion of reactants toward each other, dynamical cage effects, solvent-induced energy accumulation and relaxation, and suppression of dynamical change in molecular configuration by solvent induced friction. In attempting to sort out these different effects it is useful to note that a chemical reaction proceeds by two principal dynamical processes that appear in three stages. In the first and last stages the reactants are brought together and products are separated from each other. In the middle stage the assembled chemical system undergoes the structural/chemical change. In a condensed phase the first and last stages involve diffusion, sometimes (e.g. when the species involved are charged) in a force field. The middle stage often involves the crossing of a potential barrier. When the barrier is high the latter process is rate-determining. In unimolecular reactions the species that undergoes the chemical change is already assembled and only the barrier crossing process is relevant. On the other hand, in bi-molecular reactions with low barrier (of order kBT or less), the rate may be dominated by the diffusion process that brings the reactants together. It is therefore meaningful to discuss these two ingredients of chemical rate processes separately. Most of the discussion in this chapter is based on a classical mechanics description of chemical reactions. Such classical pictures are relevant to many condensed phase reactions at and above room temperature and, as we shall see, can be generalized when needed to take into account the discrete nature of molecular states. In some situations quantum effects dominate and need to be treated explicitly. This is the case, for example, when tunneling is a rate determining process. Another important class is nonadiabatic reactions, where the rate determining process is hopping (curve crossing) between two electronic states. Such reactions are discussed in Chapter 16.

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Quantum dressed classical mechanics: application to chemical reactions

Chemical Physics Letters ◽

10.1016/s0009-2614(01)00555-3 ◽

2001 ◽

Vol 342 (1-2) ◽

pp. 65-74 ◽

Cited By ~ 1

Author(s):

Cecilia Coletti ◽

Gert D. Billing

Keyword(s):

Chemical Reactions ◽

Classical Mechanics

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Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates

The Journal of Chemical Physics ◽

10.1063/1.1670460 ◽

1968 ◽

Vol 49 (6) ◽

pp. 2610-2616 ◽

Cited By ~ 196

Author(s):

R. A. Marcus

Keyword(s):

Chemical Reactions ◽

Analytical Mechanics

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Differential Equations

10.1093/oso/9780198822370.003.0035 ◽

2018 ◽

Cited By ~ 1

Author(s):

Peter Mann

Keyword(s):

Calculus Of Variations ◽

Lagrange Equation ◽

Shortest Paths ◽

Classical Mechanics ◽

Classical Field Theory ◽

Variational Problems ◽

Functional Derivative ◽

Mathematical Framework ◽

Analytical Mechanics ◽

Mathematical Technique

This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approach to explain how the Euler–Lagrange equation is derived using this method. It also discusses first integrals. The chapter closes by defining the functional derivative, which is used in classical field theory.

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