Molecular mechanics dynamics principles

In this chapter we will focus on one particular, recently developed DFT-based approach, namely on first-principles (Car-Parri-nello) molecular dynamics (CP-MD) [9] and its latest advancements into a mixed quantum mechanical/molecular mechanical (QM/MM) scheme [10-12] in combination with the calculation of various response properties [13-18] within DFT perturbation theory (DFTPT) and time-dependent DFT theory (TDDFT) [19]. 

The credit load for die computational chemistry laboratory course requires that the average student should be able to complete almost all of the work required for the course within die time constraint of one four-hour laboratory period per week. This constraint limits the material covered in the course. Four principal computational methods have been identified as being of primary importance in the practice of chemistry and thus in the education of chemistry students (1) Monte Carlo Methods, (2) Molecular Mechanics Methods, (3) Molecular Dynamics Simulations, and (4) Quantum Chemical Calculations. Clearly, other important topics could be added when time permits. These four methods are developed as separate units, in each case beginning with die fundamental principles including simple programming and visualization, and building to the sophisticated application of the technique to a chemical problem. 

The theoretical models proposed in Chapters 2-4 for the description of equilibrium and dynamics of individual and mixed solutions are by part rather complicated. The application of these models to experimental data, with the final aim to reveal the molecular mechanism of the adsorption process, to determine the adsorption characteristics of the individual surfactant or non-additive contributions in case of mixtures, requires the development of a problem-oriented software. In Chapter 7 four programs are presented, which deal with the equilibrium adsorption from individual solutions, mixtures of non-ionic surfactants, mixtures of ionic surfactants and adsorption kinetics. Here the mathematics used in solving the problems is presented for particular models, along with the principles of the optimisation of model parameters, and input/output data conventions. For each program, examples are given based on experimental data for systems considered in the previous chapters. This Chapter ean be regarded as an introduction into the problem software which is supplied with the book an a CD. 

In the course of these studies, it was realized that the rotation of, for example, a backbone C—C bond in n-alkane produces periodical variation in the C—C bond length as well as in the C—C—X (X = H, C) valence angles . These observations are the most striking evidence for the molecular mechanics principle, wherein the dynamics of molecules is assumed to respond to a mechanical modeP . 

The principles of molecular mechanics may be used in a molecular simulation calculation, which is a type of computational statistical me-chanics. The goal of molecular simulation is to analyze a theoretical model of molecular behavior in order to determine the macroscopic properties of a substance. In one approach, known as molecular dynamics (MD), Newton s laws of motion for individual particles and a set of potential energy terms describing the forces on the structures are applied to all of the atoms in the calculation. Integration of the resulting differential equations over a short time period leads to new locations and new velocities for the atoms. 

Kirchner B, Vrabec J, Jaramillo-Botero A, Nielsen R, Abrol R, Su J, Pascal T, Mueller J, Goddard W in First-principles-based multiscale, multiparadigm molecular mechanics and dynamics methods for describing complex chemical processes. Multiscale molecular methods in applied chemistry. Springer Berlin Heidelberg, pp 1-42. 

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