Computational Chemistry. Computer Simulation Techniques (Concise Lecture Notes in Physical Chemistry Book 3)

We describe the important role of the in-silico methods in modern Chemistry and Physics of complex systems, introduce the main underlying concepts, and overview the major techniques used in this broad field of research. The concepts of an idealised computer and virtual experiment are explained. Further, we discuss various popular computational packages used. The Born-Oppenheimer approximation for electronic configurations is introduced. Classical treatment of the motion of nuclei is then considered. Potential energy surfaces, force fields, and geometry optimisation and energy minimisation methods are discussed in detail. The Newton’s equations of motion and their numerical integration methods are presented. Numerical solution of ordinary differential equations in general is outlined. Examples of chemical reactions and Molecular dynamics are specifically considered. Study of the damped harmonic oscillator and its phase space are analysed. The Euler and Verlet algorithms are presented. Concepts of thermodynamic ensembles and calculation of various observable averages are discussed. Molecular Dynamics techniques in the NVE, NVT and NPT ensembles are considered. The need for the boundary conditions and cut-offs is discussed. Calculation of the important observables and the approach to the equilibrium state are further outlined. Simulations of gas, liquid, solid state, and of phase transitions are thoroughly reviewed. Next we proceed to the description of molecular solutions. For this, Brownian (stochastic) Dynamics, based on the Langevin equation and the use of random numbers generators, are introduced. Next, we progress to equilibrium simulations based on the Monte Carlo importance sampling methods and the Metropolis algorithm. Finally, the Schrödinger equation and the variational approach are discussed. We review various modern Quantum Chemistry methods for calculation of the electronic configurations of atomic and molecular systems.