CY6128: Computational Quantum Chemistry and Molecular Simulations

Course Objectives:
• Introduce state-of-the-art molecular level computational methods using open source and commercial codes developed and used by researchers in chemical sciences worldwide.
• To provide hands-on training in the use of standard computer codes for a few selected topics in organic, inorganic, materials and physical chemistry.
• To provide hands-on training in molecular dynamics that would help the students use molecular modeling in protein-protein, protein-ligand and DNA- ligand interactions and other biomolecular simulations.

Course Outcomes:

• Students will be able to write simple programs/use existing free software codes in numerical linear programming package known as EISPACK for diagonalization of matrices, calculation of simple integrals using quadratures and do curve-fitting experimental data for specific least-squares models.
• Students will be able to use standard features of Gaussian 16 for calculating molecular structures, energies and spectroscopic properties of simple compounds important for a variety of applications
• Each student will perform one simulation/computation extensively, in his/her own areas of interest as a project and submit the results.

Course Topics:

Introduction to Numerical methods:
• Newton-Raphson method.
• Matrix diagonalization and Householder algorithm.
• Numerical quadrature (Gaussian and Gauss-Hermite).
• Elementary concepts in parallel computing/programming.

Classical and Statistical Mechanics based Dynamics Simulations
• Definitions of ensembles, introduction to Monte Carlo Method, sampling, Metropolis Algorithm, trial moves and application.
• Definition of force fields, energy expression and force field parameters.
• Introduction and simple molecular mechanics and molecular dynamics computations using force fields. Basic introduction to AMBER, GROMACS and LAMMPS

Wave Function and Density Functional Theory Based Methods
• Variational theorem. Review of HF-theory, electron correlation and introduction to Post-HF methods.
• Basis sets, Slater orbitals, Gaussian orbitals and contraction.

• Geometry optimization, calculation of thermodynamic parameters, vibrational frequencies and intensities, NMR and ESR parameters using elementary examples and a few representative molecules using Gaussian 16.

Density Functional Theory:
• A formal definition of electron density, Thomas-Fermi Model.
• Hohenberg-Kohn theorem, Kohn-Sham method, Fermi and Coulomb Holes. Introduction to local density and X-α method, Quest for approximate exchange-correlation functional.
• LDA-GGA-Meta GGA-Hybrid DFT and their implementation in Gaussian using a few sample molecules.

References
1. Understanding Molecular Simulations, D. Frenkel and B. Smit, second edition, Elsevier, 2001.
2. Computer Simulation of Liquids, M. P. Allen and D. J. Tildesley, second edition, Oxford University Press, 2017.
3. Exploring Chemistry with Electronic Structure Methods, J. B. Foresman and Aeleen Frisch, Gaussian Inc., 2015
4. A Chemists’ Guide to Density Functional Theory, W. Koch & M. C. Holthausen, Wiley-VCH, 2001.
5. Introduction to Computational Chemistry, Frank Jensen, third edition, Wiley, 2017.
6. Modern Quantum chemistry, A. Szabo & N. S. Ostlund, McGraw-Hill, 1961 edition reprinted by Dover Publications, 1989.