CY 6122 : Numeric Methods for Computational Chemistry

Programming Tools:

Introduction to C Programming:

Variables and arithmetic expressions, Symbolic Constants, Input and Output, Arrays and functions, Data types, arithmetic, relational and logical operators, simple control-flow statements, classes and modules and ability to write small programs in C for computations such as function evaluation and elementary linear algebra.


Introduction to FORTRAN programming:

Constants and variables, arithmetic, input and output statements, control statements (Do, Go To If statements) , arrays, subprograms (Functions and subrountines), modules and ability to write small programs for computations such as function evaluation and elementary linear algebra.

Numerical Analysis:

Numerical interpolation, Polynomial and cubic spline interpolation, extrapolation of data. Numerical first and second derivatives, error analysis and Richardson‘s method.

Non-linear equations and roots of polynomials, Newton-Raphson method, secant method and Bairstow method. Numerical integration: Gaussian quadrature—Gauss-Hermite and Gauss-Legendre intervals; applications form quantum chemistry with Gaussian orbitals

Linear algebra: Householder reduction and LU decompositions, matrix inversion, determinant evaluation and eigenvalues and eigenvectors of hermitian (complex) and symmetric (real) matrices. Iterative methods for large-scale eigen value problems – Lanczos recursion, Arnoldi algorithm and Davidson‘s method. Or Fast Fourier transform, Fourier transform of real data in two and three dimensions. Introduction to finite basis representation and discrete variable. Simple applications from computational chemistry and spectroscopy.

Text Books:

  1. Press, W.H., Teukolsky, S.A., Vetterling W.T.and Flannery, B.P., Numerical Recipes; The Art of scientific Computing, Cambridge University Press, New York, 2007.
  2. Lanczos, C., Applied Analysis, Dover New York, 2010.
  3. Koonin, S.E. and Meredith , D.C., Computational Physics , Fortran Version, Version, Westview Press, U.S.A., 1998.
  4. Kerninghan, B.W. and Ritchie, D.M., The C Programming Language, Prentice Hall, New Jersey, 1988.
  5. Rajaraman , V., Computer Programming on Fortran 90 and 95, Prentice-Hall of India, New Delhi, 2006.
  6. Light, J.C. and Carrington Jr., T., Discrete Variable Representations and Their Utilization, Advances in Chemical Physics, Volume 114, pp 263-310, 2000.