Standard Article

Using Iterative Methods to Compute Vibrational Spectra

  1. Tucker Carrington Jr

Published Online: 15 SEP 2011

DOI: 10.1002/9780470749593.hrs018

Handbook of High-resolution Spectroscopy

Handbook of High-resolution Spectroscopy

How to Cite

Carrington, T. 2011. Using Iterative Methods to Compute Vibrational Spectra. Handbook of High-resolution Spectroscopy. .

Author Information

  1. Queen's University, Chemistry Department, Kingston, Ontario, Canada

Publication History

  1. Published Online: 15 SEP 2011


In this article, some modern methods for computing vibrational energies of polyatomic molecules are reviewed. The emphasis is on iterative methods with which a spectrum is obtained by evaluating matrix–vector products. To use such methods one does not need to compute or store Hamiltonian matrix elements. If each basis function is a product of functions of a single coordinate, matrix–vector products can be computed by doing sequentailly sums associated with indices of the individual coordinates. The corresponding algorithm is simple and useful, but, with current computers, it cannot be applied to compute the spectrum of a six-atom molecule. For molecules with six or more atoms (and often for molecules with five atoms), it is necessary to use basis set contraction. A contraction method is presented that has been used for methane and CH5+.


  • vibrational spectroscopy;
  • theory;
  • iterative methods;
  • Lanczos algorithm;
  • contracted bases