1. Mathematical Foundations

  1. Valerio Magnasco

Published Online: 21 FEB 2011

DOI: 10.1002/9781119971986.ch1

Models for Bonding in Chemistry

Models for Bonding in Chemistry

How to Cite

Magnasco, V. (2010) Mathematical Foundations, in Models for Bonding in Chemistry, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971986.ch1

Author Information

  1. University of Genoa, Italy

Publication History

  1. Published Online: 21 FEB 2011
  2. Published Print: 6 AUG 2010

ISBN Information

Print ISBN: 9780470667026

Online ISBN: 9781119971986



  • mathematical foundations;
  • matrices and systems of linear equations - square matrix of order two;
  • eigenvalue and eigenvector properties - matrices with idempotency, mutual exclusivity, completeness, or projectors;
  • variational approximations;
  • polar diagrams, of angular part of s, p, d, and f;
  • real regular functions - exponential (Slater-type, STO) or gaussian (GTO) radial decay;
  • AOs, solving - differential Schrödingertype eigenvalue equation;
  • Rayleigh variational principle;
  • system of atomic units - milliHartree, unit for energy of chemical bond;
  • electron distribution in molecules


This chapter contains sections titled:

  • Matrices and Systems of Linear Equations

  • Properties of Eigenvalues and Eigenvectors

  • Variational Approximations

  • Atomic Units

  • The Electron Distribution in Molecules

  • Exchange-overlap Densities and the Chemical Bond