General aspects#

In this section we will cover general aspects of electronic structure theory calculations.

  • Orbitals and basis sets
    An introduction to wave functions for single-electron systems is given.

  • Many-electron wave functions
    An introduction to many-electron wave functions is given.

  • Operators and matrix elements
    An introduction to one- and two-electron operators is given together with a presentation of their associated matrix elements.

  • Reduced particle densities
    One- and two-particle reduced densities are presented and illustrated.

  • Natural orbitals
    Natural orbitals for restricted and unrestricted calculations are introduced.

  • Integrals
    A presentation of a technique to transform integrals in the AO basis to the MO basis as needed for correlated wave function methods.

  • Electron spin
    Definitions of spin operators and a visual illustration of collinear and noncollinear spin densities.

  • Electron correlation
    Definition of correlation energy and a visual exploration of the effects of electron correlation on one- and two-particle densities.

  • Dispersion interactions
    Definition of interaction energy and visual illustration of its association with electron correlation. Dispersion correction by means of \(C_6\) coefficients is demonstrated.

  • Rayleigh–Schrödinger perturbation theory
    A presentation of the perturbation theory in a form useful for Møller–Plesset methods.

  • Second quantization
    A presentation of the occupation number formalism is given.

  • Group theory
    A presentation of group theory its application in chemistry is given.