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.