Table of Contents

Quantum Mechanics Describes Matter in Terms of Wavefunctions and Energy Levels and physical Measurements are Described in Terms of Operators Acting on Wavefunctions

Along "reaction paths", orbitals can be connected one-to-one according to their symmetries and energies. This is the origin of the Woodward-Hoffmann rules

Electrons are Placed into Orbitals to Form Configurations, Each of Which Can be Labeled by its Symmetry. The Configurations May "Interact" Strongly if They Have Similar Energies.

Electronic wavefunctions must also possess proper symmetry. These include angular momentum and point group symmetries

One must be able to evaluate the matrix elements among properly symmetry adapted N-electron configuration functions for any operator, the electronic Hamiltonian in particular. The Slater-Condon rules provide this capability

Along "reaction paths", configurations can be connected one-to-one according to their symmetries and energies. This is another part of the Woodward-Hoffmann rules

Electrons interact via pairwise Coulomb forces; within the "orbital picture" these interactions are modelled by less difficult to treat "averaged" potentials. The difference between the true Coulombic interactions and the averaged potential is not small, so to achieve reasonable (ca. 1 kcal/mol) chemical accuracy, high-order corrections to the orbital picture are needed.

The single Slater determinant wavefunction (properly spin and symmetry adapted) is the starting point of the most common mean field potential. It is also the origin of the molecular orbital concept.

Corrections to the mean-field model are needed to describe the instantaneous Coulombic interactions among the electrons. This is achieved by including more than one Slater determinant in the wavefunction.

Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be formulated in terms of the "response" (i.e., derivative) of the electronic energy with respect to the application of an external field perturbation.

Exercises, Problems, and Solutions