Because of the particular geometries of some molecules, the CSCO may be different. Instead of the CSCO that we had with the atom, we want to determine the CSCOH: the complete set of operators commuting with Ĥ. It is thus a set larger than the CSCO because the operator don’t have to commute between them. […]

The Hamiltonian quickly becomes monstrously difficult when several atoms and electrons are considered. To illustrate this point, the equations of the Hamiltonians for H, H2+ and H2 are showed below: For a molecule with M nuclei of atomic number Z1, Z2, Z3, …, ZM and n electrons, the global expression is The Hamiltonian can be […]

The presence of a second electron induces a term of repulsion between electrons. This term is positive so it increases the energy of the orbitals. The rest of the equation is similar to the Hamiltonian of the hydrogen. We can compare the energy of the orbitals with those two models. The repulsion is large in […]