PHY.K02UF Molecular and Solid State Physics
The molecular orbtials of these examples were calculated using the Hartree-Fock method. Hartre-Fock is a standard computational method that employs the Born-Oppenheimer approximation. The electron-electron interaction is partly accounted for through Coulomb- and exchange interactions. However, electron correlation - which is, loosely speaking, the fact the electrons tend to avoid each other - is neglected. In Hartree-Fock, the orbital energies can be associated with ionization energies, i.e., the energy of an orbital approximately corresponds to the energy requried to remove the electron that occupies it. This is known as Koopman's theorem.
Here, as in the lecture, all the calculation have been performed with a so-called minimal basis. This means that for each electron, only a single basis function has been provided. In other words, each hydrogen contributed one 1s function, each carbon atom one 1s, one 2s, and 3 2p functions, etc. Although this is most intuitive for the illustration of the linear combination of atomic orbitals (LCAO) approach, this represents a serious restriction for the calculation. Note that ''proper'' calculations usually much larger Slater determinants, which include atomic orbitals with higher principal quantum number and angular momentum (Such as 3d, 4f, ...). Such calculations tend to give electronic structures (and orbital energies) that are much closer to experiment than the energies reported here.