as ‘failures’ of VBT. However, these often arise from an incomplete or inaccurate use of VBT. Triplet Ground State of Oxygen It is known that O2 has a triplet ground state, but a classic Lewis structure depiction of oxygen would not indicate that any unpaired electrons exist. Perhaps because Lewis structures and VBT often depict the same structure as the most stable state, this misinterpretation has persisted. However, as has been consistently demonstrated with VBT calculations, the lowest energy state is that with two, three electron π-bonds, which is the triplet state. Ionization Energy of Methane The photoelectron spectrum (PES) of methane is commonly used as an argument as to why MO theory is superior to VBT. From an MO calculation (or even just a qualitative MOT diagram), it can be seen that the HOMO is a triply degenerate state, while the HOMO-1 is a single degenerate state. By invoking Koopman's Theorem, one can predict that there would be two distinct peaks in the ionization spectrum of methane. Those would be by exciting an electron from the t2 orbitals or the a1 orbital, which would result in a 3:1 ratio in intensity. This is corroborated by experiment. However, when one examines the VB description of CH4, it is clear that there are 4 equivalent bonds between C and H. If one were to invoke Koopman's Theorem (which is implicitly done when claiming that VBT is inadequate to describe PES), a single ionization energy peak would be predicted. However, Koopman's Theorem cannot be applied to orbitals that are not the canonical molecular orbitals, and thus a different approach is required to understand the ionization potentials of methane from VBT. To do this, the ionized product, CH4+ must be analyzed. The VB wavefunction of CH4+ would be an equal combination of 4 structures, each having 3 two-electron bonds, and 1 one-electron bond. Based on group theory arguments, these states must give rise to a triply degenerate T2 state and a single degenerate A1 state. A diagram showing the relative energies of the states is shown below, and it can be seen that there exist two distinct transitions from the CH4 state with 4 equivalent bonds to the two CH4+ states. Valence Bond Theory Methods Listed below are a few notable VBT methods that are applied in modern computational software packages. Generalized VBT (GVB) This was one of the first ab initio computational