Atomic orbitals experimental atomization energies

Alternative methods are based on the pioneering work of Hylleraas ([1928], [1964]). In these cases orbitals do not form the starting point, not even in zero order. Instead, the troublesome inter-electronic terms appear explicitly in the expression for the atomic wavefunction. However the Hylleraas methods become mathematically very cumbersome as the number of electrons in the atom increases, and they have not been very successfully applied in atoms beyond beryllium, which has only four electrons. Interestingly, one recent survey of ab initio calculations on the beryllium atom showed that the Hylleraas method in fact produced the closest agreement with the experimentally determined ground state atomic energy (Froese-Fischer [1977]). 

Although we can draw benzene-like resonance structures (Figure 16-3) for cyclobutadiene, experimental evidence shows that cyclobutadiene is unstable. Its instability is explained by the molecular orbitals, shown in Figure 16-6. Four sp2 hybrid carbon atoms form the cyclobutadiene ring, and their four p orbitals overlap to form four molecular orbitals. The lowest-energy MO is 771, the all-bonding MO with no nodes. 

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