Basis Set Choice and the Variational Wavefunction

One of the places where human decision can effect the outcome of a variational calculation is in the choice of basis. Some insight into the ways this choice effects the ultimate results is necessary if one is to make a wise choice of basis, or recognize which calculated results are physically real and which are artifacts of basis choice. 

One question we can ask is this Is a minimal basis set equally appropriate for calculating an MO wavefunction for, say, B2 as F2 In each case we use 10 AOs and 2 spin functions producing a total of 20 spin MOs. With B2, however, we have 10 electrons to go into these spin MOs, and in F2 we have 18 electrons. In all but the crudest MO calculations, the total energy is minimized in a maimer that depends on the natures of only the occupied MOs. In effect, then, the calculation for B2 produces the 10 best spin MOs from a basis set of 20 spin-AOs, whereas that for F2 produces the 18 best MOs from a different basis set of 20 spin-AOs. In a sense, then, the basis for F2 is less flexible than that for B2. Of course, the use of separated atom orbitals is a conscious effort to choose that basis that best spans the same function space as the best MOs. To the extent that this strategy is successful, the above problem is obviated (i.e., if both sets are perfect, additional flexibility is useless). The strategy is not completely successful, however, and conparison of results of minimal basis set calculations down a series of molecules such as B2, C2, N2,02, and F2 may be partially hampered by this 

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