Given the ubiquity of Gaussian basis sets in quantum chemistry, the theory of the expansion of an exponential orbital in Gaussian functions is clearly fundamental.  However, although there has been significant progress during the past 20 years, the theory remains incomplete. Gaussians lack nuclear cusps and decay too quickly, and one might have expected that their energies would therefore converge algebraically.  However, Kutzelnigg and co-workers have shown that, in a fully optimized even-tempered basis of n Gaussians, the variational energy of the ground state of the H atom converges as exp(-pv(3n)).  In this lecture, I will present some new results that shed light on the Kutzelnigg formula and that suggest how efficient basis sets may be constructed in the future.

Gaussian expansions of orbitals

244th National Meeting (2012)

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