The propagation of basis-set error and geometry optimization in ab initio calculations. II. Correlation between the balance of Gaussian basis sets and calculated molecular properties

Basis-set balance parameters, defined in terms of various projections of an abstract force vector in the space spanned by the logarithms of orbital exponents, are evaluated for a sample of 100 Gaussian basis sets. These basis sets are taken from a random Gaussian distribution of bases, centered on the best energy, fully variational uniform quality (UQ) atomic orbital (AO) basis sets. With each basis geometry optimization has been carried out for model molecule dimethyl sulfoxide, the wavefunction of which molecule is exceptionally sensitive to basis-set errors. Correlations between the balance of basis sets and calculated molecular properties are analyzed.