Quality of Gaussian basis sets: Direct optimization of orbital exponents by the method of conjugate gradients

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Abstract
Expressions are given for calculating the energy gradient vector in the exponent space of Gaussian basis sets and a technique to optimize orbital exponents using the method of conjugate gradients is described. The method is tested on the (9s5p) Gaussian basis space and optimum exponents are determined for the carbon atom. The analysis of the results shows that the calculated one‐electron properties converge more slowly to their optimum values than the total energy converges to its optimum value. In addition, basis sets approximating the optimum total energy very well can still be markedly improved for the prediction of one‐electron properties. For smaller basis sets, this improvement does not warrant the necessary expense.