Numerical Calculation of H2 and HeH+ Wavefunctions

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Abstract
Use of purely numerical techniques to evaluate integrals allows for greater flexibility in the trial functions used for variational calculations. For two‐electron problems, we have used crossed Gauss quadratures in four dimensions. Accuracy can be assessed in terms of the effect of increasing the number of integration points. Previously given formulas are modified, for singular integrands, so that results are monotonic with the number of points in any dimension, and the new formulas are tested on H2 and on the HeH+ ground state. The meaning of linear dependence of basis functions in the framework of Gauss integration is discussed. The first excited 1Σg+ state of HeH+ is investigated, and found to be nonbonding. The basis functions used here were James—Coolidge functions modified to include polar character. Another example of the flexibility of the numerical method is the use of correlation functions of simple analytical form. This is illustrated with the Gaussian exp(γr122), while formulas are given for calculation with any correlation function expressible as a power series in r12.

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