Accurate Hartree–Fock wave functions without exponent optimization

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Abstract
Basic functions with singularities matching those of the actual orbitals have been tested in analytical Hartree–Fock calculations. Such functions should provide the most rapidly convergent basis set expansions. Exponential singularities at r=∞, characterized by certain ‘‘asymptotic exponents,’’ have been identified by an asymptotic analysis of the Fock equation. Basis sets of Slater functions with these exponents give atomic energies and properties comparable to the most accurate existing analytical calculations, without significantly increasing the number of basis functions. No nonlinear optimizations were required. Calculations of the orbital moments 〈rn〉 show that only moments with n≤N, the number of Slater basis functions, can be evaluated with accuracy, whether or not the exponents are optimized. This effect appears to be caused by the neglect of certain irrational powers in asymptotic forms of the orbitals. The results for molecules suggest that basis functions which more adequately describe the nuclear cusp singularities are required to reproduce the accuracy of numerical Hartree–Fock calculations.