Two-Center, Nonintegral, Slater-Orbital Calculations: Integral Formulation and Application to the Hydrogen Molecule-Ion

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Abstract
Integrals over Slater orbitals of nonintegral principal quantum numbers centered at two nuclei are investigated, with special reference to the hydrogen molecule‐ion. All the one‐electron integrals for s orbitals are evaluated in closed form. For the hydrogen molecule‐ion, a wave function of the generalized Finkelstein—Horowitz form ψ=nsa+nsb, where ns=Nrn—1e—ζr, N being the normalization constant, n the principal quantum number, and ζ the orbital exponent, is shown to give a total energy E=—0.588085 a.u. for n=1.05759 and R=1.9866 a0 as compared with the corresponding Finkelstein—Horowitz calculation E=—0.586507 a.u. at n=1 and R=2.0033 a0, where the exact values are E=—0.60263 a.u. at R=2.000 a0. More general one‐electron integrals and some two‐electron integrals are discussed.

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