Accurate Single-Center Expansions with Slater-Type Orbitals: Hydrogen Atom and Hydrogen Molecule—Ion

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Abstract
Single‐center wavefunctions are determined for the off‐center hydrogen atom, using Slater orbitals of integral quantum number and variable orbital exponent. With the proton situated a distance R from the expansion point, for R=0.6, 1.0, 1.4, and 1.8 bohr, the approximate energies obtained are 0.49961, 0.49951, 0.49929, and 0.49913 a.u. A single‐center wavefunction is given for the 1sσg state of H2+ for the internuclear separation 2.0 bohr. The energy of this function is within 2×10−4 a.u. of the exact result. Here the earlier work of Joy and Handler has been extended by including spherical harmonics with l up to 22 and by reducing the number of nonlinear variational parameters through the rule that the high‐l orbitals peak at the protons. Wavefunctions also are presented for the 1sσg and 2pσu states for an internuclear separation of 3.6 bohr. For all of the states considered, the Joy—Handler convergence rule that the energy increment for high l is inversely proportional to l4 is verified, and extrapolations made. For the hydrogen atom, this increment also is found to be proportional to R3. By calculations of the dipole moment of the hydrogen‐atom functions and by detailed examination of the l=0 component of these functions, it is shown that the lower‐l components in single‐center wavefunctions are more sensitive to the presence of higher‐l components than had earlier been thought.

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