One-Center Molecular Calculations with Unlimited Radial Basis. H2, HeH+, and LiH Centered on One Nucleus

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Abstract
As a prelude to one‐center studies of the coordination center in ligand‐field problems, this paper gives results for LiH, HeH+, and H2 in their ground states. In each case the Hamiltonian and the orbital functions are expanded in series of spherical harmonics about the largest nucleus, the orbital expansions are truncated, and the resulting coupled integro‐differential equations are solved numerically for the radial function associated with each orbital harmonic. The result is a Hartree–Fock solution with limited angular basis but unlimited radial basis. The results for energy, quadrupole coupling constant, and other properties are reasonably close to the limiting Hartree–Fock results, and certain properties determined by the wave‐function at the nucleus are exact within the accuracy of the numerical method. For H2 at R = 1.4 bohr , the best calculated total energy is − 1.104 hartree for an expansion truncated after four spherical harmonics, s + p + d + f (− 1.128, extrapolated to many harmonics; − 1.133, Hartree–Fock limit); the calculated quadrupole coupling is 247 kHz (242, extrapolated; ∼ 232, experimental). For HeH+, a Morse curve fitted to energies at eight internuclear distances yields Req = 1.480 bohr with E = − 2.919 hartree ; for R = 1.4 bohr , E = − 2.917 (− 2.932, Hartree–Fock limit). For LiH, the results with an s + p inner shell and s + p + d + f + g + h outer shell are significantly better than for s + p + d + f inner and outer shells. The best values calculated (Hartree–Fock limit in parentheses) for energy, dipole moment, and electronic field gradient at the Li nucleus are − 7.936 (− 7.987) hartree, − 5.79 (− 5.9) D, and − 0.112 (− 0.116) a.u.

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