Integral Transform Gaussian Wavefunctions for H32+ and H3+

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Abstract
Wavefunctions obtained from a particular integral transformation of 1s Gaussian orbitals were used to calculate the ground state energies of both H32+(D3h) and H3+(D3h) molecular ions. A linear combination of integral transform Gaussian‐orbital–molecular‐orbital (LCITGO–MO) wavefunction, with basis orbitals kν(qr) placed on the nuclei, gives for H3+ a total energy of − 1.27724 a.u. at the equilibrium internuclear separation Re = 1.62 a.u. The best floating function of this type gives E = − 1.29367 a.u. at the internuclear separation R = 1.66 a.u. This accounts for 99.5% of the Hartree–Fock energy. The same integral transform of a total wavefunction, with the basis functions placed on the nuclei gives E = − 1.21243 a.u. at Re = 1.69 a.u. , while letting the orbitals float improves the energy to − 1.22292 a.u. (R = 1.66 a.u.) . The best single‐center function gives E = − 1.16021 a.u. (99.4% of the s‐limit energy) at R = 1.66 a.u. , whereas the best single‐centre total transformed wavefunction has E = − 1.13836 a.u. , also at R = 1.66 a.u. The ground state energy of the H32+(D3h) system is E = − 0.09167 a.u. (R = 1.68 a.u.) with our best non‐floating function, and becomes − 0.11708 a.u. (R = 1.68 a.u.) for our floating wavefunction. The latter is 94.6% of the exact energy. The optimum single‐center function gives E = − 0.04366 a.u. at R = 1.68 a.u.