On the accuracy of the algebraic approximation in molecular electronic structure calculations .6. Matrix Hartree-Fock and many-body perturbation theory calculations for the ground state of the water molecule

The use of distributed Gaussian basis sets in reducing the total basis set truncation error in matrix Hartree-Fock and second-order many-body perturbation theory calculations is investigated for the ground state of the water molecule at its equilibrium geometry. A distributed basis set of even-tempered Gaussian functions centred not only on the atomic nuclei bur also on the O-H bond centres and at the midpoint of the line H-H is shown to give a matrix Hartree-Fock energy of -76.067 488 mu Hartree. For diatomic molecules, distributed basis sets of this type have been shown to yield matrix Hartree-Fock energies which approach an accuracy of similar to 1 mu Hartree. The present distributed basis set, which includes functions of s, p, d and f symmetry, is employed in a second-order many-body perturbation theory study of correlation effects recovering 97.6% of an estimate of the exact second-order correlation energy given by Klopper. The effects of higher harmonics in the basis set are investigated and a basis set, which includes functions of s, p, d, f and g symmetry, is shown to be capable of recovering 98.6% of the exact second-order energy. The reliability of simple extrapolation techniques to estimate the effects of basis functions of h symmetry and higher is investigated and shown to support 99.8% of the estimate of the exact second-order correlation energy component.