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

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Abstract
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 but 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 . For diatomic molecules, distributed basis sets of this type have been shown to yield matrix Hartree - Fock energies which approach an accuracy of . 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.