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This article presents the numerical, finite difference, Hartree-Fock method as a source of reference values of total energies, multipole moments, static polarizabilities and hyperpolarizabilities (αzz, βzzz, γzzzz, Az,zz and Bzz,zz) for atoms and diatomic molecules. The finite field method is used to evaluate polarizabilities and hyperpolarizabilities as derivatives of the dipole and quadrupole moments with respect to the field. The finite difference calculations are compared with other numerical and finite basis set results. Since the finite difference Hartree-Fock method is capable of producing multipole moments with 10-12 significant figure accuracy the high quality of (hyper)polarizability values can be guaranteed. [ABSTRACT FROM AUTHOR]

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations employing the restricted Hartree-Fock model for the open-shell ground (X[sup 2] Sigma+) states of the Group IIa fluorides BeF, MgF, CaF and SrF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. By using two different grids, the accuracy of the finite difference calculations has been estimated to be of the order of 10-2 muE[sub h] . The average difference between the finite basis set and finite difference total Hartree-Fock energies is 2.75 muE[sub h] . Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values. [ABSTRACT FROM AUTHOR]

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations employing the Hartree-Fock model for the open shell ground (X 2zeta +) states of the 13-electron systems BeF, BO, CN and N+2. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The accuracy of the finite difference calculations is assessed by employing two grids of different sizes, one of 32617 points and the other of 132385 points. The total Hartree-Fock energies supported by these two grids differ by less than 0.05mu Eh. The average difference between the finite basis set and finite difference Hartreeh Fock energies is 1.3mu Eh. Dipole moments determined within the algebraic approximation are compared with the corresponding finite difference expectation values for the neutral species. [ABSTRACT FROM AUTHOR]

A comparison is made of the finite basis set approach (the algebraic approximation) and finite difference methods in calculations using the Hartree-Fock model for the ground (X1Sigma+) states of the heaviest Group IIIb fluorides: indium fluoride and thallium fluoride molecules. The XF molecules, X = In, Tl, are considered as a prototype for systems containing increasingly heavy atoms and a number of electrons. New finite difference Hartree-Fock calculations for the GaF ground state improve upon earlier results. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is discussed. For the InF molecule, the total Hartree-Fock energy obtained with a grid of 595 595 points lies 15 mu E below the finite basis set energy. For the ground h state of TlF the finite basis set energy lies about 61 mu E above the converged finite difference result obtained on a grid of 595 595 points. For the TlF molecule, the matrix element required to evaluate the electric dipole moment volume interaction for the elementary particles in the Tl nucleus is evaluated from the finite difference Hartree-Fock wavefunction. [ABSTRACT FROM AUTHOR]