Showing papers on "Basis function published in 1968"

Calculations on the 2 S Ground State of the Lithium Atom Using Wave Functions of Hylleraas Type

Abstract: A wave function was obtained for the $^{2}S$ ground state of the lithium atom using 60 basis functions of the Hylleraas type, i.e., with interelectronic distance coordinates. The energy obtained was -7.478025 atomic units as compared with the value -7.478069 calculated from experiments. The wave function was used to calculate the Fermi contact term. It was found that this basis set gave the value 2.906, which is in agreement with experiments, when both doublet spin functions were used, but a value that was 4% greater when only one spin function was used. In the first case, 100, and in the latter, 60, linear parameters were varied. The interelectronic distance coordinates are expanded according to a formula by Sack. The final integrals are evaluated analytically, and the resulting formulas, along with a short discussion of their convergence properties, are given in an Appendix.

LCAO–MO–SCF Calculations Using Gaussian Basis Functions. II. BeH2

Abstract: Results of extensive LCAO–MO–SCF calculations on BeH2 utilizing Gaussian basis functions are presented. It is established that BeH2 is linear in its ground state, and the equilibrium bond distance has been determined. Force constants and normal frequencies were obtained. Utilizing an accurate estimate of the correlation energy, the dissociation energy of BeH2 was determined to within the experimental error of the National Bureau of Standards measurement.

Calculation of the NMR Spin Coupling Constant in HD

Abstract: The NMR spin coupling constant in HD is calculated by a perturbation‐variation procedure using basis sets ranging from 2 to 12 functions. The simplicity of the HD molecule makes it possible for the coupling constant to be calculated exactly within a given basis set. It is thus possible to determine the effect on the coupling constant not only of extension of the size of the basis set but also of the inclusion of configuration interaction. Finally, the coupling constant is calculated using very accurate ground‐state wavefunctions, and the values obtained are compared with the results of the earlier 2 to 12 basis function calculations. It is found that the main contribution to the coupling comes from the Fermi contact interaction. A value of 54.06 cps is obtained for the coupling constant. The experimental value is 42.7 ± 0.5 cps.

Bare‐Nucleus Perturbation Theory: Excited States of Hydrogen Molecule

Abstract: Ground and excited Σ+ states of R = 1.4a0 are treated by perturbation theory. The full interelectronic repulsion is taken as the perturbation, and the energy of each of nine states is calculated through third order. The equation for the first‐order wavefunction is treated by the Hylleraas variational principle, using a linear variational function including up to 30 James–Coolidge basis functions. Comparisons with conventional linear variational calculations using the same basis functions, and with related calculations of other workers, are given. The perturbation results are in most cases superior to variation, especially when small basis sets are used, but it is noted that the inadequacy of the present basis set for excited states leads to slow convergence of the energies of both methods with addition of basis functions. The bare‐nucleus Hamiltonian also becomes a worse starting point for higher states because of electronic shielding, as evidenced by slower convergence of the perturbation energy series. ...

H-H-interactions in the region of small orbital overlap

Abstract: Calculations have been made on the lowest state of H2 in the region 4–6 a.u. with a view to elucidating some of the problems arising in the perturbation theory of intermolecular forces in the region of small orbital overlap. The conclusions are that a small basis set of non-orthogonal functions, which in a variation calculation gives reasonably good total energies, can give a poor approximation to the second-order perturbation energies. Variational calculations using the separate basis functions appropriate to induction, dispersion and charge-transfer energies show that these energies may be reasonably added together to reproduce the variational calculations from the total basis set.

The many-body problem in terms of particle group functions

Abstract: In the treatment of many-particle systems the particle correlations can be taken into account to a certain extent at the very beginning by choosing particle-group basis functions. However, when these basis functions do not satisfy a certain restrictive condition (“strong orthogonality”) some mathematical difficulties arise. Using a previously discovered way of overcoming these difficulties [3] we develop practical methods to solve this problem. The Green’s function formalism of Martin and Schwinger is applied using field operators for the particle groups with intrinsic degrees of freedom. Besides the possible computational advantages and the intrinsic interest of the problem this theory yields some possibilities for an ab initio microscopic theory of condensed media. In addition, it can also be useful in throwing light on some questions of relativistic field theory of structured particles.