β Scribed by Farid A. Parpia; Ajaya K. Mohanty
No coin nor oath required. For personal study only.
We have carried out relativistic molecular electronic structure calculations using the prescription of 'strict kinetic balance' applied to four-component spherical Gaussian spinors centred on the nuclei; the exponents for all atomic symmetries have been chosen according to the 'even-tempered' or 'geometric' prescription. The upper bound properties and convergence behaviour of the ground states of one-electron molecular ions with two, three and four centres have been investigated. The Dirac energy of the lO'g state of H~ at an internuclear separation of 2 bohr is computed to an accuracy of better than 1 part in 10 m. We calculate the energy of the corresponding level of the highly relativistic Th~ 79+ system at an internuclear separation of 2/90 bohr. Studies of models of three-and four-center molecular ions, H3 + and H 3+, are reported to demonstrate the applicability of the approach to arbitrary geometries. Our estimates of the relativistic energy converge monotonically from above as the basis sets are enlarged, and nonrelativistic limits obtained by increasing the speed of light used in the computations yield results in excellent agreement with calculations that are nonrelativistic from the outset.
π SIMILAR VOLUMES
A two-dimensional, fully numerical approach to the four-component first-order Dirac equation using the finite element method is employed for diatomic systems. Using the Dirac-Fock approximation with only 2601 grid points we achieve for the heavy quasi-molecule NiPb"'+ at R= 0.002 au a relative accur