D. Kolb

All-electron Dirac—Fock—Slater SCF calculations of the Au2 molecule

Abstract All-electron Dirac—Fock—Slater SCF clculations of the Au 2 molecule have been carried out using relativistic numerical atomic basis functions. In order to get a numerically accurate potential energy curve an improved calculation of the direct Coulomb potential has been taken into account. The relativistic effect inthe binding energy, the bond distance and the vibration frequency of the ground state potential energy curve have been studied in comparison with consistent non-relativistic results.

Relativistic effects in physics and chemistry of element 105. II. Electronic structure and properties of group 5 elements bromides

Relativistic self‐consistent charge Dirac–Slater discrete variational method calculations have been done for the series of molecules MBr5, where M=Nb, Ta, Pa, and element 105, Ha. The electronic structure data show that the trends within the group 5 pentabromides resemble those for the corresponding pentaclorides with the latter being more ionic. Estimation of the volatility of group 5 bromides has been done on the basis of the molecular orbital calculations. According to the results of the theoretical interpretation HaBr5 seems to be more volatile than NbBr5 and TaBr5.

H2 solved by the finite element method

Abstract We report on the solution of the Hartree-Fock equations for the ground state of the H 2 molecule using the finite element method. Both the Hartree-Fock and the Poisson equations are solved with this method to an accuracy of 10 −8 using only 26 × 11 grid points in two dimensions. A 41 × 16 grid gives a new Hartree-Fock benchmark to ten-figure accuracy.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.

ATOMIC MP2 CORRELATION ENERGIES FAST AND ACCURATELY CALCULATED BY FEM EXTRAPOLATIONS

A p-version FEM-MP2 (finite element Moller-Plesset second order perturbation) program for accurate MP2 correlation energies of closed shell atoms has been further improved: by radial transformations , inclusion of global radial factors of the form with a sloping function and discretization in x rather than r. Adding logarithmic extrapolations to a sequence , of MP2 energies obtained from low order (linear) finite-element calculations resulted in a very fast high precision approach to MP2 correlation energies. The accuracy gain over the directly calculated values is around five orders for He bare nucleus, He-HF and Be-HF, four orders for Ne-HF almost tripling the number of significant digits. Maximal effective numbers of 16 to 18 radial points were sufficient. A coupling between the maximal l-value (here ) and a suitable maximal number of radial points is observed amounting to about .

Relativistic self-consistent calculations for small diatomic molecules by the finite element method

Abstract 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 2116 grid points we achieve for H 2 an absolute accuracy of about 10 −10 au for the ground-state total energy. For the many-electron systems Li 2 and BH, we obtain a similar accuracy within the Dirac—Fock—Slater approximation which allows us to determine the relativistic contribution to the total as well as orbital energies very precisely.

An accurate solution of the two-centre Dirac equation for H+2 by the finite-element method

Abstract A two-dimensional, fully numerical approach to the four-component Dirac equation using the finite-element method (FEM) is employed for a diatomic system. For H + 2 , an absolute accuracy of about 10 −10 au for the 1σ g orbital energy is obtained by using only 2601 grid points. Using a difference method, the relativistic energy correction can be calculated with an accuracy of about 10 −13 au.

Relativistic density functional calculations using two-spinor minimax finite-element method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and Cu2, Ag2, Au2, Rg2

In previous work the authors have presented a highly accurate two-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element method (FEM) and furthermore developed a relativistic minimax two-spinor linear combination of atomic orbitals (LCAO). In the present paper the authors present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and Rg2, the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional.

Solution of the one-electron Dirac equation for the heavy diatomic quasi-molecule NiPb109+ by the finite element method

Abstract 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 109+ at R = 0.002 au a relative accuracy better than 10 −8 for orbital energies (nuclear repulsion energies ignored).

Calculations of the polycentric linear molecule H32+ with the finite element method

Abstract A fully numerical two-dimensional solution of the Schrodinger equation is presented for the linear polyatomic molecule H 3 2+ using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the lσ and 2σ orbitals is of the order of 10 −7 au.