Knut Faegri

Relativistic Gaussian basis sets for the elements K – Uuo

Abstract. A series of energy-minimized relativistic Gaussian basis sets for the elements with atomic numbers 19–118 is presented. The basis sets have been derived at the self-consistent field level as weighted average energies of the respective electronic configurations. A spherical Gaussian charge distribution has been used to model the nucleus. The basis sets are constructed as interleaving dual family sets with shared exponents within each family. The quality of the basis sets is better than double zeta.

All-electron molecular Dirac-Hartree-Fock calculations - The group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4

We describe a basis‐set‐expansion Dirac–Hartree–Fock program for molecules. Bond lengths and harmonic frequencies are presented for the ground states of the group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first‐order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first‐order perturbation theory for all molecules, but none of the sets of RECPs considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

How well does the Hartree–Fock model predict equilibrium geometries of transition metal complexes? Large‐scale LCAO–SCF studies on ferrocene and decamethylferrocene

Large scale ab initio LCAO–SCF calculations performed on ferrocene show that the Hartree–Fock model is unable to account for the experimentally observed metal to ring distance. The present results, using basis sets of better than triple zeta quality, show that both the equilibrium geometry and the orbital energies have converged already at the double zeta level (metal‐ring distance;1.89 A, i.e., 15% larger than the experimental value of 1.65 A). A comparative calculation on decamethylferrocene yields essentially the same results. These findings raise some doubts as to the adequacy of the Hartree–Fock model for predictions of equilibrium geometries of transition metal complexes in general.

THE ELECTRONIC-STRUCTURE OF THE PTH MOLECULE - FULLY RELATIVISTIC CONFIGURATION-INTERACTION CALCULATIONS OF THE GROUND AND EXCITED-STATES

Fully relativistic all‐electron self‐consistent field calculations based on the Dirac–Coulomb Hamiltonian have been performed on the three lowest lying states of the PtH molecule. The resulting four‐component Dirac–Hartree–Fock (DHF) molecular spinors are subsequently used in relativistic configuration interaction (CI) calculations on the five lower states of PtH. Spectroscopic properties are obtained by fitting the potential curve to a Morse function and show good agreement with experimental data. The effect of relativistic corrections to the Coulomb electron–electron interaction is investigated at the DHF level and is found to be insignificant for the molecular spectroscopic properties investigated by us. The CI wave functions are found to have only one dominant configuration, indicating a lack of static correlation. Dynamic correlation in the d shell is, however, important for the spectroscopic properties of PtH. The results conform with a bonding scheme in which the three lower and two upper states of...

Relativistic four‐component multiconfigurational self‐consistent‐field theory for molecules: Formalism

A formalism for relativistic four‐component multiconfigurational self‐consistent‐field calculations on molecules is presented. The formalism parallels a direct second‐order restricted‐step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses on the differences required by the use of the Dirac Hamiltonian with the incorporation of time‐reversal symmetry and point group symmetry for D2h and subgroups, providing the expressions in this framework which correspond to the nonrelativistic expressions. It is found that an efficient algorithm requires only twice the memory used by the largest nonrelativistic calculation in the equivalent basis, due to the complex arithmetic. The feasibility of the calculations is then determined more by the disk space for storage of integrals and N‐particle expansion vectors.

Energy-optimized GTO basis sets for LCAO calculations. A gradient approach

The use of gradient techniques for the development of energy‐optimized basis sets has been investigated. The region where the energy surface is approximately quadratic with a positive definite Hessian is found to be very small for large basis sets. However, scaled Newton‐Raphson methods prove quite effective even when the starting point is outside this region. The analytic calculation of the Hessian is found to be most efficient in terms of computing time.

A variational approach to relativistic effects in LCAO calculations

Abstract We suggest a simple procedure which makes it possible to include relativistic effects approximately in variational LCAO calculations. The scheme uses a free-particle projection, and is readily applicable to polyatomic systems. Pilot calculations on one-electron atoms are presented, and compared with exact Dirac solutions.

Kinetic balance and variational bounds failure in the solution of the Dirac equation in a finite Gaussian basis set

Abstract We have investigated bounds failure in calculations using Gaussian basis sets for the solution of the one-electron Dirac equation for the 2p 1 2 state of Hg79+. We show that bounds failure indicates inadequacies in the basis set, both in terms of the exponent range and the number of functions. We also show that over-representation of the small component space may lead to unphysical results. We conclude that it is important to use matched large and small component basis sets with an adequate size and exponent range.

THE CHEMISTRY OF SUPERHEAVY ELEMENTS. III. THEORETICAL STUDIES ON ELEMENT 113 COMPOUNDS

The chemistry of element 113 is investigated by theoretical methods. The results of fully relativistic calculations for (113)H and (113)F are compared with those derived by other techniques to obtain an indication of the accuracy of the more approximate models as well as the importance of including scalar and/or spin–orbit relativistic effects. Both of these effects are found to be important. The spin–orbit coupled pseudopotential approximation yields results of satisfactory accuracy, but the two relativistic methods that do not include spin–orbit coupling (Douglas–Kroll and scalar relativistic pseudopotential method) do not agree so well with each other. The calculated properties of (113)H and (113)F and a number of other hydrides and halides of element 113 are compared with the properties of the equivalent compounds of the lighter group 13 elements. In general, element 13 exhibits behavior that is consistent with its placement in group 13 of the periodic table. Some of its properties are found to be somewhat unusual however, e.g., the element is relatively electronegative, the molecules (113)H3, (113)F3, and (113)Cl3 are predicted to be T-shaped rather than trigonal planar, and the 6d electrons of element 113 participate to a significant extent in chemical bonding. Compounds where element 113 is present in the +5 oxidation state are considered as well but are predicted to be thermodynamically unstable.The chemistry of element 113 is investigated by theoretical methods. The results of fully relativistic calculations for (113)H and (113)F are compared with those derived by other techniques to obtain an indication of the accuracy of the more approximate models as well as the importance of including scalar and/or spin–orbit relativistic effects. Both of these effects are found to be important. The spin–orbit coupled pseudopotential approximation yields results of satisfactory accuracy, but the two relativistic methods that do not include spin–orbit coupling (Douglas–Kroll and scalar relativistic pseudopotential method) do not agree so well with each other. The calculated properties of (113)H and (113)F and a number of other hydrides and halides of element 113 are compared with the properties of the equivalent compounds of the lighter group 13 elements. In general, element 13 exhibits behavior that is consistent with its placement in group 13 of the periodic table. Some of its properties are found to be som...

RELATIVISTIC EFFECTS ON THE BONDING OF HEAVY AND SUPERHEAVY HYDROGEN HALIDES

Abstract The bonding in the hydrogen halides HI, HAt and HUus (Uus = element 117) has been studied using four-component Dirac-Hartree-Fock calculations and finite basis sets. The calculations show that the effect of spin-orbit splitting on the valence p-orbital dominates the bonding for the compound of the superheavy element, and even for the sixth row the spin-orbit interaction should be treated self-consistently for an accurate description of the electronic structure.