Bernd A. Heß

A mean-field spin-orbit method applicable to correlated wavefunctions

Abstract Starting from the full microscopic Breit-Pauli or no-pair spin-orbit Hamiltonians, we have devised an effective one-electron spin-orbit Hamiltonian in a well defined series of approximations by averaging the two-electron contributions to the spin-orbit matrix element over the valence shell. In addition the two-electron integrals were restricted to comprise only one-centre terms. The validity of these approximations has been tested on several palladium containing compounds. Excellent agreement of the matrix elements of the mean-field operator with corresponding full results is observed; deviations amount to a few cm −1 in absolute value or at most 0.2% on a relative scale. The newly defined mean-field operator can thus safely be employed to evaluate spin-orbit effects in transition metal containing compounds.

Relativistic ab initio CI study of the X1Σ+ and A1Σ+ states of the AgH molecule

A no-pair formalism employing external field projection operators correct to second order in the one-particle potential is used to calculate the potential curves in the neighborhood of the equilibrium geometry for the ground state X1Σ+ and the first excited state A1Σ+ of the AgH molecule, thereby determining equilibrium bond length and harmonic frequencies for these species. We report all electron calculations in the self consistent field (SCF) approximation and on configuration interaction (CI) level, for the non-relativistic hamiltonian operator as well as for its spin-free relativistic counterpart. The SCF results for the bond length of the ground state (rel. 169.2 pm, non-rel. 176.2 pm) are in good agreement with earlier all-electron Dirac-Hartree-Fock (DHF) calculations, and the CI results (rel. 162.1 pm, non-rel. 169.7 pm) show the relativistic contribution to the bond length contraction including correlation and can be compared with the experimental value of 161.8 pm.

Relativistic all-electron coupled-cluster calculations on the gold atom and gold hydride in the framework of the douglas-kroll transformation

Abstract A one-component relativistic method, based on the Douglas-Kroll transformation, is combined with the Fock-space coupledcluster method for treating electron correlation. The method is applied to the gold atom, the AuH molecule, and their ions. Excitation energies, ionization potentials, electron affinities and bond energies are calculated. Good agreement with experiment is obtained.

TDMP2 calculation of dynamic multipole polarizabilities and dispersion coefficients for the halogen anions F−, Cl−, Br− and I−

A systematic ab initio study of the dynamic multipole polarizabilities of the halogen anions F−, Cl−, Br− and I− is presented. The effects of electron correlation are included for the static as well as for the frequency-dependent polarizabilities using time-dependent second-order Mo/ller-Plesset perturbation theory. Large one-particle basis sets, optimized for polarizabilities, are used to obtain results near the MP2 basis set limit. For the anions Br− and I− also scalar relativistic effects are accounted for by means of the spin-free no-pair Hamiltonian Ĥ+sf1. For the static dipole polarizabilities of the anions F− and Cl− we find good agreement with recent correlated ab initio calculations, but for the higher multipole polarizabilities and for the anions Br− and I− the discrepancies relative to previous calculations and empirical estimates are large. The effects of electron correlation on the polarizabilities of these anions are in general extremely large, while relativistic effects are in all four inve...

Ab initio relativistic all-electron calculation of the Ar–I2 ground state potential

Correlated relativistic all-electron supermolecular ab initio calculations of the ground state potential of the Ar–I2 molecule are presented. The role of differential intramonomer spin–orbit and correlation effects in the interaction energy is investigated and found to be only of minor importance. Two energetically very similar minima of the Ar–I2 complex are found, corresponding to a linear and a T-shaped geometry of the monomers. The comparatively large isomerization barrier for the two conformations indicates the existence of two stable isomers at very low temperatures.

Relativistic all electron configuration interaction calculation of ground and excited states of the gold hydride molecule

We present relativistic configuration interaction calculations with the spin-free no-pair hamiltonian on the gold hydride molecule, treating the ground state as well as the eleven lowest excited states. The calculations provide a picture of the bonding in theX1Σ+ ground state consistent with previous work on this species using four-component spinors: compared to non-relativistic calculations, the dipole moment is reduced by a factor of two, hybridization (and thus participation ofd orbitals at the bonding) is greatly enhanced, the bond length is shortened by 20 pm, and the dissociation energy is increased by 50%. Comparison of the spin-averaged potential curves of the excited states with experiment suggests a reinterpretation of theC1Σ+ as the 0+ fine structure component of 23Π and the prediction of a weakly bound3Σ+ state with weak transitions to the ground state in the range of 2.9–3.1 eV.

A finite-nucleus model for relativistic electronic structure calculations using a Douglas-Kroll-transformed Hamiltonian*

SummaryWe report the implementation of a Gaussian finite-nucleus model in the framework of the spin-free no-pair Hamiltonian obtained from the Douglas-Kroll transformation of the no-pair operator with external-field projectors. The finite nucleus regularizes the weak singularity of the wavefunction at the locations of the nuclei and provides a means for efficient exponent optimization using a spinaveraged relativistic one-component operator. We report and discuss basis sets for the gold atom obtained from various optimization procedures, making use of a point nucleus as well as employing various finite-nucleus models.

The structure of the second-order reduced density matrix in density matrix functional theory and its construction from formal criteria

Some formal requirements for the second-order reduced density matrix are discussed in the context of density matrix functional theory. They serve as a basis for the ad hoc construction of the second-order reduced density matrix in terms of the first-order reduced density matrix and lead to implicit functionals where the occupation numbers of the natural orbitals are obtained as diagonal elements of an idempotent matrix the elements of which represent the variational parameters to be optimized. The numerical results obtained from a first realization of such an implicit density matrix functional give excellent agreement with the results of full configuration interaction calculations for four-electron systems like LiH and Be. Results for H2O taken as an example for a somewhat larger molecule are numerically less satisfactory but still give reasonable occupation numbers of the natural orbitals and indicate the capability of density matrix functional theory to cope with static electron correlation.

A new approach to density matrix functional theory

Starting from a pair-excitation multiconfiguration self-consistent field approach considering pairwise excitations of two electrons of opposite spin from a single occupied molecular orbital to a single virtual molecular orbital, we present a natural orbital functional for the electronic energy containing the natural orbitals and the pair-excitation coefficients as variational parameters to be optimized. The occupation numbers of the natural orbitals can be determined from the pair-excitation coefficients in this implicit functional. Test calculations for the water molecule give occupation numbers of the natural orbitals in reasonable agreement with the results of full configuration interaction calculations.

Calculation of orientation-dependent double-tensor moments for Coulomb-type intermolecular interactions

A new derivation is presented for the orientation-dependent interaction tensors which describe the electrostatic interaction between two multipole or multipole polarizability distributions both given in their own molecule-fixed coordinate system. This derivation leads to an explicit equations that allows easy and direct evaluation of formulae for the components of the double-tensors and also for high ranks. Such an equation is given for the real, complex spherical, and cartesian moments. The formula is suitable for providing stable computer-generated expressions for tensor operators of any rank.