W.C. Nieuwpoort

RELATIVISTIC QUANTUM-CHEMISTRY - THE MOLFDIR PROGRAM PACKAGE

In this article the Dirac-Fock-CI method is reviewed. The MOLFDIR program suite that was developed for calculations of this type on molecular systems is described in detail. Computational details of some recent applications are presented to give an impression of the computational resources necessary.

Molecular open shell configuration interaction calculations using the Dirac–Coulomb Hamiltonian : The f 6‐manifold of an embedded EuO9−6 cluster

We present results of all‐electron molecular relativistic (Hartree–Fock–Dirac) and nonrelativistic (Hartree–Fock) calculations followed by a complete open shell configuration interaction (COSCI) calculation on an EuO9−6 cluster in a Ba2GdNbO6 crystal. The results include the calculated energies of a number of states derived from the f6−manifold and 5D–7F luminescence transition wavelengths. The calculations were performed using the molecular Fock–Dirac (molfdir) program package developed in our laboratory. The theory and methods employed in this package are briefly described. The physical models used to analyze the Eu3+ impurity states range from a bare Eu3+ ion to an EuO9−6 cluster embedded in a Madelung potential representing the rest of the crystal. We show that it is necessary to use the embedded cluster model to get a reasonable description of the crystal field splittings of the states arising from the f6‐manifold. Our results indicate that the calculated splittings are very sensitive to the orbitals used. It is therefore essential that relativistic orbitals be used from the outset.

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...

The use of Gaussian nuclear charge distributions for the calculation of relativistic electronic wavefunctions using basis set expansions

Abstract It is demonstrated that the use of a Gaussian charge distribution to represent the nucleus is advantageous in relativistic quantum chemical basis set expansion calculations. It removes the singularity at the origin of the Dirac wavefunction, leading to a more rapid convergence of the ground-state energy expectation value as a function of basis set size and to a large reduction in the exponents of the optimized basis sets. Hence, smaller basis sets can be used for HFD calculations.

Ab initio SCF MO calculation of ionisation energies and charge distributions of TCNQ and its mono- and divalent anions

Abstract Ab initio SCF MO calculations using a contracted double zeta basis set of 168 gaussian type functions were performed on TCNQ + , TCNQ, TCNQ − and TCNQ 2− . The ionisation potentials obtained from total energy differences are generally 0.25-0.50 eV higher than the corresponding negative orbital energies from the TCNQ calculation and in satisfactory agreement with experimental results. The energy of the disproportionation reaction 2TCNQ − -TCNQ+TCNQ 2− is calculated to be 4.62 eV. The charge distributions as measured by the gross atomic populations generally deviate from those obtained in earlier π-electron calculations as a consequence of taking the σ-electron distribution into account. The atomic charges are in good agreement with the limited experimental data available.

Universal atomic basis sets

Abstract A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, is used to calculate matrix Hartree—Fock ground state energies for several light atoms. The resulting energies are compared with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom.

RELATIVISTIC ALL-ELECTRON MOLECULAR HARTREE-FOCK-DIRAC-(BREIT) CALCULATIONS ON CH4, SIH4, GEH4, SNH4, PBH4

SummaryResults and details of molecular Fock-Dirac-(Breit) calculations on CH4, SiH4, GeH4, SnH4, and PbH4 obtained with the MOLFDIR© program package are presented and compared with other calculations and experimental results. The relativistic ground state energies (including the Breit interaction) of the atoms C, Si, Ge, Sn, and Pb, necessary for reference purposes, have been calculated using a small relativistic CI. One of our findings is that for the heavier systems perturbation theory over-estimates the relativistic bond length contraction. The Breit interaction has only a small effect on the bond lengths.

On the use of Gaussian basis sets to solve the hartree—fock—dirac equation. I. Application to one-electron atomic systems

Abstract The solutions of the matrix representation of the Dirac equation obtained by expansion in Gaussian basis sets are examined. The basis sets consist of non-relativistically energy-optimized Cartesian Gaussians, properly balanced by a basis set constraint, or a generalized modified [σ • p ] representation. The quality of the solutions is illustrated by calculating the expectation values of various radial moments in addition to the energy eigenvalues. An expression is given for Gaussian contraction coefficients, consistent with the basis set constraint.

Electron correlation effects on the d-d excitations in NiO

The partly filled 3d shell in solid transition metal compounds is quite localized on the transition metal ion and gives rise to large electron correlation effects. With the recently developed CASSCF/CASPT2 approach electron correlation effects can be accounted for efficiently. The CASSCF step accounts for the non-dynamical correlation and part of the dynamical correlation, the following CASPT2 step takes largely care of the remaining dynamical correlation in a perturbative way. This approach is applied to the d-d excitations in NiO for which both non-dynamical and dynamical electron correlation effects have substantial influence on the energy differences. Excitation energies that compare well to the experimental data are obtained and the importance of the different electron correlation effects can be assessed.

Heisenberg exchange enhancement by orbital relaxation in cuprate compounds

Abstract We calculate the Heisenberg exchange J in the quasi-2D antiferromagnetic cuprates La 2 CuO 4 , YBa 2 Cu 3 O 6 , Nd 2 CuO 4 and Sr 2 CuO 2 Cl 2 . We apply all-electron (MC)SCF and non-orthogonal CI calculations to [Cu 2 O 11 ] 18− , [Cu 2 O 9 ] 14− , [Cu 2 O 7 ] 10− and [Cu 2 O 7 Cl 4 ] 14− cluster in a model charge embedding. The (MC)SCF triplet and singlet ground states are well characterized by Cu 2+ (d x 2 − y 2 ) and O 2− . The antiferromagnetic exchange is strongly enhanced by admixing relaxed (MC)SCF triplet and singlet excited states, in which a single electron is transferred from the central O ion to Cu. We ascribe this effect to orbital relaxation in the charge transfer component of the wavefunction. Close agreement with experiment is obtained.