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Christoph van Wüllen

Publications and source records attributed to Christoph van Wüllen.

9 recordsLinked to original sources
PubMed2006

A new type of N-heterocyclic silylene with ambivalent reactivity.

The synthesis of a novel divalent silicon compound by debromination of the corresponding dibromosilyl precursor is reported. The silylene possesses a unique reactivity toward electrophiles of the type R-X (R = H, silyl; X = halogen, triflate) in comparison with the germanium congener. DFT calculations suggest that this is due to a much higher basicity of the silylene versus that of germylene lone-pair electrons. Thus, addition of Me3SiX to the silylene (X = OSO2CF3, triflate) furnishes the corresponding (kinetically favored) 1,4-adduct which subsequently rearranges to the thermodynamically favored 1,1-adduct.

Journal Article↗
PubMed2006

Two-component relativistic density-functional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and all-electron methods.

A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.

Journal Article↗
PubMed2006

Numerical instabilities in the computation of pseudopotential matrix elements.

Steep high angular momentum Gaussian basis functions in the vicinity of a nucleus whose inner electrons are replaced by an effective core potential may lead to numerical instabilities when calculating matrix elements of the core potential. Numerical roundoff errors may be amplified to an extent that spoils any result obtained in such a calculation. Effective core potential matrix elements for a model problem are computed with high numerical accuracy using the standard algorithm used in quantum chemical codes and compared to results of the MOLPRO program. Thus, it is demonstrated how the relative and absolute errors depend an basis function angular momenta, basis function exponents and the distance between the off-center basis function and the center carrying the effective core potential. Then, the problem is analyzed and closed expressions are derived for the expected numerical error in the limit of large basis function exponents. It is briefly discussed how other algorithms would behave in the critical case, and they are found to have problems as well. The numerical stability could be increased a little bit if the type 1 matrix elements were computed without making use of a partial wave expansion.

Computer Simulation↗
PubMed2005

Accurate and efficient treatment of two-electron contributions in quasirelativistic high-order Douglas-Kroll density-functional calculations.

Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the "model potential" approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer.

Journal Article↗
PubMed2005

Density functional calculations of molecular parity-violating effects within the zeroth-order regular approximation.

A (quasirelativistic) two-component density functional theory (DFT) approach to the computation of parity-violating energy differences between enantiomers is presented which is based on the zeroth-order regular approximation (ZORA). This approach is employed herein to compute parity-violating energy differences between several P and M conformations of dihydrogen dichalcogenides (H2X2 with X=O, S, Se, Te, Po), of which some compounds have recently been suggested as potential molecular candidates for the first experimental measurement of parity-violating effects in chiral molecules. The DFT ZORA results obtained in this work with "pure" density functionals are anticipated to deviate by well less than 1% from data that would be computed within related (relativistic) four-component Dirac-Kohn-Sham-Coulomb schemes. In our implementation of the ZORA slightly larger relative deviations are expected for hybrid functionals, depending on the amount of "exact" exchange. For B3LYP (20% exact exchange) differences are estimated to amount to at most 3% in hydrogen peroxide, 2% in disulfane, and 1% or less for the heavier homologs. Thus, the present two-component approach is expected to perform excellently when compared to four-component density functional schemes while being at the same time computationally more efficient. The ZORA approach will therefore be of particular interest for the prediction of parity-violating vibrational frequency shifts, for instance, in isotopomers of H(2)Se(2) and H(2)Te(2).

Journal Article↗
PubMed2004

Relation between different variants of the generalized Douglas-Kroll transformation through sixth order.

Wolf et al. have recently investigated a generalized Douglas-Kroll transformation. From a general class of unitary transformations that can be used in the Douglas-Kroll transformation, they pick one which is supposed to give, at a given order, an optimal transformed Dirac Hamiltonian. Results were presented through the fifth order. However, no data were given to demonstrate to which extent the so-called "optimal" Douglas-Kroll transformation is superior to other choices. In this work, the Douglas-Kroll transformation is extended to the sixth order for the first time, using computer algebra algorithms to obtain the working equations. It is shown how, at a given order, different variants of the Douglas-Kroll Hamiltonians are related. Various choices of the generalized transformation are examined numerically for the ground states of the one-electron atomic ions with nuclear charges Z=20, 40, 60, 80, 100, and 120. It is shown that compared to the improvement obtained by including the next order, the differences between various choices for the generalized Douglas-Kroll transformation are almost negligible. Results closest to the Dirac eigenvalues are not obtained with the optimal Douglas-Kroll transformation given by Wolf et al., but with the parametrization originally suggested by Douglas and Kroll.

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