Christoph van Wüllen

Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations

The application of the zeroth-order regular relativistic approximation (ZORA) for molecular density functional calculations is investigated. By introducing a model potential to construct the kinetic energy operator, stationarity of the energy with respect to orbital variations is gained and most problems connected with gauge dependence of the regular approximation are eliminated. The formulation of a geometry gradient is greatly facilitated using this formalism. Calculations for the coinage metal hydrides (CuH, AgH, AuH) as well as for the homonuclear (Cu2, Ag2, Au2) and heteronuclear (CuAg, CuAu, AgAu) diatomics show that the results of ZORA calculations within the electrostatic shift approximation, as introduced by van Lenthe and co-workers, can be duplicated using the simpler scheme proposed in this work. Results for the coinage metal fluorides (CuF, AgF, AuF) and chlorides (CuCl, AgCl, AuCl) are presented as well. First-order relativistic calculations have been performed for all systems to assess the ...

The MC-IGLO method

Abstract The MC-IGLO method for the calculation of NMR chemical shifts and magnetic susceptibilities with inclusion of electron correlation effects is presented. It is a generalization of the IGLO (individual gauge for localized orbitals) approach to multiconfiguration reference functions, and is especially suited for molecules that are not well described by a single Slater determinant like ozone, B 4 H 4 , cyclobutadiene and generally molecules with both lone pairs and double bonds. In those cases where the conventional IGLO method (SCF-IGLO) - like all comparable methods - fails, MC-IGLO improves the results considerably, although the correlation effects sometimes overshoot. For closed-shell systems like H 2 O and CH 4 MC-IGLO results differ little from SCF-IGLO, and to obtain higher accuracy in these cases, the extension of the basis is more important than the inclusion of correlation effects. Explicit results are presented for H 2 O, N 2 , PN, NNO, SO 2 , B 4 H 4 and finally cyclobutadiene C 4 H 4 for geometry ranges between the rectangular equilibrium structure and a square form.

Self-consistent treatment of spin–orbit interactions with efficient Hartree–Fock and density functional methods

Efficient self-consistent field (SCF) schemes including both scalar relativistic effects and spin-orbit (SO) interactions at Hartree-Fock (HF) and density functional (DFT) levels are presented. SO interactions require the extension of standard procedures to two-component formalisms. Efficiency is achieved by using effective core potentials (ECPs) and by employing the resolution-of-the-identity approximation for the Coulomb part (RI-J) in pure DFT calculations as well as also for the HF-exchange part (RI-JK) in the case of HF or hybrid-DFT treatments. The procedures were implemented in the program system TURBOMOLE; efficiency is demonstrated for comparably large systems, such as Pb54. Relevance of SO effects for electronic structure and stability is illustrated by treatments of small Pb and Po clusters with and without accounting for SO effects.

Spectroscopic constants of gold and eka-gold (element 111) diatomic compounds: The importance of spin–orbit coupling

Scalar-relativistic density functional calculations in the zeroth-order regular approximation as well as fully relativistic Dirac–Kohn–Sham calculations have been performed to investigate spectroscopic constants of the eka-gold (element 111) compounds (111) X (X=H, F, Cl, Br, O, Au) and the dimer of element 111. For calibration, we also report results for homologous gold compounds. The bond lengths for the compounds of element 111 are similar but slightly larger than those of the gold compounds. Spin–orbit coupling increases the bond length by a few pm. For the hydride and the halides, the force constants of the eka-gold compounds are generally larger than those of the gold compounds although the dissociation energy is smaller. The oxide of eka-gold is more strongly bound than the gold oxide. The dimer of element 111 has an open shell instead of a closed-shell electronic structure and is less stable than the gold dimer. The effect of spin–orbit coupling on the dissociation energy depends on the extent to ...

A comparison of density functional methods for the calculation of phosphorus-31 NMR chemical shifts

31 P NMR chemical shifts for the phosphorus compounds PX3 (X=H, F, Cl, CH3, iC3H7 and OCH3), OPX3 (X=CH3 and OCH3), Si(PH2)4, Cr(CO5)(PH3), PX4+ (X=H, CH3), PF6−, P4 and PN have been calculated with various density functional methods as well as at the Hartree–Fock and MP2 level, using both the IGLO and GIAO variants of introducing distributed gauge origins except for MP2 (only GIAO available) and the new method proposed recently by Wilson, Amos and Handy (WAH, GIAO not available). Except for PCl3 and PN, all density functional approaches achieve comparable accuracy, better than Hartree–Fock and similar to MP2. For PCl3 and PN, the WAH method leads to a substantial improvement. The GIAO and IGLO results are of comparable accuracy. Numerical benchmark values for the absolute magnetic shielding of PN at its experimental equilibrium value are presented and compared with literature data. A theoretical analysis reveals that the approximation used by WAH makes their method lose gauge invariance.

Mechanism of Cu/Pd-Catalyzed Decarboxylative Cross-Couplings: A DFT Investigation

The reaction mechanism of decarboxylative cross-couplings of benzoates with aryl halides to give biaryls, which is cooperatively catalyzed by copper/palladium systems, was investigated with DFT methods. The geometries and energies of all starting materials, products, intermediates, and transition states of the catalytic cycle were calculated for the two model reactions of potassium 2- and 4-fluorobenzoate with bromobenzene in the presence of a catalyst system consisting of copper(I)/1,10-phenanthroline and the anionic monophosphine palladium complex [Pd(PMe3)Br](-). Several neutral and anionic pathways were compared, and a reasonable catalytic cycle was identified. The key finding is that the transmetalation has a comparably high barrier as the decarboxylation, which was previously believed to be solely rate-determining. The electronic activation energy of the transmetalation is rather reasonable, but the free energy loss in the initial Cu/Pd adduct formation is high. These results suggested that research aimed at further improving the catalyst should target potentially bridging bidentate ligands likely to assist in the formation of bimetallic intermediates. Experimental studies confirm this somewhat counterintuitive prediction. With a bidentate, potentially bridging ligand, designed to support the formation of bimetallic adducts, the reaction temperature for decarboxylative couplings was reduced by 70 °C to only 100 °C.

Spin densities in two‐component relativistic density functional calculations: Noncollinear versus collinear approach

With present day exchange‐correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar‐relativistic calculations, the spin density can be defined conventionally, but if spin‐orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the “spin density” is. In many applications, a fixed quantization axis is used to define the spin density (“collinear approach”), but one can also use the length of the local spin magnetization vector without any reference to an external axis (“noncollinear approach”). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange‐correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn‐Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I  +2 and PbF indicate that the error introduced by the collinear approximation is ∼0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort.

COMPUTATIONAL EVIDENCE FOR A NEW C84 ISOMER

Abstract Endohedral chemical shifts of all isolated pentagon isomers of C 76 and C 78 , as well as those of the most stable isolated pentagon isomers of C 84 , have been computed at the GIAO-SCF/DZP level using DFT optimized geometries (Becke88-perdew86/3-21G). The theoretical data support tentative assignments of recent experimental σ( 3 He) NMR data to the major components in a partly separated, 3 He labeled mixture. The identification of at least one new fullerene isomer, C 84 D 2d (4), is suggested, based on the endohedral chemical shift of −25.0 ppm (calc.) versus −24.4 ppm (exp.).

Calculation of nuclear magnetic resonance shieldings and magnetic susceptibilities using multiconfiguration Hartree–Fock wave functions and local gauge origins

A multiconfiguration generalization of the individual gauge for localized orbitals (IGLO) method for the calculation of magnetic properties such as susceptibilities and nuclear magnetic resonance chemical shifts is presented in detail. This includes a rederivation of the IGLO method by means of a nonlocal gauge transformation. The method is most successfully applied if strong (static) correlation effects have to be taken into account.

Zero-field splittings from density functional calculations: Analysis and improvement of known methods

Several different approaches have been proposed to calculate the zero-field splitting tensor with density functional methods. In this work, our own derivation is presented in some detail, to allow a theoretical analysis and a comparison with other methods [M. R. Pederson and S. N. Khanna, Phys. Rev. B 60, 9566 (1999); F. Neese, J. Am. Chem. Soc. 128, 10213 (2006); J. Chem. Phys. 127, 164112 (2007)]. Pedersons method can be improved by properly taking into account the quantum nature of spin when extracting the zero field splitting tensor from the magnetic anisotropy. A closed-shell molecule at large distance from an open shell complex will have a spurious contribution to the zero-field splitting tensor calculated with Neeses methods. We thus have analyzed his approach in some detail and found that it can be corrected if one properly transforms the equations used in wave function based theory to a sum-over-states type expression before one interprets it as an energy derivative. If improved along these lines, Neeses and Pedersons methods become identical down to the working equations. The theoretical analysis is illustrated by sample calculations on the well-studied Mn(III)-tris-acetylacetonato complex Mn(acac)(3), both as an isolated molecule and with a Pd(II) dichloro diammine complex at large distance as an innocent spectator.