Calculation of electric-field gradients based on higher-order generalized Douglas-Kroll transformations.

In this paper, the calculation of electric-field-like properties based on higher-order Douglas-Kroll-Hess (DKH) transformations is discussed. The electric-field gradient calculated within the Hartree-Fock self-consistent field framework is used as a representative property. The properties are expressed as an analytic first derivative of the four-component Dirac energy and the nth-order DKH energy, respectively. The differences between a "forward" transformation of the relativistic energy or the "back transformation" of the wave function is discussed in some detail. Detailed test calculations were carried out on the electric-field gradient at the halogen nucleus in the series HX (X=F,Cl,Br,I,At) for which extensive reference data are available. The DKH method is shown to reproduce (spin-free) four-component Dirac-Fock results to an accuracy of better than 99% which is significantly closer than previous DKH studies. The calculations of both the Hamiltonian and the property operator are shown to be essentially converged after the second-order transformation, even for elements as heavy as At. In addition, we have obtained results within the density-functional framework using the DKHZ and zeroth-order regular approximation (ZORA) methods. The latter results included picture-change effects at the scalar relativistic variant of the ZORA-4 level and were shown to be in quantitative agreement with earlier results obtained by van Lenthe and Baerends. The picture-change effects are somewhat smaller for the ZORA method compared to DKH. For heavier elements significant differences in the field gradients predicted by the two methods were found. Based on comparison with four-component Dirac-Kohn-Sham calculations, the DKH results are more accurate. Compared to the spin-free Dirac-Kohn-Sham reference values, the ZORA-4 formalism did not improve the results of the ZORA calculations.

Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings.

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.

A photochemical activation scheme of inert dinitrogen by dinuclear Ru(II) and Fe(II) complexes.

A general photochemical activation process of inert dinitrogen coordinated to two metal centers is presented on the basis of high-level DFT and ab initio calculations. The central feature of this activation process is the occupation of an antibonding pi* orbital upon electronic excitation from the singlet ground state S0 to the first excited singlet state S1. Populating the antibonding LUMO weakens the triple bond of dinitrogen. After a vertical excitation, the excited complex may structurally relax in the S1 state and approaches its minimum structure in the S1 state. This excited-state minimum structure features the dinitrogen bound in a diazenoid form, which exhibits a double bond and two lone pairs localized at the two nitrogen atoms, ready to be protonated. Reduction and de-excitation then yield the corresponding diazene complex; its generation represents the essential step in a nitrogen fixation and reduction protocol. The consecutive process of excitation, protonation, and reduction may be rearranged in any experimentally appropriate order. The protons needed for the reaction from dinitrogen to diazene can be provided by the ligand sphere of the complexes, which contains sulfur atoms acting as proton acceptors. These protonated thiolate functionalities bring protons close to the dinitrogen moiety. Because protonation does not change the pi*-antibonding character of the LUMO, the universal and well-directed character of the photochemical activation process makes it possible to protonate the dinitrogen complex before it is irradiated. The pi*-antibonding LUMO plays the central role in the activation process, since the diazenoid structure was obtained by excitation from various occupied orbitals as well as by a direct two-electron reduction (without photochemical activation) of the complex; that is, the important bending of N2 towards a diazenoid conformation can be achieved by populating the pi*-antibonding LUMO.

Correlated ab initio calculations of spectroscopic parameters of SnO within the framework of the higher-order generalized Douglas-Kroll transformation.

The first molecular calculations with the generalized Douglas-Kroll method up to fifth order in the external potential (DKH5) are presented. We study the spectroscopic parameters and electron affinity of the tin oxide molecule SnO and its anion SnO(-) applying nonrelativistic as well as relativistic calculations with higher orders of the DK approximation. In order to guarantee highly accurate results close to the basis set limit, an all-electron basis for Sn of at least quintuple-zeta quality has been constructed and optimized. All-electron CCSD(T) calculations of the potential energy curves of both SnO and SnO(-) reproduce the experimental values very well. Relative energies and valence properties are already well described with the established standard second-order approximation DKH2 and the higher-order corrections DKH3-DKH5 hardly affect these quantities. However, an accurate description of total energies and inner-shell properties requires superior relativistic schemes up to DKH5.

A quantum-chemical study of dinitrogen reduction at mononuclear iron-sulfur complexes with hints to the mechanism of nitrogenase.

The mechanism of biological dinitrogen reduction is still unsolved, and the structure of the biological reaction center, the FeMo cofactor with its seven iron atoms bridged by sulfur atoms, is too complicated for direct attack by current sophisticated quantum chemical methods. Therefore, iron-sulfur complexes with biologically compatible ligands are utilized as models for studying particular features of the reduction process: coordination energetics, thermodynamic stability of intermediates, relative stability of isomers of N2H2, end-on versus side-on binding of N2, and the role of states of different multiplicity at a single iron center. From the thermodynamical point of view, the crucial steps are dinitrogen binding and reduction to diazene, while especially the reduction of hydrazine to ammonia is not affected by the transition metal complex, because the complex-free reduction reaction is equally favored. Moreover, the abstraction of coordinated ammonia can be easily achieved and the complex is recovered for the next reduction cycle. Our results are discussed in the light of studies on various model systems in order to identify common features and to arrive at conclusions which are of importance for the biological mechanism.