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Markus Reiher

Publications and source records attributed to Markus Reiher.

At least 37 records · Page 2Linked to original sources
PubMed2005

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.

Journal Article↗
PubMed2005

The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation.

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.

Journal Article↗
PubMed2005

Comparative analysis of local spin definitions.

This work provides a survey of the definition of electron spin as a local property and its dependence on several parameters in actual calculations. We analyze one-determinant wave functions constructed from Hartree-Fock and, in particular, from Kohn-Sham orbitals within the collinear approach to electron spin. The scalar total spin operators S2 and Sz are partitioned by projection operators, as introduced by Clark and Davidson, in order to obtain local spin operators SASB and SzA, respectively. To complement the work of Davidson and co-workers, we analyze some features of local spins which have not yet been discussed in sufficient depth. The dependence of local spin on the choice of basis set, density functional, and projector is studied. We also discuss the results of Sz partitioning and show that SzA values depend less on these parameters than SASB values. Furthermore, we demonstrate that for small organic test molecules, a partitioning of Sz with preorthogonalized Lowdin projectors yields nearly the same results as one obtains using atoms-in-molecules projectors. In addition, the physical significance of nonzero SASB values for closed-shell molecules is investigated. It is shown that due to this problem, SASB values are useful for calculations of relative spin values, but not for absolute local spins, where SzA values appear to be better suited.

Journal Article↗
PubMed2005

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.

Journal Article↗
PubMed2005

Car-Parrinello molecular dynamics study of the initial dinitrogen reduction step in Sellmann-type nitrogenase model complexes.

We have studied reduction reactions for nitrogen fixation at Sellmann-type model complexes with Car-Parrinello simulation techniques. These dinuclear complexes are especially designed to emulate the so-called open-side FeMoco model. The main result of this work shows that in order to obtain the reduced species several side reactions have to be suppressed. These involve partial dissociation of the chelate ligands and hydrogen atom transfer to the metal center. Working at low temperature turns out to be one necessary pre-requisite in carrying out successful events. The successful events cannot be described by simple reaction coordinates. Complicated processes are involved during the initiation of the reaction. Our theoretical study emphasizes two experimental strategies which are likely to inhibit the side reactions. Clamping of the two metal fragments by a chelating phosphane ligand should prevent dissociation of the complex. Furthermore, introduction of tert-butyl substituents could improve the solubility and should thus allow usage of a wider range of (mild) acids, reductants, and reaction conditions.

Hydrogen↗
PubMed2004

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.

Journal Article↗
PubMed2004

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.

Iron↗
PubMed2004

A theoretical study of spin states in Ni-S4 complexes and models of the [NiFe] hydrogenase active site.

We have applied density functional theory, using both pure (BP86) and hybrid (B3LYP and B3LYP*) functionals, to investigate structural parameters and reaction energies for nickel(II)-sulfur coordination compounds, as well as for small cluster models of the Ni-SI and Ni-R redox state of [NiFe] hydrogenases. Results obtained investigating experimentally well-characterized complexes show that BP86 is well suited to describe the structural features of this class of compounds. However, the singlet-triplet energy splitting and even the computed ground state are strongly dependent on the applied functional. Results for the cluster models of [NiFe] hydrogenases lead to the conclusion that in the reduced protein structures characterized by X-ray diffraction a hydride bridges the two metal centres. The energy splitting of the singlet and triplet states in Ni-R and Ni-SI models is calculated to be very small and may be overcome at room temperature to allow a spin crossover. Moreover, the relative stability of the Ni-SI and Ni-R structures adopted in the present investigation is fully compatible with their involvement in the reversible heterolytic cleavage of H(2).

Binding Sites↗
PubMed2004

Exact decoupling of the Dirac Hamiltonian. I. General theory.

Exact decoupling of positive- and negative-energy states in relativistic quantum chemistry is discussed in the framework of unitary transformation techniques. The obscure situation that each scheme of decoupling transformations relies on different, but very special parametrizations of the employed unitary matrices is critically analyzed. By applying the most general power series ansatz for the parametrization of the unitary matrices it is shown that all transformation protocols for decoupling the Dirac Hamiltonian have necessarily to start with an initial free-particle Foldy-Wouthuysen step. The purely numerical iteration scheme applying X-operator techniques to the Barysz-Sadlej-Snijders (BSS) Hamiltonian is compared to the analytical schemes of the Foldy-Wouthuysen (FW) and Douglas-Kroll-Hess (DKH) approaches. Relying on an illegal 1/c expansion of the Dirac Hamiltonian around the nonrelativistic limit, any higher-order FW transformation is in principle ill defined and doomed to fail, irrespective of the specific features of the external potential. It is shown that the DKH method is the only valid analytic unitary transformation scheme for the Dirac Hamiltonian. Its exact infinite-order version can be realized purely numerically by the BSS scheme, which is only able to yield matrix representations of the decoupled Hamiltonian but no analytic expressions for this operator. It is explained why a straightforward numerical iterative extension of the DKH procedure to arbitrary order employing matrix representations is not feasible within standard one-component electronic structure programs. A more sophisticated ansatz based on a symbolical evaluation of the DKH operators via a suitable parser routine is needed instead and introduced in Part II of this work.

Journal Article↗
PubMed2004

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.

Journal Article↗
PubMed2004

Vibrational center-ligand couplings in transition metal complexes.

The mode-tracking principle [J. Chem. Phys. 2003, 118, 1634] for the direct quantum chemical calculation of preselected, characteristic molecular vibrations makes vibrational analyses of very large molecules feasible. This is demonstrated here for the [(Ph(3)PAu)(6)C](2+) complex, in which 18 phenyl groups in the ligand sphere are explicitly taken into account. We are aiming at the motion of the endohedral carbon atom, which is in an extraordinary bonding situation because it is surrounded by an octahedral core of gold atoms in this cluster. Secondary effects of the full ligand sphere on the vibrations of the [Au(6)C] core embedded in [(R(3)PAu)(6)C](2+) clusters are investigated. For this purpose, local vibrations of the octahedral core are generated, and their long-range couplings with the phosphine ligand sphere become visible in the mode-tracking iterations. The exact normal modes of these characteristic vibrations of the cluster are then obtained after convergence of the mode-tracking refinement. This protocol allows us to assess the coupling of the outer ligand sphere with the inner core of the cluster in terms of changes of the vibrational frequencies and of the collective motions of the atomic nuclei. The vibrational frequencies of the octahedral [Au(6)C] core split due to symmetry breaking in the C(1)-symmetric [(Ph(3)PAu)(6)C](2+) cluster. Our study demonstrates how effects of the periphery of a large molecule on local vibrations can be quantified. Furthermore, we predict the first set of characteristic vibrational frequencies obtained with first-principles methods for this gold cluster, whose vibrational spectra have not yet been recorded experimentally.

Journal Article↗
PubMed2003

From rare gas atoms to fullerenes: spherical aromaticity studied from the point of view of atomic structure theory.

The characteristic features of molecules like polyhedra and fullerenes, which follow the 2(N+1)(2) rule of spherical aromaticity, can be related to energetically stable closed-shell configurations of (pseudo-)atoms. This unifying view relies on a thought experiment, which produces a polyhedron in a two-step process and which can, in turn, relate the electronic configuration of any spherical polyhedron to the one of a corresponding closed-shell atom. In the first step, the electronic ground-state configuration is identified. In the second step, a group theoretical analysis can be carried out; this relates the spherically symmetric atomic orbitals to the molecular orbitals classified according to the irreducible representations of the point group of the polyhedron under consideration. This procedure explains and justifies the pseudo-l classification of molecular orbitals, which is the basis of the 2(N+1)(2) rule. For the transition from the electronic configuration of the rare gas Eka-Rn (Uuo) to the icosahedral fullerene C(20) (2+), we show how a change in the ground-state configuration leads to the phenomenologically found 2(N+1)(2) rule for spherically aromatic fullerenes.

Journal Article↗
PubMed2003

Fluorescence kinetics of aqueous solutions of tetracycline and its complexes with Mg2+ and Ca2+.

The fluorescence spectra of acidified aqueous solutions of tetracycline (tcH3+) exhibit three components with slightly different degrees of anisotropy: the 'blue' component (lambdad approximately equal to 475 nm) decays on the timescale of a few picoseconds; the second, most intense component (lambdad approximately equal to 530 nm) shows decay times of about 25 (H3O+) and 70 ps (D3O+); the third component (lambdad approximately equal to 650 nm) is longer lived (tau approximately equal to 200 ps). All three fluorescence components appear quasi-instantaneously, thus providing evidence that the relaxation processes which give rise to the unusually large Stokes shifts occur on a (sub-)picosecond timescale. The effect of H/D exchange suggests that these relaxation processes involve excited-state intramolecular proton transfer (ESIPT) of OH10 and/or OH12, but does not exclude a change in the hydrogen-bonding pattern to the solvent molecules. The low overall fluorescence yield of the fully protonated form must be correlated to the presence of a very fast decaying species. In alkaline aqueous solution, the fluorescence of the dianion (tc2-) essentially comprises two components; the decay time of the stronger, shorter-lived component is about 30 ps, that of the weaker, longer-lived one about 160 ps. The relative amplitude of the latter is larger at pH 11 than at pH 8.5, in accordance with the increase in the steady-state fluorescence intensity upon increasing the pH from 8.5 to 11. Complexation of the dianion with divalent metal ions like Mg2+ or Ca2+ leads to a strong enhancement of the steady-state fluorescence. In the time-resolved spectra, the decay time of the major fluorescence component exhibits approximately a five-fold increase in comparison to the major component of the dianion. It is about 150 ps in both types of complexes. The decay times of the minor component are increased to about 500 (Mg2+) and 320 ps (Ca2+). The absence of the ultra-fast component in the fluorescence of the dianion and its metal complexes provides evidence that a reaction of OH 12 must be responsible for the ultra-fast fluorescence component in tcH3+. The existence of a component with a lifetime of several tens of picoseconds in all samples suggests the involvement of hydrogen bonding at OH10 during the formation of the emitting species. DFT calculations for the isolated molecule provide evidence that ESIPT is indeed an energetically allowed relaxation process for those isomers that have only one intramolecular hydrogen bond to O11. The ESIPT process yields primary photoproducts that should emit at much longer wavelengths, thereby explaining the unusually large fluorescence Stokes shift.

Anti-Bacterial Agents↗
PubMed2002

Theoretical study of the Fe(phen)(2)(NCS)(2) spin-crossover complex with reparametrized density functionals.

The theoretical study of spin-crossover compounds is very challenging as those parts of the experimental findings that concern the electronic structure of these compounds can currently hardly be reproduced because of either technical limitations of highly accurate ab initio methods or because of inaccuracies of density functional methods in the prediction of low-spin/high-spin energy splitting. However, calculations with reparametrized density functionals on molecules of the thermal spin-crossover type can give improved results when compared with experiment for close-lying states of different spin and are therefore important for, e.g., transition metal catalysis. A classification of transition metal compounds within hybrid density functional theory is given to distinguish standard, critical, and complicated cases. From the class of complicated cases we choose the prominent spin-crossover compound Fe(phen)(2)(NCS)(2) and show in a first step how the electronic contribution to the energy splitting can be calculated. In a second step, the vibrational effects on the spin flip are investigated within the harmonic force-field approximation of the isolated-molecule approach. A main result of the study is the necessity of exact-exchange reduction in hybrid density functionals to arrive at reasonable electronic energy splittings. The study resolves problems that originated from the use of standard density functionals, which are not able to reproduce the electronic contribution to the low-spin/high-spin splitting correctly, and demonstrates to which extent reparametrized density functionals can be used for the prediction of the spin-crossover effect.

Journal Article↗
PubMed2002

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.

Catalysis↗
PubMed2002

The gas-phase route from Cp*2P6 to neutral hexaphosphorus.

Density functional theory has been applied to gain insight into the fragmentation and redox behavior of CpnP6+/0 and Cp*nP6+/0 cations and neutral species (n = 1, 2) in the gas phase. Particular attention is paid to the previously reported generation of neutral hexaphosphorus upon high-energy collisions of the Cp*P6+ cation. Theory provides an explanation for the experimentally observed effect that collisional electron transfer to the Cp*P6+ cation is negligible in that the associated Franck-Condon factors are predicted to be unfavorable. In contrast, dissociation of Cp*P6+ into Cp*(+) + P6 has a relatively low energy demand, thereby accounting for the efficient formation of neutral P6 in the gas phase. Theoretical exploration of the parent compound Cp2P6 reveals that the unsubstituted cyclopentadienyl ligand is much less suitable in this respect, thereby sustaining the previous suggestion that Cp* is a particularly good leaving group.

Journal Article↗