The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Core Ionization Initiates Subfemtosecond Charge Migration in the Valence Shell of Molecules.

After the ionization of a valence electron, the created hole can migrate ultrafast from one end of the molecule to another. Because of the advent of attosecond pulse techniques, the measuring and understanding of charge migration has become a central topic in attosecond science. Here, we pose the hitherto unconsidered question whether ionizing a core electron will also lead to charge migration. It is found that the created hole in the core stays put, but in response to this hole interesting electron dynamics takes place which can lead to intense charge migration in the valence shell. This migration is typically faster than that after the ionization of a valence electron and transpires on a shorter time scale than the natural decay of the core hole by the Auger process, making the subject very challenging to attosecond science.

Relativistic decay widths of autoionization processes: the relativistic FanoADC-Stieltjes method.

Electronic decay processes of ionized systems are, for example, the Auger decay or the Interatomic/ Intermolecular Coulombic Decay. In both processes, an energetically low lying vacancy is filled by an electron of an energetically higher lying orbital and a secondary electron is instantaneously emitted to the continuum. Whether or not such a process occurs depends both on the energetic accessibility and the corresponding lifetime compared to the lifetime of competing decay mechanisms. We present a realization of the non-relativistically established FanoADC-Stieltjes method for the description of autoionization decay widths including relativistic effects. This procedure, being based on the Algebraic Diagrammatic Construction (ADC), was adapted to the relativistic framework and implemented into the relativistic quantum chemistry program package Dirac. It is, in contrast to other existing relativistic atomic codes, not limited to the description of autoionization lifetimes in spherically symmetric systems, but is instead also applicable to molecules and clusters. We employ this method to the Auger processes following the Kr3d(-1), Xe4d(-1), and Rn5d(-1) ionization. Based on the results, we show a pronounced influence of mainly scalar-relativistic effects on the decay widths of autoionization processes.

The relativistic polarization propagator for the calculation of electronic excitations in heavy systems.

In this work, we present a new four-component implementation of the polarization propagator for accurate calculations of excited states in heavy systems. Differences to existing nonrelativistic realizations are detailed and the energetically lowest final states of the ns(2)np(6) → ns(2)np(5)(n + 1)s(1) and ns(2)np(6) → ns(2)np(5)(n + 1)p(1) transitions in noble gases are calculated and compared with experimental data. Already for the light atoms Ne and Ar spin-orbit coupling leads to noticeable zero field splitting that gradually increases in the heavier homologues and eventually invalidates the LS-based description of singlet and triplet excited states. For all four noble gases Ne through Xe, we observe a very good agreement with experimental transition energies in the considered energetic range where the extended version of the propagator implementation in general yields better excitation energy differences than the strict variant. In the extended version, off-diagonal first-order contributions in the two-particle-two-hole block are included that are not present in the strict variant. In case of Kr and Xe, nonrelativistic approaches already exhibit unacceptable deviations in the reproduction of transition energies and the spectral structure. The obtained excited final states are analyzed in terms of atomic contributions to the donor and acceptor orbitals constituting the corresponding wave functions. The relativistic polarization propagator provides a consistent description of electron correlation and relativistic effects especially relevant for the heavier systems where these two contributions are no longer separable.

Communication: electron transfer mediated decay enabled by spin-orbit interaction in small krypton/xenon clusters.

In this work we study the influence of relativistic effects, in particular spin-orbit coupling, on electronic decay processes in KrXe2 clusters of various geometries. For the first time it is shown that inclusion of spin-orbit coupling has decisive influence on the accessibility of a specific decay pathway in these clusters. The radiationless relaxation process is initiated by a Kr 4s ionization followed by an electron transfer from xenon to krypton and a final second ionization of the system. We demonstrate the existence of competing electronic decay pathways depending in a subtle way on the geometry and level of theory. For our calculations a fully relativistic framework was employed where omission of spin-orbit coupling leads to closing of two decay pathways. These findings stress the relevance of an adequate relativistic description for clusters with heavy elements and their fragmentation dynamics.

Plasmons in molecules: microscopic characterization based on orbital transitions and momentum conservation.

In solid state physics, electronic excitations are often classified as plasmons or single-particle excitations. The former class of states refers to collective oscillations of the electron density. The random-phase approximation allows for a quantum-theoretical treatment and a characterization on a microscopic level as a coherent superposition of a large number of particle-hole transitions with the same momentum transfer. However, small systems such as molecules or small nanoclusters lack the basic properties (momentum conservation and uniform exchange interaction) responsible for the formation of plasmons in the solid-state case. Despite an enhanced interest in plasmon-based technologies and an increasing number of studies regarding plasmons in molecules and small nanoclusters, their definition on a microscopic level of theory remains ambiguous. In this work, we analyze the microscopic properties of molecular plasmons in comparison with the homogeneous electron gas as a model system. Subsequently, the applicability of the derived characteristics is validated by analyzing the electronic excitation vectors with respect to orbital transitions for two linear polyenes within second order versions of the algebraic diagrammatic construction scheme for the polarization propagator.

A theoretical DFT-based and experimental study of the transmetalation step in Au/Pd-mediated cross-coupling reactions.

In this work a combined theoretical and experimental investigation of the cross-coupling reaction involving two metallic reaction centers, namely gold and palladium, is described. One metal center (Au) hereby is rather inert towards change in its oxidation state, whereas Pd undergoes oxidative insertion and reductive elimination steps. Detailed mechanistic and energetic studies of each individual step, with the focus on the key transmetalation step are presented and compared for different substrates and ligands on the catalytic Pd center. Different aryl halides (Cl, Br, I) and aryl triflates were investigated. Hereby the nature of the counteranion X turned out to be crucial. In the case of X=Cl and L=PMe3 the oxidative addition is rate-determining, whereas in the case of X=I the transmetalation step becomes rate-determining in the Au/Pd-cross-coupling mechanism. A variety of Au-Pd transmetalation reaction scenarios are discussed in detail, favoring a transition state with short intermetallic Au-Pd contacts. Furthermore, without a halide counteranion the transmetalation from gold(I) to palladium(II) is highly endothermic, which confirms our experimental findings that the coupling does not occur with aryl triflates and similar weakly coordinating counteranions--a conclusion that is essential in designing new Au-Pd catalytic cycles. In combination with experimental work, this corrects a previous report in the literature claiming a successful coupling potentially catalytic in both metals with weakly coordinating counteranions.

Are ß-H eliminations or alkene insertions feasible elementary steps in catalytic cycles involving gold(I) alkyl species or gold(I) hydrides?

The ß-H-elimination in the (iPr)AuEt complex and its microscopic reverse, the insertion of ethene into (iPr)AuH, were investigated in a combined experimental and computational study. Our DFT-D3 calculations predict free-energy barriers of 49.7 and 36.4 kcal mol(-1) for the elimination and insertion process, respectively, which permit an estimation of the rate constants for these reactions according to classical transition-state theory. The elimination/insertion pathway is found to involve a high-energy ethene hydride species and is not significantly affected by continuum solvent effects. The high barriers found in the theoretical study were then confirmed experimentally by measuring decomposition temperatures for several different (iPr)Au(I) -alkyl complexes which, with a slow decomposition at 180 °C, are significantly higher than those of other transition-metal alkyl complexes. In addition, at the same temperature, the decomposition of (iPr)AuPh and (iPr)AuMe, both of which cannot undergo ß-H-elimination, indicates that the pathway for the observed decomposition at 180 °C is not a ß-H-elimination. According to the calculations, the latter should not occur at temperatures below 200 °C. The microscopic reverse of the ß-H-elimination, the insertion of ethene into the (iPr)AuH could neither be observed at pressures up to 8 bar at RT nor at 1 bar at 80 °C. The same is true for the strain-activated norbornene.

Ultrafast branching in the excited state of coumarin and umbelliferone.

In the present work we have explored the ultrafast relaxation network of coumarin and umbelliferone (7-hydroxy-coumarin) using time-resolved femtosecond spectroscopy and quantum chemical calculations. Despite the importance of the photophysical properties of coumarin derivatives for applications in biomedicine, the low fluorescence quantum yield of coumarin itself has not been fully understood so far. On the basis of our combined experimental and theoretical results we suggest a model for the ultrafast decay after photoexcitation incorporating two parallel radiationless relaxation pathways: one within the initially excited state via ring opening and the other one by transition into a dark state along the carbonyl stretching mode. The fluorescence quantum yield is determined by the position of the branching point relative to the Franck-Condon region which is strongly influenced by interactions with the environment and the substitution pattern. This model is finally capable of giving a comprehensive account of the striking differences observed in the photophysical behavior of coumarin as opposed to umbelliferone.

Interatomic decay of inner-valence ionized states in ArXe clusters: relativistic approach.

In this work we investigate interatomic electronic decay processes taking place in mixed argon-xenon clusters upon the inner-valence ionization of an argon center. We demonstrate that both interatomic Coulombic decay and electron-transfer mediated decay (ETMD) are important in larger rare gas clusters as opposed to dimers. Calculated secondary electron spectra are shown to depend strongly on the spin-orbit coupling in the final states of the decay as well as the presence of polarizable environment. It follows from our calculations that ETMD is a pure interface process taking place between the argon-xenon layers. The interplay of all these effects is investigated in order to arrive at a suitable physical model for the decay of inner-valence vacancies taking place in mixed ArXe clusters.

Electronic structure and UV spectrum of hexachloroplatinate dianions in vacuo.

We present a joint experimental and theoretical study of the electronic spectrum of hexachloroplatinate dianion. We have measured electronic photodissociation and photodetachment spectra of mass-selected PtCl6(2-) ions in vacuo and compare these with calculated band positions from time-dependent density functional theory and from relativistic calculations. Excitation of an electronic transition of the dianion leads to resonant enhancement of the photodetachment cross section superimposed on direct detachment. Photoexcitation results in loss of Cl(-) and Cl(0), depending on photon energy. The photofragmentation spectrum for formation of the PtCl4(-) fragment ion mirrors the UV∕vis absorption spectrum of PtCl6(2-) in solution with a small solvatochromic shift.

Application of the scaled-opposite-spin approximation to algebraic diagrammatic construction schemes of second order.

With the concept of scaled-opposite-spin (SOS), a pragmatic semi-empirical approximation has been introduced to the extended algebraic diagrammatic construction scheme of second order (ADC(2)-x) that leads to a significant saving in computational effort. The parameters included were fitted with respect to a benchmark set of electronically excited states in standard organic molecules that include some doubly-excited states, as well. Like the original, unscaled ADC(2)-x scheme it can be used to identify electronically excited states with high double excitation character, however at reduced computational cost. At the same time, it is possible to reduce the overestimation of doubly-excited configurations that is inherent to ADC(2)-x. Additionally, a scheme for the strict variant (ADC(2)-s) was derived directly from SOS-MP2 by application of the intermediate state formalism and compared to an existing version of SOS-ADC(2)-s.

Gold catalysis: 1,3-oxazines by cyclisation of allene amides.

A series of allene amides was prepared and their gold-catalysed cyclisation was investigated. The formation of six-membered rings, 1,3-oxazines, was observed. Dihydropyrroles originating from intramolecular hydroamination of the distal C=C double bonds of the allenes were minor side products. Mechanistic studies by in situ (31)P NMR spectroscopy showed only one additional species during the conversion in each case; a computational study of the different allyl gold(I) species involved allowed this to be assigned as the σ-allyl gold species bearing the gold catalyst at the sterically less hindered methylene end. The regiospecific deuterodeauration of this intermediate confirmed a S(E) '-type mechanism for this last step of the catalytic cycle.

Possible electronic decay channels in the ionization spectra of small clusters composed of Ar and Xe: A four-component relativistic treatment.

Electronic decay of the inner-valence Ar 3s(-1) vacancy is energetically forbidden in an isolated argon atom and in all rare gas dimers where argon is present. However, if an argon atom has at least two suitable rare gas atoms in its neighborhood, the Ar 3s(-1) vacancy may decay electronically via an electron transfer mediated decay (ETMD) mechanism. An ArXe(2) cluster is considered in the present paper as an example of such systems. The single and double ionization spectra of different ArXe(2) isomers as well as of homonuclear Ar(2) and Xe(2) and heteronuclear ArXe clusters have been calculated by means of propagator methods to reveal possible electronic decay channels. A four-component version of the one-particle propagator utilizing the Dirac-Coulomb Hamiltonian was employed to obtain the single ionization potentials of the clusters studied. Hereby electron correlation, scalar relativistic effects, and spin-orbit couplings are described in a consistent manner. A two-particle propagator in its one-component form, in conjunction with effective core potentials to account consistently for correlation and scalar relativistic effects, was used to calculate the double ionization potentials. ETMD is shown to be the only possible electronic decay process of the Ar 3s(-1) vacancy in the ArXe(2) cluster. In clusters with more Xe atoms, alternative electronic decay mechanisms may appear.

Jahn-Teller distortions in the photodetachment spectrum of PtCl6(2-): a four-component relativistic study.

In this work the mutual influence of Jahn-Teller (JT) and spin-orbit effects on the photoelectron spectrum of PtCl(6)(2-) is analyzed. For this purpose potential energy surfaces of PtCl(6)(-) along the JT active modes are calculated in the four-component Dirac-Coulomb (DC) framework and the possible JT stabilizations are determined. For the relativistic calculation we set out from the one-particle propagator implemented on the basis of the DC Hamiltonian. A correlated four-component approach is favorable for complexes with a strongly relativistic central atom due to the complicated interplay of electron correlation and relativity. PtCl(6)(2-) possesses a long enough lifetime which makes it amenable to precise experimental measurements. In the photoelectron spectrum of PtCl(6)(2-) some peaks could not be unambiguously assigned either originating from a JT splitting or representing individual spin-orbit components. In previously calculated dianionic tetrahalide platinum complexes PtX(4)(2-) (X = F,Cl,Br) it was observed that spin-orbit effects dominate over the d-orbital-induced JT effects. The same trend also persists in the currently studied hexachlorocomplex where sizable platinum-induced spin-orbit splittings give rise to features that supersede any JT structures.

Photodetachment spectra of the PtX(4) (2-) (X=F,Cl,Br) dianions and their Jahn-Teller distortions: A fully relativistic study.

In this work we calculate the photoelectron spectra of the PtX(4) (2-) (X=F,Cl,Br) dianions by application of the third-order Dirac-Hartree-Fock one-particle propagator technique. Relativistic effects and electron correlation are hereby treated on a consistent theoretical basis, which is mandatory for systems containing heavy elements. An experimental PtF(4) (2-) gas phase photoelectron (PE) spectrum is not available and our calculations confirm its instability against autodetachment. For PtCl(4) (2-) potential curves for the two Jahn-Teller (JT), active modes were determined and the influence of spin-orbit splitting on the JT stabilization is discussed. The scalar relativistic and four-component potential energy curves hereby exhibit remarkable differences relevant for the correct interpretation of the spectra. A dissociation channel through the b(2g) vibrational mode was obtained for PtCl(4) (2-) in the (2)E(u) final state. For all species electron correlation strongly decreases the ionization potentials and the inclusion of spin-orbit coupling leads to alterations in the level order, which have to be taken into account for a correct peak assignment. The metal d contribution to the valence orbitals steadily decreases from the PtF(4) (2-) to the PtBr(4) (2-) compound, which rules out a pure metal d-orbital-based interpretation of the valence PE spectrum.

Possible electronic decay channels in the ionization spectra of small clusters composed of Ar and Kr: a four-component relativistic treatment.

In this work single and double ionization spectra of the homo- and heteronuclear argon/krypton dimers and trimers are calculated by means of propagator methods where a four-component implementation was employed for the single ionizations. Scalar relativistic effects play only a minor role for the outer valence spectral structure, whereas spin-orbit coupling and electron correlation have to be treated adequately in order to reproduce the features correctly. Nonradiative decay mechanisms of subvalence vacancies in the argon and krypton dimers and trimers are discussed both for the interatomic Coulombic decay and the electron transfer mediated decay (ETMD). In the heteronuclear triatomic system which serves as a model for larger clusters, a possible ETMD process of the Ar 3s vacancy is found for the linear arrangement of the atoms. In the bent configuration the ETMD channel is closed.

Four-Component Polarization Propagator Calculations of Electron Excitations: Spectroscopic Implications of Spin-Orbit Coupling Effects.

A complete implementation of the polarization propagator based on the Dirac-Coulomb Hamiltonian is presented and applied to excitation spectra of various systems. Hereby the effect of spin-orbit coupling on excitation energies and transition moments is investigated in detail. The individual perturbational contributions to the transition moments could now be separately analyzed for the first time and show the relevance of one- and two-particle terms. In some systems different contributions to the transition moments partially cancel each other and do not allow for simple predictions. For the outer valence spectrum of the H2Os(CO)4 complex a detailed final state analysis is performed explaining the sensitivity of the excitation spectrum to spin-orbit effects. Finally, technical issues of handling double group symmetry in the relativistic framework and methodological aspects of our parallel implementation are discussed.

Ensemble and single-molecule studies on fluorescence quenching in transition metal bipyridine-complexes.

Beyond their use in analytical chemistry fluorescent probes continuously gain importance because of recent applications of single-molecule fluorescence spectroscopy to monitor elementary reaction steps. In this context, we characterized quenching of a fluorescent probe by different metal ions with fluorescence spectroscopy in the bulk and at the single-molecule level. We apply a quantitative model to explain deviations from existing standard models for fluorescence quenching. The model is based on a reversible transition from a bright to a dim state upon binding of the metal ion. We use the model to estimate the stability constants of complexes with different metal ions and the change of the relative quantum yield of different reporter dye labels. We found ensemble data to agree widely with results from single-molecule experiments. Our data indicates a mechanism involving close molecular contact of dye and quenching moiety which we also found in molecular dynamics simulations. We close the manuscript with a discussion of possible mechanisms based on Förster distances and electrochemical potentials which renders photo-induced electron transfer to be more likely than Förster resonance energy transfer.

Theoretical insights into the superior activity of gold catalysts and reactions of organogold intermediates with electrophiles.

Three fundamental steps of homogeneous gold catalysis, the activiation of substrates by coordination to gold, the protodeauration after the nucleophilic addition and the transmetalation to palladium in palladium-catalysed C-C bond forming reactions using organogold intermediates have been studied and discussed in detail.