We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge-resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.

For the investigation of molecular systems with electronic ground states exhibiting multi-reference character, a spin-flip (SF) version of the algebraic diagrammatic construction (ADC) scheme for the polarization propagator up to third order perturbation theory (SF-ADC(3)) is derived via the intermediate state representation and implemented into our existing ADC computer program adcman. The accuracy of these new SF-ADC(n) approaches is tested on typical situations, in which the ground state acquires multi-reference character, like bond breaking of H2 and HF, the torsional motion of ethylene, and the excited states of rectangular and square-planar cyclobutadiene. Overall, the results of SF-ADC(n) reveal an accurate description of these systems in comparison with standard multi-reference methods. Thus, the spin-flip versions of ADC are easy-to-use methods for the calculation of “few-reference” systems, which possess a stable single-reference triplet ground state.

The extended second order algebraic-diagrammatic construction (ADC(2)-x) scheme for the polarization operator in combination with core-valence separation (CVS) approximation is well known to be a powerful quantum chemical method for the calculation of core-excited states and the description of X-ray absorption spectra. For the first time, the implementation and results of the third order approach CVS-ADC(3) are reported. Therefore, the CVS approximation has been applied to the ADC(3) working equations and the resulting terms have been implemented efficiently in the adcman program. By treating the α and β spins separately from each other, the unrestricted variant CVS-UADC(3) for the treatment of open-shell systems has been implemented as well. The performance and accuracy of the CVS-ADC(3) method are demonstrated with respect to a set of small and middle-sized organic molecules. Therefore, the results obtained at the CVS-ADC(3) level are compared with CVS-ADC(2)-x values as well as experimental data by calculating complete basis set limits. The influence of basis sets is further investigated by employing a large set of different basis sets. Besides the accuracy of core-excitation energies and oscillator strengths, the importance of cartesian basis functions and the treatment of orbital relaxation effects are analyzed in this work as well as computational timings. It turns out that at the CVS-ADC(3) level, the results are not further improved compared to CVS-ADC(2)-x and experimental data, because the fortuitous error compensation inherent in the CVS-ADC(2)-x approach is broken. While CVS-ADC(3) overestimates the core excitation energies on average by 0.61% ± 0.31%, CVS-ADC(2)-x provides an averaged underestimation of -0.22% ± 0.12%. Eventually, the best agreement with experiments can be achieved using the CVS-ADC(2)-x method in combination with a diffuse cartesian basis set at least at the triple-ζ level.

The photoabsorption spectra of C4H4O and C4D4O have been measured between ∼5.5 and 17.7 eV using a synchrotron radiation-based Fourier transform spectrometer. In addition to several broad bands due to transitions into valence states, the spectra exhibit numerous sharp bands associated with Rydberg states belonging to series converging onto the X̃2A2 or the Ã2B1 state limits. Vertical excitation energies and oscillator strengths have been computed using the second- and third-order algebraic-diagrammic construction polarisation propagator methods (ADC(2) and ADC(3)), and the equation-of-motion coupled-cluster method at the level of singles and doubles model (EOM-CCSD). Adiabatic excitation energies have been estimated using previously computed corrections. The theoretical predictions have allowed assignments to be proposed for the Rydberg series observed in the present single-photon absorption spectra and for some additional series, mainly of A2 symmetry, reported in previous multiphoton excitation studies. The assignments of some of the Rydberg series converging onto the Ã2B1 state limit have been revised and, guided by our calculations, the principal series is ascribed to the 2b1 → nda2 1B2 and 2b1 → ndb1 1A1 transitions. f-type Rydberg series, previously observed only in the multiphoton absorption spectrum of furan, have been observed and assigned. Such f-type series, converging onto either the X̃2A2 or the Ã2B1 state thresholds, contribute significantly to the single-photon absorption spectrum. Many of the absorption bands associated with Rydberg states display vibrational progressions which resemble those in the corresponding photoelectron band. It appears that some of the structure associated with the 1a2 → 3pb2 1B1 and 1a2 → 3pb1 1B2 transitions involves excitation of non-totally symmetric vibrational modes.

The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of excited states based on perturbation theory. In recent years, the second‐order ADC(2) scheme has attracted attention in the computational chemistry community because of its reliable accuracy and reasonable computational effort in the calculation of predominantly singly excited states. Owing to their size‐consistency, ADC methods are suited for the investigation of large molecules. In addition, their Hermitian structure and the availability of the intermediate state representation (ISR) allow for straightforward computation of excited‐state properties. Recently, an efficient implementation of ADC(3) has been reported, and its high accuracy for typical valence excited states of organic chromophores has been demonstrated. In this review, the origin of ADC‐based excited‐state methods in propagator theory is described, and an intuitive route for the derivation of algebraic expressions via the ISR is outlined and comparison to other excited‐state methods is made. Existing computer codes and implemented ADC variants are reviewed, but most importantly the accuracy and limits of different ADC schemes are critically examined. WIREs Comput Mol Sci 2015, 5:82–95. doi: 10.1002/wcms.1206This article is categorized under: Structure and Mechanism > Molecular Structures Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy

We report the implementation and evaluation of a perturbative, density-based correction scheme for vertical excitation energies calculated in the framework of a polarizable continuum model (PCM). Because the proposed first-order correction terms depend solely on the zeroth-order excited-state density, a transfer of the approach to any configuration interaction-type excited-state method is straightforward. Employing the algebraic-diagrammatic construction (ADC) scheme of up to third order as well as time-dependent density-functional theory (TD-DFT), we demonstrate and evaluate the approach. For this purpose, we assembled a set of experimental benchmark data for solvatochromism in molecules (xBDSM) containing 44 gas-phase to solvent shifts for 17 molecules. These data are compared to solvent shifts calculated at the ADC(1), ADC(2), ADC(3/2), and TD-DFT/LRC-ωPBE levels of theory in combination with state-specific as well as linear-response type PCM-based correction schemes. Some unexpected trends and differences between TD-DFT, the levels of ADC, and variants of the PCM are observed and discussed. The most accurate combinations reproduce experimental solvent shifts resulting from the bulk electrostatic interaction with maximum errors in the order of 50 meV and a mean absolute deviation of 20-30 meV for the xBDSM set.

The valence-shell ionization spectrum of bromobenzene, as a representative halogen substituted aromatic, was studied using the non-Dyson third-order algebraic-diagrammatic construction [nD-ADC(3)] approximation for the electron propagator. This method, also referred to as IP-ADC(3), was implemented as a part of the Q-Chem program and enables large-scale calculations of the ionization spectra, where the computational effort scales as n(5) with respect to the number of molecular orbitals n. The IP-ADC(3) scheme is ideally suited for investigating low-lying ionization transitions, so fresh insight could be gained into the cationic state manifold of bromobenzene. In particular, the present IP-ADC(3) calculations with the cc-pVTZ basis reveal a whole class of low-lying low-intensity two-hole-one-particle (2h-1p) doublet and quartet states, which are relevant to various photoionization processes. The good qualitative agreement between the theoretical spectral profile for the valence-shell ionization transitions generated with the smaller cc-pVDZ basis set and the experimental photoelectron spectrum measured at a photon energy of 80 eV on the PLÉIADES beamline at the Soleil synchrotron radiation source allowed all the main features to be assigned. Some theoretical aspects of the ionization energy calculations concerning the use of various approximation schemes and basis sets are discussed.

We report a sixth-order ab initio virial equation of state (EOS) for mercury. The virial coefficients were determined in the temperature range from 500 to 7750 K using a three-body approximation to the N-body interaction potential. The underlying two-body and three-body potentials were fitted to highly accurate Coupled-Cluster interaction energies of Hg-2 (Pahl, E.; Figgen, D.; Thierfelder, C.; Peterson, K. A.; Calvo, F.; Schwerdtfeger, P. J. Chem. Phys. 2010, 132, 114301-1) and equilateral-triangular configurations of Hg-3. We find the virial coefficients of order four and higher to be negative and to have large absolute values over the entire temperature range considered. The validity of our three-body, sixth-order EOS seems to be limited to small densities of about 1.5 g cm(-3) and somewhat higher densities at higher temperatures. Termwise analysis and comparison to experimental gas-phase data suggest a small convergence radius of the virial EOS itself as well as a failure of the three-body interaction model (i.e., poor convergence of the many-body expansion for mercury). We conjecture that the nth-order term of the virial EOS is to be evaluated from the full n-body interaction potential for a quantitative picture. Consequently, an ab initio three-body virial equation cannot describe the mercury gas phase.

The development of reliable theoretical methods and the provision of efficient computer programs for the investigation of optical spectra and photochemistry of large molecules in general is one of the most important tasks of contemporary theoretical chemistry. Here, we present an overview of the current features of our implementation of the algebraic diagrammatic construction scheme of the polarisation propagator, which is a versatile and robust approach for the theoretical investigation of excited states and their properties.

X-ray absorption spectroscopy (XAS) is a powerful tool that provides information about the electronic structure of molecules via excitation of electrons from the K-shell core region to the unoccupied molecular levels. These high-lying electronic core-excited states can be accurately calculated using the algebraic-diagrammatic construction scheme of second order ADC(2) by applying the core-valence separation (CVS) approximation to the ADC(2) working equations. For the first time, an efficient implementation of an unrestricted CVS-ADC(2) variant CVS-UADC(2) is presented for the calculation of open-shell molecules by treating α and β spins separately from each other. The potential of the CVS-UADC(2) method is demonstrated with a set of small organic radicals by comparison with standard TD-DFT/B3LYP values and experimental data. It turns out that the extended variant CVS-UADC(2)-x, in particular, provides the most accurate results with errors of only 0.1% compared to experimental values. This remarkable agreement justifies the prediction of yet nonrecorded experimental XAS spectra like the one of the anthracene cation. The cation exhibits additional peaks due to the half-filled single-occupied molecular orbital, which may help to distinguish cation from the neutral species.

The excited states of a diverse set of molecules are examined using a collection of newly implemented analysis methods. These examples expose the particular power of three of these tools: (i) natural difference orbitals (the eigenvectors of the difference density matrix) for the description of orbital relaxation effects, (ii) analysis of the one-electron transition density matrix in terms of an electron-hole picture to identify charge resonance and excitonic correlation effects, and (iii) state-averaged natural transition orbitals for a compact simultaneous representation of several states. Furthermore, the utility of a wide array of additional analysis methods is highlighted. Five molecules with diverse excited state characteristics are chosen for these tasks: pyridine as a prototypical small heteroaromatic molecule, a model system of six neon atoms to study charge resonance effects, hexatriene in its neutral and radical cation forms to exemplify the cases of double excitations and spin-polarization, respectively, and a model iridium complex as a representative metal organic compound. Using these examples a number of phenomena, which are at first sight unexpected, are highlighted and their physical significance is discussed. Moreover, the generality of the conclusions of this paper is verified by a comparison of single- and multireference ab initio methods.

Exciton sizes and electron-hole binding energies, which are central properties of excited states in extended systems and crucial to the design of modern electronic devices, are readily defined within a quasiparticle framework but are quite challenging to understand in the molecular-orbital picture. The intent of this work is to bridge this gap by providing a general way of extracting the exciton wave function out of a many-body wave function obtained by a quantum chemical excited-state computation. This methodology, which is based on the one-particle transition density matrix, is implemented within the ab initio algebraic diagrammatic construction scheme for the polarization propagator and specifically the evaluation of exciton sizes, i.e., dynamic charge separation distances, is considered. A number of examples are presented. For stacked dimers it is shown that the exciton size for charge separated states corresponds to the intermolecular separation, while it only depends on the monomer size for locally excited states or Frenkel excitons. In the case of conjugated organic polymers, the tool is applied to analyze exciton structure and dynamic charge separation. Furthermore, it is discussed how the methodology may be used for the construction of a charge-transfer diagnostic for time-dependent density-functional theory.

A variety of density matrix based methods for the analysis and visualization of electronic excitations are discussed and their implementation within the framework of the algebraic diagrammatic construction of the polarization propagator is reported. Their mathematical expressions are given and an extensive phenomenological discussion is provided to aid the interpretation of the results. Starting from several standard procedures, e.g., population analysis, natural orbital decomposition, and density plotting, we proceed to more advanced concepts of natural transition orbitals and attachment/detachment densities. In addition, special focus is laid on information coded in the transition density matrix and its phenomenological analysis in terms of an electron-hole picture. Taking advantage of both the orbital and real space representations of the density matrices, the physical information in these analysis methods is outlined, and similarities and differences between the approaches are highlighted. Moreover, new analysis tools for excited states are introduced including state averaged natural transition orbitals, which give a compact description of a number of states simultaneously, and natural difference orbitals (defined as the eigenvectors of the difference density matrix), which reveal details about orbital relaxation effects.

The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 ± 0.28 eV for singlet states and -0.18 ± 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 ± 0.38 eV and -0.70 ± 0.37 eV for singlets and 0.12 ± 0.16 eV and -0.55 ± 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 ± 0.21 eV and ADC(3) an accuracy of 0.08 ± 0.27 eV, and accordingly for the triplet states of 0.12 ± 0.10 eV and -0.10 ± 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N(6)) with system size.

The effects of parity violation (PV) on the vibrational transitions of chiral uranium compounds of the type N≡UXYZ and N≡UHXY (X, Y, Z = F, Cl, Br, I) are analysed by means of exact two-component relativistic (X2C) Hartree-Fock and density functional calculations using NUFClI and NUHFI as representative examples. The PV contributions to the vibrational transitions were found to be in the Hz range, larger than for any of the earlier proposed chiral molecules. Thus, these systems are very promising candidates for future experimental PV measurements. A detailed comparison of the N≡UHFI and the N≡WHFI homologues reveals that subtle electronic structure effects, rather than exclusively a simple Z(5) scaling law, are the cause of the strong enhancement in PV contributions of the chiral uranium molecules.

This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide-and-conquer-type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q-Chem electronic structure software uses this library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic construction methods.

Die allgemeine Relativitätstheorie lieferte die richtige Erklärung für die Präzession des Merkur-Perihels. Wie F. Calvo, P. Schwerdtfeger et al. in der Zuschrift auf S. 7731 ff. demonstrieren, liefert die spezielle Relativitätstheorie ein sogar noch bemerkenswerteres Resultat, nämlich die richtige Erklärung dafür, dass Quecksilber (Mercurium) das einzige bei Raumtemperatur flüssige Metall ist, wie Monte-Carlo-Simulationen belegen (Bild: Cameron Smorenburg). Die allgemeine Relativitätstheorie lieferte die richtige Erklärung für die Präzession des Merkur-Perihels. Wie F. Calvo, P. Schwerdtfeger et al. in der Zuschrift auf S. 7731 ff. demonstrieren, liefert die spezielle Relativitätstheorie ein sogar noch bemerkenswerteres Resultat, nämlich die richtige Erklärung dafür, dass Quecksilber (Mercurium) das einzige bei Raumtemperatur flüssige Metall ist, wie Monte-Carlo-Simulationen belegen (Bild: Cameron Smorenburg). Selbstorganisation auf Oberflächen Supramolekulare Borazinstrukturen wurden auf einer Metalloberfläche aufgebaut. A. De Vita, G. Costantini, D. Bonifazi et al. zeigen in der Zuschrift auf S. 7558 ff., dass diese Strukturen aus einem Wechselspiel von Van-der-Waals-Anziehung und Coulomb-Abstoßung resultieren.1 Mikrofluidiksysteme In der Zuschrift auf S. 7712 ff. berichten D.-P. Kim et al. über die Entwicklung eines automatisierten, kontinuierlich arbeitenden Mikrofluidiksystems, das Produkte durch serielle Synthese, Reinigung und In-situ-Verbrauch der Isocyanide ergibt.1 Katalytische Olefinhydrierung Der Schlüsselschritt der von Z. H. Li, H. Wang et al. in der Zuschrift auf S. 7644 ff. beschriebenen metallfreien Hydrierung von Olefinen mit dem Katalysator HB(C6F5)2 ist eine Boran-vermittelte σ-Bindungsmetathese über einen viergliedrigen cyclischen Übergangszustand.1