Dr. Florian Bischoff

Profil

• DFG-Sachbeihilfe: Hochgenaue Berechnung molekularer Eigenschaften mit Hilfe der Multi-Resolutions-Analyse

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 03/2014 - 01/2020 Projektleitung: Dr. Florian Bischoff

• SFB 1109/1: Quantenchemische Studien an mikrohydratisierten Gasphasen-Metalloxidclustern (TP D02)

  Quelle ↗

  Förderer: DFG Sonderforschungsbereich Zeitraum: 04/2014 - 12/2017 Projektleitung: Dr. Florian Bischoff

• VA: KOSMOS-Workshop für numerische Methoden in der Quantenchemie

  Quelle ↗

  Förderer: DFG sonstige Programme Zeitraum: 01/2018 - 08/2018 Projektleitung: Dr. Florian Bischoff

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• Explicitly Correlated R12/F12 Methods for Electronic Structure

  2011

  Chemical Reviews · 514 Zitationen · DOI

  ADVERTISEMENT RETURN TO ISSUEPREVReviewNEXTExplicitly Correlated R12/F12 Methods for Electronic StructureLiguo Kong, Florian A. Bischoff, and Edward F. Valeev*View Author Information Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States*E-mail: [email protected]Cite this: Chem. Rev. 2012, 112, 1, 75–107Publication Date (Web):December 16, 2011Publication History Received6 June 2011Published online16 December 2011Published inissue 11 January 2012https://pubs.acs.org/doi/10.1021/cr200204rhttps://doi.org/10.1021/cr200204rreview-articleACS PublicationsCopyright © 2011 American Chemical SocietyRequest reuse permissionsArticle Views6763Altmetric-Citations410LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Approximation,Basis sets,Energy,Mathematical methods,Wave function Get e-Alerts

• The MP2‐F12 method in the T<scp>URBOMOLE</scp> program package

  2011

  Journal of Computational Chemistry · 115 Zitationen · DOI

  A detailed description of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method, as implemented in the TURBOMOLE program package, is presented. The TURBOMOLE implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open- and closed-shell species, using unrestricted as well as restricted (open-shell) Hartree-Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the TURBOMOLE implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H-ZSM-5. Various basis sets are used, including the correlation-consistent basis sets specially optimized for explicitly correlated calculations (cc-pVXZ-F12).

• Atomization energies from coupled-cluster calculations augmented with explicitly-correlated perturbation theory

  2008

  Chemical Physics · 101 Zitationen · DOI

• Assessment of basis sets for F12 explicitly-correlated molecular electronic-structure methods

  2009

  Molecular Physics · 86 Zitationen · DOI

  One-electron basis sets for F12 explicitly-correlated molecular electronic-structure methods are assessed by analysing the accuracy of Hartree–Fock energies and valence-only second-order correlation energies of a test set of 106 small molecules containing the atoms H, C, N, O and F. For these molecules, near Hartree–Fock-limit energies and benchmark second-order correlation energies (accurate to within 99.95% of the basis-set limit) are provided. Absolute energies are analysed as well as the Hartree–Fock and second-order correlation contributions to the atomisation energies of the molecules. Standard basis sets such as the Karlsruhe def2-TZVPP and def2-QZVPP sets and the augmented correlation-consistent polarised valence X-tuple zeta (aug-cc-p VXZ, X = D, T, Q, 5) sets are compared with the specialised cc-pVXZ-F12 (X = D, T, Q) sets that were recently optimised by Peterson and co-workers [J. Chem. Phys. 128, 084102 (2008)] for use in F12 theory. The results obtained from F12 explicitly-correlated molecular electronic-structure calculations are compared with those that are obtained by standard electronic-structure calculations followed by basis-set extrapolation based on the X −3 convergence behaviour of the aug-cc-pVXZ basis sets. The most important conclusions are that the cc-pVXZ-F12 sets are the preferred basis sets for F12 theory and that the X −3 extrapolation from the aug-cc-pVQZ and aug-cc-pV5Z is slightly more accurate than F12 theory in the cc-pVTZ-F12 basis but less accurate than F12 theory in the cc-pVQZ-F12 basis.

• Scope and limitations of the SCS-MP2 method for stacking and hydrogen bonding interactions

  2008

  Physical Chemistry Chemical Physics · 84 Zitationen · DOI

  Fluorobenzenes are pi-acceptor synthons that form pi-stacked structures in molecular crystals as well as in artificial DNAs. We investigate the competition between hydrogen bonding and pi-stacking in dimers consisting of the nucleobase mimic 2-pyridone (2PY) and all fluorobenzenes from 1-fluorobenzene to hexafluorobenzene (n-FB, with n = 1-6). We contrast the results of high level ab initio calculations with those obtained using ultraviolet (UV) and infrared (IR) laser spectroscopy of isolated and supersonically cooled dimers. The 2PY.n-FB complexes with n = 1-5 prefer double hydrogen bonding over pi-stacking, as diagnosed from the UV absorption and IR laser depletion spectra, which both show features characteristic of doubly H-bonded complexes. The 2-pyridone.hexafluorobenzene dimer is the only pi-stacked dimer, exhibiting a homogeneously broadened UV spectrum and no IR bands characteristic for H-bonded species. MP2 (second-order Møller-Plesset perturbation theory) calculations overestimate the pi-stacked dimer binding energies by about 10 kJ/mol and disagree with the experimental observations. In contrast, the MP2 treatment of the H-bonded dimers appears to be quite accurate. Grimme's spin-component-scaled MP2 approach (SCS-MP2) is an improvement over MP2 for the pi-stacked dimers, reducing the binding energy by approximately 10 kJ/mol. When applied to explicitly correlated MP2 theory (SCS-MP2-R12 approach), agreement with the corresponding coupled-cluster binding energies [at the CCSD(T) level] is very good for the pi-stacked dimers, within +/- 1 kJ/mol for the 2PY complexes with 1-fluorobenzene, 1,2-difluorobenzene, 1,2,4,5-tetrafluorobenzene, pentafluorobenzene and hexafluorobenzene. Unfortunately, the SCS-MP2 approach also reduces the binding energy of the H-bonded species, leading to disagreement with both coupled-cluster theory and experiment. The SCS-MP2-R12 binding energies follow the SCS-MP2 binding energies closely, being about 0.5 and 0.7 kJ/mol larger for the H-bonded and pi-stacked forms, respectively, in an augmented correlation-consistent polarized valence quadruple-zeta basis. It seems that the SCS-MP2 and SCS-MP2-R12 methods cannot provide sufficient accuracy to replace the CCSD(T) method for intermolecular interactions where H-bonding and pi-stacking are competitive.

• Low-order tensor approximations for electronic wave functions: Hartree–Fock method with guaranteed precision

  2011

  The Journal of Chemical Physics · 51 Zitationen · DOI

  Here we report a formulation of the Hartree-Fock method in an adaptive multiresolution basis set of spectral element type. A key feature of our approach is the use of low-order tensor approximations for operators and wave functions to reduce the steep rise of storage and computational costs with the number of degrees of freedom that plague finite element computations. As a proof of principle we implemented Hartree-Fock method without explicit storage of the full-dimensional wave function and with guaranteed precision (microhartree precision for up to 14 electron systems is demonstrated). Even for the one-electron method the use of low-order tensor approximation reduces storage relative to the full representation, albeit with modest increase in cost. Preliminary tests for explicitly-correlated two-electron (six-dimensional) wave function suggest a factor of 50 savings in storage. At least correlated two-electron methods should be feasible with our approach on modern workstations with guaranteed precision.

• Computing many-body wave functions with guaranteed precision: The first-order Møller-Plesset wave function for the ground state of helium atom

  2012

  The Journal of Chemical Physics · 43 Zitationen · DOI

  We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

• Dissociative Water Adsorption by Al₃O₄⁺ in the Gas Phase

  2017

  The Journal of Physical Chemistry Letters · 39 Zitationen · DOI

  We use cryogenic ion trap vibrational spectroscopy in combination with density functional theory (DFT) to study the adsorption of up to four water molecules on Al₃O₄⁺. The infrared photodissociation spectra of [Al₃O₄(D₂O)_1-4]⁺ are measured in the O-D stretching (3000-2000 cm^-1) as well as the fingerprint spectral region (1300-400 cm^-1) and are assigned based on a comparison with simulated harmonic infrared spectra for global minimum-energy structures obtained with DFT. We find that dissociative water adsorption is favored in all cases. The unambiguous assignment of the vibrational spectra of these gas phase model systems allows identifying characteristic spectral regions for O-D and O-H stretching modes of terminal (μ₁) and bridging (μ₂) hydroxyl groups in aluminum oxide/water systems, which sheds new light on controversial assignments for solid Al₂O₃ phases.

• Computing molecular correlation energies with guaranteed precision

  2013

  The Journal of Chemical Physics · 39 Zitationen · DOI

  We present an approach to compute accurate correlation energies for atoms and molecules in the framework of multiresolution analysis (MRA), using an adaptive discontinuous multiresolution spectral-element representation for the six-dimensional (two-electron) pair function. The key features of our approach that make it feasible, namely (1) low-rank tensor approximations of functions and operators and (2) analytic elimination of operator singularities via explicit correlation, were retained from the previous work [F. A. Bischoff, R. J. Harrison, and E. F. Valeev, J. Chem. Phys. 137, 104103 (2012)]. Here we generalized the working equations to handle general (non-symmetric) many-electron systems at the MP2 level. The numerical performance is shown for the beryllium atom and the water molecule where literature data for the basis set limits could be reproduced to a few tens of μE(h). The key advantages of molecular MRA-MP2 are the absence of bias and arbitrariness in the choice of the basis set, high accuracy, and low scaling with respect to the system size.

• Slater-type geminals in explicitly-correlated perturbation theory: application to n-alkanols and analysis of errors and basis-set requirements

  2008

  Physical Chemistry Chemical Physics · 39 Zitationen · DOI

  In the recent years, Slater-type geminals (STGs) have been used with great success to expand the first-order wave function in an explicitly-correlated perturbation theory. The present work reports on this theory's implementation in the framework of the Turbomole suite of programs. A formalism is presented for evaluating all of the necessary molecular two-electron integrals by means of the Obara-Saika recurrence relations, which can be applied when the STG is expressed as a linear combination of a small number (n) of Gaussians (STG-nG geminal basis). In the Turbomole implementation of the theory, density fitting is employed and a complementary auxiliary basis set (CABS) is used for the resolution-of-the-identity (RI) approximation of explicitly-correlated theory. By virtue of this RI approximation, the calculation of molecular three- and four-electron integrals is avoided. An approximation is invoked to avoid the two-electron integrals over the commutator between the operators of kinetic energy and the STG. This approximation consists of computing commutators between matrices in place of operators. Integrals over commutators between operators would have occurred if the theory had been formulated and implemented as proposed originally. The new implementation in Turbomole was tested by performing a series of calculations on rotational conformers of the alkanols n-propanol through n-pentanol. Basis-set requirements concerning the orbital basis, the auxiliary basis set for density fitting and the CABS were investigated. Furthermore, various (constrained) optimizations of the amplitudes of the explicitly-correlated double excitations were studied. These amplitudes can be optimized in orbital-variant and orbital-invariant manners, or they can be kept fixed at the values governed by the rational generator approach, that is, by the electron cusp conditions. Electron-correlation effects beyond the level of second-order perturbation theory were accounted for by conventional coupled-cluster calculations with single, double and perturbative triple excitations [CCSD(T)]. The explicitly-correlated perturbation theory results were combined with CCSD(T) results and compared with literature data obtained by basis-set extrapolation.

• Chemically accurate adsorption energies for methane and ethane monolayers on the MgO(001) surface

  2018

  Physical Chemistry Chemical Physics · 37 Zitationen · DOI

  A hybrid QM:QM method that combines MP2 as high-level method on cluster models with density functional theory (PBE+D2) as low-level method on periodic models is applied to adsorption of methane and ethane on the MgO(001) surface for which reliable experimental desorption enthalpies are available. Two coverages are considered, monolayer (every second Mg2+ ion occupied) and one quarter coverage (one of eight Mg2+ ions occupied). Structure optimizations are performed at the hybrid MP2:(PBE+D2) level, with the MP2 energies and forces counterpoise corrected for basis set superposition error and extrapolated to the complete basis set limit. For the MP2 calculations on the adsorbate monolayer a two-body expansion of the lateral molecule-molecule interactions is applied. Higher order correlation effects are evaluated at the hybrid MP2:(PBE+D2) equilibrium structures as coupled cluster [CCSD(T)] - MP2 differences adopting smaller basis sets. The final adsorption energies obtained for monolayer coverage are -14.0 ± 1.0 and -23.3 ± 0.6 kJ mol-1 for CH4·MgO(001) and C2H6·MgO(001), respectively. They agree within 1 kJ mol-1 - well within chemical accuracy limits - with reference energies of -15.0 ± 0.6 and -24.4 ± 0.6 kJ mol-1, respectively. The latter have been derived from measured desorption enthalpy barriers, taking zero-point vibrational energy (ZPVE) and thermal enthalpy contributions into account.

• Temperature- and Structure-Dependent Optical Properties and Photophysics of BODIPY Dyes

  2020

  The Journal of Physical Chemistry A · 33 Zitationen · DOI

  We report on the temperature- and structural-dependent optical properties and photophysics of a set of boron dipyrromethene (BODIPY) dyes with different substitution patterns of their meso-aryl subunit. Single-crystal X-ray diffraction analysis of the compounds enabled a classification of the dyes into a sterically hindered and a unhindered group. The steric hindrance refers to a blocked rotational motion of the aryl subunit around the bond connecting this moiety to the meso-position of the BODIPY core. The energy barriers related to this rotation were simulated by DFT calculations. As follows from the relatively low rotational barrier calculated to about 17 kcal/mol, a free rotation is only possible for sterically unhindered compounds. Rotational barriers of more than 40 kcal/mol determined for the sterically hindered compounds suggest an effective freezing of the rotational motion in these molecules. With the aid of temperature-dependent spectroscopic measurements, we could show that the ability to rotate directly affects the optical properties of our set of BODIPY dyes. This accounts for the strong temperature dependence of the fluorescence of the sterically unhindered compounds which show a drastic decrease in fluorescence quantum yield and a significant shortening in fluorescence lifetime upon heating. The optical properties of the sterically hindered compounds, however, are barely affected by temperature. Our results suggest a nonradiative deactivation of the first excited singlet state of the sterically unhindered compounds caused by a conical intersection of the potential energy surfaces of the ground and first excited state which is accessible by rotation of the meso-subunit. This is in good agreement with previously reported deactivation mechanisms. In addition, our results suggest the presence of a second nonradiative depopulation pathway of the first excited singlet state which is particularly relevant for the sterically hindered compounds.

• Valence and Structure Isomerism of Al₂FeO₄⁺: Synergy of Spectroscopy and Quantum Chemistry

  2020

  Journal of the American Chemical Society · 30 Zitationen · DOI

  We provide spectroscopic and computational evidence for a substantial change in structure and gas phase reactivity of Al₃O₄⁺ upon Fe-substitution, which is correctly predicted by multireference (MR) wave function calculations. Al₃O₄⁺ exhibits a cone-like structure with a central trivalent O atom (C_3v symmetry). The replacement of the Al- by an Fe atom leads to a planar bicyclic frame with a terminal Al-O^•- radical site, accompanied by a change from the Fe^+III/O^-II to the Fe^+II/O^-I valence state. The gas phase vibrational spectrum of Al₂FeO₄⁺ is exclusively reproduced by the latter structure, which MR wave function calculations correctly identify as the most stable isomer. This isomer of Al₂FeO₄⁺ is predicted to be highly reactive with respect to C-H bond activation, very similar to Al₈O₁₂⁺ which also features the terminal Al-O^•- radical site. Density functional theory, in contrast, predicts a less reactive Al₃O₄⁺-like "isomorphous substitution" structure of Al₂FeO₄⁺ to be the most stable one, except for functionals with very high admixture of Fock exchange (50%, BHLYP).

• Second-order electron-correlation and self-consistent spin-orbit treatment of heavy molecules at the basis-set limit

  2010

  The Journal of Chemical Physics · 30 Zitationen · DOI

  Second-order perturbation theory using explicitly correlated wave functions has been introduced into a quasirelativistic two-component formalism. The convergence of the correlation energy is as much improved as for the nonrelativistic Hamiltonian, achieving basis-set-limit results in a moderate-size basis set. Equilibrium distances and vibrational frequencies of small molecules of the 6th period of the periodic system of the elements have been calculated, demonstrating the improved behavior of the explicitly correlated wave functions. Taking advantage of density-fitting techniques, the explicitly correlated approach is an economical and appealing alternative to conventional two-component second-order perturbation theory in a large one-particle basis.

• Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

  2008

  Theoretical Chemistry Accounts · 29 Zitationen · DOI

• Reactivity of titanium dimer and molecular nitrogen in rare gas matrices. Vibrational and electronic spectra and structure of Ti₂N₂

  2006

  Physical Chemistry Chemical Physics · 28 Zitationen · DOI

  The reactivity of diatomic titanium with molecular nitrogen has been investigated in rare gas matrices. The formation of Ti2N2 from the condensation of effusive beams of Ti and N2 in neon and argon matrices is observed after sample deposition. Our results also show that the in situ formation results from the spontaneous reaction at 9 K of ground state Ti2 with N2. Several low-lying excited states of Ti2N2 are also observed between 0.78 and 1.1 eV above the ground state, leading to a complex sequence of interacting vibronic transitions, merging into a broad continuum above 1.25 eV. Observations of Ti2(14)N2, Ti2(15)N2 and Ti2(14)N(15)N isotopic data enable the determination of all fundamental vibrations in the ground electronic state. Semi-empirical harmonic potential calculations lead to estimates of 3.22 N cm(-1) for the Ti-N bond force constant and 90 +/- 5 degrees for the bond angles. Comparisons with TiN diatomic data suggest a near square-planar structure with 175 +/- 3 pm TiN bond distance. Quantum chemical calculations at various levels indicate a 1A(g) ground state with a Ti-N distance close to 180 pm and 89 degrees for the NTiN bond angle, and give fundamental frequencies in excellent agreement with the experimentally observed values. Further MRCI calculations on all low-lying states enable an interpretation of the complex electronic spectrum in the NIR region.

• Numerically accurate linear response-properties in the configuration-interaction singles (CIS) approximation

  2015

  Physical Chemistry Chemical Physics · 24 Zitationen · DOI

  In the present work, we report an efficient implementation of configuration interaction singles (CIS) excitation energies and oscillator strengths using the multi-resolution analysis (MRA) framework to address the basis-set convergence of excited state computations. In MRA (ground-state) orbitals, excited states are constructed adaptively guaranteeing an overall precision. Thus not only valence but also, in particular, low-lying Rydberg states can be computed with consistent quality at the basis set limit a priori, or without special treatments, which is demonstrated using a small test set of organic molecules, basis sets, and states. We find that the new implementation of MRA-CIS excitation energy calculations is competitive with conventional LCAO calculations when the basis-set limit of medium-sized molecules is sought, which requires large, diffuse basis sets. This becomes particularly important if accurate calculations of molecular electronic absorption spectra with respect to basis-set incompleteness are required, in which both valence as well as Rydberg excitations can contribute to the molecule's UV/VIS fingerprint.

• [Al₂O₄]⁻, a Benchmark Gas-Phase Class II Mixed-Valence Radical Anion for the Evaluation of Quantum-Chemical Methods

  2016

  Journal of Chemical Theory and Computation · 23 Zitationen · DOI

  The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.

• Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis

  2017

  Journal of Chemical Theory and Computation · 22 Zitationen · DOI

  A framework to calculate CC2 approximated coupled-cluster ground state correlation energies in a multiresolution basis is derived and implemented into the MADNESS library. The CC2 working equations are formulated in first quantization which makes them suitable for real-space methods. The first quantized equations can be interpreted diagrammatically using the usual diagrams from second quantization with adjusted interpretation rules. Singularities arising from the nuclear and electronic potentials are regularized by explicitly taking the nuclear and electronic cusps into account. The regularized three- and six-dimensional cluster functions are represented directly on an adaptive grid. The resulting equations are free of singularities and virtual orbitals, which results in a low intrinsic scaling. Correlation energies close to the basis set limit are computed for small molecules. This work is the first step toward CC2 excitation energies in a multiresolution basis.

• Gas phase structures and charge localization in small aluminum oxide anions: Infrared photodissociation spectroscopy and electronic structure calculations

  2016

  The Journal of Chemical Physics · 22 Zitationen · DOI

  We use cryogenic ion trap vibrational spectroscopy in combination with quantum chemical calculations to study the structure of mono- and dialuminum oxide anions. The infrared photodissociation spectra of D2-tagged AlO1-4 (-) and Al2O3-6 (-) are measured in the region from 400 to 1200 cm(-1). Structures are assigned based on a comparison to simulated harmonic and anharmonic IR spectra derived from electronic structure calculations. The monoaluminum anions contain an even number of electrons and exhibit an electronic closed-shell ground state. The Al2O3-6 (-) anions are oxygen-centered radicals. As a result of a delicate balance between localization and delocalization of the unpaired electron, only the BHLYP functional is able to qualitatively describe the observed IR spectra of all species with the exception of AlO3 (-). Terminal Al-O stretching modes are found between 1140 and 960 cm(-1). Superoxo and peroxo stretching modes are found at higher (1120-1010 cm(-1)) and lower energies (850-570 cm(-1)), respectively. Four modes in-between 910 and 530 cm(-1) represent the IR fingerprint of the common structural motif of dialuminum oxide anions, an asymmetric four-member Al-(O)2-Al ring.

• Scalar relativistic explicitly correlated R12 methods

  2010

  The Journal of Chemical Physics · 21 Zitationen · DOI

  Combinations of explicitly correlated R12 wave functions with relativistic Douglas-Kroll-Hess (DKH) Hamiltonians are discussed. We considered several ways to incorporate the relativistic terms into the second-order Moller-Plesset R12 method and applied them to the helium isoelectronic series to investigate their accuracy and numerical stability. Among the approaches are the evaluation of the relativistic terms via double resolution-of-the-identity and the explicit evaluation of all terms up to O(c(-4)) using the Pauli Hamiltonian. Numerical collapse of the latter can be avoided if the R12 amplitudes are determined by Kato's cusp condition. Closed formulas for new two-electron integrals that include the mass-velocity term have been derived and implemented into the LIBINT2 integral library. The proposed approaches are not restricted to DKH and can be combined with other one- and two-component relativistic Hamiltonians.

• Direct determination of optimal pair-natural orbitals in a real-space representation: The second-order Moller–Plesset energy

  2020

  The Journal of Chemical Physics · 20 Zitationen · DOI

  An efficient representation of molecular correlated wave functions is proposed, which features regularization of the Coulomb electron–electron singularities via the F12-style explicit correlation and a pair-natural orbital factorization of the correlation components of the wave function expressed in the real space. The pair-natural orbitals are expressed in an adaptive multiresolution basis and computed directly by iterative variational optimization. The approach is demonstrated by computing the second-order Moller–Plesset energies of small- and medium-sized molecules. The resulting MRA-PNO-MP2-F12 method allows for the first time to compute correlated wave functions in a real-space representation for systems with dozens of atoms (as demonstrated here by computations on alkanes as large as C10H22), with precision exceeding what is achievable with the conventional explicitly correlated MP2 approaches based on the atomic orbital representations.

• Regularizing the molecular potential in electronic structure calculations. I. SCF methods

  2014

  The Journal of Chemical Physics · 20 Zitationen · DOI

  We present a method to remove the singular nuclear potential in a molecule and replace it with a regularized potential that is more amenable to be represented numerically. The singular nuclear potential is canceled by the similarity-transformed kinetic energy operator giving rise to an effective nuclear potential that contains derivative operators acting on the wave function. The method is fully equivalent to the non-similarity-transformed version. We give numerical examples within the framework of multi-resolution analysis for medium-sized molecules.

• Coupled-Cluster in Real Space. 2. CC2 Excited States Using Multiresolution Analysis

  2017

  Journal of Chemical Theory and Computation · 16 Zitationen · DOI

  We report a first quantized approach to calculate approximate coupled-cluster singles and doubles CC2 excitation energies in real space. The cluster functions are directly represented on an adaptive grid using multiresolution analysis. Virtual orbitals are neither calculated nor needed in this approach. The nuclear and electronic cusps are taken into account explicitly regularizing the corresponding equations exactly. First calculations on small molecules are in excellent agreement with the best available LCAO results.

• Gas‐Phase Vibrational Spectroscopy of the Aluminum Oxide Anions (Al₂O₃)_1–6AlO₂⁻

  2017

  ChemPhysChem · 16 Zitationen · DOI

  We use cryogenic ion trap vibrational spectroscopy in combination with density functional theory to probe how the structural variability of alumina manifests itself in the structures of the gas-phase clusters (Al₂ O₃ )_n AlO₂^- with n=1-6. The infrared photodissociation spectra of the D₂ -tagged complexes, measured in the fingerprint spectral range (400-1200 cm^-1 ), are rich in spectral features and start approaching the vibrational spectrum of amorphous alumina particles for n>4. Aided by a genetic algorithm, we find a trend towards the formation of irregular structures for larger n, with the exception of n=4, which exhibits a C_3v ground-state structure. Locating the global minima of the larger systems proves challenging.

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Name

Dr. Florian Bischoff

Titel

Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Chemie

Arbeitsgruppe

Theoretische Chemie

Telefon

+49 30 2093-82708

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26.4.2026, 01:02:43