1
|
Loos PF, Jacquemin D. A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes. J Comput Chem 2024. [PMID: 38661240 DOI: 10.1002/jcc.27358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Revised: 02/09/2024] [Accepted: 02/15/2024] [Indexed: 04/26/2024]
Abstract
In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)⋆ $$ {}^{\star } $$ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.
Collapse
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, Nantes, France
- Institut Universitaire de France (IUF), Paris, France
| |
Collapse
|
2
|
Palmer MH, Hoffmann SV, Jones NC, Coreno M, de Simone M, Grazioli C, Aitken RA, Perrault L, Patterson ILJ. The ultraviolet and vacuum ultraviolet absorption spectrum of gamma-pyrone; the singlet states studied by configuration interaction and density functional calculations. J Chem Phys 2024; 160:054305. [PMID: 38341687 DOI: 10.1063/5.0186919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 01/05/2024] [Indexed: 02/13/2024] Open
Abstract
A synchrotron based vacuum ultraviolet absorption spectrum for γ-pyrone has been interpreted in terms of singlet excited electronic states using a variety of coupled cluster, configuration interaction, and density functional calculations. The extremely weak spectral onset at 3.557 eV shows eight vibrational peaks, which following previous analyses, are attributed to a forbidden 1A2 state. A contrasting broad peak with a maximum at 5.381 eV has a relatively high cross-section of 30 Mb; this arises from three overlapping states, where a 1A1 state dominates over progressively weaker 1B2 and 1B1 states. After fitting the second band to a polynomial Gaussian function and plotting the regular residuals over 20 vibrational peaks, we have had limited success in analyzing this fine structure. However, the small separation between these three states clearly shows that their vibrational satellites must overlap. Singlet valence and Rydberg state vibrational profiles were determined by configuration interaction using the CAM-B3LYP density functional. Vibrational analysis using both the Franck-Condon and Herzberg-Teller procedures showed that both procedures contributed to the profiles. Theoretical Rydberg states were evaluated by a highly focused CI procedure. The superposition of the lowest photoelectron spectral band on the vacuum ultraviolet spectrum near 6.4 eV shows that the 3s and 3p Rydberg states based on the 2B2 ionic state are present; those based on the other low-lying ionic state (X2B1) are destroyed by broadening; this is a dramatic extension of the broadening previously witnessed in our studies of halogenobenzenes.
Collapse
Affiliation(s)
- Michael H Palmer
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh, EH9 3FJ Scotland, United Kingdom
| | - Søren Vrønning Hoffmann
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Nykola C Jones
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Marcello Coreno
- ISM-CNR, Instituto di Struttura della Materia, LD2 Unit, 34149 Trieste, Italy
| | - Monica de Simone
- IOM-CNR, Istituto Officina dei Materiali, Basovizza SS-14, Km 163.5, 34149 Trieste, Italy
| | - Cesare Grazioli
- IOM-CNR, Istituto Officina dei Materiali, Basovizza SS-14, Km 163.5, 34149 Trieste, Italy
| | - R Alan Aitken
- School of Chemistry, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9ST Scotland, United Kingdom
| | - Loëlia Perrault
- School of Chemistry, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9ST Scotland, United Kingdom
| | - Iain L J Patterson
- School of Chemistry, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9ST Scotland, United Kingdom
| |
Collapse
|
3
|
Folkestad SD, Paul AC, Ponzi A, Grazioli C, Coreno M, de Simone M, Koch H, Coriani S. Electronic Characterization of Glycolaldehyde: Experimental and Theoretical Insights from the Core- and Valence-Level Spectroscopy. J Phys Chem A 2023; 127:10621-10631. [PMID: 38084657 DOI: 10.1021/acs.jpca.3c06703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023]
Abstract
The core-level electron excitation and ionization spectra of glycolaldehyde have been investigated by photoabsorption and photoemission spectroscopy at both carbon and oxygen K-edges; the valence ionization spectra were also recorded by photoelectron spectroscopy in the UV-vis region. The spectra are interpreted by means of ab initio calculations based on the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) and coupled cluster singles, doubles, and perturbative are in good agreement with the experimental results, and many of the observed features are assigned. The photoabsorption spectra are not only dominated by transitions from core-level orbitals to unoccupied π and σ orbitals but also show structures due to Rydberg transitions.
Collapse
Affiliation(s)
- Sarai Dery Folkestad
- Department of Chemistry, NTNU─Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Alexander C Paul
- Department of Chemistry, NTNU─Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Aurora Ponzi
- Department of Physical Chemistry, R. Bošković Institute, Bijenička Cesta 54, Zagreb 10000, Croatia
| | - Cesare Grazioli
- IOM-CNR, Istituto Officina dei Materiali del Consiglio Nazionale delle Ricerche, Basovizza Area Science Park, Trieste I-34149, Italy
| | - Marcello Coreno
- ISM-CNR, Istituto di Struttura della Materia del Consiglio Nazionale delle Ricerche, Basovizza Area Science Park, Trieste I-34149, Italy
| | - Monica de Simone
- IOM-CNR, Istituto Officina dei Materiali del Consiglio Nazionale delle Ricerche, Basovizza Area Science Park, Trieste I-34149, Italy
| | - Henrik Koch
- Department of Chemistry, NTNU─Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, Kgs. Lyngby DK-2800, Denmark
| |
Collapse
|
4
|
Coutinho LH, de A Ribeiro F, Tenorio BNC, Coriani S, Dos Santos ACF, Nicolas C, Milosavljevic AR, Bozek JD, Wolff W. NEXAFS and MS-AES spectroscopy of the C 1s and Cl 2p excitation and ionization of chlorobenzene: Production of dicationic species. Phys Chem Chem Phys 2021; 23:27484-27497. [PMID: 34873605 DOI: 10.1039/d1cp03121j] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We report on single- and double-charge photofragment formation by synchrotron radiation, following C 1s core excitation and ionization and Cl 2p inner excitation and ionization of chlorobenzene, C6H5Cl. From a comparison of experimental near-edge X-ray absorption fine structure spectra and theoretical ab initio calculations, the nature of various core and inner shell transitions of the molecule and pure atomic features were identified. To shed light on the normal Auger processes following excitation or ionization of the molecule at the Cl 2p or C 1s sites, we addressed the induced ionic species formation. With energy resolved electron spectra and ion time-of-flight spectra coincidence measurements, the ionic species were correlated with binding energy regions and initial states of vacancies. We explored the formation of the molecular dication C6H5Cl2+, the analogue benzene dication C6H42+, and the singly charged species produced by single loss of a carbon atom, C5HnCl+. The appearance and intensities of the spectral features associated with these ionic species are shown to be strongly site selective and dependent on the energy ranges of the Auger electron emission. Unexpected intensities for the analogue double charged benzene C6H42+ ion were observed with fast Auger electrons. The transitions leading to C6H5Cl2+ were identified from the binding energy representation of high resolution electron energy spectra. Most C6H5Cl2+ ions decay into two singly charged moieties, but intermediate channels are opened leading to other heavy dicationic species, C6H42+ and C6H4Cl2+, the channel leading to the first of these being much more favored than the other.
Collapse
Affiliation(s)
- Lúcia H Coutinho
- Physics Institute, Federal University of Rio de Janeiro, Rio de Janeiro, 21941-972, Brazil.
| | | | - Bruno N C Tenorio
- Department of Chemistry, Technical University of Denmark, Kongens Lyngby, 2800, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kongens Lyngby, 2800, Denmark
| | - Antonio C F Dos Santos
- Physics Institute, Federal University of Rio de Janeiro, Rio de Janeiro, 21941-972, Brazil.
| | | | | | - John D Bozek
- Synchrotron SOLEIL, Gif-sur-Yvette, 91192, France
| | - Wania Wolff
- Physics Institute, Federal University of Rio de Janeiro, Rio de Janeiro, 21941-972, Brazil.
| |
Collapse
|
5
|
Auburger P, Kemeny I, Bertram C, Ligges M, Bockstedte M, Bovensiepen U, Morgenstern K. Microscopic Insight into Electron-Induced Dissociation of Aromatic Molecules on Ice. PHYSICAL REVIEW LETTERS 2018; 121:206001. [PMID: 30500234 DOI: 10.1103/physrevlett.121.206001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Indexed: 06/09/2023]
Abstract
We use scanning tunneling microscopy, photoelectron spectroscopy, and ab initio calculations to investigate the electron-induced dissociation of halogenated benzene molecules adsorbed on ice. Dissociation of halobenzene is triggered by delocalized excess electrons attaching to the π^{*} orbitals of the halobenzenes from where they are transferred to σ^{*} orbitals. The latter orbitals provide a dissociative potential surface. Adsorption on ice sufficiently lowers the energy barrier for the transfer between the orbitals to facilitate dissociation of bromo- and chloro- but not of flourobenzene at cryogenic temperatures. Our results shed light on the influence of environmentally important ice particles on the reactivity of halogenated aromatic molecules.
Collapse
Affiliation(s)
- Philipp Auburger
- Solid State Theory, Friedrich-Alexander University Erlangen-Nürnberg, Staudstr. 7B2, D-91058 Erlangen, Germany
| | - Ishita Kemeny
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany
| | - Cord Bertram
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany
- Physical Chemistry I, Ruhr-Universität Bochum, Universitätsstr. 150, D-44801 Bochum, Germany
| | - Manuel Ligges
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany
| | - Michel Bockstedte
- Solid State Theory, Friedrich-Alexander University Erlangen-Nürnberg, Staudstr. 7B2, D-91058 Erlangen, Germany
- Department of Chemistry and Physics of Materials, Paris-Lodron University Salzburg, Jakob-Haringer-Str. 2a, A-5020 Salzburg, Austria
| | - Uwe Bovensiepen
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany
| | - Karina Morgenstern
- Physical Chemistry I, Ruhr-Universität Bochum, Universitätsstr. 150, D-44801 Bochum, Germany
| |
Collapse
|
6
|
Palmer MH, Hoffmann SV, Jones NC, Coreno M, de Simone M, Grazioli C, Peterson KA, Baiardi A, Zhang T, Biczysko M. A combined theoretical and experimental study of the valence and Rydberg states of iodopentafluorobenzene. J Chem Phys 2018; 146:174301. [PMID: 28477584 DOI: 10.1063/1.4981919] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new ultraviolet (UV) and vacuum ultraviolet (VUV) spectrum for iodopentafluorobenzene (C6F5I) using synchrotron radiation is reported. The measurements have been combined with those from a recent high-resolution photoelectron spectroscopic study. A major theoretical study, which includes both Franck-Condon (FC) and Herzberg-Teller (HT) analyses, leads to conclusions, which are compatible with both experimental studies. Our observation that the VUV multiplet at 7.926 eV in the VUV spectrum is a Rydberg state rather than a valence state leads to a fundamental reassignment of the VUV Rydberg spectrum over previous studies and removes an anomaly where some previously assigned Rydberg states were to optically forbidden states. Adiabatic excitation energies (AEEs) were determined from equations-of-motion coupled cluster with singles and doubles excitation; these were combined with time dependent density functional theoretical methods. Frequencies from these two methods are very similar, and this enabled the evaluation of both FC and HT contributions in the lower valence states. Multi-reference multi-root configuration interaction gave a satisfactory account of the principal UV+VUV spectral profile of C6F5I, with vertical band positions and intensities. The UV spectral onset consists of two very weak transitions assigned to 11B1 (πσ*) and 11B2 (σσ*) symmetries. The lowest unoccupied molecular orbital of a σ*(a1) symmetry has a significant C-I* antibonding character. This results in considerable lengthening of the C-I bond for both these excited states. The vibrational intensity of the lowest 11B1 state is dominated by HT contributions; the 11B2 state contains both HT and FC contributions; the third band, which contains three states, two ππ*(11A1, 21B2) and one πσ*(21B1), is dominated by FC contributions in the 1A1 state. In this 1A1 state, and the spectrally dominant bands near 6.7 (1A1) and 7.3 eV (1A1 + 1B2), the C-I bond length is in the normal range, and FC components dominate.
Collapse
Affiliation(s)
- Michael H Palmer
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh, EH9 3FJ Scotland, United Kingdom
| | - Søren Vrønning Hoffmann
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Nykola C Jones
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | | | | | | | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| | - Alberto Baiardi
- Scuola Normale Superiore, Piazza Cavalieri 7, 56126 Pisa, Italy
| | - Teng Zhang
- Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
| | - Malgorzata Biczysko
- International Centre for Quantum and Molecular Structures, College of Sciences, Shanghai University, 99 Shangda Road, Shanghai 200444, China
| |
Collapse
|
7
|
Palmer MH, Coreno M, de Simone M, Hoffmann SV, Jones NC, Grazioli C, Peterson KA, Baiardi A, Zhang T, Biczysko M. A combined theoretical and experimental study of the ionic states of iodopentafluorobenzene. J Chem Phys 2017; 146:084302. [PMID: 28249445 DOI: 10.1063/1.4975672] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new synchrotron radiation photoelectron spectral (PES) study of iodopentafluorobenzene, together with a theoretical analysis of the spectrum, where Franck-Condon factors are discussed, gives detailed insight into the ionization processes, and this exposes the need for a reinvestigation of the vacuum ultraviolet spectral (VUV) assignments. We have calculated adiabatic ionization energies (AIEs) for several ionic states, using the equation-of-motion coupled cluster method for ionic states combined with multi-configuration self-consistent field calculation study. The AIE sequence is: X2B1 < A2A2 < B2B2 < C22B1 < D2A1 < E32B1. This symmetry sequence has a major impact on previous VUV spectral assignments, which now appear to be to optically forbidden states. Changes in the equilibrium structures for these ionic states are relatively small, but a significant decrease and increase in the C-I bond length relative to the X1A1 structure occurs for the X2B1 and C2B1 states, respectively. The PES shows major vibrational overlaps between pairs of ionic states, X with A, and A with B. The result of these overlaps is the loss of vibrational structure and considerable broadening of the higher energy PES state. Although the baseline is nearly re-established between the A and B states, where the two bands are nearly separate, the B state is also broadened by the A state. Only the C ionic state, which shows the most highly developed vibrational structure, can be regarded as free from vibrational coupling to a neighbor state. The Franck-Condon analysis of the PES bands X, A, B, and C is described in detail; the apparent simplicity of some of these bands is illusory, since almost all the observed peaks arise from super-position of several calculated vibrational states. The experimental AIE of the A state, which is submerged under the X state envelope, has been determined by the subtraction of the calculated X state envelope from the observed PES spectrum. The overlap of these PES bands and the apparent closeness of the potential energy curves describing them have been investigated, using the state-averaged, complete active space self-consistent field method. We have identified two structures, one where the potential energy curves for the X and A states cross and another for the A and B states. At these two conical intersections (ConInts), there is zero-energy difference within each pair of states. Although similar in energy, the ConInt for the crossing of the X with A states, and that for the A with B states, shows that the open-shell occupancies correspond to the 4 lowest AIE states, and all four states that are quite different from each other.
Collapse
Affiliation(s)
- Michael H Palmer
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh EH9 3FJ, Scotland, United Kingdom
| | - Marcello Coreno
- CNR-IMIP, Montelibretti, c/o Laboratorio Elettra, Trieste, Italy
| | | | - Søren Vrønning Hoffmann
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Nykola C Jones
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Cesare Grazioli
- CNR-IMIP, Montelibretti, c/o Laboratorio Elettra, Trieste, Italy
| | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| | - Alberto Baiardi
- Scuola Normale Superiore, Piazza Cavalieri 7, 56126 Pisa, Italy
| | - Teng Zhang
- Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
| | - Malgorzata Biczysko
- International Centre for Quantum and Molecular Structures, College of Sciences, Shanghai University, 99 Shangda Road, Shanghai 200444, China
| |
Collapse
|
8
|
Palmer MH, Ridley T, Vrønning Hoffmann S, Jones NC, Coreno M, de Simone M, Grazioli C, Zhang T, Biczysko M, Baiardi A, Peterson KA. Combined theoretical and experimental study of the valence, Rydberg and ionic states of fluorobenzene. J Chem Phys 2016; 144:204305. [PMID: 27250304 DOI: 10.1063/1.4949548] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
New photoelectron spectra (PES) and ultra violet (UV) and vacuum UV (VUV) absorption spectra of fluorobenzene recorded at higher resolution than previously, have been combined with mass-resolved (2 + 1) and (3 + 1) resonance enhanced multiphoton ionization (REMPI) spectra; this has led to the identification of numerous Rydberg states. The PES have been compared with earlier mass-analyzed threshold ionization and photoinduced Rydberg ionization (PIRI) spectra to give an overall picture of the ionic state sequence. The analysis of these spectra using both equations of motion with coupled cluster singles and doubles (EOM-CCSD) configuration interaction and time dependent density functional theory (TDDFT) calculations have been combined with vibrational analysis of both the hot and cold bands of the spectra, in considerable detail. The results extend several earlier studies on the vibronic coupling leading to conical intersections between the X(2)B1 and A(2)A2 states, and a further trio (B, C, and D) of states. The conical intersection of the X and A states has been explicitly identified, and its structure and energetics evaluated. The energy sequence of the last group is only acceptable to the present study if given as B(2)B2<C(2)B1<D(2)A1, a conclusion which is in agreement with most previous EOM-CCSD and other calculations. However, this symmetry ordering of the B and C states forces reconsideration of the nature of the PIRI spectrum. The coupling between these two states is induced by the a2 modes, ν12 and ν14 and we propose that the 14(1) band is observed in the B(2)B2 band in the PES for the first time, because of the improved resolution. This same assignment is given to the lowest energy band in the PIRI spectrum which was previously assigned as the origin band and further conclude that the entire PIRI spectrum is induced by ν12 and ν14. The relative intensities of the various Rydberg state peaks in the VUV absorption and REMPI spectra of fluorobenzene are very similar to those observed in the equivalent spectra of benzene.
Collapse
Affiliation(s)
- Michael H Palmer
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh, Scotland EH9 3FJ, United Kingdom
| | - Trevor Ridley
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh, Scotland EH9 3FJ, United Kingdom
| | - Søren Vrønning Hoffmann
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Nykola C Jones
- ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Marcello Coreno
- CNR-ISM, Basovizza Area Science Park, 1-34149 Trieste, Italy
| | | | | | - Teng Zhang
- Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
| | - Malgorzata Biczysko
- International Centre for Quantum and Molecular Structures, College of Sciences, Shanghai University, 99 Shangda Road, Shanghai 200444, China
| | - Alberto Baiardi
- Scuola Normale Superiore, Piazza Cavalieri 7, 56126 Pisa, Italy
| | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| |
Collapse
|