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Opoku E, Pawłowski F, Ortiz JV. Ab Initio Electron Propagators with an Hermitian, Intermediately Normalized Superoperator Metric Applied to Vertical Electron Affinities. J Phys Chem A 2024; 128:4730-4749. [PMID: 38814678 DOI: 10.1021/acs.jpca.4c02050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
New-generation ab initio electron propagator methods for calculating electron detachment energies of closed-shell molecules and anions have surpassed their predecessors' accuracy and computational efficiency. Derived from an Hermitian, intermediately normalized superoperator metric, these methods contain no adjustable parameters. To assess their versatility, a standard set (NIST-50-EA) of 50 vertical electron affinities of small closed-shell molecules based on NIST reference data has been created. Errors with respect to reference data on 23 large, conjugated organic photovoltaic (OPV23) molecules have also been analyzed. All final states are valence anions that correspond to electron affinities between 0.2 and 4.2 eV. For a given scaling of the arithmetic bottleneck, the new-generation methods obtain the lowest mean absolute errors (MAEs). The best methods with fifth-power arithmetic scaling realize MAEs below 0.1 eV. Composite models comprising cubically and quintically scaling calculations executed with large and small basis sets, respectively, produce OPV23 MAEs near 0.05 eV. The accuracy of quintically scaling methods executed with large basis sets is thereby procured with reduced computational effort. New-generation results obtained with and without the diagonal self-energy approximation in the canonical Hartree-Fock basis have been compared. These results indicate that Dyson orbitals closely resemble canonical Hartree-Fock orbitals multiplied by the square root of a probability factor above 0.85.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
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Marie A, Loos PF. Reference Energies for Valence Ionizations and Satellite Transitions. J Chem Theory Comput 2024; 20:4751-4777. [PMID: 38776293 PMCID: PMC11171335 DOI: 10.1021/acs.jctc.4c00216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Revised: 04/10/2024] [Accepted: 04/11/2024] [Indexed: 05/24/2024]
Abstract
Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
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Opoku E, Pawłowski F, Ortiz JV. New-Generation Electron-Propagator Methods for Molecular Electron-Binding Energies. J Phys Chem A 2024; 128:1399-1416. [PMID: 38377355 DOI: 10.1021/acs.jpca.3c08455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
A new generation of electron-propagator methods for the calculation of electron binding energies has surpassed its antecedents with respect to accuracy, efficiency, and interpretability. No adjustable parameters are introduced in these fully ab initio procedures. Numerical tests versus several databases of valence, vertical electron binding energies of closed-shell molecules and atoms have been performed. Easily interpreted self-energy approximations with cubic arithmetic scaling produce mean absolute errors (MAEs) of 0.2 and 0.3 eV for electron detachments and attachments, respectively. The most accurate explicitly renormalized methods with fifth-power arithmetic scaling yield MAEs below 0.1 eV for detachments and attachments. Approximate renormalization leads to more efficient fifth-power alternatives for electron detachments that achieve similar accuracy with fewer bottleneck operations. Composite protocols generate excellent predictions versus highly accurate basis-extrapolated standards and experiments. The validity of the diagonal self-energy approximation and the accuracy of the approximate renormalizations are confirmed. The success of these perturbative methods based on canonical Hartree-Fock orbitals rests on a Hermitized, intermediately normalized superoperator metric. The results of all of the new-generation calculations may be analyzed in terms of final-state orbital relaxation and differential correlation effects.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
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Opoku E, Pawłowski F, Ortiz JV. New-Generation Electron-Propagator Methods for Calculations of Electron Affinities and Ionization Energies: Tests on Organic Photovoltaic Molecules. J Chem Theory Comput 2024; 20:290-306. [PMID: 38150412 DOI: 10.1021/acs.jctc.3c00954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2023]
Abstract
A new generation of ab initio electron-propagator self-energies recently superseded its antecedents' accuracy and computational efficiency in calculating vertical ionization energies (VIEs) of closed-shell molecules. (See J. Chem. Phys. 2021, 155, 204107, J. Chem. Theory Comput. 2022, 18, 4927, J. Chem. Phys. 2023, 159, 124109.) No adjustable parameters were introduced in the generation of reference orbitals or in the construction of self-energies. The same approach has been extended in this work to vertical electron affinities (VEAs). Calculations were performed on 24 conjugated, organic photovoltaic molecules with diverse functional groups. These molecules are considerably larger than those studied in previous tests on VIEs. Several new-generation self-energies produce mean absolute errors (MAEs) below 0.1 eV versus ΔCCSD(T) (i.e., total energy differences from the coupled-cluster singles, doubles, and perturbative triples method) VIEs and VEAs obtained with identical basis sets. A composite model employs cubically and quintically scaling algorithms and power-law basis-set extrapolations based on augmented double-triple or triple-quadruple ζ data. Its MAEs are near 0.05 eV versus benchmark values, with 0.03 eV error bars for the lowest VIE and the highest VEA of each molecule. A more efficient and equally accurate composite model for calculating VIEs avoids full transformations of electron repulsion integrals to the molecular orbital basis. High probability factors support the diagonal self-energy approximation, wherein Dyson orbitals are proportional to canonical, Hartree-Fock orbitals.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
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Opoku E, Pawłowski F, Ortiz JV. A new generation of non-diagonal, renormalized self-energies for calculation of electron removal energies. J Chem Phys 2023; 159:124109. [PMID: 38127383 DOI: 10.1063/5.0168779] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 09/06/2023] [Indexed: 12/23/2023] Open
Abstract
A new generation of diagonal self-energies for the calculation of electron removal energies of molecules and molecular ions that has superseded its predecessors with respect to accuracy, efficiency, and interpretability is extended to include non-diagonal self-energies that permit Dyson orbitals to be expressed as linear combinations of canonical Hartree-Fock orbitals. In addition, an improved algorithm for renormalized methods eliminates the convergence difficulties encountered in the first studies of the new, diagonal self-energies. A dataset of outer-valence, vertical ionization energies with almost full-configuration-interaction quality serves as a standard of comparison in numerical tests. The new non-diagonal, renormalized methods are slightly more accurate than their diagonal counterparts, with mean absolute errors between 0.10 and 0.06 eV for outer-valence final states. This advantage is procured at the cost of an increase in the scaling of arithmetic bottlenecks that accompany the inclusion of non-diagonal self-energy terms. The new, non-diagonal, renormalized self-energies are also more accurate and efficient than their non-diagonal predecessors.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
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Opoku E, Pawłowski F, Ortiz JV. Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides. J Phys Chem A 2023; 127:1085-1101. [PMID: 36656801 DOI: 10.1021/acs.jpca.2c08372] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A new generation of ab initio electron-propagator self-energy approximations that are free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approximations indicate that several new methods that make the diagonal self-energy approximation in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods and their acronyms, mean absolute errors (in eV), and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV2), the approximately renormalized quasiparticle third-order method (Q3+, 0.15, O2V3) and the approximately renormalized, non-Dyson, linear, third-order method (nD-L3+, 0.1, OV4). The Brueckner doubles with triple field operators (BD-T1) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double, and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining standard data. The new methods with diagonal self-energy matrices are the foundation of a composite procedure for estimating basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
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Opoku E, Pawłowski F, Ortiz JV. Electron Propagator Self-Energies versus Improved GW100 Vertical Ionization Energies. J Chem Theory Comput 2022; 18:4927-4944. [PMID: 35822816 DOI: 10.1021/acs.jctc.2c00502] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ab initio electron propagator (EP) methods that are free of adjustable parameters in their self-energy formulae and in the generation of their orbital bases have been applied to the calculation of the lowest vertical ionization energies (VIEs) of the GW100 set. An improved set of standard results accompanied by irreducible representation assignments has been produced indirectly with coupled-cluster singles and doubles plus perturbative triples, i.e., CCSD(T), total energy differences at initial-state geometries reoptimized (in 28 cases) with the largest applicable point groups. The best compromises of accuracy and efficiency belong to a new generation of EP self-energies, several members of which may be derived from an intermediately normalized, Hermitized super-operator metric. The following diagonal self-energy methods are optimal: opposite-spin non-Dyson second order (os-nD-D2), approximately renormalized partial third order (P3+), approximately renormalized quasiparticle third order (Q3+), and non-Dyson approximately renormalized linear third order version B (nD-L3+B). Their mean absolute errors (MAEs) in electron volts and arithmetic scaling factors expressed in terms of occupied (O) and virtual (V) orbital dimensions are, respectively, (0.18, OV2), (0.14, O2V3), (0.15, O2V3), and (0.11, OV4). The 0.06 eV MAE for the non-diagonal, sixth-power (O2V4) Brueckner doubles, triple-field operator (BD-T1) EP method is exceeded by the 0.1 eV MAE with respect to experiments in seventh-power, ΔCCSD(T) calculations and indicates that BD-T1 may serve as a direct, spin-symmetry-conserving alternative in the generation of standard results for VIEs of larger, closed-shell molecules.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, United States
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Recent progress in electron-propagator, extended-Koopmans-theorem and self-consistent-field approaches to the interpretation and prediction of electron binding energies. ADVANCES IN QUANTUM CHEMISTRY 2022. [DOI: 10.1016/bs.aiq.2022.03.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Opoku E, Pawłowski F, Ortiz JV. A new generation of diagonal self-energies for the calculation of electron removal energies. J Chem Phys 2021; 155:204107. [PMID: 34852487 DOI: 10.1063/5.0070849] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A new generation of diagonal self-energy approximations in ab initio electron propagator theory for the calculation of electron removal energies of molecules and molecular ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approximately renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calculations whose accuracy approaches that of full configuration interaction. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approximately renormalized third-order quasiparticle or Q3+, (3) the renormalized third-order quasiparticle or RQ3, (4) the approximately renormalized linear third-order or L3+, and (5) the renormalized linear third-order or RL3 self-energies.
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Affiliation(s)
- Ernest Opoku
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - J V Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
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Chaudhuri RK, Chattopadhyay S. A Fock space coupled cluster based probing of the single- and double-ionization profiles for the poly-cyclic aromatic hydrocarbons and conjugated polyenes. J Chem Phys 2021; 154:114106. [PMID: 33752359 DOI: 10.1063/5.0037557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Sequential formation of a poly-cyclic aromatic hydrocarbon (PAH) dication in the H I regions of the interstellar medium (ISM) is proposed to be a function of internal energy of the doubly ionized PAHs, which, in turn, is dependent on the single- and double-ionization potentials of the system. This sets a limit on the single- and double-ionization energies of the system(s) that can further undergo sequential absorption of two photons, leading to a dication (PAH+2). Here, we report the single-ionization (I+1) and double-ionization (I+2) energies and the I+2/I+1 ratio for some selected PAHs and conjugated polyenes obtained using the Fock space coupled cluster technique, enabling simultaneous consideration of several electronic states of different characters. The I+2 to I+1 ratio bears a constant ratio, giving allowance to determine I+2 from the knowledge of single-ionization (I+1) and vice versa. Our observations are in good agreement with the established literature findings, confirming the reliability of our estimates. The measured single- and double-ionization energies further demonstrate that the sequential formation and fragmentation of a PAH dication in the H I regions of the ISM for systems such as benzene and conjugated polyenes such as ethylene and butadiene are quite unlikely because I+2-I+1 for such system(s) is higher than the available photon energy in the H I regions of the ISM. Present findings may be useful to understand the formation and underlying decay mechanisms of multiply charged ions from PAHs and related compounds that may accentuate the exploration of the phenomenon of high-temperature superconductivity.
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Affiliation(s)
| | - Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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Bintrim SJ, Berkelbach TC. Full-frequency GW without frequency. J Chem Phys 2021; 154:041101. [PMID: 33514108 PMCID: PMC7843153 DOI: 10.1063/5.0035141] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 12/13/2020] [Indexed: 01/30/2023] Open
Abstract
Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N5), and (4) enables a density-fitted implementation that reduces the scaling to O(N4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.
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Affiliation(s)
- Sylvia J. Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Palmer MH, Aitken RA, Coreno M, de Simone M, Grazioli C, Hoffmann SV, Jones NC. The ground and ionic states of cyclohepta-1,3,5-triene and their relationship to norcaradiene states: New 1H and 13C NMR spectra and analysis of a new experimental photoelectron spectrum by ab initio methods. J Chem Phys 2020; 152:144301. [DOI: 10.1063/1.5142268] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Michael H. Palmer
- School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh EH9 3FJ, Scotland, United Kingdom
| | - R. Alan Aitken
- School of Chemistry, University of St Andrews, North Haugh, St Andrews Fife, St Andrews KY16 9ST, Scotland, United Kingdom
| | - Marcello Coreno
- ISM-CNR, Istituto di Struttura della Materia, LD2 Unit, 34149 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
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Palmer MH, Coreno M, de Simone M, Grazioli C, Hoffmann SV, Jones NC. The ionic states of cyclooctatetraene: Analysis of a new experimental photoelectron spectrum by ab initio and density functional methods. J Chem Phys 2019; 150:194305. [PMID: 31117784 DOI: 10.1063/1.5096254] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
A synchrotron-based study of the photoelectron spectrum (PES) for cyclooctatetraene (COT) is reported, and this has been subjected to theoretical analysis in unprecedented detail. Weak vibrational structure was observed on the lowest ionization energy (IE1), but the peaks generally show very broad features. Multiconfiguration self-consistent field study confirms that the adiabatic IE (AIE) sequence is 12A1 < 12B1 < 22A1 < 12A2 < 22B1 < 32A1. The Tamm-Dancoff approximation gives an acceptable interpretation of the PES below 20 eV. Vibrational analysis of the PES bands by Franck-Condon methods predicts well-defined vibrational structure for these ionic states. The principal contributors to the PES envelopes are the a1 modes, and only a few are responsible for the overall shape of most bands. The high density of vibrational states, together with the known D2d ⇆ D2d interconversion process, where the C=C and C-C bonds interchange, is attributed to the lack of the observed structure. The transition state (TS) structures for the interconversion above of several ionic states of COT have been elucidated. The intrinsic reaction coordinate procedure gave a planar TS for the X1A1 (D2d) ⇆ 1A1g (D4h) ⇆ X1A1 (D2d) process; this shows alternating C-C (1.4791 Å), C=C (1.3261 Å), and C-H (1.0780 Å) bond lengths. The planar TS is a very shallow maximum, with energy varying with the method used, Hartree-Fock 0.575 eV and second order Møller-Plesset 0.653 eV. A polynomial containing quadratic, quartic, and sextic terms gives an effectively exact fit to the surface. The lowest ionic state of COT (X2A1) shows a similar TS for the process X2A1 (D2d) ⇆ 2B2u (D4h). This structure has alternating C-C (1.4366 Å), C=C (1.3572 Å), and C-H (1.0756 Å) bonds.
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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
- ISM-CNR, Istituto di Struttura della Materia, LD2 Unit, 34149 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
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14
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Peng B, Kowalski K. Green's function coupled cluster formulations utilizing extended inner excitations. J Chem Phys 2018; 149:214102. [PMID: 30525725 DOI: 10.1063/1.5046529] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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15
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Díaz–Tinoco M, Corzo HH, Pawłowski F, Ortiz JV. Do Dyson Orbitals resemble canonical Hartree–Fock orbitals? Mol Phys 2018. [DOI: 10.1080/00268976.2018.1535142] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Manuel Díaz–Tinoco
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, USA
| | - Héctor H. Corzo
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, USA
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, USA
| | - J. V. Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, USA
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Lange MF, Berkelbach TC. On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation. J Chem Theory Comput 2018; 14:4224-4236. [DOI: 10.1021/acs.jctc.8b00455] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Malte F. Lange
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy C. Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
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Local density fitting applied to second order propagator equations for core electron binding energies. COMPUT THEOR CHEM 2018. [DOI: 10.1016/j.comptc.2018.05.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Interpreting Bonding and Spectra With Correlated, One-Electron Concepts From Electron Propagator Theory. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1016/bs.arcc.2017.06.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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19
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20
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Zakrzewski VG, Dolgounitcheva O, Ortiz JV. Electron Propagator Calculations on the Ground and Excited States of C60–. J Phys Chem A 2014; 118:7424-9. [DOI: 10.1021/jp412813m] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- V. G. Zakrzewski
- Department
of Chemistry and
Biochemistry Auburn University Auburn Alabama 36849−5312, United States
| | - O. Dolgounitcheva
- Department
of Chemistry and
Biochemistry Auburn University Auburn Alabama 36849−5312, United States
| | - J. V. Ortiz
- Department
of Chemistry and
Biochemistry Auburn University Auburn Alabama 36849−5312, United States
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21
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Chong DP. Density functional theory study of the vertical ionization energies of the valence and core electrons of cyclopentadiene, pyrrole, furan, and thiophene. CAN J CHEM 2011. [DOI: 10.1139/v11-121] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The procedure abbreviated as ΔPBE0(SAOP)/et-pVQZ, based on density functional theory, was developed recently for the calculation of vertical ionization energies of the valence electrons of organic and other small molecules and succeeded in giving results with an average absolute deviation of 0.21 eV from experiment for a collection of 115 reliable test cases of nonperhalo molecules. The objective of this work is to add a number of test cases to the benchmark database. We chose the set of molecules cyclo-C4H4X, with X = CH2, NH, O, and S, previously studied by many workers both experimentally and theoretically. The results show that the ΔPBE0(SAOP)/et-pVQZ procedure is not only as good as ab initio methods such as SAC-CI, OVGF, and ADC(3) in performance, but also handles inner valence ionized cations more efficiently. Although the core-electron binding energies of the titled molecules have not been as well investigated theoretically, we apply the methods we developed in recent years to calculate the binding energies of C1s, N1s, O1s, S1s, and S2p, which compare well with available experimental data.
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Affiliation(s)
- Delano P. Chong
- Department of Chemistry, 2036 Main Mall, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
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22
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Zakrzewski VG, Dolgounitcheva O, Zakjevskii AV, Ortiz J. Ab initio Electron Propagator Calculations on Electron Detachment Energies of Fullerenes, Macrocyclic Molecules, and Nucleotide Fragments. ADVANCES IN QUANTUM CHEMISTRY 2011. [DOI: 10.1016/b978-0-12-386477-2.00009-7] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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23
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Böhm MC. Calculated Koopmans' Defects for Transition Metal Compounds in the Framework of an Effective Semiempirical Hamiltonian: Bis(π-pentadienyl)dinickel. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19820860112] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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24
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25
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Singh RK, Mishra MK. Investigation of Ethynylfurans Using the Electron Propagator Theory. J Phys Chem A 2009; 113:14150-5. [DOI: 10.1021/jp9061626] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Raman K. Singh
- Department of Chemistry, Indian Institute of Technology Bombay, Powai-400 076 India
| | - Manoj K. Mishra
- Department of Chemistry, Indian Institute of Technology Bombay, Powai-400 076 India
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Herman MF, Freed KF, Yeager DL. Analysis and Evaluation of Ionization Potentials, Electron Affinities, and Excitation Energies by the Equations of Motion-Green's Function Method. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142684.ch1] [Citation(s) in RCA: 167] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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27
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Cederbaum LS, Domcke W, Schirmer J, Niessen WV. Correlation Effects in the Ionization of Molecules: Breakdown of the Molecular Orbital Picture. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142899.ch3] [Citation(s) in RCA: 298] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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28
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von Niessen W, Cederbaum L. Many-body calculations on the ionization spectra of transition metal compounds: ZnCl2, CdCl2and NiCl2. Mol Phys 2006. [DOI: 10.1080/00268978100101751] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Fantoni R, Giardini-Guidoni A, Tiribelli R, Cambi R, Ciullo G, Sgamellotti A, Tarantelli F. An (e, 2e) spectroscopic investigation and a Green's function study of the ionization of fluoroethylene. Mol Phys 2006. [DOI: 10.1080/00268978200100661] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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31
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Deleuze MS. Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. II. Azulene, phenanthrene, pyrene, chrysene, triphenylene, and perylene. J Chem Phys 2002. [DOI: 10.1063/1.1462615] [Citation(s) in RCA: 99] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Schirmer J, Domcke W, Cederbaum LS, Niessen WV. Break-down of the molecular-orbital picture of ionization: CS, PN and P2. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3700/11/11/007] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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33
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Venkatnathan A, Mahalakshmi S, Mishra MK. Higher order decouplings of the dilated electron propagator with applications to [sup 2]P Be[sup −], [sup 2]P Mg[sup −] shape and [sup 2]S Be[sup +] (1s[sup −1]) Auger resonances. J Chem Phys 2001. [DOI: 10.1063/1.1328395] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Dolgounitcheva O, Zakrzewski VG, Ortiz JV. Electron-propagator calculations on the photoelectron spectrum of ethylene. J Chem Phys 2001. [DOI: 10.1063/1.1328393] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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35
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Deleuze MS, Giuffreda MG, François JP, Cederbaum LS. Ionization Bands and Electron Affinities of Mixed Boron−Nitrogen BnNn Clusters (n = 3,4,5). J Phys Chem A 2000. [DOI: 10.1021/jp993232x] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. S. Deleuze
- Instituut voor MateriaalOnderzoek (IMO), Departement SBG, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium
| | - M. G. Giuffreda
- Instituut voor MateriaalOnderzoek (IMO), Departement SBG, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium
| | - J.-P. François
- Instituut voor MateriaalOnderzoek (IMO), Departement SBG, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium
| | - L. S. Cederbaum
- Lehrstuhl für Theoretische Chemie, Institut für Physikalische Chemie, Universität Heidelberg, D69120 Heidelberg, Germany
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Pitarch-Ruiz J, Sánchez-Marı́n J, Maynau D. The open shell single reference size-consistent self-consistent singles and doubles configuration interaction method: Application to ionization potentials. J Chem Phys 2000. [DOI: 10.1063/1.480821] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Deleuze MS, Giuffreda MG, François JP, Cederbaum LS. Valence one-electron and shake-up ionization bands of carbon clusters. I. The Cn (n=3,5,7,9) chains. J Chem Phys 1999. [DOI: 10.1063/1.479880] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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38
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Walter O, Schirmer J. The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) for atoms. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/14/20/006] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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39
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Berman M, Kaldor U. The Schwinger variational method in electron-atom and electron-molecule scattering theory with polarisation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/14/20/023] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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40
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Berman M, Domcke W. Direct calculation of complex resonance poles in electron-molecule scattering using separable T-matrix expansions. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/17/13/006] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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42
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Deleuze MS, Cederbaum LS. Evidence for a partial breakdown of the molecular orbital picture in the ionization spectra of large saturated hydrocarbons. J Chem Phys 1996. [DOI: 10.1063/1.472585] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Deleuze MS, Cederbaum LS. Formation of satellite bands in the ionization spectra of extended systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:13326-13339. [PMID: 9983077 DOI: 10.1103/physrevb.53.13326] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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44
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Mishra MK, Medikeri MN. Characterization of Shape and Auger Resonances Using the Dilated One Electron Propagator Method. ADVANCES IN QUANTUM CHEMISTRY 1996. [DOI: 10.1016/s0065-3276(08)60253-1] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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45
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Kutz H, Meyer HD. Rotational excitation of N2 and Cl2 molecules by electron impact in the energy range 0.01-1000 eV: Investigation of excitation mechanisms. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:3819-3830. [PMID: 9912053 DOI: 10.1103/physreva.51.3819] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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46
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Deleuze M, Pickup BT, Delhalle J. Plane wave and orthogonalized plane wave many-body Green's function calculations of photoionization intensities. Mol Phys 1994. [DOI: 10.1080/00268979400101501] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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47
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Porwol T, Dömötör G, Hemmerich I, Klinkmann J, Freund H, Liegener C. Angular-resolved autoionization study of CO on Ni(110): Experiment and theory. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:10557-10571. [PMID: 10009881 DOI: 10.1103/physrevb.49.10557] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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49
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Quasiparticle approximation to the dilated electron propagator with application to 2P shape resonances in e—Be and e—Ca scattering. Chem Phys Lett 1993. [DOI: 10.1016/0009-2614(93)80151-e] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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50
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Medikeri MN, Nair J, Mishra MK. The two‐particle one hole‐Tamm‐Dancoff approximation (2ph‐TDA) decoupling of the dilated electron propagator with application to2P shape resonances ine‐Be,e‐Mg, ande‐Ca scattering. J Chem Phys 1993. [DOI: 10.1063/1.465304] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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