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Bao S, Raymond N, Nooijen M. Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics. J Chem Phys 2024; 160:094105. [PMID: 38426527 DOI: 10.1063/5.0190034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 01/28/2024] [Indexed: 03/02/2024] Open
Abstract
A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].
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Affiliation(s)
- Songhao Bao
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Neil Raymond
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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2
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Abou Taka A, Lu SY, Gowland D, Zuehlsdorff TJ, Corzo HH, Pribram-Jones A, Shi L, Hratchian HP, Isborn CM. Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue. J Chem Theory Comput 2022; 18:3039-3051. [PMID: 35472264 DOI: 10.1021/acs.jctc.1c01127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S1/S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.
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Affiliation(s)
- Ali Abou Taka
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Shao-Yu Lu
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Duncan Gowland
- Department of Physics, King's College London, London WC2R 2LS, United Kingdom
| | - Tim J Zuehlsdorff
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, United States
| | - Hector H Corzo
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Liang Shi
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Hrant P Hratchian
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Christine M Isborn
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
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3
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Zobel JP, Heindl M, Plasser F, Mai S, González L. Surface Hopping Dynamics on Vibronic Coupling Models. Acc Chem Res 2021; 54:3760-3771. [PMID: 34570472 PMCID: PMC8529708 DOI: 10.1021/acs.accounts.1c00485] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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The simulation of photoinduced non-adiabatic dynamics is of great
relevance in many scientific disciplines, ranging from physics and
materials science to chemistry and biology. Upon light irradiation,
different relaxation processes take place in which electronic and
nuclear motion are intimately coupled. These are best described by
the time-dependent molecular Schrödinger equation, but its
solution poses fundamental practical challenges to contemporary theoretical
chemistry. Two widely used and complementary approaches to this problem
are multiconfigurational time-dependent Hartree (MCTDH) and trajectory
surface hopping (SH). MCTDH is an accurate fully quantum-mechanical
technique but often is feasible only in reduced dimensionality, in
combination with approximate vibronic coupling (VC) Hamiltonians,
or both (i.e., reduced-dimensional VC potentials). In contrast, SH
is a quantum–classical technique that neglects most nuclear
quantum effects but allows nuclear dynamics in full dimensionality
by calculating potential energy surfaces on the fly. If nuclear quantum
effects do not play a central role and a linear VC (LVC) Hamiltonian
is appropriate—e.g., for stiff molecules that generally keep
their conformation in the excited state—then it seems advantageous
to combine the efficient LVC and SH techniques. In this Account, we
describe how surface hopping based on an LVC Hamiltonian (SH/LVC)—as
recently implemented in the SHARC surface hopping package—can
provide an economical and automated approach to simulate non-adiabatic
dynamics. First, we illustrate the potential of SH/LVC in a number
of showcases, including intersystem crossing in SO2, intra-Rydberg
dynamics in acetone, and several photophysical studies on large transition-metal
complexes, which would be much more demanding or impossible to perform
with other methods. While all of the applications provide very useful
insights into light-induced phenomena, they also hint at difficulties
faced by the SH/LVC methodology that need to be addressed in the future.
Second, we contend that the SH/LVC approach can be useful to benchmark
SH itself. By the use of the same (LVC) potentials as MCTDH calculations
have employed for decades and by relying on the efficiency of SH/LVC,
it is possible to directly compare multiple SH test calculations with
a MCTDH reference and ponder the accuracy of various correction algorithms
behind the SH methodology, such as decoherence corrections or momentum
rescaling schemes. Third, we demonstrate how the efficiency of SH/LVC
can also be exploited to identify essential nuclear and electronic
degrees of freedom to be employed in more accurate MCTDH calculations.
Lastly, we show that SH/LVC is able to advance the development of
SH protocols that can describe nuclear dynamics including explicit
laser fields—a very challenging endeavor for trajectory-based
schemes. To end, this Account compiles the typical costs of contemporary
SH simulations, evidencing the great advantages of using parametrized
potentials. The LVC model is a sleeping beauty that, kissed by SH,
is fueling the field of excited-state molecular dynamics. We hope
that this Account will stimulate future research in this direction,
leveraging the advantages of the SH/VC schemes to larger extents and
extending their applicability to uncharted territories.
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Affiliation(s)
- J. Patrick Zobel
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna, Austria
| | - Moritz Heindl
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna, Austria
| | - Felix Plasser
- Department of Chemistry, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Sebastian Mai
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna, Austria
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna, Austria
- Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstr. 19, 1090 Vienna, Austria
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Green JA, Jouybari MY, Aranda D, Improta R, Santoro F. Nonadiabatic Absorption Spectra and Ultrafast Dynamics of DNA and RNA Photoexcited Nucleobases. Molecules 2021; 26:1743. [PMID: 33804640 PMCID: PMC8003674 DOI: 10.3390/molecules26061743] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 03/12/2021] [Accepted: 03/14/2021] [Indexed: 11/16/2022] Open
Abstract
We have recently proposed a protocol for Quantum Dynamics (QD) calculations, which is based on a parameterisation of Linear Vibronic Coupling (LVC) Hamiltonians with Time Dependent (TD) Density Functional Theory (TD-DFT), and exploits the latest developments in multiconfigurational TD-Hartree methods for an effective wave packet propagation. In this contribution we explore the potentialities of this approach to compute nonadiabatic vibronic spectra and ultrafast dynamics, by applying it to the five nucleobases present in DNA and RNA. For all of them we computed the absorption spectra and the dynamics of ultrafast internal conversion (100 fs timescale), fully coupling the first 2-3 bright states and all the close by dark states, for a total of 6-9 states, and including all the normal coordinates. We adopted two different functionals, CAM-B3LYP and PBE0, and tested the effect of the basis set. Computed spectra are in good agreement with the available experimental data, remarkably improving over pure electronic computations, but also with respect to vibronic spectra obtained neglecting inter-state couplings. Our QD simulations indicate an effective population transfer from the lowest energy bright excited states to the close-lying dark excited states for uracil, thymine and adenine. Dynamics from higher-energy states show an ultrafast depopulation toward the more stable ones. The proposed protocol is sufficiently general and automatic to promise to become useful for widespread applications.
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Affiliation(s)
- James A. Green
- CNR—Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), Via Mezzocannone 16, I-80136 Napoli, Italy;
| | - Martha Yaghoubi Jouybari
- CNR—Consiglio Nazionale Delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area Della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy; (M.Y.J.); (D.A.)
| | - Daniel Aranda
- CNR—Consiglio Nazionale Delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area Della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy; (M.Y.J.); (D.A.)
| | - Roberto Improta
- CNR—Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), Via Mezzocannone 16, I-80136 Napoli, Italy;
| | - Fabrizio Santoro
- CNR—Consiglio Nazionale Delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area Della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy; (M.Y.J.); (D.A.)
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5
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Shen Y, Yarkony DR. Compact Bases for Vibronic Coupling in Spectral Simulations: The Photoelectron Spectrum of Cyclopentoxide in the Full 39 Internal Modes. J Phys Chem Lett 2020; 11:7245-7252. [PMID: 32787311 DOI: 10.1021/acs.jpclett.0c02199] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We report an algorithm to automatically generate compact multimode vibrational bases for the Köppel-Domcke-Cederbaum (KDC) vibronic coupling wave function used in spectral simulations of moderate-sized molecules. As a full quantum method, the size of the vibronic expansion grows exponentially with respect to the number of vibrational modes, necessitating compact bases for moderate-sized systems. The problem of generating such a basis consists of two parts: one is the choice of vibrational normal modes, and the other is the number of phonons allowed in each mode. A previously developed final-state-biased technique addresses the former part, and this work focuses on the latter part: proposing an algorithm for generating an optimal phonon distribution. By virtue of this phonon distribution, compact and affordable bases can be automatically generated for systems with on the order of 15 atoms. Our algorithm is applied to determine the nonadiabatic photoelectron spectrum of cyclopentoxide in the full 39 internal modes.
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Affiliation(s)
- Yifan Shen
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - David R Yarkony
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
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Perera A, Bartlett RJ, Sanders BA, Lotrich VF, Byrd JN. Advanced concepts in electronic structure (ACES) software programs. J Chem Phys 2020; 152:184105. [DOI: 10.1063/5.0002581] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Ajith Perera
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32605, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32605, USA
| | - Beverly A. Sanders
- Department of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida 32605, USA
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Aranda D, Cerezo J, Pescitelli G, Avila Ferrer FJ, Soto J, Santoro F. A computational study of the vibrationally-resolved electronic circular dichroism spectra of single-chain transoid and cisoid oligothiophenes in chiral conformations. Phys Chem Chem Phys 2018; 20:21864-21880. [PMID: 30105334 DOI: 10.1039/c8cp03482f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We simulate the vibronic profile of the electronic circular dichroism (ECD) spectra of oligothiophenes in cisoid and transoid chiral arrangements. We consider oligomers of different lengths, from two to fifteen units, and investigate extensively how the ECD spectral shapes depend on the inter-ring torsions. In general, the molecular structures we consider are not stationary points of the ground state potential energy surface. Therefore, in order to perform vibronic calculations, we present a new computational protocol able to define reduced-dimensionality models where the effect of the off-equilibrium modes is removed. This is done adopting a description of the vibrational motions in curvilinear internal coordinates, and vertical harmonic models coupled with an iterative application of projectors to define energy Hessians, and therefore effective normal modes, in the space complementary to the one of the off-equilibrium coordinates. Although we consider both Franck-Condon and Herzberg-Teller contributions, the results show that transoid twisted ribbons always give rise to monosignated ECD spectra, while bi-signated and multi-signated spectra are expected for cisoid helices. These findings are explained on the basis of the different transition strengths of the lowest electronic states imparted by the different spatial arrangement, that is almost linear for transoid structures and more globular for cisoid ones. We predicted the chiroptical response of a large number of possible molecular arrangements. These data are employed to critically discuss the experimental ECD of polythiophenes in different experimental conditions, forming either aggregates or host-guest complexes. The method here proposed to perform vibronic calculations in reduced-dimensionality models is of general applicability and its potential interest goes beyond the practical application presented here.
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Affiliation(s)
- Daniel Aranda
- Department of Physical Chemistry, Faculty of Science, University of Málaga, E-29071-Málaga, Spain
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8
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Powis I, Menzies RC, Holland DMP, Trofimov AB, Skitnevskaya AD, Gromov EV, Antonsson E, Patanen M, Nicolas C, Miron C. Photoionization dynamics ofcis-dichloroethene from investigation of vibrationally resolved photoelectron spectra and angular distributions. J Chem Phys 2018; 149:074305. [DOI: 10.1063/1.5042216] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- I. Powis
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - R. C. Menzies
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - D. M. P. Holland
- Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, United Kingdom
| | - A. B. Trofimov
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Str. 1, 664003 Irkutsk, Russia
- Favorsky’s Institute of Chemistry, SB RAS, Favorsky Str. 1, 664033 Irkutsk, Russia
| | - A. D. Skitnevskaya
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Str. 1, 664003 Irkutsk, Russia
| | - E. V. Gromov
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - E. Antonsson
- Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France
| | - M. Patanen
- Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France
| | - C. Nicolas
- Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France
| | - C. Miron
- Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France
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9
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Cerezo J, Aranda D, Avila Ferrer FJ, Prampolini G, Mazzeo G, Longhi G, Abbate S, Santoro F. Toward a general mixed quantum/classical method for the calculation of the vibronic ECD of a flexible dye molecule with different stable conformers: Revisiting the case of 2,2,2-trifluoro-anthrylethanol. Chirality 2018; 30:730-743. [DOI: 10.1002/chir.22853] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2018] [Revised: 02/19/2018] [Accepted: 02/20/2018] [Indexed: 12/30/2022]
Affiliation(s)
- Javier Cerezo
- Departamento de Química Física; Universidad de Murcia; Murcia Spain
| | - Daniel Aranda
- Consiglio Nazionale delle Ricerche-Istituto di Chimica dei Composti Organometallici (ICCOM-CNR); Pisa Italy
- Departamento de Química Física; Universidad de Málaga; Málaga Spain
| | | | - Giacomo Prampolini
- Consiglio Nazionale delle Ricerche-Istituto di Chimica dei Composti Organometallici (ICCOM-CNR); Pisa Italy
| | - Giuseppe Mazzeo
- Dipartimento di Medicina Molecolare e Traslazionale; Università di Brescia; Brescia Italy
| | - Giovanna Longhi
- Dipartimento di Medicina Molecolare e Traslazionale; Università di Brescia; Brescia Italy
| | - Sergio Abbate
- Dipartimento di Medicina Molecolare e Traslazionale; Università di Brescia; Brescia Italy
| | - Fabrizio Santoro
- Consiglio Nazionale delle Ricerche-Istituto di Chimica dei Composti Organometallici (ICCOM-CNR); Pisa Italy
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10
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Cerezo J, Mazzeo G, Longhi G, Abbate S, Santoro F. Quantum-Classical Calculation of Vibronic Spectra along a Reaction Path: The Case of the ECD of Easily Interconvertible Conformers with Opposite Chiral Responses. J Phys Chem Lett 2016; 7:4891-4897. [PMID: 27934048 DOI: 10.1021/acs.jpclett.6b02484] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present a novel mixed method suitable for computing the low-to-middle resolution spectra of systems characterized by a large-amplitude motion s (defined by either a reaction or an internal path) coupled to a bath of harmonic oscillators r, which change with s. The method is based on an adiabatic approximation whereby s is considered much slower than r degrees of freedom and is treated classically. We show that the spectrum can be obtained by a suitable average of quantum vibronic spectra of the fast coordinates computed at representative values of the slow coordinate along the path. By our method we calculate the electronic circular dichroism (ECD) of 2,2,2-trifluoro-anthryl-ethanol, which possesses two conformers with opposite chirality separated by a low-energy barrier. Path-averaged spectra are significantly different from those obtained only at the stable minima: Agreement with experiment is improved. The method represents a generalization of those currently based on harmonic approximation.
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Affiliation(s)
- Javier Cerezo
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
| | - Giuseppe Mazzeo
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia , Viale Europa 11, I-25123 Brescia, Italy
| | - Giovanna Longhi
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia , Viale Europa 11, I-25123 Brescia, Italy
| | - Sergio Abbate
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia , Viale Europa 11, I-25123 Brescia, Italy
| | - Fabrizio Santoro
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
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11
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Cerezo J, Santoro F. Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates. J Chem Theory Comput 2016; 12:4970-4985. [PMID: 27586086 DOI: 10.1021/acs.jctc.6b00442] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q1-frame, where Q1 are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q1-frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal modes of initial and final states in adiabatic approaches. We highlight that such a dependence of G on s is also an issue in vertical models, due to the necessity to approximate the kinetic term in the Hamiltonian when setting up the so-called GF problem. When large structural differences exist between the initial and the final-state minima, the changes in the G matrix can become too large to be disregarded.
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Affiliation(s)
- Javier Cerezo
- Istituto di Chimica dei Composti OrganoMetallici, Consiglio Nazionale delle Richerche (ICCOM-CNR) , Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
| | - Fabrizio Santoro
- Istituto di Chimica dei Composti OrganoMetallici, Consiglio Nazionale delle Richerche (ICCOM-CNR) , Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
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12
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Santoro F, Jacquemin D. Going beyond the vertical approximation with time-dependent density functional theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1260] [Citation(s) in RCA: 121] [Impact Index Per Article: 15.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Fabrizio Santoro
- CNR-Consiglio Nazionale delle Ricerche; Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR); Pisa Italy
| | - Denis Jacquemin
- CEISAM, UMR CNRS 6230; Université de Nantes; Nantes France
- Institut Universitaire de France; Paris France
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13
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de Castilho RB, Ramalho TC, Nunez CV, Coutinho LH, Santos ACF, Pilling S, Lago AF, Silva-Moraes MO, de Souza GGB. Single and double ionization of the camphor molecule excited around the C 1s edge. RAPID COMMUNICATIONS IN MASS SPECTROMETRY : RCM 2014; 28:1769-1776. [PMID: 24975258 DOI: 10.1002/rcm.6961] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2014] [Revised: 06/07/2014] [Accepted: 06/08/2014] [Indexed: 06/03/2023]
Abstract
RATIONALE An interesting class of volatile compounds, the monoterpenes, is present in some plants although their functions are not yet fully understood. We have studied the interaction of the camphor molecule with monochromatic high-energy photons (synchrotron radiation) using time-of-flight mass spectrometry and coincidence techniques. METHODS A commercial sample of S-camphor was admitted into the vacuum chamber, without purification, through an inlet system. Monochromatic light with energy around the C 1s edge was generated by the TGM beamline at the Brazilian Synchrotron Facility. A Wiley-McLaren mass spectrometer was used to characterize and detect the ions formed by the camphor photoionization. The data analysis was supported by energy calculations. RESULTS Although the fragmentation patterns were basically the same at 270 eV and 330 eV, it was observed that above the C 1s edge the contribution to the spectrum from lower mass/charge fragment ions increased, pointing to a higher degree of dissociation of the molecule. Projections of the PEPIPICO spectra demonstrated the existence of unstable doubly charged species. The Gibbs free energy was calculated using the Møller-Plesset perturbation theory (MP2) for the neutral, singly and doubly excited camphor molecule. CONCLUSIONS Our PEPIPICO spectrum clearly demonstrated the formation of doubly ionic dissociative species. From a slope analysis, we propose a secondary decay after a deferred charge separation mechanism in which, after a few steps, the camphor dication dissociates into C2 H3 (+) and C3 H5 (+) . This is the main relaxation route observed at 270 eV and 330 eV. The large energy difference between the mono and the dication (of the order of 258.2 kcal/mol) may explain the experimentally observed absence of stable dications in the spectra, because their formation is disadvantaged energetically.
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Affiliation(s)
- R B de Castilho
- Departamento de Química, Instituto de Ciências Exatas, Universidade Federal do Amazonas (UFAM), Campus Universitário, Coroado, 69077-000, Manaus, AM, Brazil
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Improta R, Ferrer FJA, Stendardo E, Santoro F. Quantum-Classical Calculation of the Absorption and Emission Spectral Shapes of Oligothiophenes at Low and Room Temperature by First-Principle Calculations. Chemphyschem 2014; 15:3320-33. [DOI: 10.1002/cphc.201402323] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2014] [Indexed: 11/11/2022]
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15
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Cerezo J, Zúñiga J, Requena A, Ávila Ferrer FJ, Santoro F. Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures. J Chem Theory Comput 2013; 9:4947-58. [DOI: 10.1021/ct4005849] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Javier Cerezo
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
| | - José Zúñiga
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
| | - Alberto Requena
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
| | - Francisco J. Ávila Ferrer
- CNR−Consiglio Nazionale
delle Ricerche, Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy and
- Physical Chemistry, Faculty of Science, University of Málaga, Málaga 29071, Spain
| | - Fabrizio Santoro
- CNR−Consiglio
Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
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Padula D, Picconi D, Lami A, Pescitelli G, Santoro F. Electronic Circular Dichroism in Exciton-Coupled Dimers: Vibronic Spectra from a General All-Coordinates Quantum-Dynamical Approach. J Phys Chem A 2013; 117:3355-68. [DOI: 10.1021/jp400894v] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Daniele Padula
- Dipartimento di Chimica e Chimica
Industriale, Università degli Studi di Pisa, via Risorgimento 35, I-56126 Pisa, Italy
| | - David Picconi
- Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, I-56126 Pisa,
Italy
- Department of Chemistry, Technische Universität München, Lichtenbergstr.
4, D-85747 Garching, Germany
| | - Alessandro Lami
- Consiglio Nazionale delle Ricerche
− CNR, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca
del CNR, Via G. Moruzzi 1, I-56124 Pisa, Italy
| | - Gennaro Pescitelli
- Dipartimento di Chimica e Chimica
Industriale, Università degli Studi di Pisa, via Risorgimento 35, I-56126 Pisa, Italy
| | - Fabrizio Santoro
- Consiglio Nazionale delle Ricerche
− CNR, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca
del CNR, Via G. Moruzzi 1, I-56124 Pisa, Italy
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Avila Ferrer FJ, Cerezo J, Stendardo E, Improta R, Santoro F. Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation. J Chem Theory Comput 2013; 9:2072-82. [PMID: 26583553 DOI: 10.1021/ct301107m] [Citation(s) in RCA: 167] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
In this work we carefully investigate the relationship between computed data and experimental electronic spectra. To that end, we compare both vertical transition energies, EV, and characteristic frequencies of the spectrum like the maximum, ν(max), and the center of gravity, M(1), taking advantage of an analytical expression of M(1) in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, experimental spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, we simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with experimental data. Our results indicate that the customary comparison of experimental ν(max) and computational EV, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the investigated systems, are on the order of 0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of experimental and computed M(1) and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs are proposed to help rationalize which kind of correction one should expect when comparing EV, M(1), and ν(max).
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Affiliation(s)
- Francisco J Avila Ferrer
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy.,University of Málaga, Physical Chemistry, Faculty of Science, Málaga, 29071, Spain
| | - Javier Cerezo
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy.,Departamento de Quı́mica Fı́sica, Universidad de Murcia, 30100 Murcia, Spain
| | - Emiliano Stendardo
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture Biommagini (IBB-CNR) Via Mezzocannone 16, I-80136, Napoli, Italy
| | - Roberto Improta
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture Biommagini (IBB-CNR) Via Mezzocannone 16, I-80136, Napoli, Italy
| | - Fabrizio Santoro
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
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Avila Ferrer FJ, Santoro F. Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra. Phys Chem Chem Phys 2013; 14:13549-63. [PMID: 22847219 DOI: 10.1039/c2cp41169e] [Citation(s) in RCA: 168] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial- and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states).
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Affiliation(s)
- Francisco José Avila Ferrer
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR), UOS di Pisa, Pisa, Italy
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19
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Stendardo E, Avila Ferrer F, Santoro F, Improta R. Vibrationally Resolved Absorption and Emission Spectra of Dithiophene in the Gas Phase and in Solution by First-Principle Quantum Mechanical Calculations. J Chem Theory Comput 2012; 8:4483-93. [DOI: 10.1021/ct300664d] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- E. Stendardo
- CNR−Consiglio Nazionale
delle Ricerche, Istituto di Biostrutture e Biommagini (IBB-CNR), Via Mezzocannone 16, I-80136, Napoli, Italy
| | - F. Avila Ferrer
- CNR−Consiglio Nazionale
delle Ricerche, Istituto di Chimica dei Composti Organo-Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G.
Moruzzi 1, I-56124 Pisa, Italy
| | - F. Santoro
- CNR−Consiglio Nazionale
delle Ricerche, Istituto di Chimica dei Composti Organo-Metallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca, via G.
Moruzzi 1, I-56124 Pisa, Italy
| | - R. Improta
- CNR−Consiglio Nazionale
delle Ricerche, Istituto di Biostrutture e Biommagini (IBB-CNR), Via Mezzocannone 16, I-80136, Napoli, Italy
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Klein K, Garand E, Ichino T, Neumark DM, Gauss J, Stanton JF. Quantitative vibronic coupling calculations: the formyloxyl radical. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-0893-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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21
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Szalay PG, Aquino AJ, Barbatti M, Lischka H. Theoretical study of the excitation spectrum of azomethane. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2010.08.013] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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22
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Dillon J, Yarkony DR, Schuurman MS. On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: Incorporation of higher order terms. J Chem Phys 2011; 134:044101. [DOI: 10.1063/1.3523344] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
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23
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Schulenburg A, Merkt F. Internal rotation in Jahn–Teller coupled systems: The ethene and allene cations. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.08.017] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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24
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F. Stanton J. On the vibronic level structure in the NO3 radical: II. Adiabatic calculation of the infrared spectrum. Mol Phys 2010. [DOI: 10.1080/00268970902740530] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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25
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Ichino T, Gauss J, Stanton JF. Quasidiabatic states described by coupled-cluster theory. J Chem Phys 2009; 130:174105. [DOI: 10.1063/1.3127246] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Reisler H, Krylov AI. Interacting Rydberg and valence states in radicals and molecules: experimental and theoretical studies. INT REV PHYS CHEM 2009. [DOI: 10.1080/01442350902989170] [Citation(s) in RCA: 80] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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27
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Hazra A, Skone JH, Hammes-Schiffer S. Combining the nuclear-electronic orbital approach with vibronic coupling theory: calculation of the tunneling splitting for malonaldehyde. J Chem Phys 2009; 130:054108. [PMID: 19206959 DOI: 10.1063/1.3068526] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The nuclear-electronic orbital (NEO) method is combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. The dynamics of the molecule are described by a vibronic Hamiltonian in a diabatic basis of two localized nuclear-electronic states for the electrons and transferring proton. This ab initio approach is computationally practical and efficient for relatively large molecules, and the accuracy can be improved systematically. The NEO-vibronic coupling approach is used to calculate the hydrogen tunneling splitting for malonaldehyde. The calculated tunneling splitting of 24.5 cm(-1) is in excellent agreement with the experimental value of 21.6 cm(-1). This approach also enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.
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Affiliation(s)
- Anirban Hazra
- Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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28
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Schuurman MS, Yarkony DR. A simulation of the photoelectron spectrum of pyrazolide. J Chem Phys 2008; 129:064304. [DOI: 10.1063/1.2961042] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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On the multimode quadratic vibronic coupling problem: An open-ended solution using a parallel Lanczos algorithm. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.09.040] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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30
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Nichols P, Hoffmann MR. A momentum-conserving Franck-Condon approximation: theory and application to the photodissociation of Li2+ in an intense laser field. J Chem Phys 2008; 128:044115. [PMID: 18247938 DOI: 10.1063/1.2821100] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
A new, computationally efficient approximation to calculating matrix elements between vibrational-electronic states that does not assume stationary nuclei is introduced. The approach emphasizes the importance of the conservation of nuclear momenta. The calculated quantities can be used wherever equivalent quantities from standard Franck-Condon treatments can be used. The new method is illustrated by a time-dependent perturbation theory description of the photodissociation of the Li(2) (+) molecular cation in an intense laser field (I=0.9x10(12) W/cm(2)), which was previously identified in a detailed study of the electronic structure [Khait et al., J. Chem. Phys. 122, 094111 (2005)] as likely to have unusual sensitivity to the initial vibrational state in dynamics. The current study confirms this speculation and shows this to be a specific instance of a situation in which nuclear dynamics during an electronic optical transition cannot be ignored.
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Affiliation(s)
- Patrick Nichols
- Chemistry Department, University of North Dakota, Grand Forks, North Dakota 58202-9024, USA
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31
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Schuurman MS, Weinberg DE, Yarkony DR. On the simulation of photoelectron spectra in molecules with conical intersections and spin-orbit coupling: The vibronic spectrum of CH3S. J Chem Phys 2007; 127:104309. [PMID: 17867749 DOI: 10.1063/1.2764052] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
A method to simulate photoelectron spectra for states coupled by conical intersections and the spin-orbit interaction is reported. The algorithm is based on the multimode vibronic coupling model and treats the spin-orbit interaction in a nonperturbative manner. Since the algorithm is not dependent on molecular symmetry, the approach is generally applicable to accidental conical intersections as well as the symmetry required intersections found in Jahn-Teller molecules. The method is also computationally efficient using energy gradient and derivative coupling information to limit the number of nuclear configurations at which ab initio data are required. This approach is applied to simulate the negative ion photoelectron spectrum of the methylthio radical. The two-state Hamiltonian employed to describe this system was determined employing ab initio gradients and derivative couplings at only 17 nuclear configurations.
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Affiliation(s)
- Michael S Schuurman
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Young RA, Yarkony DR. Towards a highly efficient theoretical treatment of Jahn-Teller effects in molecular spectra: The 1A2 and 2A2 electronic states of the ethoxy radical. J Chem Phys 2006; 125:234301. [PMID: 17190552 DOI: 10.1063/1.2402174] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Nonadiabatic effects in the two lowest electronic states of the ethoxy radical, the 1 (2)A and 2 (2)A states, are considered, using multireference configuration interaction (MRCI) wave functions comprised of over 15x10(6) configuration state functions. The lowest point on the seam of conical intersection is located. Using this point as the origin, a quasidiabatic Hamiltonian suitable for use in a multimode vibronic coupling treatment of the coupled 1 (2)A and 2 (2)A electronic states is determined. The Hamiltonian includes all contributions from all internal coordinates through second order in displacements from the origin and is comprised of over 500 parameters. By using the average energy gradient, the energy difference gradients, and the derivative couplings, all of which are obtained at little additional cost once the requisite eigenstates are known, the second order Hamiltonian is determined from MRCI calculations at only 35 nuclear configurations. This is essentially the same number of points required to obtain the frequencies for the ground state equilibrium structure using centered differences of gradients. The diabatic Hamiltonian provides a good description of the seam space, the (N(int)-2)-dimensional space of conical intersection points, continuously connected to the minimum energy crossing point, enabling, for the first time, an analysis of the changes in the branching plane induced by seam curvature in the full seam space. Comparing the diabatic representation and MRCI results we find a good agreement for the ground state equilibrium structure, R(eq)(1 (2)A), as well as the ground state energy and vertical excitation energy. In good agreement with the available experimental data are the ground state equilibrium structure and the excitation energy to the A (2)A state, predicted here to involve a cone state level. Agreement between the harmonic frequencies at R(eq)(1 (2)A) computed from the MRCI wave function and from the diabatic Hamiltonian is excellent for all but the three lowest energy normal modes where significant deviations are observed indicating the need for selected cubic and/or quartic terms. For the low-lying vibrational levels, the diabatic representation can be used to partition the normal modes into two groups, those that involve inter(diabatic) state coupling and those that are spectators as far as nonadiabatic effects are concerned. The spin-orbit coupling interaction is determined using the Breit-Pauli approximation and its incorporation into the diabatic Hamiltonian is discussed.
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Affiliation(s)
- R Andrew Young
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Xing X, Bahng MK, Wang P, Lau KC, Baek SJ, Ng CY. Rovibrationally selected and resolved state-to-state photoionization of ethylene using the infrared-vacuum ultraviolet pulsed field ionization-photoelectron method. J Chem Phys 2006; 125:133304. [PMID: 17029457 DOI: 10.1063/1.2213261] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
By preparing ethylene [C2H4(X1Ag)] in selected rotational levels of the nu11(b1u), nu2+nu12(b1u), or nu9(b2u) vibrational state with infrared (IR) laser photoexcitation prior to vacuum ultraviolet (VUV) laser photoionization, we have recorded rotationally resolved pulsed field ionization-photoelectron (PFI-PE) spectra for C2H4+(X2B3u) in the energy region of 0-3000 cm(-1) above the ionization energy (IE) of C2H4(X1Ag). Here, nu2(ag), nu9(b2u), nu11(b1u), and nu12(b1u) represent the C-C stretching, CH2 stretching, CH2 stretching, and CH2 bending modes of C2H4(X1Ag), respectively. The fully rovibrationally resolved spectra have allowed unambiguous symmetry assignments of the observed vibrational bands, which in turn have provided valuable information on the photoionization dynamics of C2H4. The IR-VUV photoionization of C2H4(X1Ag) via the nu11(b1u) or nu2+nu12(b1u) vibrational states is found to predominantly produce vibrational states of C2H4+(X2B3u) with b1u symmetry, which cannot be observed in single-photon VUV-PFI-PE measurements of C2H4(X1Ag). The analysis of the observed IR-VUV-PFI-PE bands has provided the IE(C2H4) = 84,790.2(2) cm(-1) and accurate vibrational frequencies for the nu4+(au)[84.1(2) cm(-1)], nu12+(b1u)[1411.7(2) cm(-1)], nu4+ +nu12+(b1g)[1482.5(2) cm(-1)], nu2+(ag)[1488.3(2) cm(-1)], nu2+ + nu4+(au)[1559.2(2) cm(-1)], 2nu4+ + nu12 +(b1u)[1848.5(2) cm(-1)], 4nu4+ + nu12 +(b1u)[2558.8(2) cm(-1)], nu2+ + nu12 +(b1u)[2872.7(2) cm(-1)], and nu11+(b1u)[2978.7(2) cm(-1)] vibrational states of C2H4+(X2B3u), where nu4+ is the ion torsional state. The IE(C2H4) and the nu4+(au), nu2+(ag), and nu2+ + nu4+ (au) frequencies are in excellent accord with those obtained in previous single-photon VUV-PFI-PE measurements. The other ion vibrational frequencies represent new experimental determinations. We have also performed high-level ab initio anharmonic vibrational frequency calculations for C2H4(X1Ag) and C2H4+(X2B3u) at the CCSD(T)/aug-cc-pVQZ level for guidance in the assignment of the IR-VUV-PFI-PE spectra. All theoretical vibrational frequencies for the neutral and ion, except the ion torsional frequency, are found to agree with experimental vibrational frequencies to better than 1%.
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Affiliation(s)
- Xi Xing
- Department of Chemistry, University of California at Davis, Davis, California 95616, USA
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Ichino T, Gianola AJ, Lineberger WC, Stanton JF. Nonadiabatic effects in the photoelectron spectrum of the pyrazolide-d3 anion: Three-state interactions in the pyrazolyl-d3 radical. J Chem Phys 2006; 125:084312. [PMID: 16965017 DOI: 10.1063/1.2338043] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
The 351.1 nm photoelectron spectrum of the 1-pyrazolide-d(3) anion has been measured. The photoelectron angular distributions indicate the presence of nearly degenerate electronic states of the 1-pyrazolyl-d(3) radical. Equation-of-motion ionization potential coupled-cluster singles and doubles (EOMIP-CCSD) calculations have been performed to study the low-lying electronic states. The calculations strongly suggest that three electronic states, energetically close to each other, are accessed in the photodetachment process. Strong interactions of the pseudo-Jahn-Teller type in each pair of the three states are evident in the calculations for the radical at the anion geometry. Model diabatic potentials of the three states have been constructed around the anion geometry in terms of the anion reduced normal coordinates up to the second order. An analytic method to parametrize the quadratic vibronic coupling (QVC) model potentials has been introduced. Parameters of the QVC model potentials have been determined from the EOMIP-CCSD and CCSD(T) calculations. Simulations of the 1-pyrazolide-d(3) spectrum have been performed with the model Hamiltonian, treating all vibronic interactions amongst the three states simultaneously. The simulation reproduces the fine structure of the observed spectrum very well, revealing complicated nonadiabatic effects in the low-lying states of the radical. The ground state of the 1-pyrazolyl-d(3) radical is (2)A(2) and the electron affinity is 2.935+/-0.006 eV. The first excited state is (2)B(1) with a term energy of 32+/-1 meV. While the high-symmetry (C(2v)) stationary points of the X (2)A(2) and A (2)B(1) states are minima, that of the state is a saddle point as a result of the pseudo-Jahn-Teller interactions with the other two states. The topology of the adiabatic potential energy surfaces is discussed.
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Affiliation(s)
- Takatoshi Ichino
- JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO 80309-0440, USA
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Kamiya M, Hirata S. Higher-order equation-of-motion coupled-cluster methods for ionization processes. J Chem Phys 2006; 125:074111. [PMID: 16942326 DOI: 10.1063/1.2244570] [Citation(s) in RCA: 97] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both alpha and beta ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH+ and NH+ radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the A 2Sigma- state of NH+ are predicted to be 1285, 1723, and 1705 cm(-1) by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm(-1). The small adiabatic energy separation (observed 0.04 eV) between the X 2Pi and a 4Sigma- states of NH+ also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the a 4Sigma- state has the low-spin magnetic quantum number (s(z) = 1/2). When the state with s(z) = 3/2 is sought, the energy separations converge much more rapidly with the IP-EOM-CCSD value (0.03 eV) already being close to the observed (0.04 eV).
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Affiliation(s)
- Muneaki Kamiya
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA
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Bonness S, Kirtman B, Huix M, Sanchez AJ, Luis JM. Simulation of photoelectron spectra with anharmonicity fully included: Application to the X̃A22←X̃A11 band of furan. J Chem Phys 2006; 125:014311. [PMID: 16863302 DOI: 10.1063/1.2210479] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.
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Affiliation(s)
- Sean Bonness
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
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Rodriguez-Garcia V, Yagi K, Hirao K, Iwata S, Hirata S. Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules. J Chem Phys 2006; 125:014109. [PMID: 16863289 DOI: 10.1063/1.2209676] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.
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Affiliation(s)
- Valerie Rodriguez-Garcia
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA
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