1
|
Morassut C, Ravindran A, Ciavardini A, Luppi E, De Ninno G, Coccia E. High-Harmonic Generation Spectroscopy of Gas-Phase Bromoform. J Phys Chem A 2024; 128:2015-2024. [PMID: 38469750 DOI: 10.1021/acs.jpca.3c07699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.
Collapse
Affiliation(s)
- Chiara Morassut
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, via L. Giorgieri 1, 34127 Trieste, Italy
| | - Arun Ravindran
- Laboratory of Quantum Optics, University of Nova Gorica, Si-5270 Ajdovščina, Slovenija
| | - Alessandra Ciavardini
- Laboratory of Quantum Optics, University of Nova Gorica, Si-5270 Ajdovščina, Slovenija
| | - Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
| | - Giovanni De Ninno
- Laboratory of Quantum Optics, University of Nova Gorica, Si-5270 Ajdovščina, Slovenija
- Elettra-Sincrotrone Trieste S.C.p.A., S.S. 14-km 163.5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, via L. Giorgieri 1, 34127 Trieste, Italy
| |
Collapse
|
2
|
Li Y, He F, Sato T, Ishikawa KL. Implementation of the Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Diatomic Molecules. J Phys Chem A 2024; 128:1523-1532. [PMID: 38373288 DOI: 10.1021/acs.jpca.3c06799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2024]
Abstract
We present a computational approach that implements the time-dependent complete-active-space self-consistent-field method, as introduced in [Phys. Rev. A 88, 023402 (2013)]. Our implementation addresses the challenge of diatomic molecules subjected to an intense laser pulse by considering the full dimensionality of the problem using prolate spheroidal coordinates. The method incorporates the gauge-invariant frozen-core approximation, boosts the evaluation of the electron-electron interaction term using finite-element discrete-variable representation with Neumann expansion, and utilizes an exponential time differencing scheme tailored for the stable propagation of the stiff nonlinear orbital functions. We have successfully applied this methodology to study high-harmonic generation in diatomic molecules such as H2, LiH, and N2, shedding light on the impact of electron correlations in these systems.
Collapse
Affiliation(s)
- Yang Li
- Key Laboratory for Laser Plasmas (Ministry of Education) and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Feng He
- Key Laboratory for Laser Plasmas (Ministry of Education) and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Ultra-intense Laser Science, Shanghai 201800, China
| | - Takeshi Sato
- Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kenichi L Ishikawa
- Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| |
Collapse
|
3
|
Morassut C, Coccia E, Luppi E. Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra. J Chem Phys 2023; 159:124108. [PMID: 38127378 DOI: 10.1063/5.0153825] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 08/24/2023] [Indexed: 12/23/2023] Open
Abstract
Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.
Collapse
Affiliation(s)
- C Morassut
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università di Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - E Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università di Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - E Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
| |
Collapse
|
4
|
Fu TT, Zhou SS, Chen JG, Wang J, Guo FM, Yang YJ. Minimum structure of high-order harmonic spectrum from molecular multi-orbital effects involving inner-shell orbitals. OPTICS EXPRESS 2023; 31:30171-30183. [PMID: 37710565 DOI: 10.1364/oe.495031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 08/15/2023] [Indexed: 09/16/2023]
Abstract
The spectral features of high-order harmonic spectra can provide rich information for probing the structure and dynamics of molecules in intense laser fields. We theoretically study the high harmonic spectrum with the laser polarization direction perpendicular to the N2O molecule and find a minimum structure in the plateau region of the harmonic spectrum. Through analyzing the time-dependent survival probability of different electronic orbitals and the time-dependent wave packet evolution, it is found that this minimum position is caused by the harmonic interference of HOMO a, HOMO-1, and HOMO-3 a orbitals. Moreover, this interference minimum is discovered over a wide frequency range of 0.087 a.u. to 0.093 a.u., as well as a range of driving laser intensities with peak amplitudes between 0.056 a.u. and 0.059 a.u.. This study sheds light on the multi-electron effects and ultrafast dynamics of inner-shell electrons in intense laser pulses, which are crucial for understanding and controlling chemical reactions in molecules.
Collapse
|
5
|
Luppi E, Coccia E. Role of Inner Molecular Orbitals in High-Harmonic Generation Spectra of Aligned Uracil. J Phys Chem A 2023; 127:7335-7343. [PMID: 37640677 DOI: 10.1021/acs.jpca.3c03990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In this work, we decompose the high-harmonic generation (HHG) signal of aligned gas-phase uracil into single molecular-orbital (MO) contributions. We compute HHG spectra for a pulse linearly polarized perpendicular to the molecular plane, with an intensity of 0.6 and 0.85 × 1014 W/cm2 and a wavelength of 800 nm. We use the real-time time-dependent Configuration Interaction with singles method, coupled to a Gaussian-based representation of the time-dependent wavefunction. The strong-field dynamics is affected by the energy of the ionization/recombination channels and by the coupling between the orbital symmetry and laser polarization. In the configuration studied here, we expect that π-type MOs favorably couple with the incoming pulse and play a substantial role in generating the HHG spectrum. Indeed, we show that HOMO, HOMO - 1, and HOMO - 4, which all are π-like, determine the intensity of harmonic peaks at different energies, while HOMO - 2 and HOMO - 3 provide a smaller contribution. It is worth mentioning that HOMO - 4 produces a stronger signal than that from HOMO - 1, even though the corresponding ionization energy, in an one-electron picture, is around 2.5 eV larger and more than 4 eV larger than the HOMO one.
Collapse
Affiliation(s)
- Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, via L. Giorgieri 1, Trieste 34127, Italy
| |
Collapse
|
6
|
Camper A, Ferré A, Blanchet V, Descamps D, Lin N, Petit S, Lucchese R, Salières P, Ruchon T, Mairesse Y. Quantum-Path-Resolved Attosecond High-Harmonic Spectroscopy. PHYSICAL REVIEW LETTERS 2023; 130:083201. [PMID: 36898107 DOI: 10.1103/physrevlett.130.083201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 12/08/2022] [Indexed: 06/18/2023]
Abstract
Strong-field ionization of molecules releases electrons which can be accelerated and driven back to recombine with their parent ion, emitting high-order harmonics. This ionization also initiates attosecond electronic and vibrational dynamics in the ion, evolving during the electron travel in the continuum. Revealing this subcycle dynamics from the emitted radiation usually requires advanced theoretical modeling. We show that this can be avoided by resolving the emission from two families of electronic quantum paths in the generation process. The corresponding electrons have the same kinetic energy, and thus the same structural sensitivity, but differ by the travel time between ionization and recombination-the pump-probe delay in this attosecond self-probing scheme. We measure the harmonic amplitude and phase in aligned CO_{2} and N_{2} molecules and observe a strong influence of laser-induced dynamics on two characteristic spectroscopic features: a shape resonance and multichannel interference. This quantum-path-resolved spectroscopy thus opens wide prospects for the investigation of ultrafast ionic dynamics, such as charge migration.
Collapse
Affiliation(s)
- Antoine Camper
- Université Paris-Saclay, CEA, CNRS, LIDYL, 91191 Gif-sur-Yvette, France
- Department of Physics, University of Oslo, Sem Sælandsvei 24, 0371 Oslo, Norway
| | - Amélie Ferré
- Aix Marseille Université, CNRS, LP3, 13288, Marseille, France
| | | | | | - Nan Lin
- Université Paris-Saclay, CEA, CNRS, LIDYL, 91191 Gif-sur-Yvette, France
- Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, 201800 Shanghai, China
| | - Stéphane Petit
- Université de Bordeaux-CNRS-CEA, CELIA, UMR5107 Talence, France
| | - Robert Lucchese
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Pascal Salières
- Université Paris-Saclay, CEA, CNRS, LIDYL, 91191 Gif-sur-Yvette, France
| | - Thierry Ruchon
- Université Paris-Saclay, CEA, CNRS, LIDYL, 91191 Gif-sur-Yvette, France
| | - Yann Mairesse
- Université de Bordeaux-CNRS-CEA, CELIA, UMR5107 Talence, France
| |
Collapse
|
7
|
Tuthill DR, Scarborough TD, Gorman TT, Hamer KA, Jones RR, Gaarde MB, Lopata K, Mauger F, Schafer KJ, DiMauro LF. Investigation of Interferences in Carbon Dioxide through Multidimensional Molecular-Frame High-Harmonic Spectroscopy. J Phys Chem A 2022; 126:8588-8595. [DOI: 10.1021/acs.jpca.2c04606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Daniel R. Tuthill
- Department of Physics, The Ohio State University, Columbus, Ohio43210, United States
| | | | - Timothy T. Gorman
- Department of Physics, The Ohio State University, Columbus, Ohio43210, United States
| | - Kyle A. Hamer
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana70803, United States
| | - Robert R. Jones
- Department of Physics, University of Virginia, Charlottesville, Virginia22904, United States
| | - Mette B. Gaarde
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana70803, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana70803, United States
| | - François Mauger
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana70803, United States
| | - Kenneth J. Schafer
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana70803, United States
| | - Louis F. DiMauro
- Department of Physics, The Ohio State University, Columbus, Ohio43210, United States
| |
Collapse
|
8
|
A TD-CIS study of high-harmonic generation of uracil cation fragments. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
9
|
Zhu Y, Herbert JM. High harmonic spectra computed using time-dependent Kohn-Sham theory with Gaussian orbitals and a complex absorbing potential. J Chem Phys 2022; 156:204123. [PMID: 35649850 DOI: 10.1063/5.0079910] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
High harmonic spectra for H2 and H2 + are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.
Collapse
Affiliation(s)
- Ying Zhu
- Department of Chemistry and Biochemistry, and Chemical Physics Graduate Program, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M Herbert
- Department of Chemistry and Biochemistry, and Chemical Physics Graduate Program, The Ohio State University, Columbus, Ohio 43210, USA
| |
Collapse
|
10
|
Wozniak AP, Przybytek M, Lewenstein M, Moszynski R. Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study. J Chem Phys 2022; 156:174106. [DOI: 10.1063/5.0087384] [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
In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method). The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited and continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show that when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory.
Collapse
|
11
|
Continuum Electronic States: The Tiresia Code. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27062026. [PMID: 35335385 PMCID: PMC8951385 DOI: 10.3390/molecules27062026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 03/11/2022] [Indexed: 11/17/2022]
Abstract
A multicenter (LCAO) B-spline basis is described in detail, and its capabilities concerning affording convergent solutions for electronic continuum states and wavepacket propagation are presented. It forms the core of the Tiresia code, which implements static-DFT and TDDFT hamiltonians, as well as single channel Dyson-DFT and Dyson-TDDFT descriptions to include correlation in the bound states. Together they afford accurate and computationally efficient descriptions of photoionization properties of complex systems, both in the single photon and strong field environments. A number of examples are provided.
Collapse
|
12
|
Coccia E, Luppi E. Time-dependent ab initioapproaches for high-harmonic generation spectroscopy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:073001. [PMID: 34731835 DOI: 10.1088/1361-648x/ac3608] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 11/03/2021] [Indexed: 06/13/2023]
Abstract
High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.
Collapse
Affiliation(s)
- Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, University of Trieste, via Giorgieri 1, 34127 Trieste, Italy
| | - Eleonora Luppi
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
| |
Collapse
|
13
|
Armstrong GSJ, Khokhlova MA, Labeye M, Maxwell AS, Pisanty E, Ruberti M. Dialogue on analytical and ab initio methods in attoscience. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2021; 75:209. [PMID: 34720730 PMCID: PMC8550504 DOI: 10.1140/epjd/s10053-021-00207-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 06/18/2021] [Indexed: 06/13/2023]
Abstract
The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.
Collapse
Affiliation(s)
- Gregory S. J. Armstrong
- Centre for Theoretical Atomic, Molecular, and Optical Physics, Queen’s University Belfast, Belfast, BT7 1NN UK
| | - Margarita A. Khokhlova
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489 Berlin, Germany
- Department of Physics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK
| | - Marie Labeye
- CNRS, PASTEUR, Département de chimie, Ecole Normale Supérieure, PSL University, Sorbonne Université, 75005 Paris, France
| | - Andrew S. Maxwell
- Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT UK
| | - Emilio Pisanty
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489 Berlin, Germany
- Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Marco Ruberti
- Department of Physics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK
| |
Collapse
|
14
|
Ruberti M. Quantum electronic coherences by attosecond transient absorption spectroscopy: ab initio B-spline RCS-ADC study. Faraday Discuss 2021; 228:286-311. [PMID: 33575690 DOI: 10.1039/d0fd00104j] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Here I present a fully ab initio time-resolved study of X-ray attosecond transient absorption spectroscopy (ATAS) in a prototypical polyatomic molecule, pyrazine, and demonstrate the possibility of retrieving the many-electron quantum ionic coherences arising in attosecond molecular photoionisation and pre-determining the subsequent charge-directed photochemical reactivity. Advanced first-principles many-electron simulations are performed, within a hybrid XUV pump/X-ray probe setup, to describe the interaction of pyrazine with both XUV pump and X-ray probe pulses, and study the triggered correlated many-electron dynamics. The calculations are carried out by means of the recently-developed ab initio method for many-electron dynamics in polyatomic molecules, the time-dependent (TD) B-spline Restricted Correlation Space-Algebraic Diagrammatic Construction (RCS-ADC). RCS-ADC simulates molecular ionisation from first principles, combining the accurate description of electron correlation of quantum chemistry with the full account of the continuum dynamics of the photoelectron. Complete theoretical characterisation of the atto-ionised many-electron state and photo-induced attosecond charge dynamics is achieved by calculating the reduced ionic density matrix (R-IDM) of the bipartite ion-photoelectron system, with full inclusion of the correlated shakeup states. Deviations from the sudden approximation picture of photoionisation, in the low-photon-energy limit, are presented. The effect of the multi-channel interaction between the parent-ion and the emitted photoelectron on the onset of the quantum electronic coherences is analysed. Moreover, I show how the Schmidt decomposition of the R-IDM unravels the many-electron dynamics triggered by the pump, allowing for the identification of the key channels involved. Finally, I calculate the X-ray attosecond transient absorption spectra of XUV-ionised pyrazine. The results unveil the mapping of the ATAS measurement onto the quantum electronic coherences, and related non-zero R-IDM matrix elements, produced upon ionisation by the XUV pump laser pulse.
Collapse
Affiliation(s)
- M Ruberti
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, UK.
| |
Collapse
|
15
|
Woźniak AP, Lesiuk M, Przybytek M, Efimov DK, Prauzner-Bechcicki JS, Mandrysz M, Ciappina M, Pisanty E, Zakrzewski J, Lewenstein M, Moszyński R. A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation. J Chem Phys 2021; 154:094111. [PMID: 33685145 DOI: 10.1063/5.0040879] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 1013 W/cm2 to 5 × 1014 W/cm2. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.
Collapse
Affiliation(s)
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Dmitry K Efimov
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Jakub S Prauzner-Bechcicki
- Marian Smoluchowski Institute of Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michał Mandrysz
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Marcelo Ciappina
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Emilio Pisanty
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Robert Moszyński
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| |
Collapse
|
16
|
Luppi E, Coccia E. Probing the molecular frame of uracil and thymine with high-harmonic generation spectroscopy. Phys Chem Chem Phys 2021; 23:3729-3738. [PMID: 33395454 DOI: 10.1039/d0cp05559j] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work, we present the computed high-harmonic generation (HHG) spectra of uracil and thymine molecules, by means of the real-time time-dependent formulation of Gaussian-based configuration interaction with single excitations (RT-TD-CIS). According to the experimental work [Hutchison et al., Comparison of high-order harmonic generation in uracil and thymine ablation plumes, Phys. Chem. Chem. Phys., 2013, 15, 12308], a pulse wavelength of 780 nm has been used, together with an intensity of 1014 W cm-2 and a pulse duration of 23 optical cycles. In order to examine the effect of pulse polarisation, rotationally averaged (to mimic the gas-phase sample) and single-polarisations have been computed for both molecules. Our results show that the HHG signal for both molecules possibly originates from different ionisation channels, involving HOMO, HOMO-1, HOMO-2 and HOMO-3 orbitals, which lie within 4 eV. We characterize the HHG spectrum of thymine, supporting the idea that the absence of the thymine signal in the original work does not depend on the single-molecule behaviour. Present results for uracil are consistent with the experimental data. Moreover, we have observed that states below and above the chosen ionisation threshold provide different contributions to the HHG spectrum in averaged and single-polarisation calculations.
Collapse
Affiliation(s)
- Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France and CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
| | - Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, via Giorgieri 1, 34127 Trieste, Italy.
| |
Collapse
|
17
|
Pauletti CF, Coccia E, Luppi E. Role of exchange and correlation in high-harmonic generation spectra of H 2, N 2, and CO 2: Real-time time-dependent electronic-structure approaches. J Chem Phys 2021; 154:014101. [PMID: 33412879 DOI: 10.1063/5.0033072] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
This study arises from the attempt to answer the following question: how different descriptions of electronic exchange and correlation affect the high-harmonic generation (HHG) spectroscopy of H2, N2, and CO2 molecules? We compare HHG spectra for H2, N2, and CO2 with different ab initio electronic structure methods: real-time time-dependent configuration interaction and real-time time-dependent density functional theory (RT-TDDFT) using truncated basis sets composed of correlated wave functions expanded on Gaussian basis sets. In the framework of RT-TDDFT, we employ Perdew-Burke-Ernzerhof (PBE) and long-range corrected Perdew-Burke-Ernzerhof (LC-ωPBE) functionals. We study HHG spectroscopy by disentangling the effect of electronic exchange and correlation. We first analyze the electronic exchange alone, and in the case of RT-TDDFT with LC-ωPBE, we use ω = 0.3 and ω = 0.4 to tune the percentage of long-range Hartree-Fock exchange and short-range exchange PBE. Then, we added the correlation as described by the PBE functional. All the methods give very similar HHG spectra, and they seem not to be particularly sensitive to the different description of exchange and correlation or to the correct asymptotic behavior of the Coulomb potential. Despite this general trend, some differences are found in the region connecting the cutoff and the background. Here, the harmonics can be resolved with different accuracy depending on the theoretical schemes used. We believe that the investigation of the molecular continuum and its coupling with strong fields merits further theoretical investigations in the near future.
Collapse
Affiliation(s)
| | - Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, Via Giorgieri 1, Trieste Italy
| | - Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| |
Collapse
|
18
|
Dong W, Hu H, Zhao Z. Time-resolved recombination by attosecond-controlled high harmonic generation. OPTICS EXPRESS 2020; 28:22490-22499. [PMID: 32752509 DOI: 10.1364/oe.398027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Accepted: 07/05/2020] [Indexed: 06/11/2023]
Abstract
We theoretically investigate the coherent control of strong-field high-harmonic generation in the presence of an isolated attosecond pulse. It is found that the rapid modulation of the controlled signal exhibits interference fringe structures in the delay-dependent spectra. By comparing the classical trajectory model with quantum mechanical calculation, it is demonstrated that the fringes are resulted from the interference between the photon- and the tunnelling-initiated recombination pathways. The relative recombination times for the two paths are reconstructed from the interference fringes, which provides a novel scheme for optical observation of the interplay of the photionization and tunneling ionization electron dynamics in attosecond resolution.
Collapse
|
19
|
Affiliation(s)
- E. Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, University of Trieste, Trieste, Italy
| |
Collapse
|
20
|
Perfetto E, Trabattoni A, Calegari F, Nisoli M, Marini A, Stefanucci G. Ultrafast Quantum Interference in the Charge Migration of Tryptophan. J Phys Chem Lett 2020; 11:891-899. [PMID: 31944766 DOI: 10.1021/acs.jpclett.9b03517] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Extreme-ultraviolet-induced charge migration in biorelevant molecules is a fundamental step in the complex path leading to photodamage. In this work we propose a simple interpretation of the charge migration recently observed in an attosecond pump-probe experiment on the amino acid tryptophan. We find that the decay of the prominent low-frequency spectral structure with increasing pump-probe delay is due to a quantum beating between two geometrically distinct, almost degenerate charge oscillations. Quantum beating is ubiquitous in these systems, and at least on the few-to-tens of femtosecond time scales, it may dominate over decoherence the line intensities of time-resolved spectra. We also address the experimentally observed phase shift in the charge oscillations of two different amino acids, tryptophan and phenylalanine. Our results indicate that a beyond mean-field treatment of the electron dynamics is necessary to reproduce the correct behavior.
Collapse
Affiliation(s)
- E Perfetto
- Dipartimento di Fisica , Università di Roma Tor Vergata , Via della Ricerca Scientifica 1 , 00133 Rome , Italy
- CNR-ISM , Division of Ultrafast Processes in Materials (FLASHit) , Area della Ricerca di Roma 1, Via Salaria Km 29.3 , I-00016 Monterotondo Scalo , Italy
| | - A Trabattoni
- Center for Free-Electron Laser Science (CFEL) , DESY , 22607 Hamburg , Germany
| | - F Calegari
- Center for Free-Electron Laser Science (CFEL) , DESY , 22607 Hamburg , Germany
- Institute for Photonics and Nanotechnologies , IFN-CNR , 20133 Milano , Italy
- Institut fur Experimentalphysik , Universität Hamburg , D-22761 Hamburg , Germany
| | - M Nisoli
- Institute for Photonics and Nanotechnologies , IFN-CNR , 20133 Milano , Italy
- Dipartimento di Fisica , Politecnico di Milano , 20133 Milano , Italy
| | - A Marini
- CNR-ISM , Division of Ultrafast Processes in Materials (FLASHit) , Area della Ricerca di Roma 1, Via Salaria Km 29.3 , I-00016 Monterotondo Scalo , Italy
| | - G Stefanucci
- Dipartimento di Fisica , Università di Roma Tor Vergata , Via della Ricerca Scientifica 1 , 00133 Rome , Italy
- INFN , Sezione di Roma Tor Vergata , Via della Ricerca Scientifica 1 , 00133 Rome , Italy
| |
Collapse
|
21
|
Ruberti M. Onset of ionic coherence and ultrafast charge dynamics in attosecond molecular ionisation. Phys Chem Chem Phys 2019; 21:17584-17604. [PMID: 31372608 DOI: 10.1039/c9cp03074c] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Here is presented a fully ab initio theoretical framework for simulating the correlated many-electron dynamics occurring during and emerging from molecular ionisation by attosecond laser pulses. This is based on the time-dependent (TD) version of the B-spline restricted correlation space (RCS)-algebraic diagrammatic construction (ADC) method, with the full description of the photoelectron and inclusion of electron correlation effects, such as shakeup processes and inter-channel couplings. The nature of the ultrafast charge dynamics in the molecular ion is elucidated by quantitatively predicting the degree of electronic coherence and eigenstate content of the prepared molecular cationic state, beyond the commonly used sudden approximation. The results presented here for the acetylene and ethylene molecules show that even in the high photon energy regime the simulated hole dynamics is quantitatively different from the prediction of the sudden approximation. Moreover, for high-bandwidth ionising pulse, the residual interaction between the cation, in highly-excited shake-up states, and the emitted slow photoelectron gives rise to a loss of coherence in the ionic system which can persist for the first few femtoseconds after ionisation.
Collapse
Affiliation(s)
- M Ruberti
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, UK.
| |
Collapse
|
22
|
Coccia E, Luppi E. Detecting the minimum in argon high-harmonic generation spectrum using Gaussian basis sets. Theor Chem Acc 2019. [DOI: 10.1007/s00214-019-2486-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
23
|
Perfetto E, Sangalli D, Palummo M, Marini A, Stefanucci G. First-Principles Nonequilibrium Green’s Function Approach to Ultrafast Charge Migration in Glycine. J Chem Theory Comput 2019; 15:4526-4534. [DOI: 10.1021/acs.jctc.9b00170] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- E. Perfetto
- CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016 Monterotondo Scalo, Italy
| | - D. Sangalli
- CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016 Monterotondo Scalo, Italy
| | - M. Palummo
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - A. Marini
- CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016 Monterotondo Scalo, Italy
| | - G. Stefanucci
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| |
Collapse
|
24
|
Ruberti M. Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections. J Chem Theory Comput 2019; 15:3635-3653. [PMID: 31136172 DOI: 10.1021/acs.jctc.9b00288] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.
Collapse
Affiliation(s)
- M Ruberti
- Department of Physics , Imperial College London , Prince Consort Road , London SW7 2AZ , United Kingdom
| |
Collapse
|
25
|
Gorman TT, Scarborough TD, Abanador PM, Mauger F, Kiesewetter D, Sándor P, Khatri S, Lopata K, Schafer KJ, Agostini P, Gaarde MB, DiMauro LF. Probing the interplay between geometric and electronic-structure features via high-harmonic spectroscopy. J Chem Phys 2019; 150:184308. [DOI: 10.1063/1.5086036] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- T. T. Gorman
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - T. D. Scarborough
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - P. M. Abanador
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - F. Mauger
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - D. Kiesewetter
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - P. Sándor
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - S. Khatri
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - K. Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - K. J. Schafer
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - P. Agostini
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - M. B. Gaarde
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - L. F. DiMauro
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| |
Collapse
|
26
|
Perfetto E, Stefanucci G. CHEERS: a tool for correlated hole-electron evolution from real-time simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:465901. [PMID: 30359327 DOI: 10.1088/1361-648x/aae675] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.
Collapse
Affiliation(s)
- E Perfetto
- CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della ricerca di Roma 1, Monterotondo Scalo, Italy. Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Rome, Italy
| | | |
Collapse
|
27
|
Ruberti M, Decleva P, Averbukh V. Full Ab Initio Many-Electron Simulation of Attosecond Molecular Pump–Probe Spectroscopy. J Chem Theory Comput 2018; 14:4991-5000. [DOI: 10.1021/acs.jctc.8b00479] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. Ruberti
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - P. Decleva
- Dipartimento di Scienze Chimiche, Università di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy
| | - V. Averbukh
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| |
Collapse
|
28
|
Shalashilin DV. Zombie states for description of structure and dynamics of multi-electron systems. J Chem Phys 2018; 148:194109. [PMID: 30307252 DOI: 10.1063/1.5023209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.
Collapse
|
29
|
Attosecond-Resolved Electron Dynamics in Many-Electron Atoms: Quantitative Theory and Comparison with Measurements. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8040533] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
|