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Xu Z, Hou S, Wang Z, Xie C. Neural network potentials facilitating accurate complex scaling for molecular resonances: from a model to high dimensional realistic systems. Phys Chem Chem Phys 2024. [PMID: 39104311 DOI: 10.1039/d4cp02452d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/07/2024]
Abstract
Here we propose a neural network based complex scaling (NN-CS) method for computing the complex eigenvalues (Er-iΓ/2) of molecular resonances, in which the CS of the potential part in the non-Hermitian Hamiltonian is effectively achieved by NNs. Taking a two-dimensional (2D) diabatic model including two states coupled by the conical intersection for example, the NN-CS method is shown to reproduce the eigenvalues of the resonance states quite well. Subsequently, this NN-CS method with a 2D Hamiltonian model is utilized to compute the vibronic resonances in the 1nσ*-mediated photodissociation of thioanisole based on a new NN diabatic potential energy matrix. The calculated lifetimes of the vibronic resonances are found to be in good agreement with other theoretical results and available experimental data. Finally, the NN-CS method is applied to treat a much more challenging system, namely, the resonances in the six-dimensional (6D) photodissociation continuum of NH3, due to its high dimensionalities and all three dissociative coordinates needing to be scaled in the complex scaling of the potential part. Again, the calculated energy positions and widths of the 6D resonances by the NN-CS method agree well with other theoretical results. Our calculations show that the NN-CS method is able to accurately treat the vibronic resonances involving multiple coupled electronic states and resonances in high dimensional realistic systems.
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Affiliation(s)
- Zhen Xu
- Institute of Modern Physics, Northwest University, Xi'an 710127, China.
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Siting Hou
- Institute of Modern Physics, Northwest University, Xi'an 710127, China.
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Zhimo Wang
- Institute of Modern Physics, Northwest University, Xi'an 710127, China.
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Changjian Xie
- Institute of Modern Physics, Northwest University, Xi'an 710127, China.
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
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Das S, Samanta K. Recent Advances in the Study of Negative-Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential. Chemphyschem 2023; 24:e202200546. [PMID: 36223261 DOI: 10.1002/cphc.202200546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Revised: 10/12/2022] [Indexed: 02/03/2023]
Abstract
The transient resonances are a challenge to bound state quantum mechanics. These states lie in the continuum part of the spectrum of the Hamiltonian. For this, one has to treat a continuum problem due to electron-molecule scattering and the many-electron correlation problem simultaneously. Moreover, the description of a resonance requires a wavefunction that bridges the part that resembles a bound state with another that resembles a continuum state such that the continuity of the wavefunction and its first derivative with respect to the distance between the incoming projectile and the target is maintained. A review of the recent advances in the theoretical investigation of the negative-ion resonances (NIR) is presented. The NIRs are ubiquitous in nature. They result from the scattering of electrons off of an atomic or molecular target. They are important for numerous chemical processes in upper atmosphere, space and even biological systems. A contextual background of the existing theoretical methods as well as the newly-developed multiconfigurational propagator tools based on a complex absorbing potential are discussed.
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Affiliation(s)
- Subhasish Das
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Kansapada, Argul, 752050, India
| | - Kousik Samanta
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Kansapada, Argul, 752050, India
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Dann R, Elbaz G, Berkheim J, Muhafra A, Nitecki O, Wilczynski D, Moiseyev N. Variational Solutions for Resonances by a Finite-Difference Grid Method. Molecules 2021; 26:molecules26175248. [PMID: 34500682 PMCID: PMC8434025 DOI: 10.3390/molecules26175248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Revised: 08/16/2021] [Accepted: 08/21/2021] [Indexed: 11/29/2022] Open
Abstract
We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.
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Affiliation(s)
- Roie Dann
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
- Correspondence: (R.D.); (N.M.)
| | - Guy Elbaz
- Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel; (G.E.); (A.M.); (D.W.)
| | | | - Alan Muhafra
- Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel; (G.E.); (A.M.); (D.W.)
| | - Omri Nitecki
- Schulich Faculty of Chemistry, Solid State Institute and Faculty of Physics, Technion—Israel Institute of Technology, Haifa 3200003, Israel;
| | - Daniel Wilczynski
- Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel; (G.E.); (A.M.); (D.W.)
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Solid State Institute and Faculty of Physics, Technion—Israel Institute of Technology, Haifa 3200003, Israel;
- Solid State Institute and Faculty of Physics, Technion—Israel Institute of Technology, Haifa 3200003, Israel
- Correspondence: (R.D.); (N.M.)
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Ben-Asher A, Landau A, Moiseyev N. Uniform vs Partial Scaling within Resonances via Padé Based on the Similarities to Other Non-Hermitian Methods: Illustration for the Beryllium 1 s22 p3 s State. J Chem Theory Comput 2021; 17:3435-3444. [PMID: 33945263 DOI: 10.1021/acs.jctc.1c00223] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Resonance via Padé (RVP) is an efficient method for calculating autoionization resonance states. It is based on the stabilization technique in which the basis set is scaled. The scaling can be uniform (i.e., all basis functions are scaled) or partial. Herein, we compare the two RVP scaling schemes for calculating an autoionization eigenvalue; moreover, the effect of freezing the core electrons is intertwined within this comparison. In order to study the different behavior of the RVP schemes, we associate each RVP scaling scheme with a complex contour of integration. Similarities between RVP and other non-Hermitian methods emerge from the generated contours, which suggest that RVP introduces similar outgoing boundary conditions as the complex scaling (CS), complex basis function (CBF), and reflection-free complex absorbing potential (RF-CAP) methods. A uniform-RVP contour, unlike a partial one, immediately penetrates the complex plane and influences the interaction region. Hence, uniform scaling within RVP destroys the description of the core electrons, as well as the description of the reference state, and yields less reliable results than partial scaling. The 1s22p3s 1P autoionization state of Be, at the equation-of-motion coupled-cluster level, is used as our case study model.
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Affiliation(s)
- Anael Ben-Asher
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Arie Landau
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Department of Physics and Russell-Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Pawlak M, Żuchowski PS, Jankowski P. Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule. J Chem Theory Comput 2021; 17:1008-1016. [PMID: 33475358 PMCID: PMC7877727 DOI: 10.1021/acs.jctc.0c01122] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (4He(23S) and 3He(23S)) colliding with the hydrogen isotopologues (H2, HD, D2) in the ground and first excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332-335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided.
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Affiliation(s)
- Mariusz Pawlak
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
| | - Piotr S Żuchowski
- Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Piotr Jankowski
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
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Ben-Asher A, Landau A, Cederbaum LS, Moiseyev N. Quantum Effects Dominating the Interatomic Coulombic Decay of an Extreme System. J Phys Chem Lett 2020; 11:6600-6605. [PMID: 32706968 DOI: 10.1021/acs.jpclett.0c01974] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
LiHe is an extreme open-shell system. It is among the weakest bound systems known, and its mean interatomic distance extends dramatically into the classical forbidden region. Upon 1s → 2p excitation of He, interatomic Coulombic decay (ICD) takes place in which the electronically excited helium atom relaxes and transfers its excess energy to ionize the neighboring lithium atom. A substantial part of the decay is found to be to the dissociation continuum producing Li+ and He atoms. The distribution of the kinetic energy released by the ICD products is found to be highly oscillatory. Its analysis reveals that quantum phase shifts between the decaying states and the dissociating final states are controlling this ICD reaction. The semiclassical reflection principle, which commonly explains ICD reactions, fails. The process is expected to be amenable to experiment.
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Affiliation(s)
- Anael Ben-Asher
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Arie Landau
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, Heidelberg D-69120, Germany
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, Heidelberg D-69120, Germany
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Das S, Sajeev Y, Samanta K. An Electron Propagator Approach Based on a Multiconfigurational Reference State for the Investigation of Negative-Ion Resonances Using a Complex Absorbing Potential Method. J Chem Theory Comput 2020; 16:5024-5034. [PMID: 32568537 DOI: 10.1021/acs.jctc.0c00434] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Negative-ion resonances are important metastable states that result from the collision between an electron and a neutral target. The course of many chemical processes in nature is often dictated by how an intermediate resonance state falls apart. This article reports on the development of an electron propagator (EP) based on a Hamiltonian Ĥ perturbed by a complex absorbing potential (CAP) and a multiconfigurational self-consistent field (MCSCF) initial state to study these resonances. Perturbation of Ĥ by a CAP makes the resonances amenable to a bound-state method like MCSCF. Resonances stand out among the non-resonant states as persistent complex eigenvalues of the perturbed Ĥ when the strength (η) of the CAP is varied. The MCSCF method gives a reliable and accurate description of the target states, especially when the non-dynamical correlations are dominant. The resonance energies are obtained from the poles of the EP. We propose three variants of our EP depending on how the effect of the CAP is introduced. We find that the computationally most efficient variant is the one in which the reference state of the EP is an unperturbed MCSCF wavefunction and a non-zero CAP is defined only on the virtual orbital subspace of the reference state. The onset of the CAP is carefully optimized in order to minimize the artifacts due to reflections from the CAP. An extrapolation method (based on a Padé approximant) and a de-perturbation method are adopted in order to account for the limitations of finite basis sets used and determine the resonance energy in the limit of η → 0. 2P Be-, 2Πg N2-, and 2Π CO- shape resonances are investigated. The position and width of these resonances computed in this study agree well with those reported earlier in the literature.
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Affiliation(s)
- Subhasish Das
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul 752050, India
| | - Y Sajeev
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai 400085, India
| | - Kousik Samanta
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul 752050, India
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Bhattacharya D, Landau A, Moiseyev N. Ab Initio Complex Transition Dipoles between Autoionizing Resonance States from Real Stabilization Graphs. J Phys Chem Lett 2020; 11:5601-5609. [PMID: 32579364 DOI: 10.1021/acs.jpclett.0c01519] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Electronic transition dipoles are crucial for investigating light-matter interactions. Transition dipoles between metastable (autoionizing resonance) states become complex within non-Hermitian formalism, analogous to the resonance energies. Herein, we put forward a robust method for evaluating complex transition dipoles based on real ab initio stabilization calculations. The complex transition dipoles are obtained by analytical continuation via the Padé approximant and are identified as stationary solutions in the complex plane. The capability of the new approach is demonstrated for several transition dipoles of the doubly excited helium resonance states, for which exact values are available for comparison. Nevertheless, the method presented here has no inherent limitation and is suitable for polyatomic systems.
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Affiliation(s)
- Debarati Bhattacharya
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Arie Landau
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, Heidelberg D-69120, Germany
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
- Russell-Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Landau A, Ben-Asher A, Gokhberg K, Cederbaum LS, Moiseyev N. Ab initio complex potential energy curves of the He*(1s2p 1P)–Li dimer. J Chem Phys 2020; 152:184303. [DOI: 10.1063/5.0008337] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Arie Landau
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Anael Ben-Asher
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Kirill Gokhberg
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, Heidelberg D-69120, Germany
| | - Lorenz S. Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, Heidelberg D-69120, Germany
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
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