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Esquivel RO, Molina-Espíritu M, López-Rosa S. 3 D Information-Theoretic Analysis of the Simplest Hydrogen Abstraction Reaction. J Phys Chem A 2023; 127:6159-6174. [PMID: 37477987 PMCID: PMC10405223 DOI: 10.1021/acs.jpca.3c01957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Revised: 06/08/2023] [Indexed: 07/23/2023]
Abstract
We investigate the course of an elementary chemical reaction from the perspective of information theory in 3D space through the hypersurface of several information-theoretic (IT) functionals such as disequilibrium (D), Shannon entropy (S), Fisher information (I), and the complexity measures of Fisher-Shannon (FS) and López-Mancini-Calbet (LMC). The probe for the study is the hydrogenic identity abstraction reaction. In order to perform the analysis, the reactivity pattern of the reaction is examined by use of the aforementioned functionals of the single-particle density, which is analyzed in position (r) and momentum (p) spaces. The 3D analyses revealed interesting reactivity patterns in the neighborhood of the intrinsic reaction coordinate (IRC) path, which allow to interpret the reaction mechanism for this reaction in a novel manner. In addition, the chemically interesting regions that have been characterized through the information functionals and their complexity measures are depicted and analyzed in the framework of the three-dimensional structure of the information-theoretical data of a chemical reaction, that is, the reactant/product (R/P) complexes, the transition state (TS), and the ones that are only revealed through IT measures such as the bond-cleavage energy region (BCER), the bond-breaking/forming (B-B/F) region, and the spin-coupling (SC) process. Furthermore, focus has been placed on the diagonal part of the hypersurface of the IT functionals, aside from the IRC path itself, with the purpose of analyzing the dissociation process of the triatomic transition-state complex that has revealed other interesting features of the bond-breaking (B-B) process. In other respects, it is shown throughout the combined analyses of the 3D structure of the IT functionals in conjugated spaces that the chemically significant regions occurring at the onset of the TS are completely characterized by information-theoretic aspects of localizability (S), uniformity (D), and disorder. Further, novel regions of low complexity seem to indicate new boundaries for chemically stable complex molecules. Finally, the study reveals that the chemical reaction occurs at low-complexity regions, where the concurrent phenomena take place: bond-breaking/forming (B-B/F), bond-cleavage energy reservoirs (BCER), spin-coupling (SC), and transition state (TS).
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Affiliation(s)
- Rodolfo O. Esquivel
- Departamento
de Química, Universidad Autónoma
Metropolitana, 09340 México D.F., México
- Instituto
Carlos I de Física Teórica y Computacional, Universidad de Sevilla, 41012 Sevilla, Spain
| | | | - Sheila López-Rosa
- Instituto
Carlos I de Física Teórica y Computacional, Universidad de Sevilla, 41012 Sevilla, Spain
- Departamento
de Física Aplicada II, Universidad
de Sevilla, 41012 Sevilla, Spain
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Roy R, Chakrabarti B, Chavda ND, Lekala ML. Information theoretic measures for interacting bosons in optical lattice. Phys Rev E 2023; 107:024119. [PMID: 36932481 DOI: 10.1103/physreve.107.024119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
This work reports the different information theoretic measures, i.e., Shannon information entropy, order, disorder, complexity, and their dynamical measure for the interacting bosons in an optical lattice with both commensurate and incommensurate filling factor. We solve the many-body Schrödinger equation from first principles by multiconfigurational time-dependent Hartree method which calculates all the measures with high level of accuracy. We find for both relaxed state as well as quenched state the López-Ruiz-Mancini-Calbet (LMC) measure of complexity is the most efficient depictor of superfluid (SF) to Mott-insulator transition. In the quench dynamics, the distinct structure of LMC complexity can be used as a "figure of merit" to obtain the timescale of SF to Mott state entry, Mott holding time, and the Mott state to SF state entry in the successive cycles. We also find that fluctuations in the dynamics of LMC complexity measure for incommensurate filling clearly establish that superfluid to Mott-insulator transition is incomplete. We overall conclude that distinct structure in the complexity makes it more sensitive than the standard use of Shannon information entropy.
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Affiliation(s)
- Rhombik Roy
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Barnali Chakrabarti
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - N D Chavda
- Department of Applied Physics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara-390001, India
| | - M L Lekala
- Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa
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Hazra S. A comparative study on information theoretic approach for atomic and molecular systems. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Majumdar S, Mukherjee N, Roy AK. Information entropy and complexity measure in generalized Kratzer potential. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2018.12.032] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Flores-Gallegos N. Generalized Shannon’s entropies in position and momentum spaces. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1142/s0219633617500511] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this report, we present three generalized expressions of Shannon’s entropy using the electron densities of position and momentum spaces. Such expressions were obtained using the definition of deformed logarithm introduced by Tsallis. We show that only one expression fulfils the dimensionless criterion, it is strictly positive overall space and follows a growing behavior with respect to the electron number. We also found that by using some values of [Formula: see text], it is possible to reproduce the general trends of the radial distribution in position space and momentum space of the neon atom.
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Affiliation(s)
- N. Flores-Gallegos
- Benemérita Universidad de Guadalajara, Centro Universitario de los Valles, Carretera Guadalajara — Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, México
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Alipour M, Safari Z. From information theory to quantitative description of steric effects. Phys Chem Chem Phys 2016; 18:17917-29. [DOI: 10.1039/c6cp02750d] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this study, further evidences of the efficiency of informational theory for a quantitative description of steric effects are showcased.
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Affiliation(s)
- Mojtaba Alipour
- Department of Chemistry
- College of Sciences
- Shiraz University
- Shiraz
- Iran
| | - Zahra Safari
- Department of Chemistry
- College of Sciences
- Shiraz University
- Shiraz
- Iran
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Esquivel RO, Molina-Espíritu M, López-Rosa S, Soriano-Correa C, Barrientos-Salcedo C, Kohout M, Dehesa JS. Predominant information quality scheme for the essential amino acids: an information-theoretical analysis. Chemphyschem 2015; 16:2571-81. [PMID: 26175003 DOI: 10.1002/cphc.201500282] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Revised: 05/11/2015] [Indexed: 11/05/2022]
Abstract
In this work we undertake a pioneer information-theoretical analysis of 18 selected amino acids extracted from a natural protein, bacteriorhodopsin (1C3W). The conformational structures of each amino acid are analyzed by use of various quantum chemistry methodologies at high levels of theory: HF, M062X and CISD(Full). The Shannon entropy, Fisher information and disequilibrium are determined to grasp the spatial spreading features of delocalizability, order and uniformity of the optimized structures. These three entropic measures uniquely characterize all amino acids through a predominant information-theoretic quality scheme (PIQS), which gathers all chemical families by means of three major spreading features: delocalization, narrowness and uniformity. This scheme recognizes four major chemical families: aliphatic (delocalized), aromatic (delocalized), electro-attractive (narrowed) and tiny (uniform). All chemical families recognized by the existing energy-based classifications are embraced by this entropic scheme. Finally, novel chemical patterns are shown in the information planes associated with the PIQS entropic measures.
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Affiliation(s)
- Rodolfo O Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, 09340-México, D.F. (México). .,Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada (Spain).
| | | | - Sheila López-Rosa
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada (Spain).,Departamento de Física Aplicada II, Universidad de Sevilla, 41012-Sevilla (Spain)
| | - Catalina Soriano-Correa
- Laboratorio de Química Computacional, FES-Zaragoza, Universidad Nacional Autónoma de México, 09230-Iztapalapa, México, D.F. (México)
| | - Carolina Barrientos-Salcedo
- Facultad de Bioanálisis-Veracruz, Universidad Veracruzana, Laboratorio de Química Médica y Quimiogenómica, 91700-Veracruz (México)
| | - Miroslav Kohout
- Max Planck Institute for Chemical Physics of Solids, Noethnitzer Str. 40, 01187-Dresden (Germany)
| | - Jesús S Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada (Spain)
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Alipour M. Making a happy match between orbital-free density functional theory and information energy density. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.06.073] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Martín A, López-Rosa S, Angulo J, Antolín J. Jensen–Shannon and Kullback–Leibler divergences as quantifiers of relativistic effects in neutral atoms. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.06.037] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Alipour M. Wave vector, local momentum and local coordinate from the perspective of information theory. Mol Phys 2013. [DOI: 10.1080/00268976.2013.777814] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Alipour M, Mohajeri A. Onicescu information energy in terms of Shannon entropy and Fisher information densities. Mol Phys 2012. [DOI: 10.1080/00268976.2011.649795] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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On the relationship between one-electron potential and densities of Fisher information and Shannon entropy. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.10.027] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Esquivel RO, Liu S, Angulo JC, Dehesa JS, Antolín J, Molina-Espíritu M. Fisher Information and Steric Effect: Study of the Internal Rotation Barrier of Ethane. J Phys Chem A 2011; 115:4406-15. [DOI: 10.1021/jp1095272] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Rodolfo O. Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, 09340 México D.F., México
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States
| | | | | | - Juan Antolín
- Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Bouvrie P, Antolín J, Angulo J. Generalized Quantum Similarity Index: Applications in atoms. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.03.059] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Masoller C, Rosso OA. Quantifying the complexity of the delayed logistic map. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:425-438. [PMID: 21149381 DOI: 10.1098/rsta.2010.0281] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the 'histogram-based' probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of the delay-induced dynamics: there are parameter regions where the histogram-based complexity is zero while the ordinal pattern complexity is not, and vice versa. We also show that the time series generated from the nonlinear delayed logistic map can present zero missing or forbidden patterns, i.e. all possible ordinal patterns are realized into orbits.
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Affiliation(s)
- Cristina Masoller
- Departament de Física i Enginyeria Nuclear, Escola Tecnica Superior d'Enginyeries Industrial i Aeronautica de Terrassa, Universitat Politècnica de Catalunya, Colom 11, 08222 Terrassa, Barcelona, Spain.
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Moustakidis CC, Psonis VP, Chatzisavvas KC, Panos CP, Massen SE. Statistical measure of complexity and correlated behavior of Fermi systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011104. [PMID: 20365320 DOI: 10.1103/physreve.81.011104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2009] [Revised: 10/19/2009] [Indexed: 05/29/2023]
Abstract
We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini, and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas, and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.
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Affiliation(s)
- Ch C Moustakidis
- Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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Esquivel RO, Angulo JC, Antolín J, Dehesa JS, López-Rosa S, Flores-Gallegos N. Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Phys Chem Chem Phys 2010; 12:7108-16. [DOI: 10.1039/b927055h] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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López-Rosa S, Esquivel RO, Angulo JC, Antolín J, Dehesa JS, Flores-Gallegos N. Fisher Information Study in Position and Momentum Spaces for Elementary Chemical Reactions. J Chem Theory Comput 2009; 6:145-54. [DOI: 10.1021/ct900544m] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Sheila López-Rosa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Rodolfo O. Esquivel
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Carlos Angulo
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Antolín
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Jesús S. Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Nelson Flores-Gallegos
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Esquivel RO, Flores-Gallegos N, Iuga C, Carrera EM, Angulo JC, Antolín J. Phenomenological description of the transition state, and the bond breaking and bond forming processes of selected elementary chemical reactions: an information-theoretic study. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0641-x] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Antolín J, Angulo JC, López-Rosa S. Fisher and Jensen-Shannon divergences: Quantitative comparisons among distributions. Application to position and momentum atomic densities. J Chem Phys 2009; 130:074110. [PMID: 19239287 DOI: 10.1063/1.3078050] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
The Fisher divergence (FD) and Jensen-Shannon divergence (JSD) are used in this work with the aim of providing quantitative measures of the discrepancies between two arbitrary D-dimensional distribution functions, the FD being of local character and the JSD of global one. In doing so, the concepts of Fisher information and Shannon entropy associated to a distribution are the essential quantities for building up these comparative functionals. This kind of relative measures are here applied to the study of the one-particle densities in both conjugated spaces (position and momentum) of neutral atoms, discussing the results as compared to those provided by other previous functional measures. It is clearly shown how these divergences provide relevant information on the atomic shell structure, up to a level which depends on the considered space and measure.
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Affiliation(s)
- J Antolín
- Departamento de Fisica Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Luzanov AV. Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems. J Chem Phys 2008; 129:094103. [DOI: 10.1063/1.2968607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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