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time-correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

NONLINEAR DYNAMICS 2022年第2期110卷 1597-1612页

作者： Nath, Debraj Roy, Amlan K. Vivekananda Coll Dept Math Kolkata 700063 WB India Indian Inst Sci Educ & Res IISER Kolkata Dept Chem Sci Nadia 741246 WB India

For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrodinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, and quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of the density function, with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.

关键词： Deng-Fan potential Ro-vibrational energy Average energy time-correlation function Auto-correlation function Quantum similarity index Moving boundary

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Analysis of solutions of time-dependent Schrodinger equation of a particle trapped in a spherical box

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JOURNAL OF MATHEMATICAL CHEMISTRY 2022年第6期60卷 1089-1106页

作者： Nath, Debraj Carbo-Dorca, Ramon Vivekananda Coll Dept Math 269 DH Rd Kolkata 700063 WB India Univ Girona Inst Quim Computac & Catalisi Girona 17071 Catalonia Spain Ronin Inst Montclair NJ USA

Three sets of exact solutions of the time-dependent Schrodinger equation of a particle that is trapped in a spherical box with a moving boundary wall have been calculated analytically. For these solutions, some physical quantities such as time-dependent average energy, average force, disequilibrium, quantum similarity measures as well as quantum similarity index have been investigated. Moreover, these solutions are compared concerning these physical quantities. The time-correlation functions among these solutions are investigated.

关键词： time dependent Schrodinger equation Average energy Average force time-correlation function Quantum similarity index Disequilibrium time dependent spherical box

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A model of pre-reaction complexes

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CHEMICAL PHYSICS 2024年 577卷

作者： Ozkilic, Yilmaz Istanbul Tech Univ Dept Chem TR-34469 Maslak Istanbul Turkiye

One of the main objectives of computational chemistry studies is the interpretation of chemical mechanisms whose data were obtained from quantum mechanical software packages. In these mechanisms, starting from the reactant, the reactant and the product states are connected through intermediates and transition states, in an alternating order. Generally, the reactivity of a given pathway is determined by the overall barrier height. Sometimes, a comparison becomes necessary for a given step with another possible step that can be realized within the same mechanism, and in this case as well the step with the lowest-lying transition state is preferred. However, there are some exceptions in the order of these states. There are states known as pre -reaction complexes that reside between a reactant, or an intermediate, and a transition state. Excluding some first principle quantum dynamics studies, the effect of a pre-reaction complex is generally not discussed in most of the computational chemistry studies, and the overall barrier heights become the main considerations, as usual. In this work, a mathematical model that allows obtaining the rate constant of a pathway without a pre -reaction complex, and that of a pathway with a pre-reaction complex was described. The model was built using time-dependent quantum perturbation theory and quantum time-correlation functions. This work can improve our understanding of the nature of chemical reactions that include pre-reaction complexes by enabling us to differentiate the seemingly identical reaction pathways.

关键词： Mechanism Intermediate Reaction rate Metal complex time-dependent perturbation theory time-correlation function Three-level system

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An Efficient timer and Sizer of Biomacromolecular Motions

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STRUCTURE 2020年第2期28卷 259-+页

作者： Chan, Justin Takemura, Kazuhiro Lin, Hong-Rui Chang, Kai-Chun Chang, Yuan-Yu Joti, Yasumasa Kitao, Akio Yang, Lee-Wei Natl Tsing Hua Univ Inst Bioinformat & Struct Biol 101Sect 2Kuang Fu Rd Hsinchu 30013 Taiwan Taiwan Int Grad Program Acad Sinica Inst Informat Sci Bioinformat Program Taipei Taiwan Tokyo Inst Technol Sch Life Sci & Technol 2-12-1 Ookayama Tokyo M613 Japan Natl Taiwan Univ Inst Mol & Cellular Biol Taipei Taiwan Japan Synchrotron Radiat Res Inst XFEL Utilizat Div I-1-1 KoutoSayo Cho Sayo-gun Hyogo 6795198 Japan Div Phys Natl Ctr Theoret Sci Hsinchu Taiwan

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods,'' t, for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods'' are mapped to the eigenvalues (lambda(ENM)) of the corresponding ENM modes. Thus, the power laws t(ns) = 56.1 lambda(-1.6)(ENM) and sigma(2)(angstrom(2)) = 32.7 lambda(-3.0)(ENM) can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.

关键词： protein dynamics molecular dynamics simulations principal component analysis (PCA) elastic network model (ENM) Wiener-Khintchine theorem time-correlation function power spectrum anharmonicity order parameter ribosome

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Covariant Lyapunov Analysis of Chaotic Kolmogorov Flows and time-correlation function

Covariant Lyapunov Analysis of Chaotic Kolmogorov Flows and ...

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IUTAM Symposium on 50 Years of Chaos - Applied and Theoretical

作者： Inubushi, Masanobu Kobayashi, Miki U. Takehiro, Shin-ichi Yamada, Michio Kyoto Univ Math Sci Res Inst Kyoto 6068502 Japan Univ Tokyo Collaborat Res Ctr Innovat Math Modelling Inst Ind Sci Meguro Ku Tokyo 1538505 Japan Univ Tokyo Inst Ind Sci Tokyo 1538505 Japan

We study a hyperbolic/non-hyperbolic transition of the flows on two-dimensional torus governed by the incompressible Navier-Stokes equation (Kolmogorov flows) using the method of covariant Lyapunov analysis developed by Ginelli et al.(2007) [1]. As the Reynolds number is increased, chaotic Kolmogorov flows become non-hyperbolic at a certain Reynolds number, where some new physical property is expected to appear in the long-time statistics of the fluid motion. Here we focus our attention on behaviors of the time-correlation function of vorticity across the transition point, and that the long-time asymptotic form of the correlation function changes at the Reynolds number close to that of the hyperbolic/non-hyperbolic transition, which suggests that the time-correlation function reflects the transition to non-hyperbolicity [3]. (c) 2012 Published by Elsevier Ltd. Selection and/or Peer-review under responsibility of Takashi Hikihara and Tsutomu Kambe

关键词： Covariant Lyapunov vector Kolmogorov flow time-correlation function

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Covariant Lyapunov Analysis of Chaotic Kolmogorov Flows and time-correlation function

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Procedia IUTAM 2012年 5卷 244-248页

作者： Masanobu Inubushi Miki U. Kobayashi Shin-ichi Takehiro Michio Yamada Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan Collaborative Research Center for Innovative Mathematical Modelling Institute of Industrial Science The University of Tokyo 4-6-1 Komaba Meguro-ku Tokyo 153-8505 Japan Institute of Industrial Science University of Tokyo Tokyo 153-8505 Japan

We study a hyperbolic/non-hyperbolic transition of the flows on two-dimensional torus governed by the incompressible Navier-Stokes equation (Kolmogorov flows) using the method of covariant Lyapunov analysis developed by Ginelli et al.(2007) [1] . As the Reynolds number is increased, chaotic Kolmogorov flows become non-hyperbolic at a certain Reynolds number, where some new physical property is expected to appear in the long-time statistics of the fluid motion. Here we focus our attention on behaviors of the time-correlation function of vorticity across the transition point, and that the long-time asymptotic form of the correlation function changes at the Reynolds number close to that of the hyperbolic/non-hyperbolic transition, which suggests that the time-correlation function reflects the transition to non-hyperbolicity [3] .

关键词： Covariant Lyapunov vector Kolmogorov flow time-correlation function

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Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space

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ANNUAL REVIEW OF PHYSICAL CHEMISTRY, VOL 64 2013年第1期64卷 387-413页

作者： Habershon, Scott Manolopoulos, David E. Markland, Thomas E. Miller, Thomas F., III Univ Warwick Dept Chem Coventry CV4 7AL W Midlands England Univ Oxford Phys & Theoret Chem Lab Oxford OX1 3QZ England Stanford Univ Dept Chem Stanford CA 94305 USA CALTECH Dept Chem & Chem Engn Pasadena CA 91125 USA

This article reviews the ring-polymer molecular dynamics model for condensed-phase quantum dynamics. This model, which involves classical evolution in an extended ring-polymer phase space, provides a practical approach to approximating the effects of quantum fluctuations on the dynamics of condensed-phase systems. The review covers the theory, implementation, applications, and limitations of the approximation.

关键词： quantum dynamics path integral tunneling zero-point energy time-correlation function semiclassical theory

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In search of the dark state of 5-methyl-2-hydroxypyrimidine using a numerical DFT/MRCI gradient

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MOLECULAR PHYSICS 2012年第19-20期110卷 2429-2438页

作者： Pohler, Larissa Kleinschmidt, Martin Etinski, Mihajlo Marian, Christel M. Univ Dusseldorf Inst Theoret & Computat Chem D-40225 Dusseldorf Germany Univ Belgrade Fac Phys Chem Belgrade 11000 Serbia

In a recent publication, Lobsiger et al. [Phys. Chem. Chem. Phys. 12, 5032 (2010)] presented infrared and electronic absorption spectra of supersonic jet-cooled 5-methyl-2-hydroxypyrimidine (5M2HP), the enol form of deoxythymine. In addition, they reported on the fast nonradiative decay of the S-1 population to a dark state. In the present paper, we have investigated the mechanism and rate constants of this nonradiative decay by means of quantum chemical multi-configuration methods. To this end, minima of the lowest excited singlet and triplet states as well as the minimum-energy crossing point of singlet and triplet potential energy hypersurfaces (PEHs) have been determined employing a numerical DFT/MRCI gradient where DFT/MRCI stands for a combination of density functional theory (DFT) and a semi-empirical multi-reference configuration interaction (MRCI) approach. Rate constants have been calculated in the Condon approximation using a time-dependent approach based on harmonic oscillator functions and electronic spin-orbit coupling matrix elements evaluated at the DFT/MRCI level. It is shown that the first excited triplet state possesses (3)(n ->pi*) character in the gas phase. Fast intersystem crossing is mediated by the low-lying (3)(pi ->pi*) state whose PEH crosses both, the S-1 (1)(n ->pi*) and T-1 (3)(n ->pi*) PEHs.

关键词： multireference configuration interaction numerical gradient minimum-energy crossing point spin-forbidden transition spin-orbit coupling time-correlation function

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Vibrational spectra of an LiNO₃-(CH₃)₂SO₂ system

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JOURNAL OF APPLIED SPECTROSCOPY 2012年第2期79卷 184-188页

作者： Gafurov, M. M. Rabadanov, K. Sh. Ataev, M. B. Aliev, A. R. Ahmedov, I. R. Kakagasanov, M. G. Kraminin, S. P. Russian Acad Sci Dagestan Sci Ctr Inst Phys Makhachkala 367025 Russia

Raman and IR absorption spectra were studied and molecular relaxation characteristics of vibrations of the anion and solvent were calculated for an xLiNO(3)-(1 - x)(CH3)(2)SO2 system (x = 0.1, 0.2, 0.3, 0.4 M). It was found that it is impossible to increase the concentration of free ions involved in charge transfer in such a system by either increasing the temperature or changing the concentration composition in the studied range of x.

关键词： Raman spectra vibrational dephasing time-correlation function dimethylsulfone vibrational relaxation

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Phase equilibriums, ion association, and mechanisms of solvation in the LiN(CF₃SO₂)₂-(CH₃)₂SO₂ system

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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2011年第9期85卷 1499-1504页

作者： Gafurov, M. M. Rabadanov, K. Sh. Prisyazhnyi, V. D. Tret'yakov, D. O. Gorobets, M. I. Kirillov, S. A. Ataev, M. B. Kakagasanov, M. M. Russian Acad Sci Amirkhanov Inst Phys Makhachkala 367003 Russia Russian Acad Sci Analyt Ctr Collect Use Dagestan Sci Ctr Makhachkala 367003 Russia Natl Acad Sci Ukraine Interagcy Dept Electrochem Energy Syst UA-03142 Kiev Ukraine Natl Acad Sci Ukraine Inst Sorpt & Problems Endoecol UA-03163 Kiev Ukraine

The phase diagrams, isotherms of the electrical conductivity, Raman spectra, and time correlation functions of vibrational dephasing are studied for the LiN(CF3SO2)(2)-(CH3)(2)SO2 system, which is promising for use as an electrolyte in medium-temperature lithium-ion batteries. The phase diagram of this system contains a broad supercooled region. It is shown that the concentration dependences of the electrical conductivity are typical for solutions of strong electrolytes. The Raman spectra and the time correlation functions of vibrational dephasing for the anion and the solvent indicate that in the supercooling range, cations are weakly solvated by solvent molecules and form ion pairs.

关键词： Raman spectra phase diagram solvation vibrational dephasing time-correlation function

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