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Priya, Sadhukhan M. Kinetic energy density for open-shell systems: analysis and development of a novel technique. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2136114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
Affiliation(s)
| | - Mainak Sadhukhan
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India
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Sadhukhan M, Deb B. Structure, dynamics and quantum chaos in atoms and molecules under strong magnetic fields. J INDIAN CHEM SOC 2021. [DOI: 10.1016/j.jics.2021.100112] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Kaya S, Chattaraj P, Serdaroğlu G. Two empirical formulae for estimating standard entropy of inorganic ionic solids and a possible connection between two associated electronic structure principles. Polyhedron 2021. [DOI: 10.1016/j.poly.2021.115207] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Chakraborty D, Chattaraj PK. Conceptual density functional theory based electronic structure principles. Chem Sci 2021; 12:6264-6279. [PMID: 34084424 PMCID: PMC8115084 DOI: 10.1039/d0sc07017c] [Citation(s) in RCA: 61] [Impact Index Per Article: 20.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 03/10/2021] [Indexed: 12/20/2022] Open
Abstract
In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.
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Affiliation(s)
- Debdutta Chakraborty
- Department of Chemistry, KU Leuven Celestijnenlaan 200F-2404 3001 Leuven Belgium
| | - Pratim Kumar Chattaraj
- Department of Chemistry, Indian Institute of Technology Kharagpur 721302 West Bengal India +91 3222 255303 +91 3222 283304
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
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Abstract
The chemical reactivity of a molecule as a whole or of an atom in a molecule varies during a chemical reaction. A variation of global and local reactivity descriptors in the course of a physicochemical process was studied within a quantum fluid density functional theory framework. Effects of a physical confinement and the electronic excitation therein were studied. In this Perspective, we also highlight the direction of a spontaneous chemical reaction in the light of the dynamical variants of the conceptual density functional theory-based electronic structure principles. An exhaustive state-of-the-art dynamical study is warranted in order to understand a chemical reaction from a reactivity perspective augmenting the associated molecular reaction dynamics analysis.
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Affiliation(s)
- Utpal Sarkar
- Department of Physics, Assam University, Silchar 788011, India
| | - Pratim Kumar Chattaraj
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India.,Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India
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Goel N, Gupta S, Sadhukhan M, Deb BM. Electron dynamics in H 2+ molecule-ion under a strong, oscillating magnetic field. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1676930] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- N. Goel
- Department of Chemistry and Centre for Advanced Studies in Chemistry, Panjab University, Chandigarh, India
| | - S. Gupta
- University Institute of Engineering & Technology, Panjab University, Chandigarh, India
| | - M. Sadhukhan
- Department of Chemistry, Indian Institute of Technology, Kanpur, India
| | - B. M. Deb
- Publishing Department, Visva-Bharati University, Kolkata, India
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Chakraborty D, Chattaraj PK. Bonding, Reactivity, and Dynamics in Confined Systems. J Phys Chem A 2019; 123:4513-4531. [DOI: 10.1021/acs.jpca.9b00830] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Debdutta Chakraborty
- Department of Chemistry and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, West Bengal, India
| | - Pratim Kumar Chattaraj
- Department of Chemistry and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, West Bengal, India
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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Sadhukhan M, Deb BM. An investigation into possible quantum chaos in the H 2 molecule under intense laser fields via Ehrenfest phase space (EPS) trajectories. J Mol Model 2018; 24:169. [PMID: 29931557 DOI: 10.1007/s00894-018-3698-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Accepted: 05/27/2018] [Indexed: 11/25/2022]
Abstract
By employing the Ehrenfest "phase space" trajectory method for studying quantum chaos, developed in our laboratory, the present study reveals that the H2 molecule under intense laser fields of three different intensities, I = 1 × 1014 W/cm2, 5 × 1014 W/cm2, and 1 × 1015 W/cm2, does not show quantum chaos. A similar conclusion is also reached through the Loschmidt echo (also called quantum fidelity) calculations reported here for the first time for a real molecule under intense laser fields. Thus, a long-standing conjecture about the possible existence of quantum chaos in atoms and molecules under intense laser fields has finally been tested and not found to be valid in the present case.
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Affiliation(s)
- Mainak Sadhukhan
- Department of Chemical, Biological and Macromolecular Sciences, S. N. Bose National Centre for Basic Sciences, Kolkata, 700098, India
- Physics and Materials Science Research Unit, Université du Luxembourg, 162 A, avenue de la Faïencerie, L-1511, Luxembourg City, Luxembourg
| | - B M Deb
- Publishing Department, Visva-Bharati University, 6 A. J. C. Bose Road, Kolkata, 700017, India.
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Sadhukhan M, Deb B. Ehrenfest ‘phase-space’ trajectories and quantum chaos in He atom under strong, oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory (TDQFDFT). Mol Phys 2017. [DOI: 10.1080/00268976.2017.1288277] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Mainak Sadhukhan
- Department of Chemical Sciences, Indian Institute of Science Education and Research, Mohanpur, India
- Department of Chemical, Biological and Macromolecular Sciences, S. N. Bose National Centre for Basic Sciences, Kolkata, India
| | - B.M. Deb
- V isva-Bharati University, Santiniketan, India
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Sadhukhan M, Deb BM. Dynamical deformations of the electron density in an H 2 molecule under strong, oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1241906] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Mainak Sadhukhan
- Department of Chemical Sciences, Indian Institute of Science Education and Research-Kolkata, Mohanpur, India
| | - B. M. Deb
- Visva-Bharati University, Santiniketan, India
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Chakraborty D, Kar S, Chattaraj PK. Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system. Phys Chem Chem Phys 2015; 17:31516-29. [PMID: 26033095 DOI: 10.1039/c5cp00995b] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Regular to chaotic transition takes place in a driven van der Pol oscillator in both classical and quantum domains.
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Affiliation(s)
- Debdutta Chakraborty
- Department of Chemistry and Centre for Theoretical Studies
- Indian Institute of Technology
- West Bengal
- India
| | - Susmita Kar
- Department of Chemistry and Centre for Theoretical Studies
- Indian Institute of Technology
- West Bengal
- India
| | - Pratim Kumar Chattaraj
- Department of Chemistry and Centre for Theoretical Studies
- Indian Institute of Technology
- West Bengal
- India
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Khatua M, Chattaraj PK. Molecular reactivity dynamics in a confined environment. Phys Chem Chem Phys 2013; 15:5588-614. [DOI: 10.1039/c3cp43511c] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Sarkar U, Khatua M, Chattaraj PK. A tug-of-war between electronic excitation and confinement in a dynamical context. Phys Chem Chem Phys 2012; 14:1716-27. [DOI: 10.1039/c1cp22862e] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Harbola MK, Banerjee A. Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s021963360300046x] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.
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Affiliation(s)
- Manoj K. Harbola
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
| | - Arup Banerjee
- Laser Physics Division, Centre for Advanced Technology, Indore 452013, India
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Affiliation(s)
- Pratim Kumar Chattaraj
- Department of Chemistry, Center for Theoretical Studies, Indian Institute of Technology, Kharagpur, India
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He 2++ molecular ion in a strong time-dependent magnetic field: a current-density functional study. J Comput Chem 2011; 32:2404-13. [PMID: 21598275 DOI: 10.1002/jcc.21822] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2010] [Revised: 02/10/2011] [Accepted: 03/22/2011] [Indexed: 11/07/2022]
Abstract
The He 2++ molecular ion exposed to a strong ultrashort time-dependent (TD) magnetic field of the order of 10(9) G is investigated through a quantum fluid dynamics (QFD) and current-density functional theory (CDFT) based approach using vector exchange-correlation (XC) potential and energy density functional that depend not only on the electronic charge-density but also on the current density. The TD-QFD-CDFT computations are performed in a parallel internuclear-axis and magnetic field-axis configuration at the field-free equilibrium internuclear separation R = 1.3 au with the field-strength varying between 0 and 10(11) G. The TD behavior of the exchange- and correlation energy of the He 2++ is analyzed and compared with that obtained using a [B-TD-QFD-density functional theory (DFT)] approach based on the conventional TD-DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge-density alone. The CDFT based approach yields TD exchange- and correlation energy and TD electronic charge-density significantly different from that obtained using the conventional TD-DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT-based approach is traced to the TD current-density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He 2++ molecular ion is elucidated by treating electronic charge density as an electron-"fluid" in the terminology of QFD.
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Chattaraj PK, Giri S. Electrophilicity index within a conceptual DFT framework. ACTA ACUST UNITED AC 2009. [DOI: 10.1039/b802832j] [Citation(s) in RCA: 152] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Wadehra A, Deb BM. Time-dependent quantum fluid density functional theory of hydrogen molecule under intense laser fields. J CHEM SCI 2008. [DOI: 10.1007/s12039-007-0044-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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20
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Christov IP. Time-dependent quantum Monte Carlo and the stochastic quantization. J Chem Phys 2007; 127:134110. [DOI: 10.1063/1.2779038] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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Affiliation(s)
- Pratim Kumar Chattaraj
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, IndiaThis is a Chemical Reviews Perennial Review. The root paper of this title was published in 2006 (Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065). Updates to the text appear in red type
| | - Debesh Ranjan Roy
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, IndiaThis is a Chemical Reviews Perennial Review. The root paper of this title was published in 2006 (Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065). Updates to the text appear in red type
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Ovchinnikov IV, Bartell LA, Neuhauser D. Hydrodynamic tensor density functional theory with correct susceptibility. J Chem Phys 2007; 126:134101. [PMID: 17430010 DOI: 10.1063/1.2716667] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.
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Affiliation(s)
- Igor V Ovchinnikov
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095-1569, USA
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Chapter 13 Chemical reactivity dynamics in ground and excited electronic states. ACTA ACUST UNITED AC 2007. [DOI: 10.1016/s1380-7323(07)80014-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2023]
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Ovchinnikov IV, Neuhauser D. Orbital-free tensor density functional theory. J Chem Phys 2006; 124:024105. [PMID: 16422569 DOI: 10.1063/1.2148953] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We propose a family of time-dependent orbital-free density-based theories that go beyond the usual current-density description of electrons or other particles. The theories deal with physical quantities that characterize the one-particle density matrix and consequently the kinetics of the particles. We analyze the first two theories in the family. The "lowest-order" theory is quantum hydrodynamics. The second one yields not only the longitudinal plasmon collective excitations, but also the transverse phonon modes that are associated with elementary excitations in Fermi liquids. The theories should make it feasible to do large orbital-free simulations of time-dependent and stationary systems.
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Affiliation(s)
- Igor V Ovchinnikov
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095-1569, USA
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Chu SI. Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields. J Chem Phys 2005; 123:62207. [PMID: 16122293 DOI: 10.1063/1.1904587] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.
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Affiliation(s)
- Shih-I Chu
- Department of Chemistry, University of Kansas, and Kansas Center for Advanced Scientific Computing, Lawrence, Kansas 66045, USA.
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Chattaraj PK, Maiti B, Sarkar U. Chemical reactivity of the compressed noble gas atoms and their reactivity dynamics during collisions with protons. J CHEM SCI 2003. [DOI: 10.1007/bf02704259] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Chattaraj PK, Maiti B. HSAB principle applied to the time evolution of chemical reactions. J Am Chem Soc 2003; 125:2705-10. [PMID: 12603158 DOI: 10.1021/ja0276063] [Citation(s) in RCA: 152] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Time evolution of various reactivity parameters such as electronegativity, hardness, and polarizability associated with a collision process between a proton and an X- atom/ion (X = He, Li(+), Be(2+), B(3+), C(4+)) in its ground ((1)S) and excited((1)P,(1)D,(1)F) electronic states as well as various complexions of a two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion and a proton to give rise to an XH(+) molecule. A favorable dynamical process is characterized by maximum hardness and minimum polarizability values according to the dynamical variants of the principles of maximum hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid, gradually prefers less to interact with X as has been discerned through the drop in maximum hardness value and the increase in the minimum polarizability value when the actual chemical process occurs. Among the noble gas elements, Xe is the most reactive. During the reaction: H(2) + H(+) --> H(3)(+) hardness maximizes and polarizability minimizes and H(2) is more reactive in its excited state. Regioselectivity of proton attack in the O-site of CO is clearly delineated wherein HOC(+) may eventually rearrange itself to go to the thermodynamically more stable HCO(+).
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Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach. Int J Mol Sci 2002. [DOI: 10.3390/i3040338] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Chattaraj PK, Maiti B. Reactivity Dynamics in Atom−Field Interactions: A Quantum Fluid Density Functional Study. J Phys Chem A 2000. [DOI: 10.1021/jp0019660] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- P. K. Chattaraj
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
| | - B. Maiti
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
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Hu XG, Ho TS, Rabitz H, Askar A. Solution of the quantum fluid dynamical equations with radial basis function interpolation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5967-76. [PMID: 11031661 DOI: 10.1103/physreve.61.5967] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/1999] [Indexed: 11/07/2022]
Abstract
The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation psi = exp(R + iS)/[symbol: see text]. The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density rho = magnitude of psi 2 and on the structure of R = [symbol: see text]/2 ln rho generally being simpler and smoother than rho. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase for higher dimensional systems to provide a practical computational tool.
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Affiliation(s)
- XG Hu
- Department of Chemistry, Princeton University, New Jersey 08544-1009, USA
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Chattaraj P, Sengupta S, Poddar A. Quantum fluid density functional theory of chemical reactivity in a two-state ensemble. ACTA ACUST UNITED AC 2000. [DOI: 10.1016/s0166-1280(99)00444-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Chattaraj PK, Poddar A. Molecular Reactivity in the Ground and Excited Electronic States through Density-Dependent Local and Global Reactivity Parameters. J Phys Chem A 1999. [DOI: 10.1021/jp991214+] [Citation(s) in RCA: 73] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Mayor FS, Askar A, Rabitz HA. Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems. J Chem Phys 1999. [DOI: 10.1063/1.479520] [Citation(s) in RCA: 99] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Chattaraj PK, Sengupta S. Chemical Hardness as a Possible Diagnostic of the Chaotic Dynamics of Rydberg Atoms in an External Field. J Phys Chem A 1999. [DOI: 10.1021/jp990242p] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- P. K. Chattaraj
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
| | - S. Sengupta
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
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Dey BK, Deb BM. Direct ab initio calculation of ground-state electronic energies and densities for atoms and molecules through a time-dependent single hydrodynamical equation. J Chem Phys 1999. [DOI: 10.1063/1.478527] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Chattaraj PK, Sengupta S. Popular Electronic Structure Principles in a Dynamical Context. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp961096f] [Citation(s) in RCA: 304] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- P. K. Chattaraj
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
| | - S. Sengupta
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India
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Chattaraj PK, Nath S. A dynamical study of the principle of maximum hardness. J CHEM SCI 1994. [DOI: 10.1007/bf02840746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Deb BM, Chattaraj PK. Thomas-Fermi-type method for the direct calculation of electronic densities and properties of atoms and ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:1412-1419. [PMID: 9907122 DOI: 10.1103/physreva.45.1412] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Deb BM, Chattaraj PK, Mishra S. Time-dependent quantum-fluid density-functional study of high-energy proton-helium collisions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:1248-1257. [PMID: 9905151 DOI: 10.1103/physreva.43.1248] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chattaraj PK. First-gradient corrections in Thomas-Fermi theory. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6505-6508. [PMID: 9903049 DOI: 10.1103/physreva.41.6505] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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