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Ravi S, Mukherjee S, Mukherjee B, Adhikari S, Sathyamurthy N, Baer M. Non-adiabatic coupling as a frictional force in (He, H, H)+ dynamics and the formation of HeH2+. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1811907] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Kolkata, India
| | | | - Michael Baer
- The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem, Israel
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Schild A. On the Probability Density of the Nuclei in a Vibrationally Excited Molecule. Front Chem 2019; 7:424. [PMID: 31245359 PMCID: PMC6562893 DOI: 10.3389/fchem.2019.00424] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Accepted: 05/22/2019] [Indexed: 11/24/2022] Open
Abstract
For localized and oriented vibrationally excited molecules, the qualitative features of the one-body probability density of the nuclei (one-nucleus density) are investigated. Like the familiar and widely used one-electron density that represents the probability of finding an electron at a given location in space, the one-nucleus density represents the probability of finding a nucleus at a given position in space independent of the location of the other nuclei and independent of their type. In contrast to the electrons, however, the nuclei are comparably localized. Due to this localization of the individual nuclei, the one-nucleus density provides a quantum-mechanical representation of the "chemical picture" of the molecule as an object that can largely be understood in a three-dimensional space, even though its full nuclear probability density is defined on the high-dimensional configuration space of all the nuclei. We study how the nodal structure of the wavefunctions of vibrationally excited states translates to the one-nucleus density. It is found that nodes do not necessarily lead to visible changes in the one-nucleus density: Already for relatively small molecules, only certain vibrational excitations change the one-nucleus density qualitatively compared to the ground state. It turns out that there are simple rules for predicting the shape of the one-nucleus density from the normal mode coordinates. A Python module for the computation of the one-nucleus density is provided at https://gitlab.com/axelschild/mQNMc.
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Affiliation(s)
- Axel Schild
- Laboratory for Physical Chemistry, ETH Zürich, Zurich, Switzerland
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3
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Baer M. The special theory of relativity as applied to the Born–Oppenheimer–Huang approach. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1303205] [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]
Affiliation(s)
- Michael Baer
- The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem, Israel
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Requist R, Gross EKU. Exact Factorization-Based Density Functional Theory of Electrons and Nuclei. PHYSICAL REVIEW LETTERS 2016; 117:193001. [PMID: 27858424 DOI: 10.1103/physrevlett.117.193001] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2016] [Indexed: 06/06/2023]
Abstract
The ground state energy of a system of electrons (r=r_{1},r_{2},…) and nuclei (R=R_{1},R_{2},…) is proven to be a variational functional of the electronic density n(r,R) and paramagnetic current density j_{p}(r,R) conditional on R, the nuclear wave function χ(R), an induced vector potential A_{μ}(R) and a quantum geometric tensor T_{μν}(R). n, j_{p}, A_{μ} and T_{μν} are defined in terms of the conditional electronic wave function Φ_{R}(r). The ground state (n,j_{p},χ,A_{μ},T_{μν}) can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing effective scalar and vector potentials v_{s}(r) and A_{xc}(r) that depend parametrically on R, (ii) the Schrödinger equation for χ(R), and (iii) Euler-Lagrange equations that determine T_{μν}. The theory is applied to the E⊗e Jahn-Teller model.
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Affiliation(s)
- Ryan Requist
- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
| | - E K U Gross
- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
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Baer M, Mukherjee B, Mukherjee S, Adhikari S. Time-dependent molecular fields created by the interaction of an external electro-magnetic field with a molecular system: the derivation of the wave equations. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1093183] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Michael Baer
- The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem, Israel
| | - Bijit Mukherjee
- Department of Physical Chemistry, Indian Association for Cultivation of Science, Jadavpur, India
| | - Saikat Mukherjee
- Department of Physical Chemistry, Indian Association for Cultivation of Science, Jadavpur, India
| | - Satrajit Adhikari
- Department of Physical Chemistry, Indian Association for Cultivation of Science, Jadavpur, India
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Filatov M. Assessment of Density Functional Methods for Obtaining Geometries at Conical Intersections in Organic Molecules. J Chem Theory Comput 2013; 9:4526-4541. [PMID: 24124402 PMCID: PMC3794441 DOI: 10.1021/ct400598b] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2013] [Indexed: 11/28/2022]
Abstract
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A number of commonly
available density functionals have been tested
for their ability to describe the energetics and the geometry at conical
intersections in connection with the spin-restricted ensemble referenced
Kohn–Sham (REKS) method. The minimum energy conical intersections
have been optimized for several molecular systems, which are widely
used as paradigmatic models of photochemical rearrangements and models
of biological chromophores. The results of the calculations are analyzed
using the sign-change theorem of Longuet-Higgins and a method of elementary
reaction coordinates of Haas et al. The latter approach helps to elucidate
the differences between the geometries at conical intersections as
predicted by the multireference wave function ab initio methods and by the density functional methods. Overall, the BH&HLYP
density functional yields the best results for the conical intersection
geometries and energetics.
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Affiliation(s)
- Michael Filatov
- Institut für Physikalische und Theoretische Chemie, Universität Bonn , Beringstr. 4, D-53115 Bonn, Germany
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Huix-Rotllant M, Filatov M, Gozem S, Schapiro I, Olivucci M, Ferré N. Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model. J Chem Theory Comput 2013; 9:3917-32. [PMID: 26592387 DOI: 10.1021/ct4003465] [Citation(s) in RCA: 78] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.
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Affiliation(s)
- Miquel Huix-Rotllant
- Aix-Marseille Université, CNRS, Institut de Chimie Radicalaire , 13397 Marseille Cedex 20, France
| | - Michael Filatov
- Institut für Physicalische und Theoretische Chemie, Universität Bonn , Beringstr. 4, 53115 Bonn, Germany
| | - Samer Gozem
- Department of Chemistry, Bowling Green State University , Bowling Green, Ohio 43402, United States
| | - Igor Schapiro
- Department of Chemistry, Bowling Green State University , Bowling Green, Ohio 43402, United States.,Max Planck Institute for Chemical Energy Conversion , Stiftstr. 34 - 36, Mülheim an der Ruhr, Germany
| | - Massimo Olivucci
- Department of Chemistry, Bowling Green State University , Bowling Green, Ohio 43402, United States.,Dipartimento di Chimica, Università di Siena , Siena, Italy
| | - Nicolas Ferré
- Aix-Marseille Université, CNRS, Institut de Chimie Radicalaire , 13397 Marseille Cedex 20, France
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Das A, Sahoo T, Mukhopadhyay D, Adhikari S, Baer M. Dressed adiabatic and diabatic potentials to study conical intersections for F + H2. J Chem Phys 2012; 136:054104. [DOI: 10.1063/1.3679406] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Das A, Mukhopadhyay D, Adhikari S, Baer M. Renner-Teller intersections along the collinear axes of polyatomic molecules: H2CN as a case study. J Chem Phys 2010; 133:084107. [PMID: 20815560 DOI: 10.1063/1.3479399] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The tetra-atomic C(2)H(2)(+) cation is known to form Renner-Teller-type intersections along its collinear axis. Not too long ago, we studied the nonadiabatic coupling terms (NACTs) of this molecule [G. J. Halász et al., J. Chem. Phys. 126, 154309 (2007)] and revealed two kinds of intersections. (i) By employing one of the hydrogens as a test particle, we revealed the fact that indeed the corresponding (angular) NACTs produce topological (Berry) phases that are equal to 2pi, which is a result anticipated in the case of Renner-Teller intersections. (ii) However, to our big surprise, repeating this study when one of the atoms (in this case a hydrogen) is shifted from the collinear arrangement yields for the corresponding topological phase a value that equals pi (and not 2pi). In other words, shifting (even slightly) one of the atoms from the collinear arrangement causes the intersection to change its character and become a Jahn-Teller intersection. This somewhat unexpected novel result was later further analyzed and confirmed by other groups [e.g., T. Vertesi and R. Englman, J. Phys. B 41, 025102 (2008)]. The present article is devoted to another tetra-atomic molecule, namely, the H(2)CN molecule, which just like the C(2)H(2)(+) ion, is characterized by Renner-Teller intersections along its collinear axis. Indeed, we revealed the existence of Renner-Teller intersections along the collinear axis, but in contrast to the C(2)H(2)(+) case a shift of one atom from the collinear arrangement did not form Jahn-Teller intersections. What we found instead is that the noncollinear molecule was not affected by the shift and kept its Renner-Teller character. Another issue treated in this article is the extension of (the two-state) Berry (topological) phase to situations with numerous strongly interacting states. So far the relevance of the Berry phase was tested for systems characterized by two isolated interacting states, although it is defined for any number of interacting states [M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984)]. We intend to show how to overcome this limitation and get a valid, fully justified definition of a Berry phase for an isolated system of any number of interacting states (as is expected).
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Affiliation(s)
- Anita Das
- Department of Chemistry, University of Calcutta, Kolkata 700 009, India
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