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Kawasaki A, Anderson JSM. Warning! The negative divergence of the stress-tensor does not always yield the Ehrenfest force. J Chem Phys 2023; 159:234120. [PMID: 38117022 DOI: 10.1063/5.0174905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2023] [Accepted: 10/30/2023] [Indexed: 12/21/2023] Open
Abstract
It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized.
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Affiliation(s)
- Airi Kawasaki
- Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, Japan
| | - James S M Anderson
- Instituto de Química, Universidad Nacional Autónoma de México, Universidad 300, Ciudad Universitaria, Ciudad de México 04510, Mexico
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Malcomson T, Azizi A, Momen R, Xu T, Kirk SR, Paterson MJ, Jenkins S. Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules: Excited State Photochemical Reaction Path from Benzene to Benzvalene. J Phys Chem A 2019; 123:8254-8264. [PMID: 31487180 DOI: 10.1021/acs.jpca.9b07519] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this investigation, we considered both the scalar and 3-D vector-based measures of bonding using next generation quantum theory of atoms in molecules (QTAIM), constructed from the preferred direction of electronic charge density accumulation, to better understand the photochemical reaction associated with of the formation of benzvalene from benzene. The formation of benzvalene from benzene resulted in two additional C-C bonds forming compared with the benzene. The creation of the additional C-C bonds was explained in terms of an increasing the favorability of the reaction process by maximizing the bonding density. The topological instability of the benzvalene structure was determined using the scalar and vector-based measures to explain the short chemical half-life of benzvalene in terms of the competition between the formation of unstable new C-C bonding that also destabilizes nearest neighbor C-C bonds. The explosive character of benzvalene is indicated by the unusual tendency of the C-C bonds to rupture as easily as weak bonding. The topological instability of the short strong C-C bonds was explained by the existence of measures from conventional and next generation QTAIM that previously have only been observed in weak interactions; such measures included twisted 3-D bonding descriptors.
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Affiliation(s)
- Thomas Malcomson
- Institute of Chemical Sciences, School of Engineering and Physical Sciences , Heriot-Watt University , Edinburgh , EH14 4AS , U.K
| | - Alireza Azizi
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering , Hunan Normal University , Changsha , Hunan 410081 , China
| | - Roya Momen
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering , Hunan Normal University , Changsha , Hunan 410081 , China
| | - Tianlv Xu
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering , Hunan Normal University , Changsha , Hunan 410081 , China
| | - Steven R Kirk
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering , Hunan Normal University , Changsha , Hunan 410081 , China
| | - Martin J Paterson
- Institute of Chemical Sciences, School of Engineering and Physical Sciences , Heriot-Watt University , Edinburgh , EH14 4AS , U.K
| | - Samantha Jenkins
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering , Hunan Normal University , Changsha , Hunan 410081 , China
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Xu T, Momen R, Azizi A, van Mourik T, Früchtl H, Kirk SR, Jenkins S. The destabilization of hydrogen bonds in an external E-field for improved switch performance. J Comput Chem 2019; 40:1881-1891. [PMID: 30980547 DOI: 10.1002/jcc.25843] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 03/26/2019] [Accepted: 03/31/2019] [Indexed: 01/03/2023]
Abstract
The effect of an electric field on a recently proposed molecular switch based on a quinone analogue was investigated using next-generation quantum theory of atoms in molecules (QTAIM) methodology. The reversal of a homogenous external electric field was demonstrated to improve the "OFF" functioning of the switch. This was achieved by destabilization of the H atom participating in the tautomerization process along the hydrogen bond that defines the switch. The "ON" functioning of the switch, from the position of the tautomerization barrier, is also improved by the reversal of the homogenous external electric field: this result was previously inaccessible. The "ON" and "OFF" functioning of the switch was visualized in terms of the response of the most preferred directions of motion of the electronic charge density to the applied external field. All measures from QTAIM and the stress tensor provide consistent results for the factors affecting the "ON" and "OFF" switch performance. Our analysis therefore demonstrates use for future design of molecular electronic devices. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Tianlv Xu
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan, 410081, China
| | - Roya Momen
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan, 410081, China
| | - Alireza Azizi
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan, 410081, China
| | - Tanja van Mourik
- EaStCHEM School of Chemistry, University of St Andrews, North Haugh, St Andrews, Fife KY16 9ST, United Kingdom
| | - Herbert Früchtl
- EaStCHEM School of Chemistry, University of St Andrews, North Haugh, St Andrews, Fife KY16 9ST, United Kingdom
| | - Steven R Kirk
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan, 410081, China
| | - Samantha Jenkins
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan, 410081, China
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Ikeda T, Dijkstra AG, Tanimura Y. Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra. J Chem Phys 2019; 150:114103. [DOI: 10.1063/1.5086948] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatsushi Ikeda
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Arend G. Dijkstra
- School of Chemistry and School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Tian T, Xu T, Kirk SR, Filatov M, Jenkins S. Next-generation quantum theory of atoms in molecules for the ground and excited state of DHCL. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.01.016] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Wiley TE, Konar A, Miller NA, Spears KG, Sension RJ. Primed for Efficient Motion: Ultrafast Excited State Dynamics and Optical Manipulation of a Four Stage Rotary Molecular Motor. J Phys Chem A 2018; 122:7548-7558. [DOI: 10.1021/acs.jpca.8b06472] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Theodore E. Wiley
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
| | - Arkaprabha Konar
- Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, United States
| | - Nicholas A. Miller
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
| | - Kenneth G. Spears
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
| | - Roseanne J. Sension
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
- Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, United States
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Li J, Xu T, Ping Y, van Mourik T, Früchtl H, Kirk SR, Jenkins S. Consequences of theory level choice evaluated with new tools from QTAIM and the stress tensor for a dipeptide conformer. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.02.041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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