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Jang S, Voth GA. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space. J Chem Phys 2018; 146:174106. [PMID: 28477603 DOI: 10.1063/1.4982053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
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Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, USA
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Jang S, Voth GA. Can quantum transition state theory be defined as an exact t = 0+ limit? J Chem Phys 2016; 144:084110. [DOI: 10.1063/1.4942482] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
| | - Gregory A. Voth
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics and Computation Institute, University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, USA
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Kryvohuz M. Calculation of Kinetic Isotope Effects for Intramolecular Hydrogen Shift Reactions Using Semiclassical Instanton Approach. J Phys Chem A 2014; 118:535-44. [DOI: 10.1021/jp4099073] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Maksym Kryvohuz
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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Kryvohuz M. On the derivation of semiclassical expressions for quantum reaction rate constants in multidimensional systems. J Chem Phys 2013; 138:244114. [DOI: 10.1063/1.4811221] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Kryvohuz M. Calculation of chemical reaction rate constants using on-the-fly high level electronic structure computations with account of multidimensional tunneling. J Chem Phys 2012; 137:234304. [DOI: 10.1063/1.4769195] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kryvohuz M, Marcus RA. Semiclassical evaluation of kinetic isotope effects in 13-atomic system. J Chem Phys 2012; 137:134107. [DOI: 10.1063/1.4754660] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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Kryvohuz M. Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems. J Chem Phys 2011; 134:114103. [DOI: 10.1063/1.3565425] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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Truhlar DG. Tunneling in enzymatic and nonenzymatic hydrogen transfer reactions. J PHYS ORG CHEM 2010. [DOI: 10.1002/poc.1676] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Voth GA. Path-Integral Centroid Methods in Quantum Statistical Mechanics and Dynamics. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141526.ch4] [Citation(s) in RCA: 126] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Wong IY, Gardel ML, Reichman DR, Weeks ER, Valentine MT, Bausch AR, Weitz DA. Anomalous diffusion probes microstructure dynamics of entangled F-actin networks. PHYSICAL REVIEW LETTERS 2004; 92:178101. [PMID: 15169197 DOI: 10.1103/physrevlett.92.178101] [Citation(s) in RCA: 353] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2003] [Indexed: 05/12/2023]
Abstract
We study the thermal motion of colloidal tracer particles in entangled actin filament (F-actin) networks, where the particle radius is comparable to the mesh size of the F-actin network. In this regime, the ensemble-averaged mean-squared displacement of the particles is proportional to tau(gamma), where 0<gamma<1 from 0.1<tau<100 s and depends only on the ratio of the probe radius to mesh size. By directly imaging hundreds of particles over 20 min, we determine this anomalous subdiffusion is due to the dynamics of infrequent and large jumps particles make between distinct pores in the network.
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Affiliation(s)
- I Y Wong
- Department of Physics & DEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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Schenter GK, Garrett BC, Truhlar DG. The Role of Collective Solvent Coordinates and Nonequilibrium Solvation in Charge-Transfer Reactions. J Phys Chem B 2001. [DOI: 10.1021/jp011981k] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gregory K. Schenter
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, and Department of Chemistry and Supercomputer Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431
| | - Bruce C. Garrett
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, and Department of Chemistry and Supercomputer Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431
| | - Donald G. Truhlar
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, and Department of Chemistry and Supercomputer Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431
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12
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Georgievskii Y, Stuchebrukhov AA. Concerted electron and proton transfer: Transition from nonadiabatic to adiabatic proton tunneling. J Chem Phys 2000. [DOI: 10.1063/1.1323723] [Citation(s) in RCA: 95] [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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Reichman DR, Roy PN, Jang S, Voth GA. A Feynman path centroid dynamics approach for the computation of time correlation functions involving nonlinear operators. J Chem Phys 2000. [DOI: 10.1063/1.481872] [Citation(s) in RCA: 87] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Tanaka S, Hsu CP. Theory of nonadiabatic electron transfer at electrode/liquid interfaces: Role of quantum effects. J Chem Phys 1999. [DOI: 10.1063/1.480471] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jang S, Voth GA. Path integral centroid variables and the formulation of their exact real time dynamics. J Chem Phys 1999. [DOI: 10.1063/1.479514] [Citation(s) in RCA: 176] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Liao JL, Pollak E. A test of quantum transition state theory for a system with two degrees of freedom. J Chem Phys 1999. [DOI: 10.1063/1.478127] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Shao J, Liao JL, Pollak E. Quantum transition state theory: Perturbation expansion. J Chem Phys 1998. [DOI: 10.1063/1.476446] [Citation(s) in RCA: 68] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mills G, Schenter G, Makarov D, Jónsson H. Generalized path integral based quantum transition state theory. Chem Phys Lett 1997. [DOI: 10.1016/s0009-2614(97)00886-5] [Citation(s) in RCA: 76] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Cao J, Voth GA. A unified framework for quantum activated rate processes. I. General theory. J Chem Phys 1996. [DOI: 10.1063/1.471980] [Citation(s) in RCA: 79] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Truhlar DG, Garrett BC, Klippenstein SJ. Current Status of Transition-State Theory. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp953748q] [Citation(s) in RCA: 1585] [Impact Index Per Article: 56.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Donald G. Truhlar
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Bruce C. Garrett
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle Boulevard, MS K1-96, Richland, Washington 99352
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Voth GA, Hochstrasser RM. Transition State Dynamics and Relaxation Processes in Solutions: A Frontier of Physical Chemistry. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp960317e] [Citation(s) in RCA: 156] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gregory A. Voth
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - Robin M. Hochstrasser
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
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Georgievskii Y, Pollak E. Activated rate processes: Anharmonic corrections to the quantum rate. J Chem Phys 1995. [DOI: 10.1063/1.470080] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Messina M, Schenter GK, Garrett BC. A variational centroid density procedure for the calculation of transmission coefficients for asymmetric barriers at low temperature. J Chem Phys 1995. [DOI: 10.1063/1.470227] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Makarov DE, Topaler M. Quantum transition-state theory below the crossover temperature. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:178-188. [PMID: 9963418 DOI: 10.1103/physreve.52.178] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Dakhnovskii Y, Bursulaya B, Kim HJ. Quantum tunneling in an anharmonic classical bath. Enhanced kinetic isotope effects in an Arrhenius region. J Chem Phys 1995. [DOI: 10.1063/1.468984] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zhu J, Cukier RI. An imaginary energy method‐based formulation of a quantum rate theory. J Chem Phys 1995. [DOI: 10.1063/1.468540] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Stuchebrukhov AA, Song X. Quantum effects in electron transfer reactions with strong electronic coupling. J Chem Phys 1994. [DOI: 10.1063/1.468444] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Topaler M, Makri N. Quantum rates for a double well coupled to a dissipative bath: Accurate path integral results and comparison with approximate theories. J Chem Phys 1994. [DOI: 10.1063/1.468244] [Citation(s) in RCA: 257] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sitnitsky AE. Conformational dynamics of protein side chains and enzyme-substrate interaction. J Biomol Struct Dyn 1994; 12:475-86. [PMID: 7702781 DOI: 10.1080/07391102.1994.10508752] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
The electric interaction of charged and polar protein side chains with dipole moments of the bonds of substrate molecules bound in enzyme active sites is considered. The conformational motion of the side chains leads to the fact that the electric interaction, besides a constant (electrostatic) part, contains a fluctuating one, which is a random force (noise) exerted on the substrate molecule. On the time scale of enzyme turnovers this noise can be considered as the white one with good approximation. The noise is external, and the explicit expression for its intensity has been obtained. The possible functional role of the noise as an activating factor in enzyme catalysis is discussed.
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Affiliation(s)
- A E Sitnitsky
- Laboratory of Molecular Biophysics, Institute of Biology, Tatarstan, Russia
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Hansen NF, Andersen HC. A new formulation of quantum transition state theory for adiabatic rate constants. J Chem Phys 1994. [DOI: 10.1063/1.467318] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dakhnovskii Y. Nonadiabatic chemical reactions in a strong time‐dependent electric field: An electron transfer reaction in a polar solvent. J Chem Phys 1994. [DOI: 10.1063/1.467058] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schenter GK, Messina M, Garrett BC. Centroid‐density quantum rate theory: Dynamical treatment of classical recrossing. J Chem Phys 1993. [DOI: 10.1063/1.465284] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Song X, Stuchebrukhov AA. Outer‐sphere electron transfer in polar solvents: Quantum scaling of strongly interacting systems. J Chem Phys 1993. [DOI: 10.1063/1.465310] [Citation(s) in RCA: 37] [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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Haynes GR, Voth GA. Effect of nonlinear dissipation on quantum-activated rate processes in condensed phases. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:2143-2146. [PMID: 9908353 DOI: 10.1103/physreva.46.2143] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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