51
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Hédin F, Plattner N, Doll JD, Meuwly M. Spatial Averaging: Sampling Enhancement for Exploring Configurational Space of Atomic Clusters and Biomolecules. J Chem Theory Comput 2014; 10:4284-96. [DOI: 10.1021/ct500529w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Florent Hédin
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Nuria Plattner
- Department
of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
| | - J. D. Doll
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Markus Meuwly
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
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52
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Zheng J, Xu X, Meana-Pañeda R, Truhlar DG. Army ants tunneling for classical simulations. Chem Sci 2014. [DOI: 10.1039/c3sc53290a] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
We present an algorithm, called army ants tunneling, for adding tunneling to classical trajectories by means of quantal rare event sampling.
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Affiliation(s)
- Jingjing Zheng
- Department of Chemistry
- Chemical Theory Center, and Supercomputing Institute
- University of Minnesota
- Minneapolis, USA
| | - Xuefei Xu
- Department of Chemistry
- Chemical Theory Center, and Supercomputing Institute
- University of Minnesota
- Minneapolis, USA
| | - Rubén Meana-Pañeda
- Department of Chemistry
- Chemical Theory Center, and Supercomputing Institute
- University of Minnesota
- Minneapolis, USA
| | - Donald G. Truhlar
- Department of Chemistry
- Chemical Theory Center, and Supercomputing Institute
- University of Minnesota
- Minneapolis, USA
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53
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Jasper AW, Miller JA, Klippenstein SJ. Collision Efficiency of Water in the Unimolecular Reaction CH4 (+H2O) ⇆ CH3 + H (+H2O): One-Dimensional and Two-Dimensional Solutions of the Low-Pressure-Limit Master Equation. J Phys Chem A 2013; 117:12243-55. [DOI: 10.1021/jp409086w] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ahren W. Jasper
- Combustion
Research Facility, Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969, United States
| | - James A. Miller
- Chemical
Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Stephen J. Klippenstein
- Chemical
Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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54
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Cazade PA, Meuwly M. Oxygen migration pathways in NO-bound truncated hemoglobin. Chemphyschem 2012; 13:4276-86. [PMID: 23161831 DOI: 10.1002/cphc.201200608] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2012] [Revised: 09/28/2012] [Indexed: 11/10/2022]
Abstract
Atomistic simulations of dioxygen (O(2)) dynamics and migration in nitric oxide-bound truncated Hemoglobin N (trHbN) of Mycobacterium tuberculosis are reported. From more than 100 ns of simulations the connectivity network involving the metastable states for localization of the O(2) ligand is built and analyzed. It is found that channel I is the primary entrance point for O(2) whereas channel II is predominantly an exit path although access to the protein active site is also possible. For O(2) a new site compared to nitric oxide, from which reaction with the heme group can occur, was found. As this site is close to the heme iron, it could play an important role in the dioxygenation mechanism as O(2) can remain there for hundreds of picoseconds after which it can eventually leave the protein, while NO is localized in Xe2. The present study supports recent experimental work which proposed that O(2) docks in alternative pockets than Xe close to the reactive site. Similar to other proteins, a phenylalanine residue (Phe62) plays the role of a gate along the access route in channel I. The most highly connected site is the Xe3 pocket which is a "hub" and free energy barriers between the different metastable states are ≈1.5 kcal mol(-1) which allows facile O(2) migration within the protein.
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Affiliation(s)
- Pierre-André Cazade
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056, Basel, Switzerland
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55
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Jiang R, Sibert EL. Surface hopping simulation of vibrational predissociation of methanol dimer. J Chem Phys 2012; 136:224104. [DOI: 10.1063/1.4724219] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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56
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Jasper AW, Miller JA. Theoretical Unimolecular Kinetics for CH4 + M ⇄ CH3 + H + M in Eight Baths, M = He, Ne, Ar, Kr, H2, N2, CO, and CH4. J Phys Chem A 2011; 115:6438-55. [DOI: 10.1021/jp200048n] [Citation(s) in RCA: 119] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Ahren W. Jasper
- Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969, United States
| | - James A. Miller
- Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969, United States
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57
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Jasper AW, Miller JA. Collisional Energy Transfer in Unimolecular Reactions: Direct Classical Trajectories for CH4 ⇄ CH3 + H in Helium. J Phys Chem A 2009; 113:5612-9. [DOI: 10.1021/jp900802f] [Citation(s) in RCA: 80] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ahren W. Jasper
- Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969
| | - James A. Miller
- Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969
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58
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Schmidt JR, Parandekar PV, Tully JC. Mixed quantum-classical equilibrium: Surface hopping. J Chem Phys 2008; 129:044104. [DOI: 10.1063/1.2955564] [Citation(s) in RCA: 132] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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59
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Takatsuka K. Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions. J Phys Chem A 2007; 111:10196-204. [PMID: 17676718 DOI: 10.1021/jp072233j] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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60
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Herman MF. Toward an accurate and efficient semiclassical surface hopping procedure for nonadiabatic problems. J Phys Chem A 2007; 109:9196-205. [PMID: 16833258 DOI: 10.1021/jp052652l] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The derivation of a semiclassical surface hopping procedure from a formally exact solution of the Schrodinger equation is discussed. The fact that the derivation proceeds from an exact solution guarantees that all phase terms are completely and accurately included. Numerical evidence shows the method to be highly accurate. A Monte Carlo implementation of this method is considered, and recent work to significantly improve the statistical accuracy of the Monte Carlo approach is discussed.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, LA 70118, USA
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61
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Sergeev A, Herman MF. An analysis of the accuracy of an initial value representation surface hopping wave function in the interaction and asymptotic regions. J Chem Phys 2006; 125:24107. [PMID: 16848577 DOI: 10.1063/1.2218332] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schrodinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method.
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Affiliation(s)
- Alexey Sergeev
- Department of Chemistry, Tulane University, New Orleans, LA 70118, USA
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62
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Zhu C, Jasper AW, Truhlar DG. Non-Born-Oppenheimer trajectories with self-consistent decay of mixing. J Chem Phys 2006; 120:5543-57. [PMID: 15267430 DOI: 10.1063/1.1648306] [Citation(s) in RCA: 132] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions.
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Affiliation(s)
- Chaoyuan Zhu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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63
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Takatsuka K. Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions. J Chem Phys 2006; 124:64111. [PMID: 16483200 DOI: 10.1063/1.2167648] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, Japan.
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64
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Nutt DR, Meuwly M. Studying reactive processes with classical dynamics: rebinding dynamics in MbNO. Biophys J 2005; 90:1191-201. [PMID: 16326913 PMCID: PMC1367270 DOI: 10.1529/biophysj.105.071522] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A new surface-crossing algorithm suitable for describing bond-breaking and bond-forming processes in molecular dynamics simulations is presented. The method is formulated for two intersecting potential energy manifolds which dissociate to different adiabatic states. During simulations, crossings are detected by monitoring an energy criterion. If fulfilled, the two manifolds are mixed over a finite number of time steps, after which the system is propagated on the second adiabat and the crossing is carried out with probability one. The algorithm is extensively tested (almost 0.5 mus of total simulation time) for the rebinding of NO to myoglobin. The unbound surface (Fe...NO) is represented using a standard force field, whereas the bound surface (Fe-NO) is described by an ab initio potential energy surface. The rebinding is found to be nonexponential in time, in agreement with experimental studies, and can be described using two time constants. Depending on the asymptotic energy separation between the manifolds, the short rebinding timescale is between 1 and 9 ps, whereas the longer timescale is about an order of magnitude larger. NO molecules which do not rebind within 1 ns are typically found in the Xenon-4 pocket, indicating the high affinity of NO to this region in the protein.
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Affiliation(s)
- David R Nutt
- Department of Chemistry, University of Basel, 4056 Basel, Switzerland
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65
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Herman MF, Moody MP. Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations. J Chem Phys 2005; 122:094104. [PMID: 15836109 DOI: 10.1063/1.1855313] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
A one-dimensional, two-state model problem with two well-separated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a one-dimensional model allows for the accurate numerical evaluation of both fully quantum-mechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlo surface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.
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Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA.
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66
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Amano M, Takatsuka K. Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions. J Chem Phys 2005; 122:84113. [PMID: 15836026 DOI: 10.1063/1.1854115] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.
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Affiliation(s)
- Michiko Amano
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba 153-8902, Tokyo, Japan
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