Optimal representation for semiclassical surface hopping methods

Herman, Michael F.

doi:10.1063/1.478298

Cited by 30 publications

(21 citation statements)

References 48 publications

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“…39 Suppose a two-state problem is defined in a diabatic representation, and the state wave functions are 1 d and 2 This would be the case in a molecular scattering problem, where the electronic degrees of freedom are treated quantum mechanically and the motions of the nuclei are treated semiclassically.…”

Section: A Generalized Surface Hopping Expansion Of the Wave Functionmentioning

confidence: 99%

“…Previous work 39 has shown that G is, in many cases, significantly reduced by optimizing the representation to minimize G. Previous work 39 has shown that G is, in many cases, significantly reduced by optimizing the representation to minimize G.…”

Section: B Approximate Optimal Representationmentioning

confidence: 99%

“…39 The representation A numerically efficient approximation to this optimal representation is given by multiplying the adiabatic angle, , by a crossover function which is unity far from the crossing point and goes to zero at the crossing point.…”

Section: B Approximate Optimal Representationmentioning

confidence: 99%

“…39 The second method allows for an approximate treatment of multihop terms within an interval of fixed width along the trajectory, thereby incorporating these terms into an effective one-hop term. The general surface hopping procedure is presented in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

Herman

Moody

2005

The Journal of Chemical Physics

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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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Section: A Generalized Surface Hopping Expansion Of the Wave Functionmentioning

confidence: 99%

Section: B Approximate Optimal Representationmentioning

confidence: 99%

Section: B Approximate Optimal Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

Herman

Moody

2005

The Journal of Chemical Physics

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“…37 To do so, a good first step is to develop optimal smooth diabatic PESs, which should have small diabatic and derivative couplings, along the lines of Michael Herman's suggestion. 38,39 To that end, in this paper we propose to generate such diabatic states using an implicit solvent (with Pekar factor C) to model environmental effects that are absent in our electronic structure calculations. Certainly solvent can play a role in understanding diabatic states.…”

Section: Introductionmentioning

confidence: 99%

Optimal diabatic states based on solvation parameters

Alguire

Subotnik

2012

The Journal of Chemical Physics

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A new method for obtaining diabatic electronic states of a molecular system in a condensed environment is proposed and evaluated. This technique, which we denote as Edmiston-Ruedenberg (ER)-ε diabatization, forms diabatic states as a linear combination of adiabatic states by minimizing an approximation to the total coupling between states in a medium with temperature T and with a characteristic Pekar factor C. ER-ε diabatization represents an improvement upon previous localized diabatization methods for two reasons: first, it is sensitive to the energy separation between adiabatic states, thus accounting for fluctuations in energy and effectively preventing over-mixing. Second, it responds to the strength of system-solvent interactions via parameters for the dielectric constant and temperature of the medium, which is physically reasonable. Here, we apply the ER-ε technique to both intramolecular and intermolecular excitation energy transfer systems. We find that ER-ε diabatic states satisfy three important properties: (1) they have small derivative couplings everywhere; (2) they have small diabatic couplings at avoided crossings, and (3) they have negligible diabatic couplings everywhere else. As such, ER-ε states are good candidates for so-called "optimal diabatic states."

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Theoretical exploration of ultrafast spectroscopy of small clusters

Bonačić‐Koutecký

Hartmann

Pittner

et al. 2001

Int J of Quantum Chemistry

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The central issue in femtosecond (fs) time resolved spectroscopy of clusters is the investigation of geometric relaxation and internal vibrational redistribution (IVR) after optical excitation in a nonequilibrium configuration of nuclei by laser photoelectron excitation, and corresponding time delayed probing by multiphoton‐ionization. For this purpose, we have developed multistate ab initio molecular dynamics involving adiabatic ground and excited electronic states, as well as nonadiabatic coupling between them, using the time evolution of initial thermal ensemble in Wigner representation. The combination of ab initio quantum chemical methods, used for the adiabatic and nonadiabatic molecular dynamics “on the fly,” and the Wigner distribution approach for the description of the motion of the nuclei allowed us the accurate determination of pump‐probe and pump‐dump signals also under temperature dependent initial conditions. The connection between simulated pump‐probe signals and the underlying dynamics of nuclei involving adiabatic electronic ground states has been first established for the example of the Ag\documentclass{article}\pagestyle{empty}\begin{document}$_{3}^{-}$\end{document}/Ag3/Ag\documentclass{article}\pagestyle{empty}\begin{document}$_{3}^{+}$\end{document} systems, and compared with experimental negative‐to‐neutral‐to‐positive NeNePo pump‐probe signals. Our simulations reproduced the experimental NeNePo results and determined, in addition to the timescales of geometric relaxation, the conditions under which the resonant or dissipative IVR, as well as vibrational coherence, should be found in the experimental pump‐probe signals. This can be realized in the zero electron kinetic energy NeNePo‐ZEKE experiments, which are in progress. The above combination of methods has been recently extended to the analysis of the timescales as well as of the dynamics in excited electronic states of the nonstoichiometric NanFn−1 (n=2–4) clusters with the single excess valence electron. Our approach allows the simulation of femtosecond NeExPo‐pump‐probe and NeExNe‐pump‐dump signals, based on an analytic formulation which utilizes temperature dependent ground state initial conditions of neutral system (Ne); an ensemble of trajectories carried out either on the adiabatic electronic excited state (Ex), or on both the excited and the ground states through nonadiabatic coupling in connection with the fewest switching hopping algorithm for the investigation of the dynamics of the system; and either the cationic (Po) or the neutral ground state (Ne) for the probing step. The choice of the systems has been made in order to determine the timescales of processes involving (1) fast geometric relaxation leaving the bonding frame intact versus IVR, as during the adiabatic dynamics in the first excited state of Na4F3, being the smallest prototype of F‐colored centers in the bulk; and (2) the photo‐isomerization process through the conical intersection during nonadiabatic dynamics due to the long amplitude motion, as in th...

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Optimal representation for semiclassical surface hopping methods

Cited by 30 publications

References 48 publications

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

Optimal diabatic states based on solvation parameters

Theoretical exploration of ultrafast spectroscopy of small clusters

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