Continuous surface switching: An improved time-dependent self-consistent-field method for nonadiabatic dynamics

Volobuev, Yuri L.; Hack, Michael D.; Topaler, Maria; Truhlar, Donald G.

doi:10.1063/1.481609

Cited by 119 publications

(116 citation statements)

References 95 publications

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…25,27,[32][33][34]36,[41][42][43][44]46,53 Because it has been impractical to study dynamics for systems with very small semiclassical transition probabilities, these tests have been carried out for systems with nonadiabatic probabilities of 3ϫ10 Ϫ4 and larger. The army ants algorithm allows us to extend these tests down to much lower probabilities; for example, in the present paper we present well-converged calculations for a system with a nonadiabatic transition probability of 1ϫ10…”

Section: Introductionmentioning

confidence: 99%

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Nangia¹,

Jasper²,

Miller³

et al. 2004

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping ͑TSH͒ calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme ͑called the army ants algorithm͒ for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm ͑which is efficient for strongly coupled cases͒, and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation ͑quenching͒ were found to be on the order of 10Ϫ8 . For such low-probability events the anteater sampling scheme requires a large number of trajectories (ϳ10 10 ) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10 5 trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Nangia¹,

Jasper²,

Miller³

et al. 2004

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…68 OWVP calculations have been performed more recently on a variety of model systems, including three qualitatively different types of chemical systems: (1) systems with conical intersections, [69][70][71][72][73] (2) systems with diabatic surfaces that cross and adiabatic surfaces that do not intersect, 74 and (3) systems with wide regions of weak coupling where neither the diabatic nor the adiabatic surfaces cross. 75,76 This set of calculations includes reactive 69,72,[74][75][76] and nonreactive 71,72 scattering collisions as well as unimolecular excited-state decay processes. 70,73 The availability of accurate quantum mechanical results for realistic full-dimensional non-BO systems allows for the systematic study of the accuracy of more approximate methods, and we have identified a subset of the calculations discussed above to serve as benchmark test cases.…”

Section: Quantum Mechanical Dynamicsmentioning

confidence: 99%

“…(5)) is referred to as a potential energy matrix or PEM. We include three LandauZener-Teller-type [77][78][79] PEMs (collectively referred to as the MXH family 74 of PEMs), which feature narrowly avoided crossings where the diabatic surfaces cross but the adiabatic surfaces do not.…”

Section: Quantum Mechanical Dynamicsmentioning

confidence: 99%

“…1(a). OWVP calculations with 20659 basis functions were carried out 74 for all three MXH PEMs at total energies from 1.07 to 1.13 eV. The second family of PEMs included in the set of benchmark cases is the YRH family, 75 which contains two Rosen-Zener-Demkov-type PEMs, [80][81][82] featuring wide regions of weakly coupled and nearly parallel surfaces where neither the diabatic surfaces nor the adiabatic surfaces cross.…”

Section: Quantum Mechanical Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

Self Cite

View full text Add to dashboard Cite

Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born-Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau-Zener-type and Rosen-Zener-Demkov-type reactive scattering problems are compared.

show abstract

“…This is actually a tunneling process that is classically forbidden. 6,13 Many hybrid methods have been proposed that try to combine the advantages of surface hopping and Ehrenfest mean-field like approaches, for example, the use of a smooth switching between the two types of forces in different regions, 14 Ehrenfest dynamics guided surface hopping 15 or the surface hopping dynamics with Ehrenfest excited state potential 16 approaches are two recent versions of such ideas.…”

Section: Introductionmentioning

confidence: 99%

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Huo¹,

Coker²

2012

The Journal of Chemical Physics

100

115

View full text Add to dashboard Cite

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

show abstract

Continuous surface switching: An improved time-dependent self-consistent-field method for nonadiabatic dynamics

Cited by 119 publications

References 95 publications

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

Introductory lecture: Nonadiabatic effects in chemical dynamics

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Contact Info

Product

Resources

About