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

Abstract

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.

Mechanism of Ultrafast Intersystem Crossing in 2‐Nitronaphthalene

“…Error margins for the time constants were calculated using the bootstrap method 34. Details on the fitting and bootstrapping calculations as well as discussion of minor reaction channels can be found in Sections S2.1–S2.2 of the Supporting Information.…”

Ultrafast Photoinduced Dynamics of 1,3-Cyclohexadiene Using XMS-CASPT2 Surface Hopping

“…and N S 0 = 1 − e −(t−t S 0 0 )/τ S 0 respectively, and using the bootstrap approach 58 The large-amplitude oscillation of the C 1 − C 6 interatomic distance can be explained by looking at the time evolution of the carbon ring dihedral angles as depicted in Fig. 7.…”

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

“…The “ants” approach has better statistical properties but a much higher computational cost due to trajectory branching. A third scheme called “army ants” was developed (Nangia et al, 2004) to treat weak coupling systems and sample low probability events while keeping computations feasible.…”