A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach

Abstract

We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

“…However, in the current work, the state tracking was disabled for Si NC systems because the computations become rather expensive for systems with hundreds of states. Our prior experience with model systems shows that the trivial state crossing identification becomes rather negligible in dense manifolds of states . The state tracking is included in modeling dynamics in both the graphitic C 3 N 4 monolayer and MIL-125-NH 2 MOF.…”

“…Our prior experience with model systems shows that the trivial state crossing identification becomes rather negligible in dense manifolds of states. 131 The state tracking is included in modeling dynamics in both the graphitic C 3 N 4 monolayer and MIL-125-NH 2 MOF. The corrected time−overlap matrices are used to compute the phasecorrection 132 to ensure the dynamical consistency of the wavefunctions in all steps of the MD.…”

Excited electron and spin dynamics in topological insulator: A perspective from ab initio non-adiabatic molecular dynamics

“…We use Naive Bayesian technique to sort out the multi-step transition probability matrix for each basis during the AIMD trajectory. This technique has been widely used in machine learning community and compatible for the probability character of quantum mechanics as well as this unsupervised mission of state tracking [ 30 , 31 ] See the Supplementary Material [ 22 ] for more details.…”

Generalization of the Local Diabatization Approach for Propagating Electronic Degrees of Freedom in Nonadiabatic Dynamics

“…To date, several algorithms have been designed for state tracking and handling the trivial crossing situation. These developments include the min-cost algorithm of Fernandez-Alberti and Tretiak [29] as well as a similar approach of Ryabinkin and Izmaylov, [30] the internal-consistency check by Wang and Prezhdo, [31] our stochastic state tracking algorithm, [32] and the local diabatization (LD) approach of Granucci, Persico, and co-workers. [33,34] Alternatively, Meek and Levine proposed the norm-conserving interpolation (NPI) procedure to correctly integrate TD-SE in the conical intersection regions.…”