Dependence of Electron–Hole Recombination Rates on Charge Carrier Concentration: A Case Study of Nonadiabatic Molecular Dynamics in Graphitic Carbon Nitride Monolayers

Abstract

Through systematic nonadiabatic molecular dynamics (NA-MD) calculations in a prototypical graphitic carbon nitride (C 3 N 4 ) monolayer, we demonstrate a strong dependence of electron−hole recombination time scales on the size of the simulation supercell and hence on the formal concentration of charge carriers. Using our recently developed NA-MD methodology with extended tight-binding electronic structure calculations, we have been able to conduct such calculations in C 3 N 4 monolayers containing up to 5600 atoms. The predicted time scales vary from 7 ps in the smallest (2 × 2) systems to 23 ns in the largest (8 × 8, 10 × 10) ones and depend on the NA-MD methodology and the basis of electronic excitations used. The concentration dependence becomes negligible only in very large systems, such as 8 × 8 or 10 × 10 supercells. In this limit, the time scales also become insensitive to the number of electronic excitations used in NA-MD calculations and to the inclusion of decoherence effects. We propose an effective state reduction model to explain this result.

Machine-Learned Kohn–Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

“…The nuclear trajectory is obtained using classical adiabatic MD (although with the forces that may be derived from quantum chemical calculations) and is then used as the guiding trajectory to compute the electronic Hamiltonians. In this work, we utilize the NBRA approximation of Prezhdo et al − according to which the electronic excitation is assumed not to affect the nuclear dynamics significantly, and which has been demonstrated to yield reasonable results for many nanoscale ,,,,− and rigid molecular systems. ,, Accordingly, only the adiabatic ground state forces are needed to precompute nuclear trajectories, even if electronic transitions occur. In the NBRA approach, electronic transitions do not lead to nuclear trajectory branching and, vice versa, are determined by the precomputed nuclear trajectory.…”

“…To produce the 1 ps NA-MD trajectories, we use the Hamiltonian repetition approach that consists of looping over the initial 1 ps data set of Hamiltonians obtained along the guiding trajectory. This technique has been widely used in the NBRA-based NA-MD calculations 18,21,109,116,123,124,147 although it is known to under-or overestimate the resulting time scales by nearly an order of magnitude. 148 However, since the same approach is applied equally to both the ML and direct simulations, it should not affect the validity of the current study, although the absolute values of the excitation decay time scales may not be quantitative compared to experiment.…”

“…The standard NBRA NA-MD computations typically involve precomputed nuclear trajectories (guiding trajectories) that parametrize the electronic dynamics of a system. While the guiding trajectories may be obtained relatively inexpensively using adiabatic molecular dynamics with force fields, − semiempirical or xTB methods, ,, the propagation of electronic dynamics requires more expensive DFT calculations. Obtaining accurate energies and time overlaps may require the use of expensive hybrid functionals, with the steeply increased computational expenses .…”

“…Obtaining mechanistic insights into the underlying quantum processes in materials can help optimize their properties and efficiency. Nonadiabatic molecular dynamics (NA-MD) has proven itself as a powerful tool for modeling the evolution of excited states in various molecular and nanoscale systems and provided insights into charge transfer kinetics and mechanisms, − electron–hole recombination − and hot-carrier relaxation dynamics, − carbon dioxide reduction on metal oxide surfaces, , and water splitting. , …”

Energy-Conserving and Thermally Corrected Neglect of Back-Reaction Approximation Method for Nonadiabatic Molecular Dynamics

“…Nonadiabatic molecular dynamics (NA-MD) is a widely adopted family of computational methods to model quantum dynamics of excited states in various systems. − The NA-MD simulations have found their use in describing various kinds of processes in many molecular and condensed-matter systems: modeling nonradiative electron–hole recombination and “hot” carrier relaxation in quantum dots and molecular clusters, − nanotubes, , plasmonic systems, or exotic states of matter; modeling photoinduced isomerization and reactive processes in various molecular systems; − and modeling charge transfer and charge carrier trapping processes in 2D materials, − interfaces, ,− ,, organic solids, , and pristine and defect-containing bulk semiconductors. − …”