Within this project's scope, we have notably advanced the capabilities of the open-source Libra package pioneered in my research group by implementing a broad range of algorithms, methods, and computational workflows for nonadiabatic and quantum dynamics (NAQD) simulations and conducting their comprehensive validation and assessment. Libra has become a powerful cyber-ecosystem that facilitated the development and comparative analysis of multiple NAQD methodologies and has been used by various research groups in applied studies of solar energy materials. Several research groups have made important contributions to the code and adopted it as a convenient platform for the development and delivery of their methodologies. The project resulted in about fifteen peer-reviewed publications, a book chapter, and sixteen Libra software releases ranging from version v4.4.0 as the first indexed release to version v5.8.1 as the latest one to date. The scientific and broader-picture aspects of these releases were highlighted in several peer-reviewed papers, one of which was accompanied by a publicly accessible Code Ocean capsule. Two Libra users’/developers’ workshops and summer schools were conducted, where more than 50 students were trained in Libra-specific and general topics relevant to NAQD theory and computations. The corresponding video recordings and presentations are disseminated on the dedicated websites and are freely available to everyone.

Via collaborations with the community experts, we implemented and validated a range of mixed quantum-classical and semiclassical NAQD methods: the hierarchical equations of motion methodology for modeling open quantum systems, the quantum trajectories with adaptive Gaussians, the non-equilibrium Fermi golden rule rate calculations, an algorithm for accurate nonadiabatic couplings calculations, the mapped Hamiltonian surface hopping approach, the quantum trajectories surface hopping, the global flux surface hopping, the second version of the fewest switches surface hopping method (FSSH-2) with the latter two enabling a robust integration of electronic equations of motion. Independently, we implemented the branching-corrected surface hopping which improves the internal consistency of trajectory surface hopping (TSH) calculations and accounts for decoherence effects, a range of exact factorization (XF)-based methods (XF surface hopping; mixed quantum-classical XF method; mean-field with XF). These methods naturally account for decoherence effects in dynamics and are derived from rigorous theoretical grounds via controlled approximations. Several original algorithms relevant to NAQD calculations were developed: the FSSH-3, a novel formalism for deriving the quantum state hopping probabilities via a functional optimization problem; the generalized local diabatization (LD) method, which turned out to be the most robust integration scheme of the electronic time-dependent Schrodinger equation and that became the de facto golden standard in most of our calculations; the revised decoherence-induced surface hopping (DISH) method which addressed the difficulties of the original DISH formulation. Two new trivial crossing detection algorithms were formulated that enabled tracking quantum states in the absence of wavefunction time-overlap information, a common limitation in the practical simulations of large atomistic systems. Multiple published model Hamiltonians have been implemented within the Libra package. Both through model Hamiltonians and atomistic simulations, we conducted systematic assessments and comparative studies of multiple NAQD methodologies, contributing to our understanding of the methods’ limitations and by doing that gradually building the “Jacob’s ladder” of NAQD methods.

We extended our atomistic NAQD simulation workflows to account for excitonic effects using the linear-response time-dependent density functional theory (LR-TD-DFT, within the CP2K software) or the configuration interaction within incomplete neglect of differential overlap (INDO/CI, within the MOPAC software) description of electronic excited states for both finite and periodic systems. These types of description remove the ambiguity in defining the basis of electronic/excitonic excitations present in the single-particle (orbital) description of excited states, account for the multiconfigurational nature of electronic excited states, and help improve the reliability of the corresponding atomistic simulations by going beyond the commonly adopted single-particle picture. We also implemented the NAQD workflows that rely on the inexpensive single-particle description of electronic excitations within the extended tight-binding (xTB) methodology. This development enabled modeling NAQD processes in large periodic and aperiodic systems such as metal-organic frameworks or nanocrystals, which are typically too expensive to model using traditional DFT-based approaches. Using such an xTB-based NAQD approach, we investigated the dependence of charge carrier recombination in systems with more than 6000 atoms on the carrier concentration, the largest atomistic simulation of this kind reported to date. Our revision of the computational workflows for spin-polarized periodic systems enabled the modeling of excitonic dynamics in magnetic systems. Through careful validation and code revision, we developed guidelines for reliable and robust simulations of NAQD in atomistic systems using the methodologies available in Libra. We advanced Libra’s functionalities and infrastructure for results analysis and presentation and developed multiple new tutorials highlighting the most recent Libra capabilities, which will help practitioners streamline their research projects. Thanks to this grant, Libra has gained important momentum in the NAQD and computational materials sciences communities and started making a notable impact on these research fields.

Last Modified: 02/05/2025
Modified by: Alexey V Akimov