
 To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

Deep Potentials for Materials Science

We develop a new deep potential─range correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of six nonenzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free-energy profiles generated from a target QM model. We perform these comparisons using the MNDO/d and DFTB2 semiempirical models because they differ in the way they treat orbital orthogonalization and electrostatics and produce free-energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free-energy profiles requires correction of the QM/MM interactions out to 6 A. We further find that the model's initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure, so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce four different reactions and yielded good agreement with the free-energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free-energy surfaces and 1D free-energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs but was sped up almost 100-fold when using NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free-energy applications ranging from drug discovery to enzyme design.

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Development of Range-Corrected Deep Learning Potentials for Fast, Accurate Quantum Mechanical/Molecular Mechanical Simulations of Chemical Reactions in Solution.

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron–photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm–Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.

Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis.

Recently, Wang and co-workers carried out frontier molecule orbital engineering in the design of m-Cz-BNCz, a thermally activated delayed fluorescence (TADF) molecule that emits pure green light at an external quantum efficiency of 27%. To further understand the underlying molecular design principles, we employed four advanced electronic structure analysis tools. First, an absolutely localized molecular orbitals (ALMO-) based analysis indicates an antibonding combination between the highest occupied molecular orbitals (HOMOs) of the donor 3,6-di-tert-butylcarbazole fragment and the acceptor BNCz fragment, which raises the HOMO energy and red-shifts the fluorescence emission wavelength. Second, excitation energy component analysis reveals that the S1-T1 gap is dominated by two-electron components of the excitation energies. Third, charge transfer number analysis, which is extended to use fragment-based Hirshfeld weights, indicates that the S1 and T1 excited states of m-Cz-BNCz (within time-dependent density functional theory) have notable charge transfer characters (27% for S1 and 12% for T1). This provides a balance between a small single-triplet gap and a substantial fluorescence intensity. Last, a vibrational reorganization energy analysis pinpoints the torsional motion between the BNCz and Cz moieties of m-Cz-BNCz as the source for its wider emission peak than that of p-Cz-BNCz. These four types of analyses are expected to be very valuable in the study and design of other TADF and functional dye molecules.

Elucidating the Electronic Structure of a Delayed Fluorescence Emitter via Orbital Interactions, Excitation Energy Components, Charge-Transfer Numbers, and Vibrational Reorganization Energies.

It is of important strategic significance to develop high‐efficiency narrowband organic electroluminescent materials that can be employed to fabricate ultrahigh‐definition displays with wide color gamut. This topic implies a great challenge to molecular design and synthesis, especially for the development of universality, diversity, scalability, and robustness of molecular architectonics. In this work, a synthetic methodology is demonstrated for functionalizing brominated BN‐containing multiple‐resonance (MR) frameworks with multifarious functional groups, such as donors, acceptors, and moieties without obvious push–pull electron properties. The m‐DPAcP–BNCz‐based organic light‐emitting diode (OLED) exhibits green emission with a full‐width at half‐maximum (FWHM) of 28 nm and a maximum external quantum efficiency (EQE) of 40.6%. The outstanding performance of m‐DPAcP–BNCz is attributed to the perfect integration of the inherent advantages of the MR framework and the donor–acceptor configuration, which can not only achieve bathochromic shift and narrowband emission, but also obtain high photoluminescence (PL) quantum yield (ΦPL) and horizontal emitting dipole orientation ratio (Θ//). This straightforward and efficient approach provides insightful guidance for the construction and enrichment of more high‐efficiency narrowband emitters.

Precise Functionalization of a Multiple‐Resonance Framework: Constructing Narrowband Organic Electroluminescent Materials with External Quantum Efficiency over 40%

In this article, we report a scheme to analyze and visualize the energy density fluctuations during the real-time time-dependent density functional theory (RT-TDDFT) simulations. Using Ag4–N2 complexes as examples, it is shown that the grid-based Kohn–Sham energy density can be computed at each time step using a procedure from Nakai and coworkers. Then the instantaneous energy of each molecular fragment (such as Ag4 and N2) can be obtained by partitioning the Kohn–Sham energy densities using Becke or fragment-based Hirshfeld (FBH) scheme. A strong orientation-dependence is observed for the energy flow between the Ag4 cluster and a nearby N2 molecule in the RT-TDDFT simulations. Future applications of such an energy density analysis in electron dynamics simulations are discussed.

Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations.

In this work, we report a scheme to evaluate and analysis of energy density fluctuations during the real-time time-dependent density functional theory (RT-TDDFT) simulations. Using Ag4–N2 complexes as examples, it is shown that the energy of each molecular fragment (such as Ag4 and N2) can be readily computed by partitioning Kohn-Sham energy densities using Becke or fragment-based Hirshfeld (FBH) scheme. A strong orientation-dependence is observed for theenergy flow between the Ag4 cluster and a nearby N2 molecule in the RT-TDDFT simulations. Future applications of such an energy density analysis in electron dynamics simulations arediscussed.

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Junjie Yang

Papers

Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations.

Can We See the Energy Densities? I. Insights from Real-Time Time-Dependent Density Functional Theory Simulations