Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2

We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree–Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi–Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, <i>O</i>(<i>N</i>³) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree–Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to <i>k</i>_<i>b</i><i>T</i>. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations

Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2

We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree–Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi–Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, <i>O</i>(<i>N</i>³) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree–Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to <i>k</i>_<i>b</i><i>T</i>. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations

Nonradiative Relaxation in Real-Time Electronic Dynamics OSCF2: Organolead Triiodide Perovskite

We apply our recently developed nonequilibrium real-time time-dependent density functional theory (OSCF2) to investigate the transient spectrum and relaxation dynamics of the tetragonal structure of methylammonium lead triiodide perovskite (MAPbI₃). We obtain an estimate of the interband relaxation kinetics and identify multiple ultrafast cooling channels for hot electrons and hot holes that largely corroborate the dual valence–dual conduction model. The computed relaxation rates and absorption spectra are in good agreement with the existing experimental data. We present the first <i>ab initio</i> simulations of the perovskite transient absorption (TA) spectrum, substantiating the assignment of induced bleaches and absorptions including a Pauli-bleach signal. This paper validates both OSCF2 as a good qualitative model of electronic dynamics, and the dominant interpretation of the TA spectrum of this material

Accelerating Realtime TDDFT with Block-Orthogonalized Manby–Miller Embedding Theory

Realtime time-dependent density-functional theory (RT-TDDFT) is one of the most practical techniques available to simulate electronic dynamics of molecules and materials. Promising applications of RT-TDDFT to study nonlinear spectra and energy transport demand simulations of large solvated systems over long time scales, which are computationally quite costly. In this paper, we apply an embedding technique developed for ground-state SCF methods by Manby and Miller to accelerate realtime TDDFT. We assess the accuracy and speed of these approximations by studying the absorption spectra of solvated and covalently split chromophores. Our embedding approach is also compared with less accurate, less costly QM/MM charge embeddings. We find that by mixing levels of detail the embedded mean-field theory scheme is a simple, accurate, and effective way to accelerate RT-TDDFT simulations

Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network

Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy similar to the ab initio methods used to build them. In this work, we present a neural network that predicts the energies of molecules as a sum of intrinsic bond energies. The network learns the total energies of the popular GDB9 database to a competitive MAE of 0.94 kcal/mol on molecules outside of its training set, is naturally linearly scaling, and applicable to molecules consisting of thousands of bonds. More importantly, it gives chemical insight into the relative strengths of bonds as a function of their molecular environment, despite only being trained on total energy information. We show that the network makes predictions of relative bond strengths in good agreement with measured trends and human predictions. A Bonds-in-Molecules Neural Network (BIM-NN) learns heuristic relative bond strengths like expert synthetic chemists, and compares well with ab initio bond order measures such as NBO analysis

Black-Box, Real-Time Simulations of Transient Absorption Spectroscopy

We introduce an atomistic, all-electron, black-box electronic structure code to simulate transient absorption (TA) spectra and apply it to simulate pyrazole and a GFP-chromophore derivative. The method is an application of OSCF2, our dissipative extension of time-dependent density functional theory. We compare our simulated spectra directly with recent ultrafast spectroscopic experiments. We identify features in the TA spectra to Pauli-blocking, which may be missed without a first-principles model. An important ingredient in this method is the stationary-TDDFT correction scheme recently put forward by Fischer, Govind, and Cramer that allows us to overcome a limitation of adiabatic TDDFT. We demonstrate that OSCF2 is able to reproduce the energies of bleaches and induced absorptions as well as the decay of the transient spectrum with only the molecular structure as input

Origin of the Size-Dependent Stokes Shift in CsPbBr₃ Perovskite Nanocrystals

The origin of the size-dependent Stokes shift in CsPbBr₃ nanocrystals (NCs) is explained for the first time. Stokes shifts range from 82 to 20 meV for NCs with effective edge lengths varying from ∼4 to 13 nm. We show that the Stokes shift is intrinsic to the NC electronic structure and does not arise from extrinsic effects such as residual ensemble size distributions, impurities, or solvent-related effects. The origin of the Stokes shift is elucidated via first-principles calculations. Corresponding theoretical modeling of the CsPbBr₃ NC density of states and band structure reveals the existence of an intrinsic confined hole state 260 to 70 meV above the valence band edge state for NCs with edge lengths from ∼2 to 5 nm. A size-dependent Stokes shift is therefore predicted and is in quantitative agreement with the experimental data. Comparison between bulk and NC calculations shows that the confined hole state is exclusive to NCs. At a broader level, the distinction between absorbing and emitting states in CsPbBr₃ is likely a general feature of other halide perovskite NCs and can be tuned via NC size to enhance applications involving these materials