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We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N^3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N^5) to O(N^3). We test the sRI-CC2 for different molecular systems and basis sets, and we show our sRI-CC2 method can accurately reproduce the results of deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N^2.88) for a hydrogen dimer chain, allowing us to calculate systems with nearly thousands of electrons., Comment: 19 pages, 4 figures

Accurate prediction for the electronic structure properties of halide perovskites plays a significant role in the design of highly efficient and stable solar cells. While density functional theory (DFT) within the generalized gradient approximation (GGA) offers reliable prediction in terms of lattice constants and potential energy surface for halide perovskites, it severely underestimates the band gap due to the lack of non-local exact exchange term, which exists in computationally expensive hybrid functionals. In this work, a universal Deep Kohn-Sham (DeePKS) model based on neural network is trained so as to enable electronic structure calculations with the accuracy of hybrid functional HSE06 and the efficiency comparable to GGA functional, for a plethora of halide perovskites, i.e., ABX$_3$ (A=FA, MA, Cs; B=Sn, Pb; X=Cl, Br, I). Forces, band gaps, and density of states (DOS) predicted by our DeePKS model for all aforementioned perovskites are in good agreement with the HSE06 results, with significantly improved efficiency. In addition, even though the spin-orbit coupling (SOC) effect has not been taken into consideration during the training process, DeePKS+SOC offers highly consistent band gap and DOS as compared to HSE06+SOC for Pb-containing systems. We believe such DeePKS model can be readily applied for an accurate yet efficient prediction of various properties for the family of halide perovskites.

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for high-level QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training a ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), a ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely-matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model, and then use the DeePKS model to label a much larger amount of configurations to train a ML potential. This scheme for periodic systems is implemented in a DFT package ABACUS, which is open-source and ready for use in various applications.

The accurate description of large molecular systems in complex environments remains an ongoing challenge for the field of computational chemistry. This problem is even more pronounced for photo-induced processes, as multiple excited electronic states and their corresponding non-adiabatic couplings must be taken into account. Multiscale approaches such as hybrid quantum mechanics/molecular mechanics (QM/MM) offer a balanced compromise between accuracy and computational burden. Here, we introduce an open-source software package (INAQS) for non-adiabatic QM/MM simulations that bridges the sampling capabilities of the GROMACS MD package and the excited-state infrastructure of the Q-CHEM electronic structure software. The interface is simple and can be adapted easily to other MD codes. The code supports a variety of different trajectory based molecular dynamics, ranging from Born-Oppenheimer to surface hopping dynamics. To illustrate the power of this combination, we simulate electronic absorption spectra, free energy surfaces along a reaction coordinate, and the excited state dynamics of 1,3-cyclohexadiene in solution., Comment: 45 pages, 7 figures

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and coworkers, we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. The leads to a symmetric QED-TDDFT coupling matrix, which 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 energy and composition of polaritons associated with lower-energy electronic states., Comment: 23 pages, 6 figures and 5 tables