Electronic coherences are key to understanding and controlling photo-induced molecular transformations. We identify a crucial quantum-mechanical feature of electron-nuclear correlation, the projected nuclear quantum momenta, essential to capture the correct coherence behavior. In simulations, we show that, unlike traditional trajectory-based schemes, exact-factorization-based methods approximate these correlation terms, and correctly capture electronic coherences in a range of situations, including their spatial dependence, an important aspect that influences subsequent electron dynamics and that is becoming accessible in more experiments. 

Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tDMRG) can be used to simulate isolated spin chains, the coupling with phonons make simulations significantly more challenging. The recently developed multisite tensor network path integral (MS-TNPI) method builds a framework for simulating the dynamics in extended open quantum systems by combining ideas from tDMRG and Feynman-Vernon influence functional. This MS-TNPI is used to characterize dynamics in open, extended quantum systems. Simulations are done with the commonly used sub-Ohmic, Ohmic and super-Ohmic spectral densities describing the phononic bath. We show that while the transport in presence of impurities eventually becomes diffusive, the exact details are dependent on the specifics of the interactions and amount of impurities. In contrast, the presence of a bath makes the transport diffusive irrespective of the parameters characterizing the bath.

 Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly calculate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach enables the direct use of correlation functions obtained from methods like ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.

The use of neural network potentials (NNPs) to fit ab-initio potential energy surfaces is one of the most accurate and versatile methods to expand the utility of high quality, small-scale quantum calculations, allowing for ab-initio accuracy in simulations of large systems with an increase of efficiency by several orders of magnitude. As with all neural network applications however, NNPs present challenges with respect to over-fitting and generalization. In particular, choosing and normalizing the training data can be a complex task, as biases or gaps in the data can negatively impact the NNP performance. Here, it is shown that normalizing the inputs to the NNP by a constant related to the interaction cutoff volume leads to a significant improvement in the generalization of NNPs trained for Ar, Si, and NaCl compared to the standard approach, where each input is normalized by subtracting the average and scaling by the standard deviation. Specifically, NNPs trained using inputs scaled by a constant yield more accurate energies for defect structures not in the training set, and a NNP trained on isolated Ar clusters yields an accurate potential for solid and liquid Ar. The standard approach to NNP input scaling generally yields worse defect formation energies and cannot be transferred from isolated cluster calculations to periodic systems. We note that, when using volume scaling, the first layer of the neural network effectively renormalizes the inputs, reversing trends in the input data and narrowing the distribution of input values. Seemingly, the first layer is learning the distribution of inputs and renormalizing it for processing by subsequent layers, thereby leading to improved performance by removing a priori assumptions on the input distributions.

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that, for non-empirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define a novel XC functional quality metric that includes both energy and density errors, leading to a new, improved way to rank different approximations. Judged by this metric, our machine-learned functional significantly outperforms those within the same rung of approximations.

It has been a challenge to accurately simulate Li-ion diffusion processes in battery materials at room temperature using {\it ab initio} molecular dynamics (AIMD) due to its high computational cost. This situation has changed drastically in recent years due to the advances in machine learning-based interatomic potentials. Here we implement the Deep Potential Generator scheme to \textit{automatically} generate interatomic potentials for LiGePS-type solid-state electrolyte materials. This increases our ability to simulate such materials by several orders of magnitude without sacrificing {\it ab initio} accuracy. Important technical aspects like the statistical error and size effects are carefully investigated. We further establish a reliable protocol for accurate computation of Li-ion diffusion processes at experimental conditions, by investigating important technical aspects like the statistical error and size effects. Such a protocol and the automated workflow allow us to screen materials for their relevant properties with much-improved efficiency. By using the protocol and automated workflow developed here, we obtain the diffusivity data and activation energies of Li-ion diffusion that agree well with the experiment. Our work paves the way for future investigation of Li-ion diffusion mechanisms and optimization of Li-ion conductivity of solid-state electrolyte materials.