Similar to the behavior of a free particle, the initial growth of a wide (compared to the lattice spacing) wave packet positioned on an ordered lattice is slow (its initial time derivative is zero), and its spread (root mean square displacement) linearly increases with time at long times. The irregular lattice structure results in growth being stifled for a substantial duration, in accordance with Anderson localization. Employing numerical simulations complemented by analytical insights, we study site disorder and nearest-neighbor hopping in one- and two-dimensional systems. This study indicates that the short-time growth of the particle distribution is faster on the disordered lattice than on the ordered. The faster spread occurs on time and length scales that may have importance for exciton transport in disordered materials.

Deep learning has established itself as a promising methodology for generating extremely precise predictions concerning molecular and material characteristics. Unfortunately, a significant weakness of current methods lies in the fact that neural networks offer solely point predictions, without quantifying the predictive uncertainties. Quantification efforts concerning existing uncertainties have largely relied on the standard deviation of forecasts stemming from a collection of independently trained neural networks. The computational demands of both training and prediction are substantial, causing the expense of predictions to be significantly higher. This approach employs a singular neural network to calculate predictive uncertainty, eliminating the necessity for an ensemble. Obtaining uncertainty estimates incurs practically no additional computational overhead relative to the standard training and inference processes. The quality of our uncertainty estimates is comparable to the quality of uncertainty estimates produced by deep ensembles. We delve deeper into the uncertainty estimates of our methods and deep ensembles, evaluating them against the potential energy surface, all within the configuration space of our test system. We conclude by investigating the method's applicability within an active learning setup, demonstrating results that mirror ensemble-based techniques, yet with a considerably reduced computational burden.

The complex quantum mechanical interplay between numerous molecules and the radiation field is typically deemed computationally prohibitive, necessitating the use of approximation methods. Spectroscopy, usually incorporating perturbation theory, transitions to distinct methods in regimes characterized by strong coupling. The 1-exciton model, a frequent approximation, demonstrates processes involving weak excitations using a basis formed by the ground state and its singly excited states, all within the molecular cavity mode system. Within a commonly utilized approximation in numerical work, the electromagnetic field is classically modeled, and the quantum molecular subsystem's wavefunction is treated through the mean-field Hartree approximation, considered as a product of constituent molecular wavefunctions. States exhibiting prolonged population growth are effectively disregarded by the prior method, which consequently functions as a short-term estimate. Unbound by this constraint, the latter, by its inherent properties, disregards some intermolecular and molecule-field interactions. By directly comparing results from these approximations, our work examines the optical response of molecules-in-optical cavities systems in several illustrative prototype problems. The findings of our recent model investigation, outlined in [J, are particularly important. In matters pertaining to chemistry, submit this data. The physical universe displays a sophisticated and puzzling arrangement. Employing the truncated 1-exciton approximation, a study of the interplay between electronic strong coupling and molecular nuclear dynamics (reference 157, 114108 [2022]) demonstrates excellent agreement with the semiclassical mean-field approach.

Large-scale hybrid density functional theory calculations on the Fugaku supercomputer are now facilitated by the recent advancements in the NTChem program. Employing our recently proposed complexity reduction framework, we analyze the influence of basis set and functional choices on the measures of fragment quality and interaction, using these developments. Further study of system fragmentation in a variety of energy envelopes is conducted using the all-electron representation. This analysis motivates two algorithms for the computation of orbital energies in the context of the Kohn-Sham Hamiltonian. Systems containing thousands of atoms can have their spectral properties analyzed effectively using these algorithms, which act as a valuable diagnostic tool.

As an advanced technique, Gaussian Process Regression (GPR) is implemented for thermodynamic extrapolation and interpolation. Our presented heteroscedastic GPR models allow for the automated weighting of input data, according to its estimated uncertainty. This enables the inclusion of high-order derivative information, even if it is highly uncertain. GPR models, given the derivative operator's linear property, effortlessly include derivative data. Function estimations are accurately identified using appropriate likelihood models that consider variable uncertainties, enabling identification of inconsistencies between provided observations and derivatives that arise from sampling bias in molecular simulations. As our model leverages kernels which create complete bases within the learning function space, the model's predicted uncertainty accounts for the inherent uncertainty of the functional form. This differs significantly from polynomial interpolation, which inherently assumes a fixed functional form. Across a spectrum of data inputs, we apply GPR models and assess diverse active learning methodologies, determining optimal choices for specific circumstances. Our active-learning data collection process, leveraging GPR models and derivative data, is finally applied to mapping vapor-liquid equilibrium for a single-component Lennard-Jones fluid. This approach demonstrates a powerful advancement over prior extrapolation methods and Gibbs-Duhem integration strategies. A set of instruments that enact these strategies is situated at https://github.com/usnistgov/thermo-extrap.

With the development of novel double-hybrid density functionals, accuracy is reaching new heights and fresh insights into the foundational properties of matter are emerging. Building such functionals commonly involves the use of Hartree-Fock exact exchange and correlated wave function techniques, such as the second-order Møller-Plesset (MP2) method and the direct random phase approximation (dRPA). Concerns arise regarding their high computational cost, which consequently restricts their implementation in large and periodic systems. Employing the CP2K software package, this research effort has yielded the development and integration of low-scaling methodologies for Hartree-Fock exchange (HFX), SOS-MP2, and direct RPA energy gradients. read more Sparse tensor contractions are enabled by the sparsity induced by applying the resolution-of-the-identity approximation, alongside a short-range metric and atom-centered basis functions. These operations are carried out efficiently by leveraging the Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, which demonstrate scalability across hundreds of graphics processing unit (GPU) nodes. read more Benchmarking the resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA methods required the use of large supercomputers. read more Their performance shows a favorable sub-cubic scaling as the system grows, coupled with robust strong scaling, and GPU acceleration capabilities up to a threefold increase. The forthcoming ability to perform double-hybrid level calculations on large, periodic condensed-phase systems will be more commonplace thanks to these developments.

A focus of our study is the linear energy reaction of the uniform electron gas to a harmonic external field, aiming to explicitly differentiate the contributions to the total energy. Path integral Monte Carlo (PIMC) calculations, performed at various densities and temperatures, have yielded highly accurate results for this. We offer a collection of physical insights into phenomena including screening and the comparative role of kinetic and potential energies at diverse wave numbers. The investigation unveiled a significant finding: the non-monotonic shift in induced interaction energy, switching to a negative value at intermediate wave numbers. The coupling strength profoundly influences this effect, offering further direct proof of the spatial arrangement of electrons as detailed in earlier publications [T. Their communication, Dornheim et al. In physics, there's a lot to understand. According to the 2022 report, item 5,304, we find the following proposition. Within the regime of weak perturbations, the quadratic dependence of the outcomes on the perturbation amplitude is observed, and this aligns with the quartic dependence of the correction terms from the perturbation amplitude as stipulated by both linear and nonlinear versions of the density stiffness theorem. Online access provides free PIMC simulation results, enabling benchmarking of novel methods and facilitating input for supplementary calculations.

Dcdftbmd, a large-scale quantum chemical calculation program, was incorporated into the Python-based advanced atomistic simulation program, i-PI. Hierarchical parallelization, enabled by the client-server model, respects replicas and force evaluations. The established framework demonstrated that quantum path integral molecular dynamics simulations achieve high efficiency for systems with a few tens of replicas containing thousands of atoms. Analysis of bulk water systems, employing the framework, with and without excess protons, underscored the impact of nuclear quantum effects on molecular structures, encompassing oxygen-hydrogen bond distances and radial distribution functions surrounding the hydrated excess proton.