As observed with a free particle, the initial growth of a wide (relative to the lattice spacing) wavepacket placed on an ordered lattice is slow (its initial time derivative having zero initial slope), and the spread (root mean square displacement) becomes linear with time at extended durations. A lattice exhibiting disorder leads to prolonged inhibition of growth, as observed in Anderson localization. In the context of one- and two-dimensional systems characterized by site disorder and nearest-neighbor hopping, we present numerical simulations supported by analytical calculations. These show that the particle distribution exhibits faster short-time growth in the disordered lattice than in the ordered lattice. This faster spread transpires over time and spatial scales potentially relevant to the exciton movement within disordered systems.

Deep learning's emergence presents a promising avenue for achieving highly accurate predictions of molecular and material properties. While effective, current strategies possess a common limitation: neural networks furnish only point estimations of their predictions, lacking the associated predictive uncertainties. Existing uncertainty quantification strategies have, for the most part, relied on the standard deviation derived from the predictions of a collective of independently trained neural networks. Substantial computational overhead is incurred during both training and prediction, causing a substantial increase in the cost of predictions. Employing a single neural network, we devise a method for estimating predictive uncertainty without requiring an ensemble. Standard training and inference procedures incur virtually no extra computational expense when uncertainty estimates are required. The quality of uncertainty estimates we produced is equivalent to those produced by deep ensembles. Examining the uncertainty estimates for our methods and deep ensembles across the configuration space of our test system, we compare the results to the potential energy surface. In the final analysis, the method's effectiveness is scrutinized in an active learning framework, where outcomes mirror those of ensemble strategies but with computational resources diminished by an order of magnitude.

The meticulous quantum mechanical description of the collective interaction of many molecules and the radiation field is frequently deemed computationally unfeasible, leading to the requirement of approximate calculation procedures. Although perturbation theory is typically part of standard spectroscopy, distinct approximations are invoked under circumstances of strong coupling interactions. 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. A frequently used approximation in numerical investigations describes the electromagnetic field classically, and the quantum molecular subsystem is approached using the Hartree mean-field approximation, assuming the wavefunction to be a product of each molecule's individual wavefunction. States with extended population development times are not considered by the previous approach; thus, it is essentially a short-term estimation. The latter, unhampered by this limitation, nevertheless fails to account for certain intermolecular and molecule-field correlations. This research directly compares results achieved from these approximations, as applied to numerous prototype problems, examining the optical response of molecules situated in optical cavity setups. The findings of our recent model investigation, outlined in [J, are particularly important. Kindly furnish the requested chemical details. Physically, the world is a perplexing entity. The semiclassical mean-field calculation is shown to have a strong correspondence with the truncated 1-exciton approximation's analysis of the interplay between electronic strong coupling and molecular nuclear dynamics as reported in reference 157, 114108 [2022].

A review of recent achievements in the NTChem program is provided, highlighting its capability for large-scale hybrid density functional theory calculations on the Fugaku supercomputer. 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. We use the all-electron representation to more deeply examine the fragmentation of systems across various energy profiles. Building upon this analysis, we introduce two algorithms for calculating the orbital energies of the Kohn-Sham Hamiltonian. We showcase that these algorithms can be effectively implemented on systems comprised of thousands of atoms, serving as an analytical tool that uncovers the source of spectral characteristics.

Gaussian Process Regression (GPR) is proposed as an improved approach to thermodynamic interpolation and extrapolation tasks. Our proposed heteroscedastic GPR models automatically adjust the weight given to each data point based on its uncertainty, enabling the utilization of highly uncertain, high-order derivative data. The derivative operator's linearity is exploited by GPR models for seamless integration of derivative information. This allows for the identification of estimates for functions exhibiting discrepancies between observations and derivatives, a typical consequence of sampling bias in molecular simulations, through appropriate likelihood models which accommodate heterogeneous uncertainties. Due to the utilization of kernels that create complete bases within the function space being learned, the estimated model uncertainty includes the uncertainty of the functional form itself. This contrasts significantly with polynomial interpolation, which inherently assumes a pre-defined and unvarying functional form. GPR models are applied to a multitude of data sources, and we evaluate a range of active learning strategies, noting when certain approaches are most effective. Leveraging active learning, GPR models, and derivative data, our novel data collection strategy is now applied to the task of tracing vapor-liquid equilibrium for a single-component Lennard-Jones fluid, surpassing earlier extrapolation and Gibbs-Duhem integration methods. Tools implementing these tactics are featured at the following address: https://github.com/usnistgov/thermo-extrap.

The development of novel double-hybrid density functionals is boosting accuracy to unprecedented levels and offering fresh perspectives on the fundamental makeup of matter. In order to develop these functionals, one must often utilize Hartree-Fock exact exchange and correlated wave function techniques, including the second-order Møller-Plesset (MP2) and the direct random phase approximation (dRPA). Their high computational cost is a limiting factor in their application to large and periodic systems. This work presents the development and implementation of low-scaling methods for Hartree-Fock exchange (HFX), SOS-MP2, and direct RPA energy gradients, incorporated into the CP2K software suite. selleck chemicals llc The use of short-range metrics and atom-centered basis functions, in conjunction with the resolution-of-the-identity approximation, results in sparsity, allowing sparse tensor contractions. The newly developed Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries facilitate the efficient execution of these operations, allowing scalability across hundreds of graphics processing unit (GPU) nodes. selleck chemicals llc To benchmark the methods resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA, large supercomputers were necessary. selleck chemicals llc System size has a favorable effect on the sub-cubic scaling, and there is a marked improvement in strong scaling. Additionally, GPU acceleration provides a speed boost of up to three times. Regular calculations of large, periodic condensed-phase systems will now be possible at a double-hybrid level thanks to these advancements.

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. This outcome was facilitated by comprehensive ab initio path integral Monte Carlo (PIMC) calculations conducted at diverse temperatures and densities. The analysis yields a number of physical understandings of screening and the comparative influence of kinetic and potential energies across various wave numbers. A striking conclusion is derived from the non-monotonic variation of the induced interaction energy, becoming negative at intermediate wave numbers. The pronounced reliance on coupling strength underscores this effect, providing further direct confirmation of the spatial alignment of electrons, as previously posited in earlier works [T. The communication of Dornheim et al. Physics, a fascinating field of study. The observation made in document number 5,304 of the year 2022 was as follows. Linear and nonlinear variations of the density stiffness theorem both concur with the quadratic dependence of observed effects on the perturbation amplitude under weak perturbation conditions, and the quartic influence on corrective terms stemming from the perturbation amplitude. Utilizing PIMC simulation results, freely accessible online, researchers can benchmark new methodologies or employ them in other calculations.

Using the advanced atomistic simulation program, i-PI, a Python-based tool, and the large-scale quantum chemical calculation program, Dcdftbmd, are now interconnected. The client-server model facilitated hierarchical parallelization, considering 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. The framework's examination of bulk water systems, encompassing both the presence and absence of an excess proton, showed that nuclear quantum effects are substantial in shaping intra- and inter-molecular structural properties, specifically oxygen-hydrogen bond lengths and radial distribution functions around the hydrated excess proton.