A wavepacket of significant width (relative to lattice spacing) positioned on an ordered lattice, similar to a free particle, grows slowly initially (with zero initial time derivative), and its spread (root mean square displacement) follows a linear time dependence at large times. On a haphazard lattice, growth is hindered for an extended period, a phenomenon known as Anderson localization. We examine site disorder with nearest-neighbor hopping within one- and two-dimensional systems, demonstrating through numerical simulations, corroborated by analytical analysis, that the short-time evolution of particle distribution is more rapid on the disordered lattice compared to the ordered lattice. The accelerated distribution happens at time and length scales that are possibly pertinent to exciton motion in disordered systems.

Deep learning's emergence presents a promising avenue for achieving highly accurate predictions of molecular and material properties. Current approaches, however, unfortunately, have a common shortcoming: neural networks only offer point estimations of their predictions, without providing the accompanying uncertainties. Existing uncertainty quantification methodologies have, in the main, depended on the standard deviation of predictions produced by a group of separately trained neural networks. Substantial computational overhead is incurred during both training and prediction, causing a substantial increase in the cost of predictions. A method for estimating predictive uncertainty based on a single neural network, rather than an ensemble, is proposed here. Uncertainty estimations are possible using virtually no additional computational resources beyond the usual training and inference steps. Our uncertainty estimations demonstrate a comparable quality to those derived from deep ensembles. Our test system's configuration space is used to further examine and compare the uncertainty estimates of our methods and deep ensembles 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.

A thorough quantum mechanical examination of the collaborative interaction of many molecules with the electromagnetic field is usually regarded as numerically intractable, making the use of approximate models essential. Standard spectroscopic procedures frequently involve perturbation theory; however, different estimations are employed when coupling is substantial. 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. For numerical studies, a frequently utilized approximation describes the electromagnetic field classically, and within the Hartree mean-field approximation, the quantum molecular subsystem's wavefunction is considered as a product of individual molecular wavefunctions. The previous method, inherently a short-term approximation, neglects states with substantial population growth durations. Unfettered by this restriction, the latter, by its very nature, overlooks some intermolecular and molecule-field correlations. This investigation presents a direct comparison of results from these approximations, as applied to diverse prototype problems concerning the optical response of molecules within optical cavity environments. A critical aspect of our recent model investigation, detailed in [J], is presented here. Please provide this chemical data. The physical world exhibits an intricate and perplexing design. A comparison of the truncated 1-exciton approximation's treatment of the interplay between electronic strong coupling and molecular nuclear dynamics (documented in 157, 114108 [2022]) with the semiclassical mean-field calculation reveals remarkable agreement.

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. We evaluate the consequences of basis set and functional selection on fragment quality and interaction measures, employing these developments in tandem with our recently proposed complexity reduction framework. To further investigate system fragmentation within various energy ranges, we leverage the all-electron representation. From this analysis, we develop two algorithms for computing the orbital energies of the Kohn-Sham Hamiltonian system. The algorithms' capability to analyze systems with thousands of atoms is demonstrated, highlighting their role as diagnostic tools in revealing the origin of spectral properties.

Gaussian Process Regression (GPR) is introduced as a sophisticated method for both thermodynamic extrapolation and interpolation. The heteroscedastic GPR models we introduce automatically tailor the weighting of the provided information based on its estimated uncertainty, facilitating the inclusion of high-order derivative data, even if its uncertainty is significant. 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. We employ kernels that form complete bases within the function space for learning. This leads to uncertainty estimations that encompass the uncertainty in the functional form, unlike polynomial interpolation, which operates under the assumption of a predefined, fixed functional form. We utilize GPR models across a range of data sources, examining various active learning approaches to determine the optimal strategies in different contexts. We've successfully implemented active learning data collection, integrating GPR models and derivative information, to analyze vapor-liquid equilibrium in a single-component Lennard-Jones fluid. This novel method represents a substantial advancement from prior strategies like extrapolation and Gibbs-Duhem integration. A group of instruments utilizing these strategies are found at the repository https://github.com/usnistgov/thermo-extrap.

Fresh double-hybrid density functionals are demonstrating unprecedented accuracy and are producing significant advancements in our comprehension of matter's fundamental characteristics. The creation of such functionals invariably calls for the utilization of Hartree-Fock exact exchange and correlated wave function methods, like the second-order Møller-Plesset (MP2) and the direct random phase approximation (dRPA). Because of their demanding computational requirements, their application in large and recurring systems is restricted. 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. HG106 cost Using the resolution-of-the-identity approximation, a short-range metric, and atom-centered basis functions, sparsity is created, thereby enabling sparse tensor contractions. With the new Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, these operations are executed with efficiency, demonstrating scalability across hundreds of graphics processing unit (GPU) nodes. HG106 cost Large supercomputers were employed to benchmark the newly developed methods: resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA. HG106 cost Sub-cubic scaling with respect to system size is positive, along with a robust display of strong scaling, and GPU acceleration that may improve performance up to a factor of three. By virtue of these advancements, double-hybrid level calculations for large, periodic condensed-phase systems can now be performed with greater regularity.

An investigation into the linear energy response of a uniform electron gas under harmonic external forcing, emphasizing the breakdown of the overall energy into its constituent parts. Path integral Monte Carlo (PIMC) calculations, performed at various densities and temperatures, have yielded highly accurate results for this. We present several physical understandings of phenomena like screening, examining the comparative significance of kinetic and potential energies across various wave numbers. The observed interaction energy change exhibits a fascinating non-monotonic pattern, becoming negative at intermediate wave numbers. This effect's strength is inextricably linked to coupling strength, constituting further, direct evidence for the spatial alignment of electrons, a concept introduced in earlier works [T. Dornheim et al. presented in their communication. The physics involved are complex. The 2022 record, entry 5,304, offered this observation. The quadratic relationship observed between perturbation amplitude and the outcome, in the context of weak perturbations, and the quartic dependence of correction terms tied to the perturbation amplitude are both in agreement with the linear and nonlinear formulations of the density stiffness theorem. Publicly accessible PIMC simulation results are available online, permitting the benchmarking of new methodologies and incorporation into other computational endeavors.

The advanced atomistic simulation program, i-PI, now incorporates the large-scale quantum chemical calculation program, Dcdftbmd. The implementation of the client-server model enabled hierarchical parallelization, concerning replicas and force evaluations. The established framework highlighted the high efficiency of quantum path integral molecular dynamics simulations for systems comprising a few tens of replicas and thousands of atoms. Applying the framework to bulk water systems, with or without an excess proton, confirmed that nuclear quantum effects significantly affect intra- and inter-molecular structural properties, including oxygen-hydrogen bond distance and the radial distribution function for the hydrated excess proton.