Like a free particle, the initial growth of a broad (compared to lattice spacing) wavepacket on an ordered lattice is sluggish (with a zero initial time derivative), and its spread (root mean square displacement) becomes linear in time at long times. Long-term growth inhibition on a disordered lattice is a characteristic of Anderson localization. We investigate site disorder with nearest-neighbor hopping in one- and two-dimensional systems, and present numerical simulations supported by analytical results. These simulations reveal that the particle distribution develops more quickly in the short term on the disordered lattice than on the ordered one. Such expedited propagation takes place across temporal and spatial scales, which might be crucial for exciton behavior in disordered systems.
Deep learning provides a promising paradigm for achieving highly accurate predictions regarding the properties of both molecules and materials. A recurring limitation of current methodologies, though, is the inherent nature of neural networks, which offer only point estimates for predictions, failing to account for the uncertainties associated with these estimations. The standard deviation of predictions from an ensemble of independently trained neural networks has been central to many existing uncertainty quantification endeavors. This training and prediction process places a significant computational load on the system, resulting in an order of magnitude increase in the expense of predictions. A single neural network is employed in this method to estimate predictive uncertainty without resorting to 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. By scrutinizing the configuration space of our test system, we assess the uncertainty estimates of our methods and deep ensembles, comparing them to the potential energy surface. The method's efficiency in an active learning environment is studied, and the results align with ensemble-based approaches, while experiencing a drastic reduction in computational cost by an order of magnitude.
Calculating the exact quantum mechanical description of the collective interaction of many molecules with the radiant field is often deemed computationally too complex, requiring the use of approximation methods. Perturbation theory, a common element in standard spectroscopy, gives way to different approximations in the face of intense coupling. The 1-exciton model, a common approximation, describes weak excitation processes using a basis set comprising the ground state and single excited states of 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 former method inherently prioritizes speed over accuracy, creating a short-term approximation for states with prolonged population growth patterns. Unconstrained in this manner, the latter nonetheless neglects certain intermolecular and molecule-field correlations. This work directly compares the outcomes obtained using these approximations, applied to several illustrative problems concerning the optical response of molecular systems in optical cavities. Our recent model study, detailed in [J, underscores an important aspect. The requested chemical information must be returned. Physically, the world manifests in intricate ways. The analysis of the interplay between electronic strong coupling and molecular nuclear dynamics, performed using the truncated 1-exciton approximation (reference 157, 114108 [2022]), strongly corroborates the results obtained from the semiclassical mean-field calculation.
Large-scale hybrid density functional theory calculations on the Fugaku supercomputer are now facilitated by the recent advancements in the NTChem program. By integrating these developments with our recently introduced complexity reduction framework, we can analyze the impact of basis set and functional choices on the measures of fragment quality and interaction. We further analyze system fragmentation in differing energy bands by employing the all-electron representation. 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 demonstrated to be a more effective method for thermodynamic interpolation and extrapolation. Our newly developed heteroscedastic GPR models dynamically weight input information according to its estimated uncertainty, facilitating the integration of highly uncertain, high-order derivative data. GPR models readily incorporate derivative information given the derivative operator's linearity. Appropriate likelihood models, accounting for variable uncertainties, enable them to detect estimations of functions where provided observations and derivatives exhibit inconsistencies due to the sampling bias common in molecular simulations. 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. 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 set of instruments that enact these strategies is situated at https://github.com/usnistgov/thermo-extrap.
Groundbreaking double-hybrid density functionals are achieving superior accuracy and producing invaluable insights into the essential qualities of matter. To construct such functionals, Hartree-Fock exact exchange and correlated wave function methods, including second-order Møller-Plesset (MP2) and direct random phase approximation (dRPA), are typically necessary. Their application to large and periodic systems is hampered by their high computational expense. This research describes the development and implementation of novel low-scaling methods for Hartree-Fock exchange (HFX), SOS-MP2, and direct RPA energy gradients directly within the CP2K software environment. Metabolism inhibitor 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. Efficiently handling these operations is achieved with the newly developed Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, which scale seamlessly to hundreds of graphics processing unit (GPU) nodes. Metabolism inhibitor Large supercomputers were employed to benchmark the newly developed methods: resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA. Metabolism inhibitor The system exhibits a positive sub-cubic scaling relationship with its size, coupled with excellent strong scaling characteristics, and accelerated GPU performance up to a three-fold gain. By virtue of these advancements, double-hybrid level calculations for large, periodic condensed-phase systems can now be performed with greater regularity.
Investigating the linear energy response of the uniform electron gas to an external harmonic perturbation, we seek to isolate and understand each part of the total energy. This outcome was facilitated by comprehensive ab initio path integral Monte Carlo (PIMC) calculations conducted at diverse temperatures and densities. Our findings reveal several physical aspects of screening and the comparative impact of kinetic and potential energies for different wave numbers. A noteworthy observation arises from the non-monotonic trend in the induced interaction energy alteration, transitioning to a negative value at intermediate wave numbers. This effect is heavily influenced by the magnitude of the coupling strength, offering further direct evidence that electrons are spatially aligned, as indicated in previous studies [T. Communication by Dornheim et al. The physics involved are complex. The 2022 record, entry 5,304, offered this observation. 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. Online access provides free PIMC simulation results, enabling benchmarking of novel methods and facilitating input for supplementary 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. Replicas and force evaluations were subject to hierarchical parallelization, a result of the client-server model's implementation. Quantum path integral molecular dynamics simulations, as demonstrated by the established framework, perform with high efficiency for systems containing thousands of atoms and a few tens of replicas. 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.