Regions Of Configuration Space Research Articles

A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons.

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for abinitio non-adiabatic dynamics in the near future.

"On-the-fly" : How to reliably and automatically characterize and construct potential energy surfaces.

In this work, the code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H O), (reduced-dimensional) methane (CH ), and methylene imine (CH NH).

Curvature-driven pathways interpolating between stationary points: the case of the pure spherical 3-spin model

This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical p-spin model with p = 3. The study investigates pairs of stationary points (local minima or rank-1 saddles), analyzing the energy profile along geodesic paths and comparing them with ‘perturbed’ pathways correlated to the landscape curvature. The goal is to assess the extent to which information from the local Hessian matrices around stationary points can identify paths with lower energy barriers. Surprisingly, unlike findings in other systems, the direction of softest local curvature is not a reliable predictor of low-energy paths, except in the case in which the direction of softest curvature corresponds to an isolated mode of the Hessian. However, other information encoded in the local Hessian does allow the identification of pathways associated with lower energy barriers. We conclude commenting on implications for the system’s activated dynamics.

ETune: Efficient configuration tuning for big-data software systems via configuration space reduction

Configuration tuning for big-data software systems is generally challenging due to the complex configuration space and costly performance evaluation. The workload changes over time in the context of big data making this problem even more difficult. To address the low efficiency issue caused by the need to retune from scratch after workload changes, we present ETune based on a combination of an Bayesian Optimization (BO) based tuner and configuration space reduction techniques to efficiently find high-performance configurations for big-data systems. For configuration space reduction, we develop two approaches: (1) shrinking the configuration space by trading off the exploitation and exploration between the impactful parameters and other parameters in the tuning process, (2) generating the promising regions of configuration space by transferring knowledge across past tuning tasks. The two configuration space reduction methods aim to reduce the huge configuration space to a compact but promising one, and searching in the reduced configuration space can further accelerate the configuration tuning. The extensive experiments show that our configuration space reduction methods considerably boost the BO-based tuner, and ETune significantly improves the tuning efficiency compared with the transfer learning based state-of-the-arts.

Understanding and eliminating spurious modes in variational Monte Carlo using collective variables

The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin chain, this approach can produce unreliable wave function approximations. One of the most obvious signs of failure is the occurrence of random, persistent spikes in the energy estimate during training. These energy spikes are caused by regions of configuration space that are over-represented by the wave function density, which are called ``spurious modes'' in the machine learning literature. After exploring these spurious modes in detail, we demonstrate that a collective-variable-based penalization yields a substantially more robust training procedure, preventing the formation of spurious modes and improving the accuracy of energy estimates. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC where a reasonable choice of collective variable is available.

Uncertainty-driven dynamics for active learning of interatomic potentials

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo

Variational Monte Carlo (VMC) is an approach for computing ground-state wave functions that has recently become more powerful due to the introduction of neural network-based wave-function parametrizations. However, efficiently training neural wave functions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence at no more than twice the computational cost. Second, to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when the sampler moves between metastable regions of configuration space. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and $XXZ$ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200 parameter updates.

Deconvolving the components of the sign problem

Auxiliary field Quantum Monte Carlo simulations of interacting fermions require sampling over a Hubbard-Stratonovich field $h$ introduced to decouple the interactions. The weight for a given configuration involves the products of the determinant of matrices $M_\sigma(h)$, where $\sigma$ labels the species, and hence is typically not positive definite. Indeed, the average sign $\langle {\cal S} \rangle$ of the determinants goes to zero exponentially with increasing spatial size and decreasing temperature for most Hamiltonians of interest. This statement, however, does not explicitly separate two possible origins for the vanishing of $\langle {\cal S} \rangle$. Does $\langle {\cal S} \rangle \rightarrow 0$ because {\it randomly} chosen field configurations have ${\rm det}\big(M(h)\big) < 0$, or does the `sign problem' arise because the specific subset of configurations chosen by the weighting function have a greater preponderance of negative values? In the latter case, the process of weighting the configurations with $|{\rm det}\big(M(h)\big)|$ might steer the simulation to a region of configuration space of $h$ where positive and negative determinants are equally likely, even though randomly chosen $h$ would preferentially have determinants with a single dominant sign. In this paper we address the relative importance of these two mechanisms for the vanishing of $\langle {\cal S} \rangle$ in quantum simulations.

Reinforcement learning of rare diffusive dynamics.

We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.

Combining phonon accuracy with high transferability in Gaussian approximation potential models.

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that accurately predict vibrational properties in specific regions of configuration space while retaining flexibility and transferability to others. We use an adaptive regularization of the GAP fit that scales with the absolute force magnitude on any given atom, thereby exploring the Bayesian interpretation of GAP regularization as an "expected error" and its impact on the prediction of physical properties for a material of interest. The approach enables excellent predictions of phonon modes (to within 0.1 THz-0.2 THz) for structurally diverse silicon allotropes, and it can be coupled with existing fitting databases for high transferability across different regions of configuration space, which we demonstrate for liquid and amorphous silicon. These findings and workflows are expected to be useful for GAP-driven materials modeling more generally.

Frozen-planet resonances in doubly excited helium atom; adiabatic approach

An improved adiabatic method is applied to study the highly excited asymmetric two-electron configurations of helium atom known as frozen-planet resonances. It is shown that our approach provides much better agreement with numerically calculated resonance positions than the previously used Born–Oppenheimer type approximation. Wide range of states were studied, related to N = 7 − 15 first-ionization thresholds. We show that estimates of tunneling widths of these states however are not reliable, because of the breakdown of adiabatic approximation in the underbarrier region of configuration space. We also provide computational evidence that a single-potential approximation in hyperspherical coordinates would be inferior to our approach.

Funnel hopping Monte Carlo: An efficient method to overcome broken ergodicity.

Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice, however, sampling of the complete configuration space is often hindered by high energy barriers between different regions of configuration space, which can make ergodic sampling completely infeasible within accessible simulation times. Although several extensions to the conventional Monte Carlo scheme have been developed, which enable the treatment of such systems, these extensions often entail substantial computational cost or rely on the harmonic approximation. In this work, we propose an exact method called Funnel Hopping Monte Carlo (FHMC) that is inspired by the ideas of smart darting but is more efficient. Gaussian mixtures are used to approximate the Boltzmann distribution around local energy minima, which are then used to propose high quality Monte Carlo moves that enable the Monte Carlo simulation to directly jump between different funnels. We demonstrate the method's performance on the example of the 38 as well as the 75 atom Lennard-Jones clusters, which are well known for their double funnel energy landscapes that prevent ergodic sampling with conventional Monte Carlo simulations. By integrating FHMC into the parallel tempering scheme, we were able to reduce the number of steps required significantly until convergence of the simulation.

Distribution of rare saddles in the p -spin energy landscape

We compute the statistical distribution of index-1 saddles surrounding a given local minimum of the p -spin energy landscape, as a function of their distance to the minimum in configuration space and of the energy of the latter. We identify the saddles also in the region of configuration space in which they are subdominant in number (i.e. rare) with respect to local minima, by computing large deviation probabilities of the extremal eigenvalues of their Hessian. As an independent result, we determine the joint large deviation probability of the smallest eigenvalue and eigenvector of a GOE matrix perturbed with both an additive and multiplicative finite-rank perturbation.

Hierarchical Markov State Model Building to Describe Molecular Processes.

Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.

Asymptotics of a semiclassical type for wave functions of quasimolecules in problems of ion-molecular collisions

Purpose. To construct an asymptotics of a quasiclassical type for the two-center wave function of the tunneliding electron used for calculating of the two-electron exchange interaction in the problems of ion-molecular collisions with particle rearrangement. Methods. The semiclassical method and the Green’s function formalism have been used for construction of the asymptotically correct two-center wave functions of a homonuclear diatomic molecule and a dipole-bound anion in the vicinity of a perturbing multiply charged ion. Results.We have constructed the semiclassical representation for the two-center one-electronic wave function of the quasimolecular system, which consist of the atomic ion and diatomic homonuclear molecule or dipole-bound anion, in the whole region of configuration space at large separation between colliding particles. Conclusions. An analytical study of the asymptotic properties (at large distances between interacting particles) of the quasimolecular systems that consists of an ion and a homonuclear diatomic molecule or dipole-bound anion has been carried out. The new analytical representations for the two-center one-electronic wave functions of the quasimolecular systems in the whole region of configuration space at large separation between colliding particles has been obtained in the framework of the semiclassical version of the asymptotic approach and the method of Green’s function

Cluster reducibility of multiquark operators

It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of completely compact multiquark bound states. Multiquark operators still play a crucial role in the description of exotic states in regions of configuration space where the hadronic clusters are close to each other. Our proof gives a foundation for a unified viewpoint, where the multiquark-type and the molecular-type approaches play complementary roles, at the gauge-invariant nonlocal operator level.

Car-Parrinello Monitor for More Robust Born-Oppenheimer Molecular Dynamics.

Born-Oppenheimer molecular dynamics (BOMD) is a promising simulation method for exploring the possible reaction pathways of a chemical system, but one significant challenge is the increased difficulty of converging the self-consistent field (SCF) calculation that often accompanies the breaking and forming of chemical bonds. To address this challenge, we developed an enhancement to the BOMD simulation method called the Car-Parrinello monitor (CPMonitor) that uses Car-Parrinello molecular dynamics (CPMD) to recover from SCF convergence failures. CPMonitor works by detecting SCF convergence failures in BOMD and switching to a CPMD Hamiltonian to propagate through the region of configuration space where the SCF calculation is unable to converge, then switching back to BOMD when good convergence behavior is re-established. We present a series of simulation studies that use CPMonitor, including detailed studies of the thermodynamic and dynamical properties of simple systems, as well as ab initio nanoreactor simulations containing transition metal atoms that were previously not possible to simulate using standard BOMD methods. Our studies show that CPMonitor can make BOMD simulations robust to SCF convergence difficulties and improve simulation performance and stability in reaction discovery applications.

Reproducing global potential energy surfaces with continuous-filter convolutional neural networks.

Neural networks fit to reproduce the potential energy surfaces of quantum chemistry methods offer a realization of analytic potential energy surfaces with the accuracy of ab initio methods at a computational cost similar to classical force field methods. One promising class of neural networks for this task is the SchNet architecture, which is based on the use of continuous-filter convolutional neural networks. Previous work has shown the ability of the SchNet architecture to reproduce density functional theory energies and forces for molecular configurations sampled during equilibrated molecular dynamics simulations. Due to the large change in energy when bonds are broken and formed, the fitting of global potential energy surfaces is normally a more difficult task than fitting the potential energy surface in the region of configurational space sampled during equilibrated molecular dynamics simulations. Herein, we demonstrate the ability of the SchNet architecture to reproduce the energies and forces of the potential energy surfaces of the H + H2 and Cl + H2 reactions and the OCHCO+ and H2CO/cis-HCOH/trans-HCOH systems. The SchNet models reproduce the potential energy surface of the reactions well with the best performing SchNet model having a test set root-mean-squared error of 0.52 meV and 2.01 meV for the energies of the H + H2 and Cl + H2 reactions, respectively, and a test set mean absolute error for the force of 0.44 meV/bohr for the H + H2 reaction. For the OCHCO+ and H2CO/cis-HCOH/trans-HCOH systems, the best performing SchNet model has a test set root-mean-squared error of 2.92 meV and 13.55 meV, respectively.

Robot Motion Planning Method Based on Incremental High-Dimensional Mixture Probabilistic Model

The sampling-based motion planner is the mainstream method to solve the motion planning problem in high-dimensional space. In the process of exploring robot configuration space, this type of algorithm needs to perform collision query on a large number of samples, which greatly limits their planning efficiency. Therefore, this paper uses machine learning methods to establish a probabilistic model of the obstacle region in configuration space by learning a large number of labeled samples. Based on this, the high-dimensional samples’ rapid collision query is realized. The influence of number of Gaussian components on the fitting accuracy is analyzed in detail, and a self-adaptive model training method based on Greedy expectation-maximization (EM) algorithm is proposed. At the same time, this method has the capability of online updating and can eliminate model fitting errors due to environmental changes. Finally, the model is combined with a variety of sampling-based motion planners and is validated in multiple sets of simulations and real world experiments. The results show that, compared with traditional methods, the proposed method has significantly improved the planning efficiency.

Accurate quantum molecular dynamics for multidimensional systems by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method.

Quantum phenomena are quite often of critical importance in chemical reactions. Thus the development of quantum molecular dynamics approaches is required to study the role of quantum effects such as tunnelling in chemical processes. The basis expansion leaping multi-configuration Gaussian (BEL MCG) method has been developed to obtain time-propagated wave packets describing reactive molecular systems. Here we examine the applicability of BEL MCG to double well problems in several dimensions. We pay particular attention to what is required to yield highly accurate dynamics with respect to several key features of the BEL MCG propagation. The importance of using basis functions of a width appropriate to the nature of the potential energy surface in the region of configuration space where each basis function is located is highlighted, which has implications for virtually all quantum molecular dynamics methods utilising Gaussian basis functions.