Benchmarking the exponential ansatz for the Holstein model.

Polarons are quasiparticles formed as a result of lattice distortions induced by charge carriers. The single-electron Holstein model captures the fundamentals of single polaron physics. We examine the power of the exponential ansatz for the polaron ground-state wavefunction in its coupled cluster, canonical transformation, and (canonically transformed) perturbative variants across the parameter space of the Holstein model. Our benchmark serves to guide future developments of polaron wavefunctions beyond the single-electron Holstein model.

Correlation functions from tensor network influence functionals: The case of the spin-boson model.

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry.

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models.

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Variational Lang-Firsov Approach Plus Møller-Plesset Perturbation Theory with Applications to Ab Initio Polariton Chemistry.

We apply the Lang-Firsov (LF) transformation to electron-boson coupled Hamiltonians and variationally optimize the transformation parameters and molecular orbital coefficients to determine the ground state. Møller-Plesset (MP-n, with n = 2 and 4) perturbation theory is then applied on top of the optimized LF mean-field state to improve the description of electron-electron and electron-boson correlations. The method (LF-MP) is applied to several electron-boson coupled systems, including the Hubbard-Holstein model, diatomic molecule dissociation (H2, HF), and the modification of proton transfer reactions (malonaldehyde and aminopropenal) via the formation of polaritons in an optical cavity. We show that with a correction for the electron-electron correlation, the method gives quantitatively accurate energies comparable to that by exact diagonalization or coupled-cluster theory. The effects of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions.

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained (CG) approaches in k-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher order contributions. We propose a systematic framework for constructing a faithful Fourier-space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular CG models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parameterization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

Electron and Spin Delocalization in [Co6 Se8 (PEt3 )6 ]0/+1 Superatoms.

Molecular clusters can function as nanoscale atoms/superatoms, assembling into superatomic solids, a new class of solid-state materials with designable properties through modifications on superatoms. To explore possibilities on diversifying building blocks, here we thoroughly studied one representative superatom, Co6 Se8 (PEt3 )6 . We probed its structural, electronic, and magnetic properties and revealed its detailed electronic structure as valence electrons delocalize over inorganic [Co6 Se8 ] core while ligands function as an insulated shell. 59 Co SSNMR measurements on the core and 31 P, 13 C on the ligands show that the neutral Co6 Se8 (PEt3 )6 is diamagnetic and symmetric, with all ligands magnetically equivalent. Quantum computations cross-validate NMR results and reveal degenerate delocalized HOMO orbitals, indicating aromaticity. Ligand substitution keeps the inorganic core nearly intact. After losing one electron, the unpaired electron in [Co6 Se8 (PEt3 )6 ]+1 is delocalized, causing paramagnetism and a delocalized electron spin. Notably, this feature of electron/spin delocalization over a large cluster is attractive for special single-electron devices.

Instantons and the quantum bound to chaos.

The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.

Response properties in phaseless auxiliary field quantum Monte Carlo.

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.

Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo.

We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures.

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Finding defects in glasses through machine learning.

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Due to their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods.

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Ultrafast imaging of polariton propagation and interactions.

Semiconductor excitations can hybridize with cavity photons to form exciton-polaritons (EPs) with remarkable properties, including light-like energy flow combined with matter-like interactions. To fully harness these properties, EPs must retain ballistic, coherent transport despite matter-mediated interactions with lattice phonons. Here we develop a nonlinear momentum-resolved optical approach that directly images EPs in real space on femtosecond scales in a range of polaritonic architectures. We focus our analysis on EP propagation in layered halide perovskite microcavities. We reveal that EP-phonon interactions lead to a large renormalization of EP velocities at high excitonic fractions at room temperature. Despite these strong EP-phonon interactions, ballistic transport is maintained for up to half-exciton EPs, in agreement with quantum simulations of dynamic disorder shielding through light-matter hybridization. Above 50% excitonic character, rapid decoherence leads to diffusive transport. Our work provides a general framework to precisely balance EP coherence, velocity, and nonlinear interactions.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity.

Recent experiments suggest that ground state chemical reactivity can be modified when placing molecular systems inside infrared cavities where molecular vibrations are strongly coupled to electromagnetic radiation. This phenomenon lacks a firm theoretical explanation. Here, we employ an exact quantum dynamics approach to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials.

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multilayered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multilayered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond.

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 - N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry.

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy.

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.