Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales

Analytical evaluations of the path integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator

By using the recently derived universal discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically and evaluated numerically at each imaginary time step for any short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth-order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing thermodynamic energy, converges extremely slowly with an increasing number of beads.

A collection of forcefield precursors for metal-organic frameworks

A host of important performance properties for metal-organic frameworks (MOFs) and other complex materials can be calculated by modeling statistical ensembles. The principle challenge is to develop accurate and computationally efficient interaction models for these simulations. Two major approaches are (i) ab initio molecular dynamics in which the interaction model is provided by an exchange-correlation theory (e.g., DFT + dispersion functional) and (ii) molecular mechanics in which the interaction model is a parameterized classical force field. The first approach requires further development to improve computational speed. The second approach requires further development to automate accurate forcefield parameterization. Because of the extreme chemical diversity across thousands of MOF structures, this problem is still mostly unsolved today. For example, here we show structures in the 2014 CoRE MOF database contain more than 8 thousand different atom types based on first and second neighbors. Our results showed that atom types based on both first and second neighbors adequately capture the chemical environment, but atom types based on only first neighbors do not. For 3056 MOFs, we used density functional theory (DFT) followed by DDEC6 atomic population analysis to extract a host of important forcefield precursors: partial atomic charges; atom-in-material (AIM) C6, C8, and C10 dispersion coefficients; AIM dipole and quadrupole moments; various AIM polarizabilities; quantum Drude oscillator parameters; AIM electron cloud parameters; etc. Electrostatic parameters were validated through comparisons to the DFT-computed electrostatic potential. These forcefield precursors should find widespread applications to developing MOF force fields.

New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 1. Theory and accuracy

Polarizabilities and London dispersion forces are important to many chemical processes. Force fields for classical atomistic simulations can be constructed using atom-in-material polarizabilities and C n (n = 6, 8, 9, 10…) dispersion coefficients. This article addresses the key question of how to efficiently assign these parameters to constituent atoms in a material so that properties of the whole material are better reproduced. We develop a new set of scaling laws and computational algorithms (called MCLF) to do this in an accurate and computationally efficient manner across diverse material types. We introduce a conduction limit upper bound and m-scaling to describe the different behaviors of surface and buried atoms. We validate MCLF by comparing results to high-level benchmarks for isolated neutral and charged atoms, diverse diatomic molecules, various polyatomic molecules (e.g., polyacenes, fullerenes, and small organic and inorganic molecules), and dense solids (including metallic, covalent, and ionic). We also present results for the HIV reverse transcriptase enzyme complexed with an inhibitor molecule. MCLF provides the non-directionally screened polarizabilities required to construct force fields, the directionally-screened static polarizability tensor components and eigenvalues, and environmentally screened C6 coefficients. Overall, MCLF has improved accuracy compared to the TS-SCS method. For TS-SCS, we compared charge partitioning methods and show DDEC6 partitioning yields more accurate results than Hirshfeld partitioning. MCLF also gives approximations for C8, C9, and C10 dispersion coefficients and quantum Drude oscillator parameters. This method should find widespread applications to parameterize classical force fields and density functional theory (DFT) + dispersion methods.

Molecular-scale remnants of the liquid-gas transition in supercritical polar fluids

An electronically coarse-grained model for water reveals a persistent vestige of the liquid-gas transition deep into the supercritical region. A crossover in the density dependence of the molecular dipole arises from the onset of nonpercolating hydrogen bonds. The crossover points coincide with the Widom line in the scaling region but extend farther, tracking the heat capacity maxima, offering evidence for liquidlike and gaslike state points in a "one-phase" fluid. The effect is present even in dipole-limit models, suggesting that it is common for all molecular liquids exhibiting dipole enhancement in the liquid phase.

Signature properties of water: Their molecular electronic origins

Water challenges our fundamental understanding of emergent materials properties from a molecular perspective. It exhibits a uniquely rich phenomenology including dramatic variations in behavior over the wide temperature range of the liquid into water's crystalline phases and amorphous states. We show that many-body responses arising from water's electronic structure are essential mechanisms harnessed by the molecule to encode for the distinguishing features of its condensed states. We treat the complete set of these many-body responses nonperturbatively within a coarse-grained electronic structure derived exclusively from single-molecule properties. Such a "strong coupling" approach generates interaction terms of all symmetries to all orders, thereby enabling unique transferability to diverse local environments such as those encountered along the coexistence curve. The symmetries of local motifs that can potentially emerge are not known a priori. Consequently, electronic responses unfiltered by artificial truncation are then required to embody the terms that tip the balance to the correct set of structures. Therefore, our fully responsive molecular model produces, a simple, accurate, and intuitive picture of water's complexity and its molecular origin, predicting water's signature physical properties from ice, through liquid-vapor coexistence, to the critical point.

High-order path-integral Monte Carlo methods for solving quantum dot problems

The conventional second-order path-integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of antisymmetric free-fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work we show that optimized fourth-order path-integral Monte Carlo methods, which use no more than five free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.

Electronically coarse-grained model for water

We introduce an electronically coarse-grained description of water representing all long range, many-body electronic responses via an embedded quantum oscillator. Leading-order response coefficients and gas phase electrostatic moments are exactly reproduced. Molecular dynamics, using electronic path integral sampling, shows that this framework is sufficient for a realistic liquid to emerge naturally with transferability extending further to nonambient state points and to the free water surface. The model allows the strength of many-body dispersion and polarization to be adjusted independently and these are found to have significant effects on the condensed phase.