arXiv subjects

Thomas F. Miller III

Publications and source records attributed to Thomas F. Miller III.

At least 37 records · Page 2Linked to original sources

arXiv2020

Sum-Frequency Signals in 2D-Terahertz-Terahertz-Raman Spectroscopy

We demonstrate that halogenated methane 2D-Terahertz Terahertz Raman (2D-TTR) spectra are determined by the complicated structure of the instrument response function (IRF) along $f_1$ and by the molecular coherences along $f_2$. Experimental improvements have helped increase the resolution and dynamic range of the measurements, including accurate THz pulse shape characterization. Sum-frequency excitations convolved with the IRF are found to quantitatively reproduce the 2D-TTR signal. A new Reduced Density Matrix model which incorporates sum-frequency pathways, with linear and harmonic operators fully supports this (re)interpretation of the 2D-TTR spectra.

physics.chem-ph↗

arXiv2020

Nuclear Quantum Effects in Scattering of H and D from Graphene

We present a detailed study of the nuclear quantum effects in H/D sticking to graphene, comparing classical, quantum and mixed quantum/classical simulations to results of scattering experiments. Agreement with experimentally derived sticking probabilities is improved when nuclear quantum effects are included using ring polymer molecular dynamics. Specifically, the quantum motion of the carbon atoms enhances sticking, showing that an accurate description of graphene phonons is important to capturing the adsorption dynamics. We also find an inverse H/D isotope effect arising from Newtonian mechanics.

physics.chem-ph↗

arXiv2020

Dimension-free path-integral molecular dynamics without preconditioning

Convergence with respect to imaginary-time discretization is an essential part of any path-integral-based calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics (PIMD) - including ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) - is that for a given MD timestep, the overlap between the exact ring-polymer Boltzmann-Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte-Carlo/MD sampling schemes. We show that these problems can be avoided through the introduction of "dimension-free" numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. We show that dimension freedom can be achieved via mollification of the forces from the physical potential and with the BCOCB integration scheme. The dimension-free numerical integration schemes yield finite error bounds for a given MD timestep as the number of beads is taken to infinity; these conclusions are proven for harmonic potential and borne out numerically for anharmonic systems, including water. The numerical results for BCOCB are particularly striking, allowing for three-fold increases in the stable timestep for liquid water with respect to the Bussi-Parrinello (OBABO) and Leimkuhler (BAOAB) integrators while introducing negligible errors in the statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

physics.chem-ph↗

arXiv2020

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates, for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime.

cond-mat.stat-mech↗

arXiv2019

Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning

Machine learning (ML) in the representation of molecular-orbital-based (MOB) features has been shown to be an accurate and transferable approach to the prediction of post-Hartree-Fock correlation energies. Previous applications of MOB-ML employed Gaussian Process Regression (GPR), which provides good prediction accuracy with small training sets; however, the cost of GPR training scales cubically with the amount of data and becomes a computational bottleneck for large training sets. In the current work, we address this problem by introducing a clustering/regression/classification implementation of MOB-ML. In a first step, regression clustering (RC) is used to partition the training data to best fit an ensemble of linear regression (LR) models; in a second step, each cluster is regressed independently, using either LR or GPR; and in a third step, a random forest classifier (RFC) is trained for the prediction of cluster assignments based on MOB feature values. Upon inspection, RC is found to recapitulate chemically intuitive groupings of the frontier molecular orbitals, and the combined RC/LR/RFC and RC/GPR/RFC implementations of MOB-ML are found to provide good prediction accuracy with greatly reduced wall-clock training times. For a dataset of thermalized geometries of 7211 organic molecules of up to seven heavy atoms, both implementations reach chemical accuracy (1 kcal/mol error) with only 300 training molecules, while providing 35000-fold and 4500-fold reductions in the wall-clock training time, respectively, compared to MOB-ML without clustering. The resulting models are also demonstrated to retain transferability for the prediction of large-molecule energies with only small-molecule training data. Finally, it is shown that capping the number of training datapoints per cluster leads to further improvements in prediction accuracy with negligible increases in wall-clock training time.

physics.chem-ph↗

arXiv2019

Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics

Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostatted (i.e., canonical) equations of motion, it leads to non-ergodicity of the sampling. These pathologies are generally proven to arise at integration timesteps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based molecular dynamics - including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD - providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD timestep. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD timesteps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.

physics.chem-ph↗

arXiv2019

Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding

Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of density functional theory. Here, we present the derivation, implementation, and numerical demonstration of analytical nuclear gradients for projection-based wavefunction-in-density functional theory (WF-in-DFT) embedding. The gradients are formulated in the Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. An important aspect of the gradient theory is that WF contributions to the total WF-in-DFT gradient can be simply evaluated using existing WF gradient implementations without modification. Another simplifying aspect is that Kohn-Sham (KS) DFT contributions to the projection-based embedding gradient do not require knowledge of the WF calculation beyond the relaxed WF density. Projection-based WF-in-DFT embedding gradients are thus easily generalized to any combination of WF and KS-DFT methods. We provide numerical demonstration of the method for several applications, including calculation of a minimum energy pathway for a hydride transfer in a cobalt-based molecular catalyst using the nudged-elastic-band method at the CCSD-in-DFT level of theory, which reveals large differences from the transition state geometry predicted using DFT.

physics.chem-ph↗

arXiv2019

Energy Conversion via Metal Nanolayers

Current approaches for electric power generation from nanoscale conducting or semi-conducting layers in contact with moving aqueous droplets are promising as they show efficiencies of around 30 percent, yet, even the most successful ones pose challenges regarding fabrication and scaling. Here, we report stable, all-inorganic single-element structures synthesized in a single step that generate electrical current when alternating salinity gradients flow along its surface in a liquid flow cell. 10 nm to 30 nm thin nanolayers of iron, vanadium, or nickel produce several tens of mV and several microA cm^-2 at aqueous flow velocities of just a few cm s^-1. The principle of operation is strongly sensitive to charge-carrier motion in the thermal oxide nano-overlayer that forms spontaneously in air and then self terminates. Indeed, experiments suggest a role for intra-oxide electron transfer for Fe, V, and Ni nanolayers, as their thermal oxides contain several metal oxidation states, whereas controls using Al or Cr nanolayers, which self-terminate with oxides that are redox inactive under the experimental conditions, exhibit dramatically diminished performance. The nanolayers are shown to generate electrical current in various modes of application with moving liquids, including sliding liquid droplets, salinity gradients in a flowing liquid, and in the oscillatory motion of a liquid without a salinity gradient.

physics.app-ph↗

arXiv2019

Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature

We extend the coupled-cluster method to correlated quantum dynamics of both closed and open systems at finite temperatures using the thermo-field formalism. The approach expresses the time-dependent density matrix in an exponential ansatz and describes time-evolution along the Keldysh path contour. A distinct advantage of the approach is exact trace-preservation as a function of time, ensuring conservation of probability and particle number. Furthermore, the method avoids the computation of correlated bra-states, simplifying the computational implementation. We develop the method in a thermal quasi-particle representation, which allows seamless connection to the projection method and diagrammatic techniques of the traditional coupled-cluster formalism. For comparison, we also apply the thermo-field framework to renormalization-group methods to obtain reference results for closed and open systems at finite temperatures. We test the singles and doubles approximation to the density-matrix coupled-cluster method on the correlated electronic dynamics of the single-impurity Anderson model, demonstrating that the new method successfully captures the correlated dynamics of both closed systems at finite temperature and driven-dissipative open systems. This encouraging performance motivates future applications to non-equilibrium quantum many-body dynamics in realistic systems.

quant-ph↗

arXiv2019

Interpretation of the THz-THz-Raman Spectrum of Bromoform

Nonlinear THz-THz-Raman (TTR) liquid spectroscopy offers new possibilities for studying and understanding condensed-phase chemical dynamics. Although TTR spectra carry rich information about the systems under study, the response is encoded in a three-point correlation function comprising of both dipole and polarizability elements. Theoretical methods are necessary for the interpretation of the experimental results. In this work, we study the liquid-phase dynamics of bromoform, a polarizable molecule with a strong TTR response. Previous work based on reduced density matrix (RDM) simulations suggests that unusually large multi-quanta dipole matrix elements are needed to understand the measured spectrum of bromoform. Here, we demonstrate that a self-consistent definition of the time coordinates with respect to the reference pulse leads to a simplified experimental spectrum. Furthermore, we analytically derive a parametrization for the RDM model by integrating the dipole and polarizability elements to the 4th order in the normal modes, and we enforce inversion symmetry in the calculations by numerically cancelling the components of the response that are even with respect to the field. The resulting analysis eliminates the need to invoke large multi-quanta dipole matrix elements to fit the experimental spectrum; instead, the experimental spectrum is recovered using RDM simulations with dipole matrix parameters that are in agreement with independent ab initio calculations. The fundamental interpretation of the TTR signatures in terms of coupled intramolecular vibrational modes remains unchanged from the previous work.

physics.chem-ph↗

arXiv2019

Path-accelerated molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-timescale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics (PAMD) method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to MD timesteps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action with respect to time and by initializing the path configurations from a non-equilibrium distribution, the algorithm enables significant speedups in terms of the length of MD trajectories that can be integrated in a given amount of wall-clock time. The method is demonstrated for Brownian dynamics, although it is generalizable to other stochastic equations of motion including open systems. We apply the method to two simple systems, a harmonic oscillator and a Lennard-Jones liquid, and we show that in comparison to the conventional Euler integration scheme for Brownian dynamics, the new method can reduce the wall-clock time for integrating trajectories of a given length by more than three orders of magnitude in the former system and more than two in the latter. This new method for parallelizing MD in the dimension of time can be trivially combined with algorithms for parallelizing the MD force evaluation to achieve further speedup.

physics.comp-ph↗

arXiv2019

A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules

We address the degree to which machine learning can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based machine learning (MOB-ML) method is applied to several test systems. Strikingly, for the MP2, CCSD, and CCSD(T) levels of theory, it is shown that the thermally accessible (350 K) potential energy surface for a single water molecule can be described to within 1 millihartree using a model that is trained from only a single reference calculation at a randomized geometry. To explore the breadth of chemical diversity that can be described, MOB-ML is also applied to a new dataset of thermalized (350 K) geometries of 7211 organic models with up to seven heavy atoms. In comparison with the previously reported $Δ$-ML method, MOB-ML is shown to reach chemical accuracy with three-fold fewer training geometries. Finally, a transferability test in which models trained for seven-heavy-atom systems are used to predict energies for thirteen-heavy-atom systems reveals that MOB-ML reaches chemical accuracy with 36-fold fewer training calculations than $Δ$-ML (140 versus 5000 training calculations).

physics.chem-ph↗

arXiv2018

Even-handed subsystem selection in projection-based embedding

Projection-based embedding offers a simple framework for embedding correlated wavefunction methods in density functional theory. Partitioning between the correlated wavefunction and density functional subsystems is performed in the space of localized molecular orbitals. However, during a large geometry change--such as a chemical reaction--the nature of these localized molecular orbitals, as well as their partitioning into the two subsystems, can change dramatically. This can lead to unphysical cusps and even discontinuities in the potential energy surface. In this work, we present an even-handed framework for localized orbital partitioning that ensures consistent subsystems across a set of molecular geometries. We illustrate this problem and the even-handed solution with a simple example of an SN2 reaction. Applications to a nitrogen umbrella flip in a cobalt-based CO2 reduction catalyst and to the binding of CO to Cu clusters are presented. In both cases, we find that even-handed partitioning enables chemically accurate embedding with modestly-sized embedded regions for systems in which previous partitioning strategies are problematic.

physics.chem-ph↗

arXiv2018

Transferability in Machine Learning for Electronic Structure via the Molecular Orbital Basis

We present a machine learning (ML) method for predicting electronic structure correlation energies using Hartree-Fock input.The total correlation energy is expressed in terms of individual and pair contributions from occupied molecular orbitals, and Gaussian process regression is used to predict these contributions from a feature set that is based on molecular orbital properties, such as Fock, Coulomb, and exchange matrix elements. With the aim of maximizing transferability across chemical systems and compactness of the feature set, we avoid the usual specification of ML features in terms of atom- or geometry-specific information, such atom/element-types, bond-types, or local molecular structure. ML predictions of MP2 and CCSD energies are presented for a range of systems, demonstrating that the method maintains accuracy while providing transferability both within and across chemical families; this includes predictions for molecules with atom-types and elements that are not included in the training set. The method holds promise both in its current form and as a proof-of-principle for the use of ML in the design of generalized density-matrix functionals.

physics.chem-ph↗

arXiv2016

Enhancing Cation Diffusion and Suppressing Anion Diffusion via Lewis-Acidic Polymer Electrolytes

Solid polymer electrolytes (SPE) have the potential to increase both the energy density and stability of lithium-based batteries, but low Li-ion conductivity remains a barrier to technological viability. SPEs are designed to maximize Li-ion diffusivity relative to the anion, while maintaining sufficient salt solubility. It is thus remarkable that polyethylene oxide (PEO), the most widely used SPE, exhibits Li-ion diffusivity that is an order of magnitude smaller than that of typical counter-ions, such as TFSI, at moderate salt concentrations. Here, we show that Lewis-basic polymers like PEO intrinsically favor slow cation and rapid anion diffusion while this relationship can be reversed in Lewis-acidic polymers. Using molecular dynamics (MD) simulations, Lewis-acidic polyboranes are identified that achieve up to a ten-fold increase in Li-ion diffusivity and a significant decrease in anion diffusivity, relative to PEO. The results for this new class of Lewis-acidic SPEs illustrate a general principle for increasing Li-ion diffusivity and transference number with polymer chemistries that exhibit weaker cation and stronger anion coordination.

physics.chem-ph↗

arXiv2014

Kinetically Constrained Ring-Polymer Molecular Dynamics for Non-adiabatic Chemical Reactions

We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force.

cond-mat.stat-mech↗

arXiv2012

Density functional theory embedding for correlated wavefunctions: Improved methods for open-shell systems and transition metal complexes

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and we develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential (OEP) calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in the dispersion interactions due to conventional exchange-correlation (XC) functionals while simultaneously avoiding errors due to subsystem partitioning across covalent bonds. Application of WFT-in-DFT embedding to the calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II) cation reveals that the majority of the dependence on the DFT XC functional can be eliminated by treating only the single transition-metal atom at the WFT level; furthermore, these calculations demonstrate the substantial effects of open-shell contributions to the embedding potential, and they suggest that restricted open-shell WFT-in-DFT embedding provides better accuracy than unrestricted open-shell WFT-in-DFT embedding due to the removal of spin contamination.

physics.chem-ph↗

arXiv2012

Flux-correlation approach to characterizing reaction pathways in quantum systems: A study of condensed-phase proton-coupled electron transfer

We introduce a simple method for characterizing reactive pathways in quantum systems. Flux auto- correlation and cross-correlation functions are employed to develop a quantitative measure of dynamical coupling in quantum transition events, such as reactive tunneling and resonant energy transfer. We utilize the method to study condensed-phase proton-coupled electron transfer (PCET) reactions and to determine the relative importance of competing concerted and sequential reaction pathways. Results presented here include numerically exact quantum dynamics simulations for model condensed-phase PCET reactions. This work demonstrates the applicability of the new method for the analysis of both approximate and exact quantum dynamics simulations.

cond-mat.stat-mech↗