Condensed Phase Systems Research Articles

Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional.

We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.

An Iterative Fragment Scheme for the ACKS2 Electronic Polarization Model: Application to Molecular Dimers and Chains.

The treatment of electrostatic interactions is a key ingredient in the force field-based simulation of condensed phase systems. Most approaches used fixed, site-specific point charges. Yet, it is now clear that many applications of force fields (FFs) demand more sophisticated treatments, prompting the implementation of charge equilibration methods in polarizable FFs to allow the redistribution of charge within the system. One approach allowing both, charge redistribution and site-specific polarization, while at the same time solving methodological shortcomings of earlier methods, is the first-principles-derived atom-condensed Kohn-Sham density functional theory method approximated to the second order (ACKS2). In this work, we present two fragment approaches to ACKS2, termed f-ACKS2 and a self-consistent version, scf-ACKS2, that treat condensed phase systems as a collection of electronically polarizable molecular fragments. The fragmentation approach to ACKS2 not only leads to a more transferable and less system-specific collection of electronic response parameters but also opens up the method to large condensed phase systems. We validate the accuracies of f-ACKS2 and scf-ACKS2 by comparing polarization energies and induced dipole moments for a number of charged hydrocarbon dimers against DFT reference calculations. Finally, we also apply both fragmented ACKS2 variants to calculate the polarization energy for electron-hole pair separation along a chain of anthracene molecules and find excellent agreement with reference DFT calculations.

Two-dimensional Raman spectroscopy of Lennard-Jones liquids via ring-polymer molecular dynamics.

The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.

Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization

Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with N<105 fermionic modes can be performed with roughly O(1) and O(N2) T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.

Fast and Accurate Quantum Chemical Modeling of Infrared Spectra of Condensed-Phase Systems.

An efficient approach for an accurate quantum mechanical (QM) modeling of infrared (IR) spectra of condensed-phase systems is described. An ensemble of energetically low-lying cluster structures of a solute molecule surrounded by an explicit shell of solvent molecules is efficiently generated at the semiempirical tight-binding QM level and then reoptimized at the density functional theory level of theory. The IR spectrum of the solvated molecule is obtained as a thermodynamic average of harmonically computed QM spectra for all significantly populated cluster structures. The accuracy of such simulations in comparison to experimental data for some organic compounds and their solutions is shown to be the same or even better than the corresponding QM computations of the gas-phase IR spectrum for the isolated molecule.

Trajectory Surface Hopping Nonadiabatic Molecular Dynamics with Kohn-Sham ΔSCF for Condensed-Phase Systems.

We present an efficient approach for surface hopping-based nonadiabatic dynamics in the condensed phase. For the systems studied, a restricted Kohn-Sham orbital formulation of the delta self-consistent field (ΔSCF) method was used for efficient calculation of excited electronic states. Time-dependent density functional theory (DFT) is applied to aid excited-state SCF convergence and provide guess electronic state densities. Aside from that the Landau-Zener procedure simplifies the surface hopping between electronic states. By utilizing the combined Gaussian and plane waves approach with periodic boundary conditions the method is easily applicable to full atomistic DFT simulations of condensed-phase systems and was used to study the nonradiative deactivation mechanism of photoexcited diimide in water solution.

Efficient and Accurate Approach To Estimate Hybrid Functional and Large Basis-Set Contributions to Condensed-Phase Systems and Molecule-Surface Interactions.

We present a graph theoretic approach to adaptively compute contributions from many-body approximations in an efficient manner and perform accurate hybrid density functional theory (DFT) electronic structure calculations for condensed-phase systems. The salient features of the approach are ONIOM-like. (a) The full-system calculation is performed at a lower level of theory (pure DFT) by enforcing periodic boundary conditions. (b) This treatment is then improved through a correction term that captures many-body interactions up to any given order within a higher (in this case, hybrid DFT) level of theory. (c) In the spirit of ONIOM, contributions from the many-body approximations that arise from the higher level of theory [i.e., from (b) above] are included through extrapolation from the lower level calculation. The approach is implemented in a general, system-independent, fashion using the graph-theoretic functionalities available within Python. For example, the individual one-body components within the unit cell are designated as "nodes" within a graph. The interactions between these nodes are captured through edges, faces, tetrahedrons, and so forth, thus building a many-body interaction hierarchy. Electronic energy extrapolation contributions from all of these geometric entities are included within the above-mentioned ONIOM paradigm. The implementation of the method simultaneously uses multiple electronic structure packages. Here, for example, we present results which use both the Gaussian suite of electronic structure programs and the Quantum ESPRESSO program within a single calculation. Thus, the method integrates both plane-wave basis functions and atom-centered basis functions within a single structure calculation. The method is demonstrated for a range of condensed-phase problems for computing (i) hybrid DFT energies for condensed-phase systems at pure DFT cost and (ii) large, triple-zeta, multiply polarized, and diffuse atom-centered basis-set energies at computational costs commensurate with much smaller sets of basis functions. The methods are demonstrated through calculations performed on (a) homogeneous water surfaces as well as heterogeneous surfaces that contain organic solutes studied using two-dimensional periodic boundary conditions and (b) bulk simulations of water enforced through three-dimensional periodic boundary conditions. A range of structures are considered, and in all cases, the results are in good agreement with those obtained using large atom-centered basis and hybrid DFT calculations on the full periodic systems at significantly lower cost.

Learning macro from micro

Machine Learning Determining atomic structural correlations in condensed-phase systems is crucial for understanding material properties and their behavior at the macroscale. It represents one of the central challenges in modern statistical mechanics because of the complex collective behavior emerging from microscopic many-body interactions. Using two classical condensed-phase models, a Lennard-Jones system and a hard-sphere fluid, Craven et al. show that machine learning methods trained on a set of optimally short molecular dynamics simulations can predict radial distribution functions with increased accuracy by an order of magnitude or even greater compared with traditional analytical approaches. The proposed methodology is general and could be applied more broadly across diverse condensed-phase systems. J. Phys. Chem. Lett. 10.1021/acs.jpclett.0c00627 (2020).

NWChem: Past, present, and future.

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

Ex Machina Determination of Structural Correlation Functions.

Determining the structural properties of condensed-phase systems is a fundamental problem in theoretical statistical mechanics. Here we present a machine learning method that is able to predict structural correlation functions with significantly improved accuracy in comparison with traditional approaches. The usefulness of this ex machina (from the machine) approach is illustrated by predicting the radial distribution functions of two paradigmatic condensed-phase systems, a Lennard-Jones fluid and a hard-sphere fluid, and then comparing those results to the results obtained using both integral equation methods and empirically motivated analytical functions. We find that application of the developed ex machina method typically decreases the predictive error by more than an order of magnitude in comparison with traditional theoretical methods.

A self-consistent coulomb bath model using density fitting.

A self-consistent Coulomb bath model is presented to provide an accurate and efficient way of performing calculations for interfragment electrostatic and polarization interactions. In this method, a condensed-phase system is partitioned into molecular fragment blocks. Each fragment is embedded in the Coulomb bath due to other fragments. Importantly, the present Coulomb bath is represented using a density fitting method in which the electron densities of molecular fragments are fitted using an atom-centered auxiliary basis set of Gaussian type. The Coulomb bath is incorporated into an effective Hamiltonian for each fragment, with which the electron density is optimized through an iterative double self-consistent field (DSCF) procedure to realize the mutual many-body polarization effects. In this work, the accuracy of interfragment interaction energies enumerated using the Coulomb bath is tested, showing a good agreement with the exact results from an energy decomposition analysis. The qualitative features of many-body polarization effects are visualized by electron density difference plots. It is also shown that the present DSCF method can yield fast and robust convergence with near-linear scaling in performance with increase in system size.

TRAVIS-A free analyzer for trajectories from molecular simulation.

TRAVIS ("Trajectory Analyzer and Visualizer") is a program package for post-processing and analyzing trajectories from molecular dynamics and Monte Carlo simulations, mostly focused on molecular condensed phase systems. It is an open source free software licensed under the GNU GPL, is platform independent, and does not require any external libraries. Nine years after the original publication of TRAVIS, we highlight some of the recent new functions and features in this article. At the same time, we shortly present some of the underlying algorithms in TRAVIS, which contribute to make trajectory analysis more efficient. Some modern visualization techniques such as Sankey diagrams are also demonstrated. Many analysis functions are implemented, covering structural analyses, dynamical analyses, and functions for predicting vibrational spectra from molecular dynamics simulations. While some of the analyses are known since several decades, others are very recent. For example, TRAVIS has been used to compute the first ab initio predictions in the literature of bulk phase vibrational circular dichroism spectra, bulk phase Raman optical activity spectra, and bulk phase resonance Raman spectra within the last few years.

Accurate and Efficient Prediction of NMR Parameters of Condensed-Phase Systems with the Generalized Energy-Based Fragmentation Method.

We have implemented the calculations of NMR parameters within the generalized energy-based fragmentation (GEBF) method for condensed-phase systems with periodic boundary conditions (PBC). In this PBC-GEBF approach, NMR parameters of molecules in a unit cell are assembled as a linear combination of the corresponding quantities from a series of small embedded subsystems. To treat condensed-phase systems containing large molecules, we propose a novel "fragment-based" strategy for building subsystems, while our previously reported "molecule-based" strategy for construction of subsystems is appropriate for periodic systems with small molecules. The "fragment-based" strategy in PBC-GEBF is demonstrated to be much more efficient than its "molecule-based" counterpart to treat crystals of large molecules. With the "molecule-based" PBC-GEBF method, we obtained consistently good NMR parameters of liquid water with B3LYP on top of neural-network-potential-based ab initio molecular dynamics (AIMD) snapshots. With the "fragment-based" PBC-GEBF approach, we predicted the 1H chemical shifts of a large macrocycle in solution based on a series of classical MD snapshots. The calculated results are in good accord with the experimental chemical shifts. Therefore, the PBC-GEBF method is expected to be a reliable and efficient tool for predicting NMR parameters of large complex systems in solutions.

The central portions of the Cu–Fe–Se phase system at temperatures from 900 to 300 °C

ABSTRACTThe central portions of the condensed phase system Cu–Fe–Se were investigated by means of dry syntheses in evacuated silica glass tubes at 900, 750, 600, 500, 450, 350, and 300 °C. Synthesis products were studied by reflected-light microscopy and electron microprobe analyses. The field of sulfide melt is extensive at 900 °C and retreats progressively towards the Cu–Se side at 750 °C; residual selenide melt persists at 600 °C. The selenium analogue of iss was found only at and below 600 °C; eskebornite becomes individualized at and below 500 °C, whereas the selenium analogue of bornite solid solution is present at all investigated temperatures, although with reduced extent on temperature decrease. The three iron selenides (β, γ, δ) display considerable solubility of copper, which for the mackinawite-like β FeSe reaches 14 at.% Cu at 300 °C. FeSe2 displays an immiscibility gap with isotropic solid solution (Cu,Fe)Se2, the composition of which gradually changes towards Cu-rich with decreasing temperature. Similarities and differences with the sulfur-based system are highlighted.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance.

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H2O)256) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

EMPIRE: a highly parallel semiempirical molecular orbital program: 3: Born-Oppenheimer molecular dynamics

Direct NDDO-based Born-Oppenheimer molecular dynamics (MD) have been implemented in the semiempirical molecular orbital program EMPIRE. Fully quantum mechanical MD simulations on unprecedented time and length scales are possible, since the calculation of self-consistent wavefunctions and gradients is performed in a massively parallel manner. MD simulations can be performed in the NVE and NVT ensembles, using either deterministic (Berendsen) or stochastic (Langevin) thermostats. Furthermore, dynamics for condensed-phase systems can be performed under periodic boundary conditions. We show three exemplary applications: the dynamics of molecular reorganization upon ionization, long timescale dynamics of an endohedral fullerene, and calculation of the vibrational spectrum of a nanoparticle consisting of more than eight hundred atoms.Graphical A snapshot from an MNDO-H simulation of NH4+@C60 at 4000 K shortly before a proton crosses the fullerene wall to give NH3@C60H+.

FCHL revisited: Faster and more accurate quantum machine learning.

We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical accuracy on the scale of milliseconds. FCHL19 is a revision of our previous work [F. A. Faber et al., J. Chem. Phys. 148, 241717 (2018)] where the representation is discretized and the individual features are rigorously optimized using Monte Carlo optimization. Combined with a Gaussian kernel function that incorporates elemental screening, chemical accuracy is reached for energy learning on the QM7b and QM9 datasets after training for minutes and hours, respectively. The model also shows good performance for non-bonded interactions in the condensed phase for a set of water clusters with a mean absolute error (MAE) binding energy error of less than 0.1 kcal/mol/molecule after training on 3200 samples. For force learning on the MD17 dataset, our optimized model similarly displays state-of-the-art accuracy with a regressor based on Gaussian process regression. When the revised FCHL19 representation is combined with the operator quantum machine learning regressor, forces and energies can be predicted in only a few milliseconds per atom. The model presented herein is fast and lightweight enough for use in general chemistry problems as well as molecular dynamics simulations.

Charge Displacement Analysis-A Tool to Theoretically Characterize the Charge Transfer Contribution of Halogen Bonds.

Theoretical bonding analysis is of prime importance for the deep understanding of the various chemical interactions, covalent or not. Among the various methods that have been developed in the last decades, the analysis of the Charge Displacement function (CD) demonstrated to be useful to reveal the charge transfer effects in many contexts, from weak hydrogen bonds, to the characterization of σ hole interactions, as halogen, chalcogen and pnictogen bonding or even in the decomposition of the metal-ligand bond. Quite often, the CD analysis has also been coupled with experimental techniques, in order to give a complete description of the system under study. In this review, we focus on the use of CD analysis on halogen bonded systems, describing the most relevant literature examples about gas phase and condensed phase systems. Chemical insights will be drawn about the nature of halogen bond, its cooperativity and its influence on metal-ligand bond components.

ScMile: A Script to Investigate Kinetics with Short Time Molecular Dynamics Trajectories and the Milestoning Theory.

Studies of complex and rare events in condensed phase systems continue to attract considerable attention. Milestoning is a useful theory and algorithm to investigate the long-time dynamics of activated molecular events. It is based on launching a large number of short trajectories and statistical analysis of the outcome. The implementation of the theory in a computer script is described that enables more efficient Milestoning calculation, reducing user time and errors, and automating a significant fraction of the algorithm. The script exploits a molecular dynamics engine, which at present is NAMD, to run the short trajectories. However, since the script is external to the engine, the script can be easily adapted to different molecular dynamics codes. The outcomes of the short trajectories are analyzed to obtain a kinetic and thermodynamic description of the entire process. While many examples of Milestoning were published in the past, we provide two simple examples (a conformational transition of alanine dipeptide in a vacuum and aqueous solution) to illustrate the use of the script.

Short solvent model for ion correlations and hydrophobic association

Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent-solvent and solute-solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.