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

Tucker Tensor Approach for Accelerating Fock Exchange Computations in a Real-Space Finite-Element Discretization of Generalized Kohn-Sham Density Functional Theory

The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO2 cluster with 3684 electrons.

Born-Oppenheimer Molecular Dynamics with a Linear Combination of Atomic Orbitals and Hybrid Functionals for Condensed Matter Simulations Made Possible. Theory and Performance for the Microcanonical and Canonical Ensembles

The implementation of an original Born-Oppenheimer molecular dynamics module is presented, which is able to perform simulations of large and complex condensed phase systems for sufficiently long time scales at the level of density functional theory with hybrid functionals, in the microcanonical (NVE) and canonical (NVT) ensembles. The algorithm is fully integrated in the Crystal code, a program for quantum mechanical simulations of materials, whose peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals to describe the wave function. The corresponding efficiency in the evaluation of the exact Fock exchange series has led to the implementation of a rich variety of hybrid density functionals at a low computational cost. In addition, the molecular dynamics implementation benefits also from the effective MPI parallelization of the code, suited to exploit high-performance computing resources available on current generation supercomputer architectures. Furthermore, the information contained in the trajectory of the dynamics is extracted through a series of postprocessing algorithms that provide the radial distribution function, the diffusion coefficient and the vibrational density of states. In this work, we present a detailed description of the theoretical framework and the algorithmic implementation, followed by a critical evaluation of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach, when ice and liquid water simulations are performed in the microcanonical and canonical ensembles.

Mechanism of arsenic release process from arsenopyrite chemical oxidation

Oxidation of arsenopyrite is one of the main causes of arsenic pollution in the environment. This study, examind changes in the surface properties of arsenopyrite in the presence of oxygen. Furthermore, X-ray photoelectron spectroscopy, in situ Raman analysis, high-resolution transmission electron microscopy, and ab initio molecular dynamics were carried out on arsenopyrite, and the oxidation properties and processes of the arsenopyrite surface, along with the Fe/As/S oxidation processes, were analysed In situ-Raman spectroscopy data clearly showed that in the presence of oxygen, Fe2+ ions were transformed into Fe3+ ions on the surface of arsenopyrite at 207 cm-1, and the content of iron oxides on the surface of arsenopyrite increased significantly over time. The presence of iron promoted the oxidation of As(III), and the oxidation process was found to affect the oxidation of As atoms on the surface of arsenopyrite due to the presence of FeS bonds. The presence of As3+ intensified the oxidation of arsenopyrite surface (139 cm-1).The main reason was the presence of O2·-/HO2· on the surface of arsenopyrite, the change of Fe2+ → FeOH2+ → Fe3+ on the surface of arsenopyrite, and the change of As3+ → As4+ → As5+, which strengthened the overflow of As, leading to reconstruction and changes on the surface of arsenopyrite.

Complex-Valued K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Large-Scale Hybrid Functional Enabled Ab Initio Molecular Dynamics Simulations within Plane Waves

K-means clustering, as a classic unsupervised machine learning algorithm, is the key step to select the interpolation sampling points in interpolative separable density fitting (ISDF) decomposition for hybrid functional electronic structure calculations. Real-valued K-means clustering for accelerating the ISDF decomposition has been demonstrated for large-scale hybrid functional enabled ab initio molecular dynamics (hybrid AIMD) simulations within plane-wave basis sets where the Kohn-Sham orbitals are real-valued. However, it is unclear whether such K-means clustering works for complex-valued Kohn-Sham orbitals. Here, we propose an improved weight function defined as the sum of the square modulus of complex-valued Kohn-Sham orbitals in K-means clustering for hybrid AIMD simulations. Numerical results demonstrate that the K-means algorithm with a new weight function yields smoother and more delocalized interpolation sampling points, resulting in smoother energy potential, smaller energy drift, and longer time steps for hybrid AIMD simulations compared to the previous weight function used in the real-valued K-means algorithm. In particular, we find that this improved algorithm can obtain more accurate oxygen-oxygen radial distribution functions in liquid water molecules and a more accurate power spectrum in crystal silicon dioxide compared to the previous K-means algorithm. Finally, we describe a massively parallel implementation of this ISDF decomposition to accelerate large-scale complex-valued hybrid AIMD simulations containing thousands of atoms (2,744 atoms), which can scale up to 5,504 CPU cores on modern supercomputers.

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning

The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health. However, theoretical study of the interactions of such organic adsorbates on the surface of water, and their bulk concerted properties, often necessitates the use of ab initio methods to properly incorporate the long-range electronic properties that govern these extended systems. Notable theoretical treatments of "on-water" reactions thus far have employed hybrid DFT and semilocal DFT, but the interactions involved are weak interactions that may be best described using post-Hartree-Fock theory. Here, we aim to demonstrate the utility of a graph-theoretic approach to molecular fragmentation that accurately captures the critical "weak" interactions while maintaining an efficient ab initio treatment of the long-range periodic interactions that underpin the physics of extended systems. We apply this graph-theoretical treatment to study PFOA on the surface of water as a model system for the study of weak interactions seen in the wide range of surface interactions and reactions. The approach divides a system into a set of vertices, that are then connected through edges, faces, and higher order graph theoretic objects known as simplexes, to represent a collection of locally interacting subsystems. These subsystems are then used to construct ab initio molecular dynamics simulations and for computing multidimensional potential energy surfaces. To further improve the computational efficiency of our graph theoretic fragmentation method, we use a recently developed transfer learning protocol to construct the full system potential energy from a family of neural networks each designed to accurately model the behavior of individual simplexes. We use a unique multidimensional clustering algorithm, based on the k-means clustering methodology, to define our training space for each separate simplex. These models are used to extrapolate the energies for molecular dynamics trajectories at PFOA water interfaces, at less than one-tenth the cost as compared to a regular molecular fragmentation-based dynamics calculation with excellent agreement with couple cluster level of full system potential energies.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

Selected Columns of the Density Matrix in an Atomic Orbital Basis I: An Intrinsic and Non-iterative Orbital Localization Scheme for the Occupied Space

In this work, we extend the selected columns of the density matrix (SCDM) methodology [J. Chem. Theory Comput. 2015, 11, 1463-1469]─a non-iterative and real-space procedure for generating localized occupied orbitals for condensed-phase systems─to the construction of local molecular orbitals (LMOs) in systems described using non-orthogonal atomic orbital (AO) basis sets. In particular, we introduce three different theoretical and algorithmic variants of SCDM (referred to as SCDM-M, SCDM-L, and SCDM-G) that can be used in conjunction with the AO basis sets used in standard quantum chemistry codebases. The SCDM-M and SCDM-L variants are based on a pivoted QR factorization of the Mulliken and Löwdin representations of the density matrix and are tantamount to selecting a well-conditioned set of projected atomic orbitals (PAOs) and projected (symmetrically-) orthogonalized atomic orbitals, respectively, as proto-LMOs that can be orthogonalized to exactly span the occupied space. The SCDM-G variant is based on a real-space (grid) representation of the wavefunction, and therefore has the added flexibility of considering a large number of grid points (or δ functions) when selecting a set of well-conditioned proto-LMOs. A detailed comparative analysis across molecular systems of varying size, dimensionality, and saturation level reveals that the LMOs generated by these three non-iterative/direct SCDM variants are robust, comparable in orbital locality to those produced with the iterative Boys or Pipek-Mezey (PM) localization schemes, and completely agnostic toward any single orbital locality metric. Although all three SCDM variants are based on the density matrix, we find that the character of the generated LMOs can differ significantly between SCDM-M, SCDM-L, and SCDM-G. In this regard, only the grid-based SCDM-G procedure (like PM) generates LMOs that qualitatively preserve σ-π symmetry (in systems such as s-trans alkenes), and are well-aligned with chemical (i.e., Lewis structure) intuition. While the direct and standalone use of SCDM-generated LMOs should suffice for most chemical applications, our findings also suggest that the use of these orbitals as an unbiased and cost-effective (initial) guess also has the potential to improve the convergence of iterative orbital localization schemes, in particular for large-scale and/or pathological molecular systems.

Efficient implementation of analytical gradients for periodic hybrid functional calculations within fitted numerical atomic orbitals from NAO2GTO

The NAO2GTO scheme provides an efficient way to evaluate the electron repulsion integrals (ERIs) over numerical atomic orbitals (NAOs) with auxiliary Gaussian-type orbitals (GTOs). However, the NAO2GTO fitting will significantly impact the accuracy and convergence of hybrid functional calculations. To address this issue, here we propose to use the fitted orbitals as a new numerical basis to properly handle the mismatch between NAOs and fitted GTOs. We present an efficient and linear-scaling implementation of analytical gradients of Hartree-Fock exchange (HFX) energy for periodic HSE06 calculations with fitted NAOs in the HONPAS package. In our implementation, the ERIs and their derivatives for HFX matrix and forces are evaluated analytically with the auxiliary GTOs, while other terms are calculated using numerically discretized GTOs. Several integral screening techniques are employed to reduce the number of required ERI derivatives. We benchmark the accuracy and efficiency of our implementation and demonstrate that our results of lattice constants, bulk moduli, and band gaps of several typical semiconductors are in good agreement with the experimental values. We also show that the calculation of HFX forces based on a master-worker dynamic parallel scheme has a very high efficiency and scales linearly with respect to system size. Finally, we study the geometry optimization and polaron formation due to an excess electron in rutile TiO2 by means of HSE06 calculations to further validate the applicability of our implementation.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xx operator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V^xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H₂O)₆₄ configurations (with densities spanning 0.4-1.7 g/cm³), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H₂O)₆₄ configurations. Using an out-of-sample set of (H₂O)₅₁₂ configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method

In this article, we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when a Gaussian basis set with pseudopotentials is used. The usual algorithm for evaluating exchange matrix scales cubically with the system size because one has to perform O(N²) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matrix without the need to do FFT, albeit at the cost of additional memory requirement. Although the basic idea of using auxiliary functions is not new, our algorithm is cheaper due to a combination of three ingredients: (a) we use a robust pseudospectral method that allows us to use a relatively small number of auxiliary basis to obtain high accuracy; (b) we use occ-RI exchange, which eliminates the need to construct the full exchange matrix; and (c) we use the (interpolative separable density fitting) ISDF algorithm to construct these auxiliary basis sets that are used in the robust pseudospectral method. The resulting algorithm is accurate, and we note that the error in the final energy decreases exponentially rapidly with the number of auxiliary functions.

Reaction dynamics of Diels-Alder reactions from machine learned potentials

Recent advances in the development of reactive machine-learned potentials (MLPs) promise to transform reaction modelling. However, such methods have remained computationally expensive and limited to experts. Here, we employ different MLP methods (ACE, NequIP, GAP), combined with automated fitting and active learning, to study the reaction dynamics of representative Diels-Alder reactions. We demonstrate that the ACE and NequIP MLPs can consistently achieve chemical accuracy (±1 kcal mol^-1) to the ground-truth surface with only a few hundred reference calculations. These strategies are shown to enable routine ab initio-quality classical and quantum dynamics, and obtain dynamical quantities such as product ratios and free energies from non-static methods. For ambimodal reactions, product distributions were found to be strongly dependent on the QM method and less so on the type of dynamics propagated.

Structural and Dynamic Properties of Solvated Hydroxide and Hydronium Ions in Water from Ab Initio Modeling

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water has been a challenging task from ab initio molecular dynamics (AIMD). The difficulty mainly comes from a lack of accurate and efficient exchange-correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly-constrained and appropriately normed (SCAN) meta-GGA functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange-correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice in describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. Our AIMD simulations indicate hydroxide diffuses slower than hydronium in water, which is consistent with the experiments.

Improving the scaling and performance of multiple time stepping-based molecular dynamics with hybrid density functionals

Density functionals at the level of the generalized gradient approximation (GGA) and a plane-wave basis set are widely used today to perform ab initio molecular dynamics (AIMD) simulations. Going up in the ladder of accuracy of density functionals from GGA (second rung) to hybrid density functionals (fourth rung) is much desired pertaining to the accuracy of the latter in describing structure, dynamics, and energetics of molecular and condensed matter systems. On the other hand, hybrid density functional based AIMD simulations are about two orders of magnitude slower than GGA based AIMD for systems containing ~100 atoms using ~100 compute cores. Two methods, namely MTACE and s-MTACE, based on a multiple time step integrator and adaptively compressed exchange operator formalism are able to provide a speed-up of about 7-9 in performing hybrid density functional based AIMD. In this work, we report an implementation of these methods using a task-group based parallelization within the CPMD program package, with the intention to take advantage of the large number of compute cores available on modern high-performance computing platforms. We present here the boost in performance achieved through this algorithm. This work also identifies the computational bottleneck in the s-MTACE method and proposes a way to overcome it.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Massively parallel linear-scaling Hartree-Fock exchange and hybrid exchange-correlation functionals with plane wave basis set accuracy

We extend our linear-scaling approach for the calculation of Hartree-Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree-Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory-Based Ab Initio Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles

In the previous paper of this series [Ko, H.-Y. et al. J. Chem. Theory Comput. 2020, 16, 3757-3785], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the exact exchange (EXX) interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid message-passing interface MPI/OpenMP implementation of this approach in Quantum ESPRESSO (QE) that enables linear scaling hybrid density functional theory (DFT)-based ab initio molecular dynamics (AIMD) in the microcanonical/canonical (NVE/NVT) ensembles of condensed-phase systems containing 500-1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend the current capabilities of exx to enable hybrid DFT-based AIMD simulations of large-scale condensed-phase systems with general and fluctuating cells in the isobaric-isoenthalpic/isobaric-isothermal (NpH/NpT) ensembles. The theoretical extensions to this approach include an analytical derivation of the EXX contribution to the stress tensor for systems in general simulation cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that (i) handle both static and fluctuating simulation cells with non-orthogonal lattice symmetries, (ii) solve Poisson's equation in general/non-orthogonal cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. Using this approach, we perform a case study on a variety of condensed-phase systems (including liquid water, a benzene molecular crystal polymorph, and semi-conducting crystalline silicon) and demonstrate that the EXX contributions to the energy and stress tensor simultaneously converge with an appropriate choice of exx parameters. This is followed by a critical assessment of the computational performance of the extended exx module across several different high-performance computing architectures via case studies on (i) the computational complexity due to lattice symmetry during NpT simulations of three different ice polymorphs (i.e., ice Ih, II, and III) and (ii) the strong/weak parallel scaling during large-scale NpT simulations of liquid water. We demonstrate that the robust and highly scalable implementation of this approach in the extended exx module is capable of evaluating the EXX contribution to the stress tensor with negligible cost (<1%) as well as all other EXX-related quantities needed during NpT simulations of liquid water (with a very tight 150 Ry planewave cutoff) in ≈5.2 s ((H₂O)₁₂₈) and ≈6.8 s ((H₂O)₂₅₆) per AIMD step. As such, the extended exx module presented in this work brings us another step closer to routinely performing hybrid DFT-based AIMD simulations of sufficient duration for large-scale condensed-phase systems across a wide range of thermodynamic conditions.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.

Achieving an Order of Magnitude Speedup in Hybrid-Functional- and Plane-Wave-Based Ab Initio Molecular Dynamics: Applications to Proton-Transfer Reactions in Enzymes and in Solution

Ab initio molecular dynamics (MD) with hybrid density functionals and a plane wave basis is computationally expensive due to the high computational cost of exact exchange energy evaluation. Recently, we proposed a strategy to combine adaptively compressed exchange (ACE) operator formulation and a multiple time step integration scheme to reduce the computational cost significantly [J. Chem. Phys. 2019, 151, 151102 ]. However, it was found that the construction of the ACE operator, which has to be done at least once in every MD time step, is computationally expensive. In the present work, systematic improvements are introduced to further speed up by employing localized orbitals for the construction of the ACE operator. By this, we could achieve a computational speedup of an order of magnitude for a periodic system containing 32 water molecules. Benchmark calculations were carried out to show the accuracy and efficiency of the method in predicting the structural and dynamical properties of bulk water. To demonstrate the applicability, computationally intensive free-energy computations at the level of hybrid density functional theory were performed to investigate (a) methyl formate hydrolysis reaction in neutral aqueous media and (b) proton-transfer reaction within the active-site residues of the class C β-lactamase enzyme.

Cost-effective composite methods for large-scale solid-state calculations

Following the development in recent years of progressively more accurate approximations to the exchange-correlation functional, the use of density functional theory (DFT) methods to examine increasingly large and complex systems has grown, in particular for solids and other condensed matter systems. However the cost of these calculations is high, often requiring the use of specialist HPC facilities. As such, for the purpose of large-scale high-throughput screening of material properties, a hierarchy of simplified DFT methods has been proposed that allows rapid electronic structure calculation of large systems, and we have recently extended this scheme to the solid state (sol-3c). Here, we analyze the applicability and scaling of the new sol-3c DFT methods to molecules and crystals composed of light-elements, such as small proteins and model DNA-helices. Furthermore, the calculation of the electronic structure of large to very large porous systems, such as metal-organic frameworks and inorganic nanoparticles, is discussed. The new composite methods have been implemented in the CRYSTAL17 code, which efficiently implements hybrid functionals and enables routine application of the new methods to large-scale calculations of such materials with excellent performance, even with small-scale computing resources.

Faster exact exchange in periodic systems using single-precision arithmetic

Density-functional theory simplifies many-electron calculations by approximating the exchange and correlation interactions with a one-electron operator that is a functional of the density. Hybrid functionals incorporate some amount of exact exchange, improving agreement with measured electronic and structural properties. However, calculations with hybrid functionals require substantial computational resources, limiting their use. By calculating the exchange interaction of periodic systems with single-precision arithmetic, the computation time is cut nearly in half with a negligible loss in accuracy. This improvement makes exact exchange calculations quicker and more feasible, especially for high-throughput calculations. Example hybrid density-functional theory calculations of band energies, forces, and x-ray absorption spectra show that this single-precision implementation maintains accuracy with significantly reduced runtime and memory requirements.

Iron's Wake: The Performance of Quantum Mechanical-Derived Versus General-Purpose Force Fields Tested on a Luminescent Iron Complex

Recently synthetized iron complexes have achieved long-lived excited states and stabilities which are comparable, or even superior, to their ruthenium analogues, thus representing an eco-friendly and cheaper alternative to those materials based on rare metals. Most of computational tools which could help unravel the origin of this large efficiency rely on ab-initio methods which are not able, however, to capture the nanosecond time scale underlying these photophysical processes and the influence of their realistic environment. Therefore, it exists an urgent need of developing new low-cost, but still accurate enough, computational methodologies capable to deal with the steady-state and transient spectroscopy of transition metal complexes in solution. Following this idea, here we focus on the comparison between general-purpose transferable force-fields (FFs), directly available from existing databases, and specific quantum mechanical derived FFs (QMD-FFs), obtained in this work through the Joyce procedure. We have chosen a recently reported Fe^III complex with nanosecond excited-state lifetime as a representative case. Our molecular dynamics (MD) simulations demonstrated that the QMD-FF nicely reproduces the structure and the dynamics of the complex and its chemical environment within the same precision as higher cost QM methods, whereas general-purpose FFs failed in this purpose. Although in this particular case the chemical environment plays a minor role on the photo physics of this system, these results highlight the potential of QMD-FFs to rationalize photophysical phenomena provided an accurate QM method to derive its parameters is chosen.