Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels.

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. We demonstrate the portability of this approach and its performance in benchmark problems.

Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics.

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

A fast, dense Chebyshev solver for electronic structure on GPUs.

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [Liang et al., J. Chem. Phys. 119, 4117-4125 (2003)] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics.

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

Eigenvector centrality for characterization of protein allosteric pathways.

Determining the principal energy-transfer pathways responsible for allosteric communication in biomolecules remains challenging, partially due to the intrinsic complexity of the systems and the lack of effective characterization methods. In this work, we introduce the eigenvector centrality metric based on mutual information to elucidate allosteric mechanisms that regulate enzymatic activity. Moreover, we propose a strategy to characterize the range of correlations that underlie the allosteric processes. We use the V-type allosteric enzyme imidazole glycerol phosphate synthase (IGPS) to test the proposed methodology. The eigenvector centrality method identifies key amino acid residues of IGPS with high susceptibility to effector binding. The findings are validated by solution NMR measurements yielding important biological insights, including direct experimental evidence for interdomain motion, the central role played by helix h[Formula: see text], and the short-range nature of correlations responsible for the allosteric mechanism. Beyond insights on IGPS allosteric pathways and the nature of residues that could be targeted by therapeutic drugs or site-directed mutagenesis, the reported findings demonstrate the eigenvector centrality analysis as a general cost-effective methodology to gain fundamental understanding of allosteric mechanisms at the molecular level.

Graph-based linear scaling electronic structure theory.

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Accurate line shapes from sub-1 cm(-1) resolution sum frequency generation vibrational spectroscopy of α-pinene at room temperature.

Despite the importance of terpenes in biology, the environment, and catalysis, their vibrational spectra remain unassigned. Here, we present subwavenumber high-resolution broad-band sum frequency generation (HR-BB-SFG) spectra of the common terpene (+)-α-pinene that reveal 10 peaks in the C-H stretching region at room temperature. The high spectral resolution resulted in spectra with more and better resolved spectral features than those of the Fourier transform infrared, femtosecond stimulated Raman spectra in the bulk condensed phase and those of the conventional BB-SFG and scanning SFG spectroscopy of the same molecule on a surface. Experiment and simulation show the spectral line shapes with HR-BB-SFG to be accurate. Homogeneous vibrational decoherence lifetimes of up to 1.7 ps are assigned to specific oscillators and compare favorably to lifetimes computed from density functional tight binding molecular dynamics calculations. Phase-resolved spectra provided their orientational information. We propose the new spectroscopy as an attractive alternative to time domain vibrational spectroscopy or heterodyne detection schemes for studying vibrational energy relaxation and vibrational coherences in molecules at molecular surfaces or interfaces.

Photoelectrochemical hole injection revealed in polyoxotitanate nanocrystals functionalized with organic adsorbates.

We find that crystallographically resolved Ti17O24(OPr(i))20 nanoparticles, functionalized by covalent attachment of 4-nitrophenyl-acetylacetonate or coumarin 343 adsorbates, exhibit hole injection into surface states when photoexcited with visible light (λ = 400-680 nm). Our findings are supported by photoelectrochemical measurements, EPR spectroscopy, and quantum dynamics simulations of interfacial charge transfer. The underlying mechanism is consistent with measurements of photocathodic currents generated with visible light for thin layers of functionalized polyoxotitanate nanocrystals deposited on FTO working electrodes. The reported experimental and theoretical analysis demonstrates for the first time the feasibility of p-type sensitization of TiO2 solely based on covalent binding of organic adsorbates.

Linker rectifiers for covalent attachment of transition-metal catalysts to metal-oxide surfaces.

Linkers that favor rectification of interfacial electron transfer are likely to be required for efficient photo-driven catalysis of multi-electron reactions at electrode surfaces. Design principles are discussed, together with the synthesis and characterization of a specific pair of molecular linkers, related by inversion of the direction of an amide bond in the heart of the molecule. The linkers have a terpyridyl group that can covalently bind Mn as in a well-known water oxidation catalyst and an acetylacetonate group that allows attachment to TiO2 surfaces. The appropriate choice of the sense of the amide linkage yields directionality of interfacial electron transfer, essential to enhance electron injection and slow back-electron transfer. Support comes from electron paramagnetic resonance and terahertz spectroscopic measurements, as well as computational modeling characterizing the asymmetry of electron transfer properties.

S0-State model of the oxygen-evolving complex of photosystem II.

The S0 → S1 transition of the oxygen-evolving complex (OEC) of photosystem II is one of the least understood steps in the Kok cycle of water splitting. We introduce a quantum mechanics/molecular mechanics (QM/MM) model of the S0 state that is consistent with extended X-ray absorption fine structure spectroscopy and X-ray diffraction data. In conjunction with the QM/MM model of the S1 state, we address the proton-coupled electron-transfer (PCET) process that occurs during the S0 → S1 transition, where oxidation of a Mn center and deprotonation of a µ-oxo bridge lead to a significant rearrangement in the OEC. A hydrogen bonding network, linking the D1-D61 residue to a Mn-bound water molecule, is proposed to facilitate the PCET mechanism.

Characterization of an amorphous iridium water-oxidation catalyst electrodeposited from organometallic precursors.

Upon electrochemical oxidation of the precursor complexes [Cp*Ir(H(2)O)(3)]SO(4) (1) or [(Cp*Ir)(2)(OH)(3)]OH (2) (Cp* = pentamethylcyclopentadienyl), a blue layer of amorphous iridium oxide containing a carbon admixture (BL) is deposited onto the anode. The solid-state, amorphous iridium oxide material that is formed from the molecular precursors is significantly more active for water-oxidation catalysis than crystalline IrO(2) and functions as a remarkably robust catalyst, capable of catalyzing water oxidation without deactivation or significant corrosion for at least 70 h. Elemental analysis reveals that BL contains carbon that is derived from the Cp* ligand (∼ 3% by mass after prolonged electrolysis). Because the electrodeposition of precursors 1 or 2 gives a highly active catalyst material, and electrochemical oxidation of other iridium complexes seems not to result in immediate conversion to iridium oxide materials, we investigate here the nature of the deposited material. The steps leading to the formation of BL and its structure have been investigated by a combination of spectroscopic and theoretical methods. IR spectroscopy shows that the carbon content of BL, while containing some C-H bonds intact at short times, is composed primarily of components with C═O fragments at longer times. X-ray absorption and X-ray absorption fine structure show that, on average, the six ligands to iridium in BL are likely oxygen atoms, consistent with formation of iridium oxide under the oxidizing conditions. High-energy X-ray scattering (HEXS) and pair distribution function (PDF) analysis (obtained ex situ on powder samples) show that BL is largely free of the molecular precursors and is composed of small, <7 Å, iridium oxide domains. Density functional theory (DFT) modeling of the X-ray data suggests a limited set of final components in BL; ketomalonate has been chosen as a model fragment because it gives a good fit to the HEXS-PDF data and is a potential decomposition product of Cp*.

Anchoring sites to the STM tip can explain multiple peaks in single molecule conductance histograms.

Accelerated molecular dynamics and quantum conductance calculations are employed to shed light onto the electrochemical properties of the Au|1,8-octanedithiol|Au junction. Widely different contact geometries with varying degrees of roughness are examined. Strikingly, the two extreme situations considered in this work, tip-tip and tip-perfect surface junctions, give almost indistinguishable conductances. This result contrasts the usual notion that different S-Au bonding geometries combined with molecular torsions provide the explanation for the experimentally observed sets (low, medium, high) of conductance peaks. In this work, we provide an alternative explanation for the occurrence of these sets in terms of the specific anchoring sites of the molecule to the tip, which in turn determines the interaction of a portion of the carbon chain with the tip.

A methodology to generate crystal-based molecular structures for atomistic simulations.

We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal 'slabs' with periodic boundary conditions (PBCs) and non-periodic solids such as Wulff structures. We also introduce a method to build crystal slabs with orthogonal PBC vectors. These methods are integrated into our code,Los Alamos Crystal Cut(LCC), which is open source and thus fully available to the community. Examples showing the use of these methods are given throughout the manuscript.

Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices.

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

A QUBO formulation for top-τ eigencentrality nodes.

The efficient calculation of the centrality or "hierarchy" of nodes in a network has gained great relevance in recent years due to the generation of large amounts of data. The eigenvector centrality (aka eigencentrality) is quickly becoming a good metric for centrality due to both its simplicity and fidelity. In this work we lay the foundations for solving the eigencentrality problem of ranking the importance of the nodes of a network with scores from the eigenvector of the network, using quantum computational paradigms such as quantum annealing and gate-based quantum computing. The problem is reformulated as a quadratic unconstrained binary optimization (QUBO) that can be solved on both quantum architectures. The results focus on correctly identifying a given number of the most important nodes in numerous networks given by the sparse vector solution of our QUBO formulation of the problem of identifying the top-τ highest eigencentrality nodes in a network on both the D-Wave and IBM quantum computers.

Toward a QUBO-Based Density Matrix Electronic Structure Method.

Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree-Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave's new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. We also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores.

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective.

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia's A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent the fractional occupation numbers of the electronic states at finite temperatures.

Reduction of the molecular hamiltonian matrix using quantum community detection.

Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree-Fock methods as future advances in quantum hardware become available.