Joshua Finkelstein

We present several finite-temperature recursive Fermi–operator expansion schemes based on the second-order spectral projection (SP2) method. Our approach builds on a previous observation that the electronic structure problem, as formulated through a recursive SP2 expansion, can be mapped onto the architecture of a deep neural network. Using this perspective, we generalize SP2 to finite electronic temperatures by constructing machine learning models that determine optimized recursive expansion coefficients. The same approach is also applied to the prediction of the electronic entropy for fractional occupation numbers. The coefficients are trained for a specified chemical potential and electronic temperature and are not available in closed analytical form. However, by employing an appropriate affine rescaling strategy to the Hamiltonian matrix, we eliminate the need to retrain the model for different temperatures and chemical potentials. Our approach avoids explicit diagonalization and relies solely on highly optimized matrix–matrix multiplication kernels. Compared to state-of-the-art diagonalization, we achieve an order-of-magnitude speedup in the single-particle finite-temperature density matrix calculation for small and moderately sized matrices on modern graphics processing units and dense matrix multiply units.

We present a series of simulations of the oxygen reduction reaction (ORR) using a novel framework for atomistic simulations of surface catalysis under electrochemical bias. The framework makes use of quantum-mechanical extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) simulations, which provide the speed and accuracy required for explicit atomistic treatment of both electrode and electrolyte. Simulations of solvated O2 near nitrogen-doped graphene (NG) were performed to gain insight into the ORR, and different mechanisms were observed, depending on the applied bias. Under higher bias the ORR occurred by an outer-sphere mechanism, without adsorption of O2 to NG. In this mechanism, electron transfer between the catalyst and the O2 was mediated by the solvent. Under lower bias the ORR occurred by an inner-sphere mechanism involving adsorption of O2 to NG, leading to direct electron transfer. Our extensive, all-atom quantum-mechanical molecular dynamics simulations also show clear differences between the kinetics of the ORR on this ideally polarizable electrode and commonly used kinetic theories, leading to new insights regarding mechanistic changes with varied overpotentials. Combining quantum accuracy with explicit solvation and electrostatic potential bias, XL-BOMD opens a route to predictive, atomistic insight into electrocatalytic processes, as demonstrated with the ORR.

Graph-based electronic structure theory offers a scalable approach to study large, complex atomistic systems using distributed and hybrid computational platforms. We demonstrate the coupling of graph-based linear scaling electronic structure theory, as implemented in the Scalable Ecosystem, Driver, and Analyzer for Complex Chemistry Simulations (SEDACS), with semiempirical quantum chemistry methods as implemented in the PySEQM code, with Graphics Processing Unit (GPU) acceleration. This powerful combination enables efficient, scalable electronic structure calculations over many nodes, significantly reducing computational cost while naturally harnessing parallelism. Detailed analyses of parallelization efficiency, computational accuracy, and communication overheads are provided, highlighting an order-of-magnitude speedup for systems of up to 10,000 atoms.

We present an extended Lagrangian shadow molecular dynamics scheme with an interatomic Born-Oppenheimer potential determined by the relaxed atomic charges of a second-order charge equilibration model. To parametrize the charge equilibration model, we use machine learning with neural networks to determine the environment-dependent electronegativities and chemical hardness parameters for each atom, in addition to the charge-independent energy and force terms. The approximate shadow molecular dynamics potential in combination with the extended Lagrangian formulation improves the numerical stability and reduces the number of Coulomb potential calculations required to evaluate accurate conservative forces. We demonstrate efficient and accurate simulations with excellent long-term stability of the molecular dynamics trajectories. The significance of choosing fixed or environment-dependent electronegativities and chemical hardness parameters is evaluated. Finally, we compute the infrared spectrum of molecules via the dipole autocorrelation function and compare to experiments to highlight the accuracy of the shadow molecular dynamics scheme with a machine learned flexible charge potential.

We present an extended Lagrangian shadow molecular dynamics scheme with an interatomic Born-Oppenheimer potential determined by the relaxed atomic charges of a second-order charge equilibration model. To parameterize the charge equilibration model, we use machine learning with neural networks to determine the environment-dependent electronegativities and chemical hardness parameters for each atom, in addition to the charge-independent energy and force terms. The approximate shadow molecular dynamics potential in combination with the extended Lagrangian formulation improves the numerical stability and reduces the number of Coulomb potential calculations required to evaluate accurate conservative forces. We demonstrate efficient and accurate simulations with excellent long-term stability of the molecular dynamics trajectories. The significance of the choosing fixed or environment-dependent electronegativities and chemical hardness parameters is evaluated. Finally, we compute the infrared spectrum of molecules via the dipole auto-correlation function and compare to experiments to highlight the accuracy of the shadow molecular dynamics scheme with a machine learned flexible charge potential.

Density matrix perturbation theory based on recursive Fermi-operator expansions provides a computationally efficient framework for time-independent response calculations in quantum chemistry and materials science. From a perturbation in the Hamiltonian, we can calculate the first-order perturbation in the density matrix, which then gives us the linear response in the expectation values for some chosen set of observables. We present an alternative, dual formulation, where we instead calculate the static susceptibility of an observable, which then gives us the linear response in the expectation values for any number of different Hamiltonian perturbations. We show how the calculation of the susceptibility can be performed with the same expansion schemes used in recursive density matrix perturbation theory, including generalizations to fractional occupation numbers and self-consistent linear response calculations, i.e., similar to density functional perturbation theory. As with recursive density matrix perturbation theory, the dual susceptibility formulation is well suited for numerically thresholded sparse matrix algebra, which has linear scaling complexity for sufficiently large sparse systems. Similarly, the recursive computation of the susceptibility also seamlessly integrates with the computational framework of deep neural networks used in artificial intelligence (AI) applications. This integration enables the calculation of quantum response properties that can leverage cutting-edge AI-hardware, such as NVIDIA Tensor Cores or Google Tensor Processing Units. We demonstrate performance for recursive susceptibility calculations using NVIDIA Graphics Processing Units and Tensor Cores.

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S^-1. This factorization of S^-1, written as ZZ^T = S^-1, is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix-matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.