arXiv subjects

Vikram Gavini

Publications and source records attributed to Vikram Gavini.

At least 19 recordsLinked to original sources

arXiv2026

Large-scale pseudopotential density functional theory calculations using orthogonalized enriched finite element basis

We present an efficient and scalable computational framework for pseudopotential Kohn-Sham density functional theory (KS-DFT) calculations using an enriched finite element (EFE) basis. The EFE basis is formed by augmenting the classical finite element (CFE) basis with compact atom-centered functions, which we term enrichment functions. The key idea is to combine the completeness of a finite element basis with the efficiency of an atom-centered basis. We orthogonalize the enrichment functions with respect to the underlying CFE basis to simultaneously improve the conditioning of the EFE basis and the efficiency of evaluating the inverse of the overlap matrix. To efficiently solve the Kohn-Sham eigenvalue problem, we employ a residual-based Chebyshev subspace iteration approach that is tolerant to approximations in the evaluation of the inverse of the overlap matrix. We demonstrate the accuracy of the framework as compared to the widely available DFT packages. For benchmark non-periodic calculations, ranging up to 39,083 electrons, the EFE basis offers a $5-7\times$ reduction in degrees of freedom over the CFE basis. As a result of this, EFE achieves a $5-9\times$ reduction in computational cost over the CFE basis. The EFE basis also provides a $4-5\times$ reduction in the required memory compared to the CFE basis, thus allowing for optimal utilization of computational resources. Finally, we demonstrate that the EFE basis affords good parallel scalability. Overall, the EFE basis offers a systematically convergent, fast, scalable, resource-efficient basis for pseudopotential DFT calculations.

cond-mat.mtrl-sci↗

arXiv2026

Intrinsic ductility enhancement in Mg alloys elucidated via large-scale ab-initio calculations

Magnesium is the lightest structural alloy, yet its practical use is limited by its low ductility. Recent studies suggest ductility enhancement in dilute Mg alloys may stem from favorable solute modification of pyramidal I/II screw dislocation core energy difference, activating slip via a double cross-slip mechanism. This work conducts large-scale DFT calculations, reaching ~6,000 atoms, of dislocation energetics in Mg and Mg-Y/Zn alloys. We find that relative solute strengthening effects on pyramidal I and II screw dislocation glide are crucial for cross-slip enhancement in Mg-Y, in contrast to prior investigations, that find solute-mediated dislocation-core energy modification as the main driver. Our predictions align with single- and poly-crystal experimental results and also capture the transition from pyramidal II to I preferred slip in Mg-Y.

cond-mat.mtrl-sci↗

arXiv2025

Field theoretic atomistics: Learning thermodynamic and variational surrogate to density functional theory

The Hohenberg-Kohn (HK) theorem -- the bedrock of density functional theory (DFT) -- establishes a universal map from the external potential to the energy. It also relates the electron density and atomic forces to the variation of the energy with the external potential. But the HK map is rarely utilized in atomistics, wherein interatomic potentials are defined using the molecular or crystal structure rather than the external potential. As a break from this tradition, we present a field theoretic atomistics framework where the external potential assumes the central quantity. We machine learn the HK energy map while satisfying the thermodynamic limit. Further, we obtain both forces and electron density from the variation of the HK energy map, that are exact relations. Our models attain good accuracy across diverse benchmarks and compete with state-of-the-art machine learned interatomic potentials. Through electron density, we predict accurate dipole and quadrupole moments, otherwise nontrivial for interatomic potentials. Our formulation paves the way for a scalable electronic structure surrogate to DFT.

physics.chem-ph↗

arXiv2025

invDFT: A CPU-GPU massively parallel tool to find exact exchange-correlation potentials from groundstate densities

Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique functional of the electron density. Despite 50 years of active research, existing XC approximations remain far from general purpose chemical accuracy of various thermochemical and materials properties. In that light, the inverse DFT problem, of finding the exact XC potential corresponding to an accurate groundstate density, offers an insightful tool to understand the nature of the XC functional as well as aid in the development of more accurate functionals. However, solving the inverse DFT problem is fraught with several numerical challenges, such as non-uniqueness or spurious oscillations in the solution and non-convergence. We present invDFT as an open-source framework to address the outstanding challenges in inverse DFT and computed XC potentials solely from a target density. We do so by use of a systematically convergent finite-element basis and asymptotic corrections to the target density. We also employ several numerical and high-performance computing (HPC) advances that affords both efficiency and parallel scalability, on CPU-GPU hybrid architectures. We demonstrate the accuracy and scalability of invDFT using accurate full-configuration interaction (FCI) densities as well as model densities, ranging up to 100 electrons and spanning both weakly and strongly correlated molecules.

physics.comp-ph↗

arXiv2025

An Atomic Cluster Expansion Potential for Twisted Multilayer Graphene

Twisted multilayer graphene, characterized by its moiré patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising approach to model such systems. Our work develops a method to generate training and test datasets for fitting MLIPs that capture all possible misalignments but remain small-scale to facilitate efficient data generation and parameter estimation. To achieve this, we generate configurations with periodic boundary conditions suitable for DFT calculations, and then introduce an internal twist and shift within those supercell structures. Using this technique, supplemented with an active learning workflow, we fit an Atomic Cluster Expansion potential for simulating twisted multilayer graphene and test it for accuracy and robustness on a range of simulation tasks.

physics.comp-ph↗

arXiv2024

MiMiC: A High-Performance Framework for Multiscale Molecular Dynamics Simulations

MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an interoperable approach based on a multiple-program multiple-data (MPMD) paradigm, serving as an intermediary responsible for fast data exchange and interactions between the subsystems. The main goal of MiMiC is to avoid interfering with the underlying parallelization of the external programs, including the operability on hybrid architectures (e.g., CPU/GPU), and keep their setup and execution as close as possible to the original. At the moment, MiMiC offers an efficient implementation of electrostatic embedding QM/MM that has demonstrated unprecedented parallel scaling in simulations of large biomolecules using CPMD and GROMACS as QM and MM engines, respectively. However, as it is designed for high flexibility with general multiscale models in mind, it can be straightforwardly extended beyond QM/MM. In this article, we illustrate the software design and the features of the framework, which make it a compelling choice for multiscale simulations in the upcoming era of exascale high-performance computing.

physics.chem-ph↗

arXiv2024

Learning local and semi-local density functionals from exact exchange-correlation potentials and energies

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functionals by utilizing the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN) based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies, densities, atomization energies, and barrier heights for hundreds of molecules outside the training set. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA, highlighting the promise of using the XC potential in modeling XC functionals. We expect this approach to pave the way for systematic learning of increasingly accurate and sophisticated XC functionals.

physics.chem-ph↗

arXiv2024

Accelerating inverse Kohn-Sham calculations using reduced density matrices

The Ryabinkin-Kohut-Staroverov (RKS) and Kanungo-Zimmerman-Gavini (KZG) methods offer two approaches to find exchange-correlation (XC) potentials from ground state densities. The RKS method utilizes the one- and two-particle reduced density matrices to alleviate any numerical artifacts stemming from a finite basis (e.g., Gaussian- or Slater-type orbitals). The KZG approach relies solely on the density to find the XC potential, by combining a systematically convergent finite-element basis with appropriate asymptotic correction on the target density. The RKS method, being designed for a finite basis, offers computational efficiency. The KZG method, using a complete basis, provides higher accuracy. In this work, we combine both the methods to simultaneously afford accuracy and efficiency. In particular, we use the RKS solution as initial guess to the KZG method to attain a significant $3-11\times$ speedup. This work also presents a direct comparison of the XC potentials from the RKS and the KZG method and their relative accuracy on various weakly and strongly correlated molecules, using their ground state solutions from accurate configuration interaction calculations solved in a Slater orbital basis.

physics.chem-ph↗

arXiv2024

Exponential time propagators for elastodynamics

We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as to express the solution in the form of a Magnus expansion. With any spatial discretization, it entails computing the exponential of a matrix acting upon a vector. We employ an adaptive Krylov subspace approach to inexpensively and and accurately evaluate the action of the exponential matrix on a vector. In particular, we use an apriori error estimate to predict the optimal Kyrlov subspace size required for each time-step size. We show that the Magnus expansion truncated after its first term provides quadratic and superquadratic convergence in the time-step for nonlinear and linear elastodynamics, respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam, soft tissue elastomer, and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displacement, and velocity, our method allows for $10-100\times$ larger time-steps than conventional time-marching schemes such as Newmark-$β$ method. Computationally, it translates to a $\sim$$1000\times$ and $\sim$$10-100\times$ speed-up over conventional time-marching schemes for linear and nonlinear elastodynamics, respectively.

math.NA↗

arXiv2024

Quasicrystal bulk and surface energies from density functional theory

Are quasicrystals stable or metastable? Density functional theory (DFT) is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing sizes, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases--revealing that translational symmetry is not a necessary condition for the T = 0 K stability of inorganic solids. Although we find the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is nucleation-limited, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques here broadly open the door to first-principles investigations into the structure-bonding-stability relationships of aperiodic materials.

cond-mat.mtrl-sci↗

arXiv2024

Examining the Impact of Local Condition Violations on Energy Computations in DFT

This work introduces Extent of Violation Indices (EVIs), a novel metric for quantifying how well exchange-correlation functionals adhere to local conditions. Applying EVIs to a diverse set of molecules for GGA functionals reveals widespread violations, particularly for semi-empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a link emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific conditions, but definitive conclusions about error cancellation require advancements in both functional accuracy and our understanding of cancellation mechanisms. Overall, this study highlights EVIs as a powerful tool for analyzing functional behavior and adherence to local conditions, paving the way for future research to fully elucidate the impact of violations on energy errors.

physics.chem-ph↗

arXiv2024

Tucker tensor approach for accelerating 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 3-dimensional convolutional integrals into a tensor product of 1-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overalapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency is demonstrated on various systems, including Pt clusters of various sizes and a $\text{TiO}_{\text{2}}$ cluster with 3,684 electrons.

cond-mat.mtrl-sci↗

arXiv2023

Exact and model exchange-correlation potentials for open-shell systems

The conventional approaches to the inverse density functional theory problem typically assume non-degeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle non-interacting ensemble-v-representable densities, as opposed to just non-interacting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems -- four atoms (Li, C, N, and O) and two molecules (CN and $\text{CH}_2$) -- using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using non-local (B3LYP, SCAN0) and local/semi-local (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of $\mathcal{O}(10^{-3}-10^{-2})$, the relative errors in the model XC potentials remain substantially large -- $\mathcal{O}(10^{-1}-10^0)$.

physics.chem-ph↗

arXiv2023

Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally-efficient semi-local approximations for the exchange-correlation energy. The accuracy of a semi-local density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, as known for about 30 years. The conventional explanation is that Hartree-Fock theory yields the more accurate density. This article presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H$_2$ + F $\rightarrow$ HHF $\rightarrow$ H + HF, and finds a strong, understandable cancellation between positive (excessively over-corrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions [Kaplan et al., J. Chem. Theory Comput. 19, 532--543 (2023)] based on 76 barrier heights and three less reliable, but less expensive, fully-nonlocal density-functional proxies for the exact density.

physics.chem-ph↗

arXiv2023

Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis

Ryabinkin-Kohut-Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, Full Configuration Interaction computations in the Slater orbitals are employed to give quality input to RKS method, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. The RKS method will be shown to be an efficient algorithm to arrive at exchange correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. Examples of weakly and strongly correlated molecular systems will demonstrate the main features of Slater RKS.

physics.chem-ph↗

arXiv2023

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous SCF iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from $\sim$ 100-1100 atoms ($\sim$ 500--20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized $d$ orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20--30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed point iteration in some cases. Finally, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4$\times$ reduction in computational cost for the total ground-state calculation compared to other preconditioners.

cond-mat.mtrl-sci↗

arXiv2022

Efficient all-electron time-dependent density functional theory calculations using an enriched finite element basis

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with compactly supported numerical atom centered basis, obtained from atomic groundstate DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on \textit{a priori} error estimates to guide our choice of an adaptive finite element mesh as well as the time-step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization. Notably, we attain a $50-100\times$ speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear response by studying the absorption spectrum in sodium clusters, the linear to nonlinear response transition in green fluorescence protein chromophore, and the higher harmonic generation in magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to $\sim1000$ processors, using a benchmark system of 50-atom sodium nanocluster.

physics.chem-ph↗

arXiv2022

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

cond-mat.mtrl-sci↗