arXiv subjects

Phani Motamarri

Publications and source records attributed to Phani Motamarri.

At least 19 recordsLinked to original sources

arXiv2026

Prototype-Guided Latent Alignment for Data-Efficient Fine-Tuning of Molecular Foundation Models

Machine learning interatomic potentials (MLIPs) have transformed materials discovery by leveraging graph neural networks (GNNs) to predict material properties with near density functional theory (DFT) accuracy. While large-scale pretrained foundation models offer transferable baseline representations, they frequently struggle to generalise to out-of-distribution (OOD) target systems -- a common challenge in modelling complex or chemically diverse materials. Fine-tuning is the standard remedy, but the high cost of generating DFT-labelled configurations confines adaptation to data-scarce regimes, where over-parameterised GNNs amplify overfitting and degrade target-domain performance. To address this, we propose a prototype-based alignment approach for data-efficient fine-tuning of MLIPs. Our method identifies local structural similarities between the source and target domains by grouping atoms with analogous chemical environments based on their latent representations. Each target-domain atom's energy contribution is aligned to its source-domain prototype, introducing an inductive bias that anchors fine-tuned representations to the pretrained structure, encouraging effective reuse of learned interactions and improving generalisation without restrictive assumptions on the target chemistry. We evaluate our method on the rMD17 benchmark using equivariant MACE and invariant SchNet across varying data budgets, and extend evaluation to the MACE-OFF foundation models on the SPICE dataset. Our approach consistently improves predictive accuracy in the low-data regime, reducing energy MAE by up to 18% over standard fine-tuning baselines.

cond-mat.mtrl-sci↗

arXiv2026

Towards exascale fully relativistic pseudopotential density functional theory calculations enabled by mixed-precision computation and compressed-communication using residual based subspace iteration

Materials exhibiting noncollinear magnetism or strong spin-orbit-coupling underpin many spintronic and topological applications, but their simulations require complex two-component spinors and costs substantially more than scalar density functional theory (DFT). We present a GPU-centric exascale finite-element DFT framework with noncollinear magnetism and spin-orbit-coupling, combining (i) adaptive higher-order finite-element discretization, (ii) a matrix-free Poisson solver, (iii) residual-based Chebyshev filtered subspace iteration (R-ChFSI) for sparse generalized eigenproblems, (iv) R-ChFSI-enabled mixed precision computation with block floating-point compressed MPI communication, and (v) communication-efficient band partitioning. R-ChFSI permits inexact matrix-multivector products and $4\times$--$6.4\times$ compression of communicated data relative to FP64 while preserving double-precision robustness and reducing computation and data movement. Results demonstrate strong scaling on Aurora and Frontier, with up to $3.4\times$ faster Chebyshev filtering. On Aurora, total self-consistent-field (SCF) solve wall time reduces by $2\times$. An 800-node (9,600-GPU) calculation demonstrates fully relativistic pseudopotential DFT for $\sim$80,000 electrons in under 7 minutes per SCF iteration.

cond-mat.mtrl-sci↗

arXiv2026

Accelerating finite-element-based projector augmented-wave density functional theory calculations with scalable GPU-centric computational methods

Accurate large-scale Kohn-Sham density functional theory (DFT) calculations are essential for modeling complex material systems, including interfaces, defects, nanoclusters, and twisted two-dimensional heterostructures. Achieving chemical accuracy at scales of $10^4$-$10^5$ electrons with practical time-to-solution, however, remains challenging for existing DFT implementations. We present GPU-centric computational methods and algorithmic innovations within a finite-element (FE) discretized projector augmented-wave (PAW) formulation (PAW-FE) for accurate, efficient, and scalable electronic-structure calculations on modern exascale systems. The FE discretization, developed within a collinear spin formalism, accommodates generic boundary conditions and employs multi-resolution quadrature for accurate evaluation of atom-centered PAW integrals on coarse grids. The resulting generalized Hermitian eigenproblem is solved using residual-based Chebyshev filtered subspace iteration (R-ChFSI). Exploiting R-ChFSI's tolerance to inexact matrix-multivector products, we employ an approximate inverse PAW overlap matrix, mixed-precision arithmetic (FP32/TF32), and low-precision nearest-neighbor communication (BF16) during filtered subspace construction, along with block-wise computation-communication overlap to reduce cost while preserving robustness. These strategies yield up to $8\times$ and $20\times$ CPU-GPU speedups on Intel and AMD GPU architectures, respectively. Compared to plane-wave PAW methods, PAW-FE achieves close to 8$\times$ reduction in time-to-solution for 10,000-electron systems on NVIDIA GPUs, with larger gains at scale, and around 6$\times$ over norm-conserving FE approaches. We demonstrate scalability to 130,000-electron systems, establishing PAW-FE as an exascale-ready method for chemically accurate first-principles simulations.

physics.comp-ph↗

arXiv2026

ChemXDyn: Dynamics-informed species and reaction detection methodology from atomistic simulations

Accurate identification of chemical species and reaction pathways from molecular dynamics (MD) trajectories is a prerequisite for deriving predictive chemical-kinetic models and for mechanistic discovery in reactive systems. However, state-of-the-art trajectory analysis methods infer bonding from instantaneous distance thresholds, which can misclassify transient, nonreactive encounters as bonds and thereby introduce spurious intermediates, distorted reaction networks, and biased rate estimates. Here, we introduce ChemXDyn, a dynamics-aware computational methodology that leverages time-resolved interatomic distance signatures as a core principle to robustly identify chemically consistent bonded interactions and, consequently, extract meaningful reaction pathways. In particular, ChemXDyn propagates molecular connectivity through time while enforcing atomic valence and coordination constraints to distinguish genuine bond-breaking and bond-forming events from transient, nonreactive encounters. We evaluate ChemXDyn on ReaxFF MD simulations of hydrogen and ammonia oxidation and on neural-network potential MD simulations of methane oxidation, and benchmark its performance against widely used trajectory analysis methods. Across these cases, ChemXDyn suppresses unphysical species prevalent in static analyses, recovers experimentally consistent reaction pathways, and improves the fidelity of rate constant estimation. In ammonia oxidation, ChemXDyn removes unphysical intermediates and resolves key NOx- and N2O-forming and -consuming routes. In methane oxidation, it reconstructs the canonical progression from CH4 to CO2. By linking atomistic dynamics to chemically consistent reaction identification, ChemXDyn provides a transferable foundation for MD-derived reaction networks and kinetics, with potential utility spanning combustion, catalysis, plasma chemistry, and electrochemical environments.

physics.comp-ph↗

arXiv2025

Matrix-free algorithms for fast ab initio calculations on distributed CPU architectures using finite-element discretization

Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while accommodating generic boundary conditions. However, the dominant computational bottleneck in FE-based DFT arises from the repeated application of the discretised sparse Hamiltonian to large blocks of trial vectors during iterations in an iterative eigensolver. Traditional sparse matrix-vector multiplications and FE cell-matrix approaches encounter memory limitations and high data-movement overheads, particularly at higher polynomial orders, typically used in DFT calculations. To overcome these challenges, this work develops matrix-free algorithms for FE-discretised DFT that substantially accelerate these products by doing on-the-fly operations that utilize structured tensor contractions over 1D basis functions and quadrature data. A unified multilevel batched data layout that handles both real and complex-valued operators is introduced to maximise cache reuse and SIMD utilisation on Frontier (AVX2), Param Pravega (AVX512) and Fugaku (SVE). We also combine terms for optimal cache reuse, even-odd decomposition to reduce FLOP, and mixed-precision intrinsics. Extensive benchmarks show that for large multivector pseudopotential DFT calculations, the matrix-free kernels deliver 1.5-4x speedups over the state-of-the-art cell-matrix approach baselines. For all-electron DFT calculations, the matrix-free operator achieves gains of up to 5.8x due to its efficient implementation and superior arithmetic intensity. When integrated with an error-tolerant Chebyshev-filtered subspace iteration eigensolver, the matrix-free formalism yields substantial reductions in end-to-end time-to-solution using FE meshes that deliver desired accuracies in ground-state properties.

physics.comp-ph↗

arXiv2025

Real-space methods for ab initio modelling of surfaces and interfaces under external potential bias

Accurate ab initio modelling of surfaces and interfaces, especially under an applied external potential bias, is important for describing and characterizing various phenomena that occur in electronic, catalytic, and energy storage devices. Leveraging the ability of real-space density functional theory (DFT) codes to accommodate generic boundary conditions, we introduce two methods for applying an external potential bias that can be suitable for modelling surfaces and interfaces. In the first method, an external constant electric field is applied by modifying the DFT Hamiltonian via the introduction of an auxiliary linear potential while solving the electrostatic potential arising in DFT using a Poisson equation with zero-Neumann boundary conditions. The second method directly enforces the desired external potential bias by imposing constraints on the electrostatic potential, thereby naturally mimicking experimental conditions. We describe the underlying DFT governing equations for the two setups within the real-space formalism employing finite-element discretization. First, we validate the constant electric field setup within real-space finite-element DFT (DFT-FE) with an equivalent approach using plane-wave DFT (i.e., using periodic boundary conditions) on three representative benchmark systems, namely La-terminated Li$_7$La$_3$Zr$_2$O$_{12}$, GaAs (111), and Al FCC (111) slabs. Subsequently, we present a comprehensive evaluation of the two setups in terms of the average ground-state properties, such as surface and adsorption energies. The methods developed in our work provide an attractive alternative to plane-wave DFT approaches in applying external potential bias that usually suffer from the periodic boundary conditions restrictions and poor scalability on parallel computing architectures.

cond-mat.mtrl-sci↗

arXiv2025

Residual-based Chebyshev filtered subspace iteration for sparse Hermitian eigenvalue problems tolerant to inexact matrix-vector products

Chebyshev Filtered Subspace Iteration (ChFSI) is widely used for computing a small subset of extremal eigenpairs from large matrices, particularly when the eigenpairs must be computed repeatedly as the system matrix evolves within an outer nonlinear iteration. In this work, we propose R-ChFSI, a residual-based reformulation that recasts the Chebyshev polynomial recurrence in terms of residuals rather than eigenvector estimates, which achieves robust convergence even when matrix--vector products are computed inexactly. We derive convergence guarantees under such approximations and show that R-ChFSI can naturally leverage (i) the use of inexpensive approximate inverses for generalized eigenproblems of the form $\textbf{A} \textbf{x} = \lambda \textbf{B} \textbf{x}$, where exact factorizations of $\textbf{B}$ are prohibitively expensive, (ii)~low-precision arithmetic (FP32, TF32) for both standard and generalized eigenproblems, and (iii)~reduced-precision (BF16) inter-process communication in distributed sparse matrix--vector products. Controlled experiments on dense random matrices quantitatively verify the convergence bounds derived in this work and confirm the robustness of R-ChFSI to prescribed approximation errors for both standard and generalized eigenproblems. Large-scale experiments on finite-element discretized DFT generalized eigenproblems with up to 85 million grid points and 13,500 eigenpairs demonstrate that R-ChFSI achieves residual norms orders of magnitude below those of standard ChFSI when approximate inverses are employed, and reliably meets target tolerances of $10^{-8}$ even when employing reduced precision, yielding filtering speedups of up to $2.7{\times}$ ($2.1{\times}$ for the full eigensolver) on GPU accelerators

physics.comp-ph↗

arXiv2024

Finite-element methods for noncollinear magnetism and spin-orbit coupling in real-space pseudopotential density functional theory

We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the open-source DFT-FE computational framework, fills a significant gap in real-space DFT calculations using finite element basis sets, which offer several advantages over traditional DFT basis sets. In particular, we leverage the local reformulation of DFT electrostatics to derive the finite-element (FE) discretized governing equations involving two-component spinors. We subsequently utilize an efficient self-consistent field iteration approach based on Chebyshev filtered subspace iteration procedure exploiting the sparsity of local and non-local parts of FE discretized Hamiltonian to solve the underlying nonlinear eigenvalue problem based on a two-grid strategy. Furthermore, we propose using a generalized functional within the framework of noncollinear magnetism and spin-orbit coupling with a stationary point at the minima of the Kohn-Sham DFT energy functional to develop a unified framework for computing atomic forces and periodic unit-cell stresses. Validation studies against plane-wave implementations show excellent agreement in ground-state energetics, vertical ionization potentials, magnetic anisotropy energies, band structures, and spin textures. The proposed method achieves up to 8x-11x speed-ups for semi-periodic and non-periodic systems with $\sim$5000-7000 electrons in terms of minimum wall times compared to widely used plane-wave implementations on CPUs in addition to exhibiting significant computational advantage on GPUs.

cond-mat.mtrl-sci↗

arXiv2024

Fast and scalable finite-element based approach for density functional theory calculations using projector-augmented wave method

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. To the best of our knowledge, this is the first real-space approach for DFT calculations, combining the efficiency of PAW formalism involving smooth electronic fields with the ability of systematically improvable higher-order finite-element basis to achieve significant computational gains. In particular, we have developed efficient strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigenspace in each self-consistent field iteration. These strategies leverage the low-rank perturbation of the FE basis overlap matrix in conjunction with reduced order quadrature rules to invert the discretized PAW overlap matrix while also exploiting the sparsity of both the local and non-local parts of the discretized PAW Hamiltonian and overlap matrices. Using the proposed approach, we benchmark the accuracy and performance on various representative examples involving periodic and non-periodic systems with plane-wave-based PAW implementations. Furthermore, we also demonstrate a considerable computational advantage ($\sim$ 5$\times$ -- 10$\times$) over state-of-the-art plane-wave methods for medium to large-scale systems ($\sim$ 6,000 -- 35,000 electrons). Finally, we show that our approach (PAW-FE) significantly reduces the degrees of freedom to achieve the desired accuracy, thereby enabling large-scale DFT simulations ($>$ 50,000 electrons) at an order of magnitude lower computational cost compared to norm-conserving pseudopotential calculations using finite-element discretized calculations.

physics.comp-ph↗

arXiv2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modelling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for $N$ smallest eigenvector-eigenvalue pairs with $N$ proportional to the number of electrons in the material system. These calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn-Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh-Ritz projection step of the discretized Kohn-Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node CPU and GPU architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behaviour and energy efficiency.

physics.comp-ph↗

arXiv2023

Chemical bonding in large systems using projected population analysis from real-space density functional theory calculations

We present an efficient and scalable computational approach for conducting projected population analysis from real-space finite-element (FE) based Kohn-Sham density functional theory calculations (DFT-FE). This work provides an important direction towards extracting chemical bonding information from large-scale DFT calculations on materials systems involving thousands of atoms while accommodating periodic, semi-periodic or fully non-periodic boundary conditions. Towards this, we derive the relevant mathematical expressions and develop efficient numerical implementation procedures that are scalable on multi-node CPU architectures to compute the projected overlap and Hamilton populations. The population analysis is accomplished by projecting either the self-consistently converged FE discretized Kohn-Sham orbitals, or the FE discretized Hamiltonian onto a subspace spanned by a localized atom-centred basis set. The proposed methods are implemented in a unified framework within DFT-FE code where the ground-state DFT calculations and the population analysis are performed on the same FE grid. We further benchmark the accuracy and performance of this approach on representative material systems involving periodic and non-periodic DFT calculations with LOBSTER, a widely used projected population analysis code. Finally, we discuss a case study demonstrating the advantages of our scalable approach to extract the quantitative chemical bonding information of hydrogen chemisorbed in large silicon nanoparticles alloyed with carbon, a candidate material for hydrogen storage.

physics.comp-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↗

arXiv2022

Fast hardware-aware matrix-free algorithm for higher-order finite-element discretized matrix multivector products on distributed systems

Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work proposes efficient matrix-free algorithms for evaluating FE discretized matrix-multivector products on both multi-node CPU and GPU architectures. We address a critical gap in existing matrix-free implementations, which are well suited only for the action of FE discretized matrices on a single vector. We employ batched evaluation strategies, with the batchsize tailored to underlying hardware architectures, leading to better data locality and enabling further parallelization. On CPUs, we utilize even-odd decomposition, SIMD vectorization, and overlapping computation and communication strategies. On GPUs, we employ strategies to overlap compute and data movement in conjunction with GPU shared memory, constant memory, and kernel fusion to reduce data accesses. Our implementation outperforms the baselines for Helmholtz operator action, achieving up to 1.4x improvement on one CPU node and up to 2.8x on one GPU node, while reaching up to 4.4x and 1.5x improvement on multiple nodes for CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively. We further benchmark the performance of the proposed implementation for solving a model eigenvalue problem for 1024 smallest eigenvalue-eigenvector pairs by employing the Chebyshev Filtered Subspace Iteration method, achieving up to 1.5x improvement on one CPU node and up to 2.2x on one GPU node while reaching up to 3.0x and 1.4x improvement on multinode CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively.

physics.comp-ph↗

arXiv2022

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

We present DFT-FE 1.0, building on DFT-FE 0.6 [Comput. Phys. Commun. 246, 106853 (2020)], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ~ $100,000$ electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation -- via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency -- as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our implementation, which yields $\sim 20 \times$ CPU-GPU speed-up by using GPU acceleration on hybrid CPU-GPU nodes. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of $80-140$ seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing ~ $6,000-15,000$ electrons.

physics.comp-ph↗

arXiv2021

Tensor-structured algorithm for reduced-order scaling large-scale Kohn-Sham density functional theory calculations

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn-Sham Hamiltonian and an $L_1$ localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2,000 electrons.

physics.comp-ph↗

arXiv2019

DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching $\sim 100,000$ electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn-Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn-Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used plane-wave codes---both in CPU-times and wall-times, and on both non-periodic and periodic systems---at systems sizes beyond a few thousand electrons, with over $5-10$ fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated on up to 192,000 MPI tasks.

physics.comp-ph↗

arXiv2017

Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of a material point $\textbf{x}$. These configurational forces that result from the inner variations of the Kohn-Sham energy functional provide a unified framework to compute atomic forces as well as stress tensor for geometry optimization. Importantly, owing to the variational nature of the formulation, these configurational forces inherently account for the Pulay corrections. The formulation presented in this work treats both pseudopotential and all-electron calculations in single framework, and employs a local variational real-space formulation of Kohn-Sham DFT expressed in terms of the non-orthogonal wavefunctions that is amenable to reduced-order scaling techniques. We demonstrate the accuracy and performance of the proposed configurational force approach on benchmark all-electron and pseudopotential calculations conducted using higher-order finite-element discretization. To this end, we examine the rates of convergence of the finite-element discretization in the computed forces and stresses for various materials systems, and, further, verify the accuracy from finite-differencing the energy. Wherever applicable, we also compare the forces and stresses with those obtained from Kohn-Sham DFT calculations employing plane-wave basis (pseudopotential calculations) and Gaussian basis (all-electron calculations). Finally, we verify the accuracy of the forces on large materials systems involving a metallic aluminum nanocluster containing 666 atoms and an alkane chain containing 902 atoms, where the Kohn-Sham electronic ground state is computed using a reduced-order scaling subspace projection technique (P. Motamarri and V. Gavini, Phys. Rev. B 90, 115127).

physics.comp-ph↗

arXiv2016

Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations

We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core-subspace, spanned by the core eigenfunctions, and its complement, the valence-subspace, and thereby enables an efficient computation of the Fermi-operator expansion by reducing the expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The key ideas used in our approach are: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate non-orthogonal localized functions spanning the Chebyshev-filtered subspace; (ii) compute the Kohn-Sham Hamiltonian projected onto the valence-subspace; (iii) employ Fermi-operator expansion in terms of the valence-subspace projected Hamiltonian to compute the density matrix, electron-density and band energy. We demonstrate the accuracy and performance of the method on benchmark materials systems involving silicon nano-clusters up to 1330 electrons, a single gold atom and a six-atom gold nano-cluster. The benchmark studies on silicon nano-clusters revealed a staggering five-fold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of $\sim 10^{-4} Ha/atom$ with respect to reference calculations. Further, numerical investigations on gold suggest that spectrum splitting is indispensable to achieve meaningful accuracies, while employing Fermi-operator expansion.

physics.comp-ph↗