Kohn-Sham Density Functional Theory Calculations Research Articles

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves.

Density functional perturbation theory (DFPT) is a crucial tool for accurately describing lattice dynamics. The adaptively compressed polarizability (ACP) method reduces the computational complexity of DFPT calculations from O(N4) to O(N3) by combining the interpolative separable density fitting (ISDF) algorithm. However, the conventional QR factorization with column pivoting (QRCP) algorithm, used for selecting the interpolation points in ISDF, not only incurs a high cubic-scaling computational cost, O(N3), but also leads to suboptimal convergence. This convergence issue is particularly pronounced when considering the complex interplay between the external potential and atomic displacement in ACP-based DFPT calculations. Here, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a more efficient quadratic-scaling O(N2) alternative to the computationally intensive cubic-scaling O(N3) QRCP algorithm. We implement this efficient K-means-based ISDF algorithm to accelerate plane-wave DFPT calculations in KSSOLV, which is a MATLAB toolbox for performing Kohn-Sham density functional theory calculations within plane waves. We demonstrate that this K-means algorithm not only offers comparable accuracy to QRCP in ISDF but also achieves better convergence for ACP-based DFPT calculations. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly 2 orders of magnitude compared to QRCP in ISDF.

Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data.

Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.

High-Throughput Aqueous Electrolyte Structure Prediction Using IonSolvR and Equivariant Graph Neural Network Potentials.

Neural network potentials have recently emerged as an efficient and accurate tool for accelerating ab initio molecular dynamics (AIMD) in order to simulate complex condensed phases such as electrolyte solutions. Their principal limitation, however, is their requirement for sufficiently large and accurate training sets, which are often composed of Kohn-Sham density functional theory (DFT) calculations. Here we examine the feasibility of using existing density functional tight-binding (DFTB) molecular dynamics trajectory data available in the IonSolvR database in order to accelerate the training of E(3)-equivariant graph neural network potentials. We show that the solvation structure of Na+ and Cl- in aqueous NaCl solutions can be accurately reproduced with remarkably small amounts of data (i.e., 100 MD frames). We further show that these predictions can be systematically improved further via an embarrassingly parallel resampling approach.

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory.

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

Real-space solution to the electronic structure problem for nearly a million electrons.

We report a Kohn-Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix-vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

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 toward extracting chemical bonding information from large-scale DFT calculations on materials systems involving thousands of atoms while accommodating periodic, semiperiodic, or fully nonperiodic boundary conditions. Toward this, we derive the relevant mathematical expressions and develop efficient numerical implementation procedures that are scalable on multinode 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-centered basis set. The proposed methods are implemented in a unified framework within the 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 nonperiodic 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.

GPU acceleration of local and semilocal density functional calculations in the SPARC electronic structure code.

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing Kohn-Sham density functional theory calculations within the local density and generalized gradient approximations. In particular, we develop a modular math-kernel based implementation for NVIDIA architectures wherein the computationally expensive operations are carried out on the GPUs, with the remainder of the workload retained on the central processing units (CPUs). Using representative bulk and slab examples, we show that relative to CPU-only execution, GPUs enable speedups of up to 6× and 60× in node and core hours, respectively, bringing time to solution down to less than 30s for a metallic system with over 14 000 electrons and enabling significant reductions in computational resources required for a given wall time.

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 G\^ateaux derivatives of the residual of fixed point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these G\^ateaux 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.

Hybrid finite element / multipole expansion method for atomic Kohn-Sham density functional theory calculations

A numerical framework is developed for aspherical atomic Kohn-Sham density functional theory calculations. The framework invokes higher-order finite elements as a radial discretization in combination with a multipole expansion for controlling the spherical resolution. Both all-electron and nonlocal pseudopotential calculations are addressed in a unified setting. The overall approach is validated through a range of numerical examples which demonstrate the systematic convergence of the radial and spherical discretizations as well as the outstanding accuracy that can be efficiently obtained in the presence of strong aspherical external fields. Overall, the presented approach offers a route to adaptive local enrichment for electronic structure calculation in the context of the finite element method.

On the bending of rectangular atomic monolayers along different directions: an ab initio study

We study the bending of rectangular atomic monolayers along different directions from first principles. Specifically, choosing the phosphorene, GeS, TiS3, and As2S3 monolayers as representative examples, we perform Kohn–Sham density functional theory calculations to determine the variation in transverse flexoelectric coefficient and bending modulus with the direction of bending. We find that while the flexoelectric coefficient is nearly isotropic, there is significant and complex anisotropy in bending modulus that also differs between the monolayers, with extremal values not necessarily occurring along the principal directions. In particular, the commonly adopted orthotropic continuum plate model with uniform thickness fails to describe the observed variations in bending modulus for GeS, TiS3, and As2S3. We determine the direction-dependent effective thickness for use in such continuum models. We also show that the anisotropy in bending modulus is not associated with the rehybridization of atomic orbitals.

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods.

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i) A linearized scheme of the quadratic equation used to determine the cluster amplitudes. ii) The effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.

Plane-wave-based stochastic-deterministic density functional theory for extended systems

Traditional finite-temperature Kohn-Sham density functional theory (KSDFT) has an unfavorable scaling with respect to the electron number or at high temperatures. The evaluation of the ground-state density in KSDFT can be replaced by the Chebyshev trace (CT) method. In addition, the use of stochastic orbitals within the CT method leads to the stochastic density functional theory [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic density functional theory [Phys. Rev. Lett. 125, 055002 (2020)] (MDFT). We have implemented the above four methods within the first-principles package ABACUS. All of the four methods are based on the plane-wave basis set with the use of norm-conserving pseudopotentials and the periodic boundary conditions with the use of $k$-point sampling in the Brillouin zone. By using the KSDFT calculation results as benchmarks, we systematically evaluate the accuracy and efficiency of the CT, SDFT, and MDFT methods via examining a series of physical properties, which include the electron density, the free energy, the atomic forces, stress, and density of states for a few condensed phase systems. The results suggest that our implementations of CT, SDFT, and MDFT not only reproduce the KSDFT results with a high accuracy, but also exhibit several advantages over the tradition KSDFT method. We expect these methods can be of great help in studying high-temperature and large-size extended systems such as warm dense matter and dense plasma.

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ∼8-fold GPU-CPU speedup for these operations on the largest systems studied. The computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ∼7,000 atoms. Program summaryProgram Title: TTDFT: Tucker tensor density functional theory codeCPC Library link to program files:https://doi.org/10.17632/8dgmcs8ys2.1Licensing provisions: LGPLProgramming language: C/C++External routines/libraries: TuckerMPI (https://gitlab.com/tensors/TuckerMPI), cuBLAS (https://docs.nvidia.com/cuda/cublas/index.html), cuSparse (https://docs.nvidia.com/cuda/cusparse/index.html), ALGLIB (http://www.alglib.net/), Boost (https://www.boost.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es)Nature of problem: Real-space Kohn-Sham density functional theory calculations using localized Tucker tensor basis.Solution method: We present a real-space Kohn-Sham density functional theory code based on tensor-structured techniques with GPU acceleration. Tensor-structured techniques are adopted for computing a Tucker tensor basis, representing the eigenfunctions of an additive separable approximation to the Kohn-Sham Hamiltonian. The Tucker tensor basis is further localized using L1 regularization to improve the sparsity of the Kohn-Sham Hamiltonian matrix, and improve the computational efficiency and parallel scalability of the proposed algorithm. The solution to the Kohn-Sham problem in the localized Tucker tensor basis is computed using the Chebyshev filtered subspace iteration (ChFSI) method.Additional comments including restrictions and unusual features: The code works with Troullier-Martin (TM) pseudopotentials in Kleinman-Bylander form. The current release supports only non-periodic DFT calculations with the local density approximation (LDA) for exchange-correlation functional.This TTDFT project uses GitHub via Git, a free distributed version control software. The archived version at the time of submission of this work can be found on the CPC program library through program files DOI provided above. The GitHub repository of this project can be found on https://github.com/ttdftdev/ttdft_public.

Insights on the enhanced nitrogen dioxide sensing using doped boron nitride nanosheets through the quantum chemical studies

A comprehensive analysis of the effect of different dopant atoms (Cr, Ni, Al, C, Si, O and S) on the sensing capacity of boron nitride nanosheets (BNNs) towards NO2 gas is reported in this study. The calculations were based on the Kohn-Sham density functional theory calculations. The quantum chemical analysis was based on the molecular electrostatic potential maps, HOMO-LUMO distributions, DOS plots, Mullikan charges and quantum descriptors were studied. The NO2 positioning over the nanosheets was optimized at CAM_B3LYP/6-31G level of theory. The infrared spectra obtained from the first principle computations indicated a frequency shift for the NO symmetric stretching vibrations. The computed Mullikan charges showed a charge transfer from nanosheets to NO2. HOMO-LUMO energies and their distributions confirmed the charge transfer. The reactivity descriptors for Cr and Si-doped BNNs suggested their better ability to adsorb NO2 than other nanosheets. The thermodynamics of the sensing was studied using the adsorption energies that ranged between −0.3 to −2.6 eV, confirming the chemical nature of sensing. Overall, the analysis showed that Cr/BNNs and Ni/BNNs exhibited greater sensing activity towards NO2 than the other doped BNNs.

Conditional probability density functional theory

We present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the CP density from a series of independent Kohn-Sham (KS) DFT calculations. By directly calculating CP densities, we bypass the need for an approximate XC energy functional. In this work we discuss and derive several key properties of the CP density and corresponding CP-KS potential. Illustrative examples are used throughout to help guide the reader through the various concepts and theory presented. We explore a suitable CP-DFT approximation and discuss exact conditions, limitations, and results for selected examples.

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. We describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples. Program summaryProgram title: Kohn-Sham Solver 2.0 (KSSOLV 2.0)CPC Library link to program files:https://doi.org/10.17632/pp8vgvfcv4.1Developer's repository link:https://bitbucket.org/berkeleylab/kssolv2.0/src/release/Licensing provisions: BSD 3-clauseProgramming language:: MATLABNature of problem: KSSOLV2.0 is used to perform Kohn-Sham density functional theory based electronic structure calculations to study chemical and material properties of molecules and solids. The key problem to be solved is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem.Solution method: The KSSOLV 2.0 implements both the self-consistent field (SCF) iteration with a variety of acceleration strategies and a direct constrained minimization algorithms. It is written completely in MATLAB and uses MATLAB's object oriented programming features to make it easy to use and modify.

Density Functional Theory Perspective on the Nonlinear Response of Correlated Electrons across Temperature Regimes.

We explore a new formalism to study the nonlinear electronic density response based on Kohn–Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wavenumbers q < 2qF, with qF being the Fermi wavenumber. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the nonlinear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods.

Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition.

Range-separated hybrid functionals making use of a smooth separation of the Coulomb operator in terms of the error function and its complement have proven to be a valuable tool for improving Kohn-Sham density functional theory (DFT) calculations. This holds in particular for obtaining accurate excitation energies from linear-response time-dependent DFT. Evaluating the long-range exchange contributions represents one of the most time-consuming tasks in such calculations. Prefitted auxiliary basis sets can be employed to speed up this step. Here, we present a way to generate auxiliary basis sets optimized to fit the long-range exchange contributions only, contrary to the common optimization strategies on the basis of the full Coulomb operator. For this purpose, we use the atomic Cholesky decomposition technique. The basis sets are generated on-the-fly using the specific range-separation parameter defined in the exchange-correlation functional. We obtain excitation energies and oscillator strengths which are of similar or better accuracy than those obtained with conventional resolution-of-the-identity auxiliary basis sets while drastically reducing the number of auxiliary functions required. This is demonstrated for the QUESTDB#5 benchmark set. In addition, we outline the benefits of this approach in sequences of calculations employing varying range-separation parameters, as is the case in the optimally tuned range-separation strategy. Finally, we illustrate the efficiency of this approach for real-world examples, namely, a chlorophyll tetramer from photosystem II and a carotenoid-porphyrin-C60 triad.

First-principles derivation and properties of density-functional average-atom models

Finite-temperature Kohn-Sham density functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remains uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modeling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analyzing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model---such as boundary conditions and XC functionals---on common properties in WDM, for example equation-of-state data, ionization degree and the behavior of the frontier energy levels. Furthermore, drawing upon insights from ground-state KS-DFT, we discuss the likely sources of error in KS-AA models and possible strategies for mitigating such errors.

Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature

Kohn-Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present a density matrix based method for Kohn-Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann-Feynman forces, and Hellmann-Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw-Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.