Orbital-free density functional theory (OF-DFT) is an electronic structure method with a low computational cost that scales linearly with the number of simulated atoms, making it suitable for ...large-scale material simulations. It is generally considered that OF-DFT strictly requires the use of local pseudopotentials, rather than orbital-dependent nonlocal pseudopotentials, for the calculation of electron-ion interaction energies, as no orbitals are available. This is unfortunate situation since the nonlocal pseudopotentials are known to give much better transferability and calculation accuracy than local ones. We report here the development of a theoretical scheme that allows the direct use of nonlocal pseudopotentials in OF-DFT. In this scheme, a nonlocal pseudopotential energy density functional is derived by the projection of nonlocal pseudopotential onto the non-interacting density matrix (instead of "orbitals") that can be approximated explicitly as a functional of electron density. Our development defies the belief that nonlocal pseudopotentials are not applicable to OF-DFT, leading to the creation for an alternate theoretical framework of OF-DFT that works superior to the traditional approach.
Million-atom quantum simulations are in principle feasible with orbital-free density functional theory (OF-DFT) because the algorithms only require simple functional minimizations with respect to the ...electron density function. In this context, OF-DFT has been useful for simulations of warm dense matter, plasma, cold metals, and alloys. Unfortunately, systems as important as quantum dots and clusters (having highly inhomogeneous electron densities) still fall outside OF-DFT's range of applicability. In this Rapid Communication, we make considerable progress in addressing this century old problem by devising and implementing an accurate, transferable, and universal family of nonlocal noninteracting kinetic energy density functionals that feature correct asymptotics and can handle highly inhomogeneous electron densities. We show that OF-DFT achieves close to chemical accuracy for the electronic energy and reproduces the electron density to about 5% of the benchmark for semiconductor quantum dots and metal clusters. Therefore, this work shows that OF-DFT can reliably simulate systems with highly inhomogeneous electron density, such as clusters and quantum dots, with applicability to the rational design of materials.
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn–Sham density-functional theory. This problem must be ...addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn–Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn–Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.
Program title: ELSI Interface
Program Files doi:http://dx.doi.org/10.17632/y8vzhzdm62.1
Licensing provisions: BSD 3-clause
Programming language: Fortran 2003, with interface to C/C++
External routines/libraries: MPI, BLAS, LAPACK, ScaLAPACK, ELPA, libOMM, PEXSI, ParMETIS, SuperLU_DIST
Nature of problem: Solving the electronic structure from a generalized or standard eigenvalue problem in calculations based on Kohn–Sham density functional theory (KS-DFT).
Solution method: To connect the KS-DFT codes and the KS electronic structure solvers, ELSI provides a unified software interface with reasonable default parameters, hierarchical control over the interface and the solvers, and automatic conversions between input and internal working matrix formats. Supported solvers are: ELPA (dense generalized eigensolver), libOMM (orbital minimization method), and PEXSI (pole expansion and selected inversion method).
Restrictions: The ELSI interface requires complete information of the Hamiltonian matrix.
By invoking a divide-and-conquer strategy, subsystem DFT dramatically reduces the computational cost of large-scale, ab initio electronic structure simulations of molecules and materials. The central ...ingredient setting subsystem DFT apart from Kohn–Sham DFT is the nonadditive kinetic energy functional (NAKE). Currently employed NAKEs are at most semilocal (i.e., they only depend on the electron density and its gradient), and as a result of this approximation, so far large-scale simulations only included systems composed of weakly interacting subsystems. In this work, we advance the state-of-the-art by introducing fully nonlocal NAKEs in subsystem DFT simulations for the first time. A benchmark analysis based on the S22-5 test set shows that nonlocal NAKEs considerably improve the computed interaction energies and electron densities compared to commonly employed GGA NAKEs, especially when increasing intersubsystem electron density overlap is considered. Most importantly, we resolve the long-standing problem of too attractive interaction energy curves typically resulting from the use of GGA NAKEs.
We present the one-orbital ensemble self-consistent field (OE-SCF), an alternative orbital-free DFT solver that extends the applicability of DFT to beyond nanoscale system sizes, retaining the ...accuracy required to be predictive. OE-SCF treats the Pauli potential as an external potential updating it iteratively, dramatically outperforming current solvers because only few iterations are needed to reach convergence. OE-SCF enabled us to carry out the largest ab initio simulations for silicon-based materials to date by employing only 1 CPU. We computed the energy of bulk-cut Si nanoparticles as a function of their diameter up to 16 nm, and the polarization and interface charge transfer when a Si slab is sandwiched between two metal slabs where lattice matching mandated a large contact area. Additionally, OE-SCF opens the door to adopting even more accurate functionals in orbital-free DFT simulations while still tackling large system sizes.
In this work, we extend the applicability of standard Kohn–Sham DFT (KS-DFT) to model realistically sized molecule–metal interfaces where the metal slabs venture into the tens of nanometers in size. ...Employing state-of-the-art noninteracting kinetic energy functionals, we describe metallic subsystems with orbital-free DFT and combine their electronic structure with molecular subsystems computed at the KS-DFT level resulting in a multiscale subsystem DFT method. The method reproduces within a few millielectronvolts the binding energy difference of water and carbon dioxide molecules adsorbed on the top and hollow sites of an Al(111) surface compared to KS-DFT of the combined supersystem. It is also robust for Born–Oppenheimer molecular dynamics simulations. Very large system sizes are approached with standard computing resources thanks to a parallelization scheme that avoids accumulation of memory at the gather–scatter stage. The results as presented are encouraging and open the door to ab initio simulations of realistically sized, mesoscopic molecule–metal interfaces.
The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of ...low-density/high reduced density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals, retaining the computational complexity of typical semilocal functionals. Crucially, this functional depends on the inter-subsystem density overlap. The new functional reproduces Kohn–Sham DFT and benchmark CCSD(T) interaction energies of weakly interacting dimers in the S22-5 and S66 test sets with a mean absolute deviation well below 1 kcal/mol.
By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the ...nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, available semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve dramatically the accuracy of sDFT simulations by (1) implementing nonlocal nonadditive kinetic energy functionals based on the LMGP family of functionals; (2) adapting Quantum ESPRESSO's implementation of rVV10 and vdW-DF nonlocal exchange-correlation functionals to be employed in sDFT simulations; (3) implementing “deorbitalized” meta GGA functionals (e.g., SCAN-L). We carefully assess the performance of the newly implemented tools on the S22-5 test set. eQE 2.0 delivers excellent interaction energies compared to conventional Kohn-Sham DFT and CCSD(T). The improved performance does not come at a loss of computational efficiency. We show that eQE 2.0 with nonlocal nonadditive functionals retains the same linear scaling behavior achieved previously in eQE 1.0 with semilocal nonadditive functionals.
Program title: eQE
CPC Library link to program files:https://doi.org/10.17632/g55n9xmnt2.1
Developer's repository link:https://gitlab.com/Pavanello/eqe
Licensing provisions: GPLv2
Programming language: Fortran 90
External routines/libraries: BLACS, MPI
Nature of problem: Solving the electronic structure of molecules and materials with subsystem density functional theory
Solution method: This version of eQE uses subsystem Density-Functional Theory (DFT) to compute the electronic structure of molecules and materials. Subsystem DFT is a divide-and-conquer version of DFT that can be massively parallelized and is linear scaling in work and data. However, it requires the use of density functionals for kinetic and exchange-correlation energies. eQE can now employ nonlocal functionals as well as meta-GGA functionals for these energy terms.
Additional comments: Url of stable release http://eqe.rutgers.edu
Kohn–Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ...ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn–Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.
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