Nonlocal Kinetic Energy Functionals By Functional Integration

Since the seminal works of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting Kinetic Energy, $T_s[\rho]$, the subject of this work. The typical paradigm is to first approximate the energy functional, and then take its functional derivative, $\frac{\delta T_s[\rho]}{\delta \rho(r)}$, yielding a potential that can be used in orbital-free DFT, or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for $T_s[\rho]$ is prescribed (which we dub MGP) having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential derives from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (BCC, FCC) and semiconducting (CD) phases of Silicon as well as of III-V semiconductors. MGP functional is found to be numerically stable typically reaching selfconsistency within 12 iteration of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter (WT) nonlocal functional or any GGA functional

Constructing optimal local pseudopotentials from first principles

Local pseudopotential (LPP) is an important component of the orbital free density functional theory (OF-DFT), which is a promising large scale simulation method that can still maintain information of electron state in materials. Up to date, LPP is usually extracted from the solid state DFT calculations. It is unclear how to assess its transferability while applying to a much different chemical environment. Here we reveal a fundamental relation between the first principles norm-conserving PP (NCPP) and the LPP. Using the optimized effective potential method developed for exchange functional, we demonstrate that the LPP can be constructed optimally from the NCPP for a large number of elements. Our theory also reveals that the existence of an LPP is intrinsic to the elements, irrespective to the parameters used for the construction. Our method provides a unified method in constructing and assessing LPP in the framework of first principles pseudopotentials

Nonlocal Subsystem Density Functional Theory

By invoking a divide-and-conquer strategy, subsystem DFT dramatically reduces the computational cost of large-scale, \textit{ab-initio} electronic structure simulations of molecules and materials. The central ingredient setting subsystem DFT apart from Kohn-Sham DFT is the non-additive 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 only systems composed of weakly interacting subsystems have been successfully tackled. 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 density compared to commonly employed GGA NAKEs, especially when the inter-subsystem electron density overlap is high. Most importantly, we resolve the long standing problem of too attractive interaction energy curves typically resulting from the use of GGA NAKEs

Orbital-Free DFT Correctly Models Quantum Dots When Asymptotics, Nonlocality and Nonhomogeneity Are Accounted For

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 work, we address this century old problem by devising and implementing an accurate, transferable and universal family of nonlocal Kinetic Energy density functionals that feature correct asymptotics and can handle highly inhomogenous electron densities. For the first time to date, 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 demonstrates that OF-DFT is no longer limited to simulations of systems with nearly homogeneous electron density but it can venture into simulations of clusters and quantum dots with applicability to rational design of novel materials

Absence of BLM leads to accumulation of chromosomal DNA breaks during both unperturbed and disrupted S phases

Bloom's syndrome (BS), a disorder associated with genomic instability and cancer predisposition, results from defects in the Bloom's helicase (BLM) protein. In BS cells, chromosomal abnormalities such as sister chromatid exchanges occur at highly elevated rates. Using Xenopus egg extracts, we have studied Xenopus BLM (Xblm) during both unperturbed and disrupted DNA replication cycles. Xblm binds to replicating chromatin and becomes highly phosphorylated in the presence of DNA replication blocks. This phosphorylation depends on Xenopus ATR (Xatr) and Xenopus Rad17 (Xrad17), but not Claspin. Xblm and Xenopus topoisomerase III{alpha} (Xtop3{alpha}) interact in a regulated manner and associate with replicating chromatin interdependently. Immunodepletion of Xblm from egg extracts results in accumulation of chromosomal DNA breaks during both normal and perturbed DNA replication cycles. Disruption of the interaction between Xblm and Xtop3{alpha} has similar effects. The occurrence of DNA damage in the absence of Xblm, even without any exogenous insult to the DNA, may help to explain the genesis of chromosomal defects in BS cells

A linear scaling method to evaluate the ion-electron potential of crystalline solids

We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge distribution and corresponding boundary conditions on the unit cell. Given that no quadratic scaling structure factor is required---as used in traditional methods---the expression shows inherent linear behavior, and is well suited to simulating large-scale systems within orbital-free density functional theory. The scheme is implemented in the ATLAS software package and benchmarked by using a solid Mg bcc lattice containing tens of thousands of atoms in the unit cell. The test results show that the method can efficiently model large crystals with high computational accuracy.Comment: 5 pages, 5 figure

Ab-initio structure and dynamics of supercritical CO2

Green technologies rely on green solvents and fluids. Among them, supercritical CO2 already finds many important applications. The molecular level understanding of the dynamics and structure of this supercritical fluid is a prerequisite to rational design of future green technologies. Unfortunately, the commonly employed Kohn-Sham DFT is too computationally demanding to produce meaningfully converged dynamics within a reasonable time and with a reasonable computational effort. Thanks to subsystem DFT, we analyze finite-size effects by considering simulations cells of varying sizes (up to 256 independent molecules in the cell) and finite-time effects by running 100 ps-long trajectories. We find that the simulations are in reasonable and semiquantitative agreement with the available neutron diffraction experiments and that, as opposed to the gas phase, the CO2 molecules in the fluid are bent with an average OCO angle of 175.8 degrees. Our simulations also confirm that the dimer T-shape is the most prevalent configuration. Our results further strengthen the experiment-simulation agreement for this fluid when comparing radial distribution functions and diffusion coefficient, confirming subsystem DFT as a viable tool for modeling structure and dynamics of condensed-phase systems

eQE 2.0: Subsystem DFT Beyond GGA Functionals

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, 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 in eQE 1.0 with semilocal nonadditive functionals

DFTpy: An efficient and object-oriented platform for orbital-free DFT simulations

In silico materials design is hampered by the computational complexity of Kohn-Sham DFT, which scales cubically with the system size. Owing to the development of new-generation kinetic energy density functionals (KEDFs), orbital-free DFT (OFDFT, a linear-scaling method) can now be successfully applied to a large class of semiconductors and such finite systems as quantum dots and metal clusters. In this work, we present DFTpy, an open source software implementing OFDFT written entirely in Python 3 and outsourcing the computationally expensive operations to third-party modules, such as NumPy and SciPy. When fast simulations are in order, DFTpy exploits the fast Fourier transforms (FFTs) from PyFFTW. New-generation, nonlocal and density-dependent-kernel KEDFs are made computationally efficient by employing linear splines and other methods for fast kernel builds. We showcase DFTpy by solving for the electronic structure of a million-atom system of aluminum metal which was computed on a single CPU. The Python 3 implementation is object-oriented, opening the door to easy implementation of new features. As an example, we present a time-dependent OFDFT implementation (hydrodynamic DFT) which we use to compute the spectra of small metal cluster recovering qualitatively the time-dependent Kohn-Sham DFT result. The Python code base allows for easy implementation of APIs. We showcase the combination of DFTpy and ASE for molecular dynamics simulations (NVT) of liquid metals. DFTpy is released under the MIT license

ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory

Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler--Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al$_{3}$Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations