Search for: All records

For an electronic system, given a mean field method and a distribution of orbital occupation numbers that are close to the natural occupations of the correlated system, we provide formal evidence and computational support to the hypothesis that the entropy (or more precisely −σS, where σ is a parameter and S is the entropy) of such a distribution is a good approximation to the correlation energy. Underpinning the formal evidence are mild assumptions: the correlation energy is strictly a functional of the occupation numbers, and the occupation numbers derive from an invertible distribution. Computational support centers around employing different mean field methods and occupation number distributions (Fermi–Dirac, Gaussian, and linear), for which our claims are verified for a series of pilot calculations involving bond breaking and chemical reactions. This work establishes a formal footing for those methods employing entropy as a measure of electronic correlation energy (e.g., i-DMFT [Wang and Baerends, Phys. Rev. Lett. 128, 013001 (2022)] and TAO-DFT [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)]) and sets the stage for the widespread use of entropy functionals for approximating the (static) electronic correlation. 

Abstract Optical transmission and scattering spectroscopic microscopy at the visible and adjacent wavelengths denote one of the most informative and inclusive characterization methods in material research. Unfortunately, restricted by the diffraction limit of light, it cannot resolve the nanoscale variation in light absorption and scattering, diagnostics of the local inhomogeneity in material structure and properties. Moreover, a large quantity of nanomaterials has anisotropic optical properties that are appealing yet hard to characterize through conventional optical methods. There is an increasing demand to extend the optical hyperspectral imaging into the nanometer length scale. In this work, we report a super-resolution hyperspectral imaging technique that uses a nanoscale white light source generated by superfocusing the light from a tungsten-halogen lamp to simultaneously obtain optical transmission and scattering spectroscopic images. A 6-nm spatial resolution in the visible to near-infrared wavelength regime (415–980 nm) is demonstrated on an individual single-walled carbon nanotube (SW-CNT). Both the longitudinal and transverse optical electronic transitions are measured, and the SW-CNT chiral indices can be identified. The band structure modulation in a SW-CNT through strain engineering is mapped. 

Abstract The accuracy of charge‐transfer excitation energies, solvatochromic shifts, and other environmental effects calculated via various density‐embedding techniques depend critically on the approximations employed for the nonadditive noninteracting kinetic energy functional,. Approximating this functional remains an important challenge in electronic‐structure theory. To assist in the development and testing of approximations for, we derive two virial relations for fragments in molecules. These establish separate connections between the nonadditive kinetic energies of the noninteracting and interacting systems of electrons, and quantities such as the electron‐nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn‐Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules. 

Abstract 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) 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 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 clusters recovering qualitatively the time‐dependent Kohn–Sham DFT result. The Python codebase allows for easy implementation of application programming interfaces. We showcase the combination of DFTpy and ASE for molecular dynamics simulations of liquid metals. DFTpy is released under the MIT license. This article is categorized under:Software > Quantum ChemistryElectronic Structure Theory > Density Functional TheoryData Science > Computer Algorithms and Programming