Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

Abstract

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. 1 arXiv:1812.08952v1 [cond-mat.mtrl-sci] 21 Dec 2018 Metal clusters and quantum dots constitute an important class of systems of pivotal importance for materials design particularly in photovoltaics [1], catalysis [2], and even quantum computing [3]. Although these fields are already strongly shaped by computeraided design, the high computational cost of available quantum-mechanical methods such as Kohn-Sham density functional theory (KS-DFT) [4, 5] is hampering futher progress. In this playing field, what is really needed is a breakthrough in techniques alternative to the current standard, and among them [6-12] Orbital-Free Density Functional Theory (OF-DFT) is a promising candidate. OF-DFT is a promising and intriguing alternative because approximate density functionals for the kinetic energy entirely replace the need to solve for a Schrödinger equation. This completely bypasses its inherent complexity. Particularly, OF-DFT algorithms are promising because they involve a computational scaling of at most O(N ln N ), where N is a measure of the system size, and a memory requirement of only O(N ) [13-15].Unfortunately, even though OF-DFT has already proven to be successful for simulations of million-atom systems involving crystalline and liquid metals and alloys [15][16][17][18], as well as plasmas and warm dense matter [19][20][21], its applicability has been severely limited by the accuracy of the available Kinetic Energy density functionals (KEDFs). For example, finite systems such as metal clusters and quantum dots have been outside the range of applicability of OF-DFT.In this work, we achieve a breakthrouth by carefully balancing three important aspects defining the KEDFs: asymptotics of the corresponding potential, intrinsic nonlocality, and ability to handle nonhomogeneous systems. Th...

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

“…This prompted a number of additional development by several groups, [27][28][29][30] including our recent work. 8,31 In this section, we will focus on the functionals developed by our group, and specifically LMGP and LWT family of functionals. However, the techniques and conclusions drawn here are general and encompass other new-generation functionals, such as HC 26 and LDAK.…”

“…Unfortunately, HC was deemed too computationally expensive to become a workhorse for realistically sized model systems. This prompted a number of additional development by several groups, 27–30 including our recent work 8,31 . In this section, we will focus on the functionals developed by our group, and specifically LMGP and LWT family of functionals.…”

“…In Reference 8, we developed a technique to generalize WT as well as MGP/A/G functionals to approach localized, finite systems by invoking spline techniques to obtain kernels no longer dependent only on the average electron density but instead dependent locally on the full electron density function. The resulting functionals are dubbed LWT, LMGP/A/G depending on the kernels mentioned in Equations ) and ().…”

“…Commonly adopted KEDF approximants are not accurate enough to describe strongly directional chemical bonds—a category which unfortunately includes most molecules 6,7 . However, new‐generation nonlocal KEDFs allow OFDFT to model quantum dots and semiconductors 8,9 . Hence, OFDFT is to be considered an emerging technique for computational materials science, chemistry, and physics.…”

Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

“…Both semilocal and non-local functionals have achieved mixed successe in treating condensed phases and their ingredient atoms, molecules, and clusters and solids. Such functionals are either constraint-based and non-empirical [8][9][10][11][12][13][14][15][16][17][18] or semi-empirical 19,20 . With any significant ground-state advance, an obvious, important associated step is generalization to a non-interacting free energy functional F s .…”