Oepp Pseudopotential And ATLAS Software For Real-space Calculations Based On Orbital-free Density Functional Theory

Orbital-Free Density Functional Theory(OF-DFT) is an exact quantum mechanics based theoretical approach for obtaining the ground state properties of many-electrons system just with the electron density, in principle. Due to the elimination of evaluation of wavefunctions, the computational cost of OF-DFT is linear scaling with the simulation system instead of high nonlinear scaling for conventional orbital-based Kohn-Sham(KS)-DFT. With the huge advantage in computational cost, OF-DFT can realize quantum mechanics based simulation for large systems with more than millions of atoms which overcome the limitation(~1,000 atoms) of conventional KS-DFT. Compared with empirical method, in OF-DFT, the information of electron density – the most basic physical quantities to determine the basic structures and properties of materials are retained, thus it has much applicability. With the increasing proposed kinetic energy density functional(KEDF) in the recent two decades, OF-DFT has become a suitable first-principles approach for large scale(Millions of atoms) materials simulations, since it can well balance the computational cost and accuracy in large-scale simulations.However, in OF-DFT, no information of orbital(wavefunction) is included, and all physical quantities are only the functionals of electron density function. For this reason, the orbital-based nonlocal pseudopotentials used in KS-DFT scheme can not be applied to OF-DFT directly. Currently, many schemes have been proposed to construct local pseudopotentials(LPPs), but most of the accurate LPPs are obtained by fitting or deriving from the bulk properties. Just as Prof. Karasiev and Trikey stated in 2012 that it is a challenging issue to construct good LPPs from the existing nonlocal pseudopotentials. Obviously, it is a key and challenging problem needing to be solved in OF-DFT to construct high quality(accurate and transferable) LPP from first principles. In addition, in comparison with KS-DFT, OF-DFT is undeveloped and lacks of corresponding softwares, which has become an obstacle for widespread application of OF-DFT in large-scale simulations. Thus, to improve the performance of theoretical methods and the corresponding software package suitable for large-scale simulations is another key problem needing to be solved for promoting the development and application of OF-DFT. In this thesis, we focus on solving these two problems to promote the development of OF-DFT. On one hand, we first reveal the fundamental relation between(nonlocal) normal-conserving pseudopotential and LPP using optimized effective potential(OEP) method with the normal-conserving condition in theory. Based on this relation, we propose a method to construct the first principles optimized effective local pseudopotential(OEPP) from normal-conserving pseudopotential. On the other hand, we propose an OF-DFT based first principles method for large-scale materials simulations by using the advantage of both real-space finite-difference method and a direct energy-minimization algorithm. The method is coded into a software package ATLAS. The main innovative results are as follows:1. Transferability is a crucial property of pseudopotential. The strong transferability of nonlocal pseudopotentials can be ensured by the general or specific normal-conserving conditions. For now, many schemes for the construction of local pseudopotentials have been put forward. These LPPs can be roughly categorized as two types:1) Model or empirical LPPs; 2) the LPP is derived from the bulk KS-DFT calculation results. Thus, LPPs constructed by all these method cannot meet requirement of transferability. Therefore, we first reveal the relation between norm-conserving(nonlocal) pseudopotential and the norm-conserving local pseudopotential using the(OEP) method with normal-conserving condition. With this relation, a new scheme is proposed for the construction of the optimized effective orbital-independent LPPs from the corresponding orbital-dependent normal-conserving nonlocal pseudopotential. The testing results of both the electron structure of free atom and bulk properties all indicate that(with a typical exception of second row elements in the periodic table), for most of s-block elements and many p-block elements, OEPPs are accurate and transferable. Our research results also indicate that the feasibility of construction of an accurate and transferable local pseudopotential for an given element is the intrinsic property of the element. Our work solve the longstanding key problem for construction of transferable local pseudopotential in OF-DFT.2. In large-scale simulations, apart from beside the computational accuracy, the important issues also include the computational cost, parallel efficiency, and numerical stability. Thus, to make OF-DFT be the most widely used method in large-scale simulation, it is necessary to propose an effective method for the implementation of OF-DFT. In comparison with the traditional basis based methods real-space finite-difference method has huge advantage in dealing with various boundary conditions and has good parallel efficiency. Many researchers also reported that, in large-scale simulations, due to long-range Coulomb interactions the so called “charge sloshing” problem will easily arise and is numerical unstable. The direct energy-minimization algorithm is the most effective way to overcome this problem. Thus, we developed a novel approach to engage the advantage of both RS-FD method and the direct energy-minimization scheme for OF-DFT calculations. The method is coded into the ATLAS software package. We benchmarked ATLAS using crystal solid Mg, Al, and Al3 Mg. The test results indicate that our implementation can achieve high accuracy, efficiency, and numerical stability for large simulations. Our method has more advantage in computational cost in comparison with the conventional plan-wave based method especially for the large-scale simulations. ATLAS will provide an alternative for large-scale simulations. We expect our work will accelerate the development of OF-DFT.