The Development Of Method And Software For Large-Scale First-Principles Simulations

The materials simulation methods based on the first principles usually include the wave function theory(WFT)and density functional theory(DFT).The WFT,such as the configuration interaction theory and the coupled-cluster theory,has the advantages of high accuracy and transferability.However,it often takes expensive computational cost to solve the multi-particle Schr?dinger equation of the system.Therefore,the simulated cell is usually limited to dozens of atoms.In principle,DFT can avoid solving the Schr?dinger equation for multi-particle system.Thus,DFT requires a smaller computational cost,making it possible to simulate the large-scale materials.For example,the well-known Kohn-sham density functional theory(KS-DFT)ingeniously borrows a noninteracting multi-particle auxiliary system to avoid directly solving the multi-body Schr?dinger equation and can simulate the systems containing hundreds of atoms.Currently,KS-DFT has become a "work horse" in physics,chemistry and materials science because of its reliable accuracy and superior efficiency.It has become the most popular method to simulations of the crystal and molecular systems.However,the solution of nonlinear equations is required in KS-DFT to obtain Kohn-sham orbitals and the ground state electron density.Currently,the self-consistent field(SCF)iteration scheme has been successful applied to solve Kohn-sham equation.However,the computation cost of SCF scales cubically with the system size,making its use prohibitive for large-scale systems containing more than a few thousand atoms.Orbital-free density functional theory(OF-DFT)has attracted considerable attention as an alternative to KS-DFT because of its quasi-linear computation-scale cost.In OF-DFT,the total energy of the system and ground state electron density can be obtained by directly minimizing the total energy density functional.Its quasi-linear computational scaling behavior makes it possible to simulate the system contains millions of atoms,which is an ideal first-principles method for large-scale material simulations.Due to the lack of accurate kinetic energy density functional(KEDF)and universal pseudopotential,OF-DFT is,therefore,still limited to some specific systems.To sum up,the development of the first-principles methods with high accuracy and high computational efficiency is still a long-standing challenge.Here,we have developed the first-principles methods for large-scale simulations based on both OF-DFT and KS-DFT,and achieved the following innovative scientific research results:1.Despite a large number of nonlocal kinetic energy density functionals(KEDFs)available for large-scale calculations,most of those nonlocal KEDFs designed for the extended systems can not be directly applied to isolated systems.In order to overcome this problem,we propose a generalized scheme to construct nonlocal KEDFs via the local density approximation kernels and construct a family of KEDFs for simulations of isolated systems.The performance of KEDFs has been demonstrated by several clusters encompassing Mg,Si,and Ga As.The results show that our KEDFs can achieve high numerical accuracy and stability for random clusters.It is also noteworthy that the density oscillation behaviors of the bonding region of Si50 cluster has been successfully reproduced by our KEDFs.2.In order to further investigate the KEDFs for simulations of the extended systems,we propose a new scheme to construct a nonlocal KEDF from “scratch” by the line integrals,in which the corrected response behavior deviation from the uniform electron gas is included.Particularly,we firstly chose the integral path from the uniform electron gas to the real electron density.Then,we extended the linear response function of uniform electron gas(Lindhard function)by using the symmetry requirement of the integrand along the integral path.Finally,a new nonlocal KEDF,named Xu-Wang-Ma,was obtained by line integrals.XWM has been benchmarked on a range of model systems with different chemical environments.Numerical tests show that,in general,XWM can quantitatively reproduce the Kohn-Sham predictions of the basic bulk properties,electron density and vacancy formation energies.Particularly,the XWM functional is found to be numerically stable for random structures of both simple metals and several phases of silicon.The high accuracy and numerical stability of XWM functional yield improvements over most of KEDFs currently in use for applications,providing more insight into the development of new KEDFs.3.Because there are no orbitals in OF-DFT,the local pseudopotential is used to describe the ion-electron interaction in traditional OF-DFT.However,local pseudopotential can not reproduce the scattering properties of the real ion cores.Therefore,we proposed the nonlocal pseudopotential energy density functional to describe the ion-electron interaction in OF-DFT and applied it to simulate the properties of Li.The results show that the idea of nonlocal pseudopotential energy density functional can effectively improve the accuracy and transferability of OF-DFT,providing a theoretical foundation for the wide applications of OF-DFT.4.Due to the limitations of the transferability and accuracy of KEDF and local pseudopotential,OF-DFT is limited to some specific systems.While KS-DFT has been proved as a general method for materials simulations.However,the traditional self-consistent field(SCF)approach of solving the equation using iterative diagonalization exhibits an inherent cubic scaling behavior and becomes prohibitive for large systems.We employed a combination of the real space finite-difference formulation and Che FSI to solve the Kohn–Sham equation,and implemented this approach in ab initio Real-space Electronic Structure(ARES)software in a multi-processor,parallel environment.An improved scheme was proposed to generate the initial subspace of Chebyshev filtering in ARES efficiently,making it suitable for large-scale simulations.The accuracy,stability,and efficiency of the ARES software were illustrated by simulations of large-scale crystalline systems containing thousands of atoms.