Optimization Of Algorithms And Programs For First-Principles Calculations And High-Throughput Screening Of Materials

First-principles calculations have become an important tool for studying the physical and chemical properties of substances and exploring the internal mechanisms of chemical reactions.Among them,density functional theory based on the Kohn-Sham equation is one of the most widely used methods.However,density functional theory has two main problems.Firstly,although the density functional theory is complete,the exchange-correlation functional is unknown.Therefore the accuracy of the calculated results depends heavily on the approximate exchange-correlation functional.Secondly,although density functional theory has simplified the 3N-dimensional many-body problem to a 3-dimensional problem,its computational complexity is still as high as O(N3),and the complexity of advanced electronic structure methods such as hybrid functional calculations and time-dependent density functional theory have even higher complexity.Therefore,in recent years,research on algorithms based on density functional theory has focused on achieving higher accuracy,faster speed and the ability to handle larger systems.For example,exchange-correlation functionals with higher accuracy have been developed to improve computational accuracy.Additionally,linear scaling algorithms have been employed to enhance the computational scale of density functional theory,thereby enabling the computation of larger systems.On the other hand,first-principles calculations play an important role in the discovery and verification of novel functional materials,but the traditional scheme of calculating the properties of a single material is too inefficient to search for target functional materials.Therefore,it is necessary to develop database-oriented high-throughput calculation methods.The work presented in this thesis focuses on the these goals,primarily on the optimization and acceleration of first-principles algorithms within plane-wave basis sets and high-throughput screening of materials with low lattice thermal conductivity.The details are as follows.Chapter 1 introduces the historical development and theoretical foundations of density functional theory.The chapter begins by reviewing the treatment of manybody systems in first-principles calculations,highlighting the significance of the BornOppenheimer and Hartree-Fock approximations in simplifying the problems.Subsequently,we introduces the fundamental principles of density functional theory,including the Hohenberg-Kohn theorem and the Kohn-Sham equation.Furthermore,we elucidate two significant extensions of density functional theory,time-dependent density functional theory(TDDFT)and density functional perturbation theory(DFPT).Finally,we acquaint readers with several first-principles packages and present an overview of the principal topics covered in this thesis.Chapter 2 mainly introduces the basis sets usually used in first-principles calculations,including plane-wave basis sets,atomic orbital basis sets and adaptive basis sets.The characteristics of plane wave basis sets and their processing methods in density functional theory calculations are elucidated.Then,the low-rank approximation algorithms within the plane-wave base sets used in this thesis are introduced,including the interpolative separable density fitting(ISDF)decomposition and the adaptively compressed exchange(ACE)operator.ISDF primarily focuses on the low-rank decomposition of orbital pairs,which can be divided into two steps:computing interpolation points and interpolation vectors.This technique has significant applications in hybrid functional calculations,time-dependent density functional theory calculations,and density functional perturbation theory.The ACE is a low-rank approximation of the exchange operator in hybrid functional,thereby reducing the computational complexity when exchange operator is applied to the wavefunctions.Chapter 3 introduces the acceleration of hybrid functional calculations in real-time time-dependent density functional theory(hybrid RT-TDDFT)within plane-wave basis sets by combining ISDF decomposition and ACE operator(ACE-ISDF).Hybrid functional can effectively improve the computational accuracy of RT-TDDFT,but its computational complexity is very high.The strategies for lowering computational demands in hybrid RT-TDDFT calculations include increasing the time step and reducing the computational cost of each time step.In our study,we have chosen the latter approach by utilizing the ACE-ISDF algorithm to accelerate the hybrid functional calculations for each time step of RT-TDDFT,which can yield accurate excited state dynamics results and is five times faster than the traditional method.In addition,we implement the ACEISDF algorithm to accelerate the massive parallelism of hybrid functional RT-TDDFT.From our results,we can realize RT-TDDFT simulations for the systems containing thousands of atoms(1,728 atoms),which can scale up to 3,456 CPU cores on modern supercomputers.Chapter 4 introduces the application of K-means clustering algorithm to accelerate the density functional perturbation theory.The recently proposed adaptively compressed polarizability(ACP)algorithm successfully lowers the computational complexity of density functional perturbation theory(DFPT)from O(N4)to O(N3),where the number of Sternheimer equations to be solved is reduced from O(N2)to O(N)using ISDF decomposition.The interpolation points in the ISDF algorithm are obtained by the QRCP procedure,whose computational complexity is O(N3),which will significantly increase the computational cost as the system size grows.And QRCP will seriously compromise the convergence of the Dyson equation when the number of interpolation points is small.We apply the K-means clustering algorithm to accelerate DFPT in KSSOLV software,demonstrating the accuracy and better convergence of K-means algorithm with a O(N2)cost.Chapter 5 introduces the CPU-GPU heterogeneous implementation of the PPCG algorithm.The PPCG algorithm is a diagonalization method proposed in recent years,which is suitable for large-scale system calculations within plane-wave basis sets.Compared with Davidson and LOBPCG algorithms,the PPCG algorithm relaxes the optimality of the search direction,so that the eigenvalue problem of 3N ×3N is transformed into N/k 3k × 3k subproblems,which reduces the Rayleigh-Ritz cost for large systems.We designed a CPU-GPU heterogeneous parallel scheme for PPCG algorithm,which was successfully applied to the domestic C86 supercomputing platform.The PPCG algorithm allows us to adjust the size of subproblems according to the characteristics of the computing platform to obtain optimal computing performance.On the GPU of the C86 platform,we can achieve an order of magnitude or more improvement in terms of computing efficiency.Finally,we demonstrate that our program can achieve massively parallel computing of the systems containing thousands of atoms on 2000 GPU cards.Chapter 6 introduces the high-throughput screening of rattling-induced ultralow lattice thermal conductivity in semiconductors.Low thermal conductivity is necessary for efficient thermoelectric conversion.Firstly,we introduce the rattling model and its ability to induce strong anharmonicity,leading to low thermal conductivity.Subsequently,we propose a structural descriptor suitable for high-throughput screening based on the rattling model.By employing this descriptor,we efficiently identify over 500 materials with low thermal conductivity from a database containing more than 100,000 materials.We demonstrate that the materials with halide double perovskites structures generally have low lattice thermal conductivity,where Rb2SnBr6 has lattice thermal conductivity of 0.1 Wm-1K-1 at 300K,which is the lowest of all known materials with rattling model to date.Chapter 7 makes a conclusion of the thesis,and prospects the development of algorithms and programs for high-accuracy first-principles calculations,as well as highthroughput calculations.