Linear-scaling Implemention of HSE06 Hybrid Functional and Theoretical Studies of Physical Properties of Novel Materials

Author:Qin Xin Ming

Supervisor:yang jin long


Degree Year:2019





Due to its combination of relatively high accuracy and low computational cost,density functional theory(DFT)is the most widely used method for electronic structure calculations in molecules and condensed matter systems.Despite its great successes,pure DFT with traditional local or semiloca functionals have some inherent drawbacks.For example,they always severely underestimate band gaps of semiconductors.The Heyd-Scuseria-Emzerhof(HSE06)screened hybrid functional can systematically im-prove calculation results for solids by including only the short-range parts of exact nonlocal Hartree-Fock-type exchange(HFX).However,the large computational effort required to evaluate HFX limits its applications in large systems.Thus,it is of great importance to further develop and implement fast linear-scaling(O(N))methods for large-scale HSE06 calculations.This is one of the main works in this thesis.On the other hand,first-principles calculations based on DFT can provide reliable results inde-pendently from experiments,and it has become an integral tool in materials investiga-tions,aiding to explain experimental data,guiding experimental design and predicting novel materials and properties.In this thesis,the ground state electronic structures,lat-tice dynamics,electron-phonon coupling and superconductivity of some novel materials are also investigated from first-principles.The first chapter provides an introduction to the theoretical framework of Kohn-Sham DFT.The basic idea of DFT is to describe a many-body interacting system in terms of the electron density rather than the many-body wavefunction.In Kohn-Sham DFT,the original interacting system is mapped onto a much easier-to-solve non-interacting system by introducing an unkown exchange-correlation term.Searching for better exchange-correlation functionals is one of the most important topics of DFT,and some modern functionals are reviewed.In the end of this chapter,we introduce briefly the DFT pack-ages used in the current work.In the second chapter,we introduce the O(N)methods for DFT.O(N)methods take advantage of the decay property of the density matrix or Wannier functions in real space,that is the sparse matrix representations of the density matrix in a local basis,and thus the computational cost can scale linearly with system size.Numerical atomic orbitals(NAOs)are well suited to O(N)methods because they are very flexible,can be strictly localized,and few of them are needed for accurate results.Focusing on NAOs,we review the O(N)approaches to construct the Hamiltonian matrix and to solve the density matrix.In the last,we also introduce the O(N)DFT package HONPAS developed by our group.In chapter 3,we present a development and improvement of O(N)HSE06 hybrid functional implementation for extended systems with NAOs.In our early implemen-tation,a NA02GT0 scheme using auxiliary GTOs to represent NAOs has been estab-lished to calculate the electron repulse integrals(ERIs)analytically,and several integral screening techniques are employed to make HSE06 calculations scale linearly.Based on these implementations,we improve the Schwarz-screening method by fitting two center integrals of different types to parametrized screening functions related to their distances.With these screening functions,the upper bounds for both primitive and con-tracted ERIs can be estimated more fast.We add density matrix screening in order to fully exploit the sparsity of the density matrix,which further improves the screening ef-ficiency.The initial density matrix is obtained from a converged post-PBE calculation.In addition,we also finish the O(N)implementation of HSE06 forces.Since the density matrix has been completely converged,the calculation of the forces is less expensive than the construction of the HFX matrix in the SCF process.Finally,we propose a sim-ple and efficient parallelization scheme for the computation of ERIs,HFX and forces,and some test calculations demonstrate that our program has good performance in both speed and accuracy.In chapter 4,two theoretical works on the structural and electronic properties of the thermoelectric material AgBiSe2 and the self-assembled two-dimensional(2D)molec-ular superstructures are presented in cooperation with the experimental group.Firstly,we propose a theoretical explanation to the mechanism of the reversible p-n-p conduc-tion type switching experimently observed in AgBiSe2 during its rhombohedral-cubic phase transition.We choose suitable supercells to model different phases and defects forAgBiSe2.After comparing formation energies of different defects,we find that Ag vacancies are the intrinsic point defects,which make AgBiSe2 p-type semiconducting in both the rhombohedral and disordering cubic phase.Our theoretical calculations indi-cate that the Ag/Bi bimetal exchange through Ag vacancies in Ag-Se-Bi-Se-…chains palys an important role in the p-n-p switching.During the rhombohedral-cubic phase transition process,Ag-Bi atoms exchange produces an intermediate quasi-metallic state with dominant Ag-Se-Ag-Se-…chains,which eventually leads to the switching be-tween p-and n-type conduction.As AgBiSe2 transforms into cubic phase,Ag and Bi atoms are full disordering in lattice,their indistinguishability makes the Ag-Se-Bi-Se-…chains still be dominant,and thus the conduction type changes back to p-type conduction due to the presence of Ag vacancies.Secondly,we investigate the en-ergy level realignment mechanism in the binary molecular networks CuPc-F16CuPc on highly oriented pyrolytic graphite(HOPG)substrate.From CuPc/graphene and F16CuPc/graphene to their binary superstructures,an unusual energy level realignment has been observed in experiment.We simulate the self-assembled molecular networks by using supercells with CuPc,F16CuPc and CuPc-F16CuPc monolayer adsorbed on the graphene substrate.Through comparing the changes in structure,electronic state and charge transfer behavior between single-component and binary superstructures,we find that the formation of weak intermolecular hydrogen bonds between neighboring CuPc and F16CuPc can significantly affect the interface charge transfer behaviors and induce the energy level realignment.In chapter 5,we focus on studying the electron-phonon coupling(EPC)and su-perconductivity in 2D monolayer materials from first-principles.At the beginning,we introduce the first-principles methods for calculating the EPC constant λ and the su-perconducting transition temperature Tc,and aslo review the current progress in the research of 2D superconductivity.Then,we predicit 2D phonon-mediated supercon-ductivity in three kinds of pristine monolayer materials.The first one is the graphene-like C5N monolayer that may have been successfully synthesized.Our estimated λ and Tc are 0.32 and 1.3 K for pristine C5N monolayer,respectively.The EPC is majorly from 7r*-states coupling with the in-plane optical phonons of high frequency.Further calculations show that both tensile strain and doping by alkaline metal adatoms can sig-nificantly enhance the superconductivity C5N monolayer,and Tc can be increased up to 39.8 K by 12%biaxial tensile strain.The other two are Cu2Si monolayer and Cu2Ge monolayer which have been theoretically predicted to be stable due to the existence of muticenter a bonds.We predict that both of them are phonon-mediated supercondutors with Tc of 2.6 K and 2.1 K,respectively.The strong coupling between muticenter σ-states and out-of-plane modes is the main reason for their supercondcutivity.For com-parison,we also explore the EPC and possible superconductivity in the carrier-doped Be2C monolayer.We find that only the hole-doped Be2C monolayer has similar EPC behavior and therefore can be superconducting.