Implementation Of Nonlocal Exchange And Correlation Interaction In Extended Systems With Numerical Atomic Basis Set

In the past decade, strictly localized numerical atomic basis set is shining inthe implementation of linear scaling methods, which is possible to calculate largesystems. Numerical atomic basis set has draw more and more attention and havebeen widely used.Most of the softwares using numerical basis set only have traditional densityfunctionals based on the local density approximation (LDA) or the generalizedgradient approximation (GGA), which sometimes are not accurate enough. Apossible remedy is to add nonlocal Hartree-Fock type exchange (HFX) into localor semilocal density functionals. Such hybrid functionals can be used to treatdynamical and nondynamical correlations.However, implementation of nonlocal electron interaction with numericalatomic basis set is not an easy task. Very recently, following Talman’s earlywork, Toyoda and Ozaki tried to calculate the electron repulsion integrals (ERIs)in the reciprocal space with numerical atomic basis set. However, as they men-tioned, the computational time for a single ERI is 3.0 second on an 3.2 GHz IntelXeon processor. Such a low e?ciency makes their HFX calculation unfeasible forany practical system.In resent years, our group has been focus on the implementation of nonlocalelectron interaction using numerical atomic orbital: the ?rst one is a straightforward integration method; And the second one is a more complex NAO2GTOscheme. We will show our methods in the following chapters.In the ?rst chapter, we will discuss recent progress in electronic structurecalculations with numerical atomic basis set. Principles of numerical basis setand Hamiltonian construction are introduced ?rstly. Then we give an overviewon the direction of our future development. In the second chapter, a method to calculate Hartree-Fork type exact ex-change has been implemented in the electronic structure code SIESTA based onlocalized numerical atomic orbital basis set. In our implementation, the elec-tron repulsion integrals are calculated by solving Poisson’s equation using theinterpolating scaling functions method and then doing numerical integration inreal-space. Test calculations for both isolated and periodic systems are performed,and good agreement with results calculated by GAUSSIAN 03 or CRYSTAL 06packages is obtained.In the third chapter, we present an e?cient O(N) implementation of screenedhybrid density functional for periodic systems with numerical atomic orbitalsNAOs of valence electrons ?tted with gaussian type orbitals, which is convenientfor the calculation of electron repulsion integrals and the construction of Hartree-Fock exchange matrix elements. All other parts of Hamiltonian matrix elementsare constructed directly with NAOs. The strict locality of NAOs is adopted as ane?cient two-electron integral screening technique to speed up calculations.In the fourth chapter, we will show our method to calculate the second-orderM?ller-Plesset perturbation(MP2) correlation energy using numerical atomic basisset. We have implemented both canonical formulation and laplace-transformedMP2 theory for extended systems. These two kinds of methods can get same resultwith the same computation parameters. The laplace-transformed MP2 methodtakes less time than canonical method by avoiding multidimensional k-integration.Using the localization of NAO, the laplace-transformed MP2 can deal with largesystems.In the ?fth chapter, the implementation of ?rst derivation of screened hybriddensity functional energy is discussed. So the geometry optimization can be donewith HSE06 functional using our code.In the appendix, we will show how to compile and how to use SIESTA code.After that, I will propose a new mechanism originated from quantum interferencefor negative di?erential resistance.