Scaling Correction Method For Improving Energy Gap Predictions Of Molecules And Solids With Density Functional Calculation

This dissertation focuses on the elimination of the delocalization error that plagues the density functional approximations in density functional theory (DFT),to improve the energy gap predictions of molecules and solids. The energy gap is a fundamental property of molecules and solids, and it is critical to relevant researches and applications. The density functional methods are widely used to predict many kinds of physical and chemical properties of these systems, because of its outstanding balance between accuracy and computational cost. However,the intrinsic delocalization error associated with the density functional approximations makes the predictions of energy gaps inaccurate, despite the fact that DFT itself is an exact theory. This dissertation elaborates the development of the nonempirical scaling correction method that eliminates the delocalization error. With the information on orbital relaxation, the scaling corrected Kohn-Sham(KS) frontier orbital energies are capable to predict accurate ionization potentials,electron affinities, and molecular gaps. The scaling correction method is significant to the researches of the electronegativity, hardness, reactivity, etc. Its numerical implementation is discussed in the main text. The localized orbital scaling correction (LOSC) method for periodic solids is also presented. LOSC method for solids improves substantially and systematically the prediction of fundamental gaps for a wide range of solids, including metals, semiconductors, transition metal oxides, ionic crystals, noble gas crystals, and organic polymer chains. Moreover,its numerical implementation is very efficient.The dissertation is organized as follows.In Chapter I, the basis of DFT is briefly presented. The researches in this dissertation are based on the framework of DFT. The concept of delocalization error is also introduced, which is one of the main issues in DFT. Then the scaling correction to the delocalization error is discussed, and it is the theoretical basis of the following chapters.In Chapter II, the development of scaling correction method with the KS frontier orbital relaxation is elaborated. The information of the orbital relaxation is then used to improve the accuracy of predicted KS frontier orbital energies by Hartree-Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scaling correction method provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent field calculations for (N ± 1)-electron systems.Chapter III shows the scaling corrected KS frontier orbital energies are capable to predict accurate molecular electron affinities (EAs). In fact, accurate prediction of EA is difficult with DFT methods. The somewhat large error of the calculated EA originates mainly from the intrinsic delocalization error associated with the approximate exchange-correlation functional. In this work, the EA is given by the scaling corrected KS frontier orbital energy of the neutral molecule, without the need to carry out the self-consistent field calculation for the anion.In Chapter ?,the LOSC method is extended to periodic solids. The LOSC method introduced in Chapter I achieves a universal alleviation of delocalization error for finite systems. By using Wannier functions to characterize local fractional electron distributions, the LOSC method is extended to periodic solids and polymer chains. It is demonstrated that the application of LOSC improves substantially and systematically the prediction of fundamental gaps for various types of solids, ranging from zero-gap metals to wide-gap insulators.