Multistate Density Functional Theory For Modelling Strongly Correlated Systems And Electron Excited State

Kohn-Sham density functional theory（KSDFT）has become indispensable tools for studying of atoms and molecules as well as condensed-phase materials due to its balanced trade-off between accuracy and efficiency in handling dynamic electron cor-relations.Despite the remarkable success,KSDFT,on the basis of a single Slater deter-minant is incapable of describing:（1a）systems that require multi-determinants to form the spin-adapted state to ensure spin symmetry?（1b）closed-shell system with correct spin symmetry but the HOMO-LUMO gap is close to zero,in which multi-determinants are required for the degenerate or nearly degenerate electronic states.For excited state,linear response time-dependent density functional theory（LR-TDDFT）with adiabatic approximation has been enormously successful in predicting the excitation energies.Since it is also based on a single Slater determinant,it inherits the above two problems of KS-DFT.In addition,the use of the adiabatic approximation gives rise to the follow-ing problems:（2a）inability to describe excited states with multi-electronic excitation properties?（2b）failure to describe excited states with severe orbital relaxation effects.In addition,LR-TDDFT performs poorly on charge transfer state,which can be par-tially remedied by mixture of the Hartree-Fock exchange or applying range-separated functionals.In principle,these strong correlation problems can be solved by multiref-erence wave function theory（MR-WFT）.However,MR-WFT requires a huge amount of memory to compute the dynamic correlation and the computational cost increases exponentially with the active space,which limits its application.In this thesis,we present a multi-state density functional theory（MSDFT）for mod-elling strongly correlated systems and electron excited state.In MSDFT,the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches.MSDFT provides a dynamic-then-static framework for treating electron correlation.First,dynamic correlation is incorporated into in-dividual determinants through block-localized Kohn-Sham density functional theory（BLKS-DFT）.Then,nonorthogonal state interaction（NOSI）is performed to treat static correlation.Because molecular orbitals are optimized separately for each determinant by including Kohn–Sham dynamic correlation,a small number of configurations in the active space is sufficient to yield the adiabatic states.Therefore,this method is computa-tional efficienct to treat strongly correlated systems that are problematic for KSDFT（1a,1b）but too large for accurate multireference wave function methods.In MSDFT,?SCF or block-localized excitation method（a fragment-based?SCF method）is used to opti-mize excited determinants,which ensures that multi-electronic excitation properties and orbital relaxation effect can be described（2a,2b）.This thesis divides into the following:Introduction to excited state DFT method is provided in the first chapter.Chapter2 presents the rigorous theoretical framework of MSDFT and the approximated formu-lation of MSDFT,NOSI.We discuss various techniques in NOSI that can be used to compute excited-state properties and our recent advance.Including developing（1）a new block-localized method,i.e.targeted state orbitals（TSO）method,for excited con-figuration optimization.This method“freezes”the target orbitals that are not desired to be occupied by electrons in order to circumvent the variational collapse problem?（2）a new approach for constructing transition density functional（TDF）.This is achieved by enforcing the degeneracy condition of spin multiplets of the same total spin states and then define the effective exchange integrals between spin-contaminate configura-tions to solve the double counting of electron correlation.These methods have been inplemented into a computational quantum chemistry software.In applications,we selects some electron excitation problems which TDDFT are failure to describe.In chapter 3,we use BLKS-DFT method to construct block lo-calized configurations in order to describe local valence excitation and inter-fragment charge transfer states.We have applied our method to three systems which conven-tional TDDFT methods previously fail to describe,i.e.charge transfer stabilization of valence exicted states on the anthracene excimer complex,charge transfer states of aryl-tetracyanoethene complexes,and local excitation and charge transfer of a set of bi-molecule complex.The results showed that MSDFT is able to provide a good de-scription of covalent and charge transfer excited states comparable to experimental and computational results obtained using high level theories.Because of the simplicity and interpretive capability through diabatic configuration weights,the method may be use-ful in dynamic simulations of charge transfer and nonadiabatic processes.In Chapter 4,we focus on solving orbital relaxation and multiple electron excitation issues.We inves-tigated the core excitation of open-shell doublet and triplet radical molecules,such as NO,NH₂⁺and benzene cation,from a core orbital in the ground state to the singly occu-pied molecular orbital（SOMO）and to the lowest unoccupied molecular orbital（LUMO）.The results show that MSDFT can adequately describe orbital relaxation effects of core excitation.And our new approach for constructing transition density functional（TDF）can effectively define spin-adapted states in the open-shell systems.In Chapter 5,we in-vestigated a special type of molecule obtained via delayed fluorescence from inverted singlet and triplet excited states（DFIST）process.In particular,the lowest triplet（T₁）has a higher energy than the lowest singlet excited state（S₁）.During the fluorescence process,T₁state is able to relax to S₁state via spin-orbit coupling freely without incur-ring thermal activation process,this process allows 100%internal quantum efficiency which makes this type of molecules useful for building highly efficient organic light-emitting diodes（OLEDs）.S₁and T₁of these molecules are generally dominated by the single-excitation configuration from the HOMO to LUMO.At the same time,double-excitation is the key to stabilize S₁state,making the S₁state energy lower than T₁.We constructed a minimal active space consists of only two unpaired electrons in two or-bitals.We showed that MAS-MSDFT predicted the inverted singlet and triplet exicited state gap at an accuracy comparable to the high level DLPNO-STEOM-CCSD method.