Development And Applications Of Block-Correlated Electronic Structure Method

The unremitting pursuit of developing electronic structure theory is to accurately predict molecular geometries,energies and various chemical and physical properties.Traditional single-reference electron correlation methods based on the Hartree-Fock(HF)reference have achieved great success for weakly correlated systems.Such single-reference methods include,for example,many-body perturbation theory and coupled cluster(CC)theory.However,the accuracy of these methods decreases dramatically for strongly correlated systems(e.g,multiple-bond breaking,transition metal compounds),in which the HF wave function is no longer a suitable starting point.Multireference(MR)electron correlation methods have been developed to deal with strongly correlated systems.Those methods,especially multireference CC(MRCC),which are based on the linear combination of many determinants as the reference function,have been demonstrated to provide satisfactory descriptions for small strongly correlated systems.However,the computational cost of all of the existing MRCC methods increases exponentially with the size of the active space,so they can only be applied to small systems.In our opinion,instead of improving the existing MRCC methods,totally different MRCC methods should be developed.First,we need to build new MRCC methods with a more effective multireference reference function,which should recover a portion of static correlation.Second,new MRCC methods based on this new reference function should effectively deal with the missing static correlation and dynamic correlation to get highly accurate results.Previous works have shown that the generalized valence bond(GVB)wave function may be a better reference function than the HF reference function for systems with strong multireference character.However,none of the existing algorithms for the GVB methods can allow GVB calculations of large systems to be done routinely in a black-box way.The main work of this thesis is:(1)to develop a new algorithm to achieve black-box GVB calculations for large systems;(2)to develop a block-correlated CC method(BCCC)based on the GVB reference function(GVB-BCCC in short),which can provide satisfactory descriptions for electronic structures of strongly correlated systems.In chapter 2,we will introduce how to automatically construct the initial GVB orbitals for various systems,and demonstrate that our procedure can allow GVB calculations to be done for quite large systems in a black-box way,which has never been reported previously.Thus,the GVB wave function is now easily available for subsequent MR electron correlation calculations.In chapter 3,we will propose a GVB-based BCCC method(GVB-BCCC)for accurate electron correlation calculations of strongly correlated systems.The wave function ansatz,and the general procedure of deriving the formulations,and implementation details of GVB-BCCC will be introduced in detail.In chapter 4,we will apply the GVB-BCCC method to investigate the bond dissociation processes in a series of molecules,the accuracy and applicability of the GVB-BCCC method will be evaluated and compared with other theoretical methods.The main contributions and innovations of this thesis are summarized as follows:In Chapter 2,we propose an efficient general strategy for generating initial orbitals for GVB calculations,which makes routine black-box GVB calculations on large systems feasible.Depending on whether the restricted HF wavefunction is stable or not,two schemes are suggested to obtain different active occupied orbitals and active virtual ones.Then,these orbitals are separately transformed to localized orbitals.Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres algorithm and are used as the initial guess for the GVB orbitals.With this procedure,GVB energies have been obtained for the lowest singlet and triplet states of polyacenes(up to decacene with 96 pairs)and the singlet ground state of two di-copper-oxygen-ammonia complexes.In addition,we have shown that analysis of the GVB orbitals in strongly correlated pairs may be used to achieve an automatic definition of the minimum active space for multireference electronic structure calculations.In Chapter 3,a block correlated coupled cluster(BCCC)method based on the GVB wave function(GVB-BCCC in short)is proposed and implemented at the ab initio level,which represents an attractive multireference electronic structure method for strongly correlated systems.This method is a generalization of the traditional orbital-based coupled cluster method,in which the cluster operators are defined in terms of many-electron block states.We will introduce in detail the principle of the GVB-BCCC method,the derivation of working equations,and the implementation details of the corresponding computer program.The features of the GVB-BCCC method will also be introduced.In Chapter 4,the GVB-BCCC method will be applied to investigate double bond breaking processes in two molecules(H₂O and C₂H₄),and triple bond breaking processes in two molecules(BH₃ and N₂).The accuracy of the GVB-BCCC method will be evaluated with other theoretical methods.Then we will apply the GVB-BCCC method to investigate the bond dissociation processes of several relatively large strongly correlated systems.The GVB-BCCC method is demonstrated to provide accurate descriptions for multiple bond breaking in small molecules,although the GVB reference function is qualitatively wrong for the studied processes.For a challenging prototype of strongly correlated systems,tridecane with all 12 single C-C bonds at various distances,our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method from the weakly correlated region to the highly correlated region.