The Improved Local Contracted CISD Method And Its Applications

Quantum chemistry has become an important tool in predicting the structures, en-ergetics and properties of chemical systems. Electron correlation is essential for the ac-curate description of various chemical phenomena. On the basis of canonical molecular orbitals the computational cost of conventional electron correlation methods increases steeply with the molecular size, making them impractical in the calculation of large-sized molecules. To circumvent this dilemma and achieve low and even linear scaling of electron correlation methods, the short-range character of electron correlation poten-tial is extensively explored.The present work aims to develop low and even linear scaling electron correlation method for both the ground state and low-lying excited states. The main idea is to exploit the locality of correlation and excitation. The external contraction is employed in configuration interaction (CI) method to save the computational cost. To further improve the accuracy of local contracted CI method, the dressing technique derived from the intermediate Hamiltonian is implemented. In a similar philosophy to local contracted scheme, by assuming the excited states as the linear combination of local excitations, the renormalized excitionic method is implemented within the ab initio Hamiltonian. The main context of this dissertation can be summarized as follows.In chapter 2, we presented local contracted (LC) CISD scheme using the localized molecular orbitals. LC-CISD consists of two steps:the first step is the definition of intra and inter bond vectors through relatively small local IEPA correlation, and the subsequent step is the consideration of the couplings between these bond vectors by constructing the LC-CISD matrix of the whole system and diagonalizing it directly. Through the contraction of virtual MOs, the size of final LC-CISD subspace scale as only no2 with no being the number of occupied MOs. The computational cost can be re-duced by further truncation of virtual space and neglect of interactions between distant bond pairs. The results show that the loss of correlation energy due to the contraction of the doubly excited determinants is only of the order of a few percent.In chapter 3, we implement the renormalized excitonic method using the FCI wave function by expanding the low-lying excited states of the whole system as a linear combination of local excitations. We test the ionized potential and the energy gap between singlet ground state and the lowest triplet state for linear hydrogen and linear polyenes. We investigate the factors influencing the accuracy of REM. It shows that the reasonable results can be obtained provided that the near degenerate problems of the model space are circumvented and the interactions between blocks are consider sufficiently.In order to correct the size-inconsistency error, in chapter 4, we translate the LC-CISD formalism to various CEPA variants with the aid of dressing technique derived from intermediate Hamiltonian theory. Both the global and determinant specific dress-ings are introduced. Determinant specific CEPA-3 dressing can qualitatively describe the single bond breaking processes. In the local contracted context, we also introduced the effect of triples and quadruples via four-electron full CI correlations. By using the localized MOs, most of the effects of the triples and quadruples are captured through this correction due to the prevalence of the intrabond double excitations. Our results show that our LC-CEPA-3 incorporated the effects of triples and quadruples present ac-curate description of the single bond breaking processes, as well as the good description of the properties around equilibrium geometries. We also suggest the coupled cluster dressing in the local contracted framework.Finally, a brief conclusion and outlook for the future work are summarized in chap-ter 5.In conclusion, by exploiting the localized orbitals, external contraction and the dressing technique, we have broaden the application of CI method towards the large systems with improved accuracy. The exploration of ab initio REM also provides an alternative clue in the calculation of low-lying excited states of large systems.