Coupled-cluster methods for open-shell molecular and other many-fermion systems.

摘要

The description of the electronic structure of radicals and other open-shell molecular systems represents a significant challenge for current theoretical methodologies. Since the low-lying electronic states of open-shell species often possess a manifestly multi-determinantal character, it is difficult to perform calculations for these systems that are both highly accurate and practical enough to be applied to a wide range of chemical problems of interest. To overcome these difficulties, we have developed two new classes of coupled-cluster (CC) methods, which are capable of accounting for the high-level electron correlation effects that characterize open-shell systems at a relatively low computational cost. The first class of methods, the active-space variants of the electron-attached (EA) and ionized (IP) equation-of-motion CC (EOMCC) theories, utilize the idea of applying a linear electron-attaching or ionizing operator to the correlated, ground-state CC wave function of an N -electron closed-shell system in order to generate the ground and excited states of the related (N +/- 1)-electron radical species. Furthermore, these approaches use a physically motivated set of active orbitals to a priori select the dominant higher-order correlation effects to be included in the calculation, which significantly reduces the costs of the high-level approximations needed for obtaining accurate results for open-shell species without sacrificing accuracy. The second class consists of the size extensive, left-eigenstate completely-renormalized (CR) CC approaches based on the biorthogonal formulation of the method of moments of CC equations, in which noniterative corrections due to higher-order excitations are added to the energies obtained with the standard CC approximations, such as CCSD (CC with singles and doubles). We have extended one of the best methods in this category, termed CR-CC(2,3) or CR-EOMCC(2,3), in which a noniterative correction due to triple excitations is added to the CCSD or EOMCCSD energy, and its higher-order CR-CC(2,4)/CR-EOMCC(2,4) approach, in which a noniterative correction due to triple and quadruple excitations is added to the CCSD/EOMCCSD energy, to open-shell systems. In this thesis the theoretical details of all of these new methodologies as well as a sample of benchmark examples that illustrate their performance in studies of ground and excited states of open-shell molecular systems are discussed. In addition, since there is nothing in the underlying theoretical framework specific to electronic structure, the CC approaches developed in this thesis are not restricted to molecular cases and can be applied to other many- fermion systems, such as atomic nuclei. Representative examples of applications of the new CC methods developed in this thesis research in the context of quantum chemistry to studies of nuclear structure are given as well.