Development Of Coupled Cluster Methods Based On Orbital Pair Excitations

In the past decades, quantum chemistry has been widely used in the areas of chemistry, material science, physics, biology, and etc. The accurate description of molecular potential energy surfaces (PESs) is an important problem in quantum chemistry. For small and medium molecules, the coupled-cluster (CC) method is widely used for PES calculations. The traditional CC methods, such as CC with singles and doubles (CCSD), can provide accurate results for most closed-shell systems near their equilibrium geometries. But if the chemical bonds are stretched (or broken), the accuracy of traditional CC methods deteriorates significantly because the Hartree-Fock (HF) reference determinant is quasidegenerate or degenerate to some other determinants during the bond-breaking processes. So, it is necessary to add higher-than-double excitation operators within the single-reference CC framework to obtain more accurate results. Unfortunately, the storage requirement and computational scaling increase rapidly with the inclusion of more excitation operators, which limits the applications of traditional CC methods. Thus, the development of faster and more accurate CC methods has become an important task in quantum chemistry.In this thesis, in order to provide accurate descriptions for the bond breaking processes of small molecules, we develop new CC methods based on the orbital pair excitations in the framework of single-reference CC (SRCC). The expansion of the cluster operator in terms of "orbital pairs" in the SRCC framework is a new concept first proposed by us. In this manner, our CC methods can include some parts of higher excitations, which are not included in the corresponding traditional CC methods with similar disk storage and computational cost. Thus, these CC methods can obtain more accurate results than the traditional CC approaches. With the second-quantization formalism, we have developed a computer program to derive the working equations and generate the computational code of these CC methods automatically. Main contributions of the present work can be summarized as follows:In Chapter 2, we first introduce the concept of "orbital pair" and then truncate the cluster operator in terms of excitations up to five orbital pairs, which defines the CC5P method. The computational cost of this method scales as the seventh power of the system size. The UHF reference is used in all CC5P calculations within this work. Before CC5P calculations, we need to transform occupied (or virtual) canonical molecular orbitals into corresponding orbitals (or orbital pairs) so that eachα-spin orbital is uniquely paired with oneβ-spin orbital. In comparison with full configuration interaction (FCI) results, the UHF-based CC5P (UCC5P) and its approximate versions are demonstrated to provide much more accurate descriptions for single-bond breaking processes than the UHF-based CCSD(T) [UCCSD(T)] method, which has the same computational scaling as UCC5P. For multiple bond breaking processes, UCC5P could also provide slightly better results than UCCSD(T).In Chapter 3, we develop the CC approach with excitations up to six orbital pairs, which is named as CC6P. Since only some parts of the higher-than-triple excitation operators are included, the computational scaling of CC6P is similar to that of CCSDT. Here, we choose the RHF (or ROHF) determinant as the reference determinant to avoid the spin contamination. Because CC6P and its approximate variants are not invariant to the unitary transformation among occupied or virtual orbitals, the occupied and virtual orbitals need to be localized separately, before CC calculations are carried out, to guarantee the size extensivity of CC6P and its approximate schemes. Then these approaches are applied to study the bond-breaking PESs in four molecules (F2, H2O, N2 and F2+). By comparing with the FCI results, CC6P and its approximate schemes are demonstrated to provide very accurate descriptions for the single-bond breaking process in F2 and considerably better results for the multi-bond breaking processes than the CCSDT method.In Chapter 4, we present the CC approach with excitations up to seven orbital pairs, denoted as CC7P, which computationally scales as the ninth power of the system size. Similar to the CC6P method in Chapter 3, the RHF (or ROHF) reference determinant is employed to avoid the spin contamination, and canonical occupied (and virtual) orbitals need to be localized separately to ensure CC7P and its approximate schemes (CC7P-4 and CC7P-5) to be size extensive. Then we apply CC7P-4 and CC7P-5 approaches to investigate the bond-breaking PESs in four systems (OF, HFH-, H2O and N2). In comparison with the FCI results, the CC7P-4 and CC7P-5 approaches are able to provide very accurate results in the bond breaking process in OF, and the CC7P-5 method could also give accurate description on the potential energy surface of simultaneous dissociation of two O-H bonds in H2O, which can not be quantitatively described by the CCSDTQ method.