Development Of Hybrid Coupled Cluster Methods

In the past decades, the applications of quantum chemistry to various problems in chemistry, physics, and biology have increased rapidly. Methods like density functional theory (DFT), with relatively low computational scalings (N3～4), have been successful in studying molecules or materials near their equilibrium geometries. Combining with the molecular mechanics (MM), the QM/MM method is now widely used to study certain problems in large biological systems. However, there are many problems that require more accurate ab initio correlation methods. For example, accurate evaluation of reaction barriers for some simple reactions requires very accurate correlation methods. The traditional coupled-cluster (CC) method, such as CC singles and doubles with perturbative triples, CCSD(T), can provide very accurate results for closed-shell systems near their equilibrium geometries, and has been called "the gold standard of quantum chemistry". However, for open-shell systems, radicals, and systems in the bond breaking regions, where degeneracy or quasidegeneracy of determinants occurs, all single-reference electron correlation methods will not work without inclusion of higher excitations. Simple extensions of CC methods to a higher excitation level, like CCSDT and CCSDTQ, will lead to a rapid increase in the computational scaling so that these two methods are limited to very small systems. To tackle the problem, several multireference (MR) CC methods have been developed. However, there are still problems within multireference methods. We feel that the development of fast and accurate single-reference (SR) CC methods is still appealing.The main part of this thesis is about the further development of the hybrid coupled cluster methods by combining active space CC methods with CCSD(T) to deal with ground-state electronic structures of molecules with certain multi-reference character. Especially, the implementation of the CCSD(T)q-h, a hybrid model between CCSDtq and CCSD(T), is first reported. To allow hybrid CC methods feasible for medium-sized systems, non-iterative schemes for solving the CCSD(T)-like equations are proposed. With these new developments, the hybrid CC methods are expected to become promising tools for studying potential energy surfaces and molecules with diradical characters. The main findings and innovations are summarized as follows:In Chapter2, we develop and implement two hybrid coupled cluster methods, named CCSD(T)-h and CCSD(T)q-h, by combining the active-space CC methods (CCSDt and CCSDtq) with CCSD(T) to deal with electronic structures of molecules with significant multireference character. A general procedure for constructing the active orbitals is proposed, which is based on the unrestricted HF calculation. Non-iterative schemes for solving the CCSD(T)-like equations in the two hybrid methods are introduced so that the storage of all triple excitation amplitudes is avoided. We will describe the automatic derivation of the CC formulations and generation of the computer program.In Chapter3, the CCSD(T)-h and CCSD(T)q-h approaches are applied to investigate the ground-state PESs for a number of bond-breaking processes. The results are compared with those obtained from their parent CC methods, CCSDT and CCSDTQ, and also the full configuration interaction (FCI). Our results have shown that CCSD(T)-h and CCSD(T)q-h are excellent approximations to CCSDT and CCSDTQ, respectively. The CCSD(T)-h approach has also been applied to study the energy barriers of several typical reactions, and spectroscopic constants of diatomic open-shell molecules. In all cases, numerical results have shown that CCSD(T)-h and CCSD(T)q-h can offer a significant improvement over the popular CCSD(T) method.In Chapter4, an efficient implementation of the CC singles, doubles, and hybrid triples based on the split virtual orbitals, SVO-CCSD(T)-h, is presented. In this method, virtual orbitals with a large basis set are split into two subsets by taking a smaller basis set as an auxiliary reference. The triples are thus divided into two subsets and treated in a hybrid way as in the CCSD(T)-h approach. The use of quasi-canonical orbitals greatly simplifies the solution of the CCSD(T)-like equations, which allows the SVO-CCSD(T)-h method feasible for medium-sized systems. The S VO-CCSD(T)-h is then applied to study the reaction barriers for a number of simple reactions and spectroscopic constants in several open-shell molecules. Results have shown that the SVO-CCSD(T)-h method provides a significant improvement upon the CCSD(T) method in many cases.