Theoretical Study And Application Of Linearized Coupled Cluster And Multireference Perturbation Theory

For the post-Hartree-Fock method for calculating electron correlation energy,it can be simply divided into two categories:single-reference state method and multi-reference state method.The wave function constructed by the multi-reference state method is more perfect than that of the single-reference state method,which can describe the various properties of the system more accurately.The multi-reference state method performs better than the single-reference state method in computing the molecular with excited state,describing the potential energy curve of molecular dissociation,or other situations.However,the multi-reference state method often has some problems,such as invasive state,no size consistency,and the calculation process is much more complex than the single-reference state method.Therefore,the study of multi-reference state methods still needs to be improved and developed.The main contents of this paper are as follows:In this paper,we proposed a new multi-reference state single-double coupling cluster method(MRLCCSD),and its performance is tested comprehensively.MRLCCSD is exploited to calculate the ground state energies of HF,H2O,NH3,CH4,N2,BF and C2 with basis sets,cc-pVDZ,cc-pVTZ and cc-pVQZ.The equilibrium bond length and vibration frequency of HF,HCl,Li2,LiH,LiF,LiBr,BH and AlF are computed with MRLCCSD and compared with the experimental data.The electron affinities of F and CH as well as the proton affinities of H2O and NH3 are also calculated MRLCCS.These results are compared with the results produced withMP2,linearized coupled-cluster doubles(LCCD),coupled-cluster doubles(CCD),CCSD and CCSD(T).It is shown that all results obtained with MRLCCSD are reliable and accurate.In this paper,a new multireference Rayleigh-Schrodinger perturbation theory(MRSPT)based on the complete active space multireference wavefunctionis proposed.MRSPT is derived with the assumptionthat the orbital energies of active orbitals are the same as ?,an unknown parameter.In this work,? is optimized at the MRSPT2 level.The second and third order perturbation theories are shown numerically to be size extensive.The size consistency of the method was verified by numerically computing of the supermolecules and complexscomposed of H2,BH and Li2 molecules.The second order perturbation theory is exploited to compute the ground state energies of F2,AlH,HCI and P2,and calculated the extrapolated energies with the infinite basis set.And optimized the equilibrium bond lengths and harmonic vibrational frequencies of BH,BF,P2,HF and F2.These results are compared with the results produced withcomplete active spaceself-consistent field(CASSCF),second-order perturbation theory(MP2),coupled-cluster singles anddoubles(CCSD),coupled-cluster singles and doubles with triples correction(CCSD(T)).The rationality and accuracy of MRSPT2 are analyzed in detail.The dissociation behaviors of NH3 and OH-have also been investigated.When other methods can not describe the potential energy curve reasonably,the potential energy curve of MRSPT2 performs well,reflecting the superiority of MRSPT method.Divergences of the single reference perturbation theories due to the addition of diffusion basis functions have been investigated for both closed-shell and open-shell molecular systems.Feenberg transformation is exploited to treat the problems.In this paper,two closed shell systems with non-convergent perturbation energies,N3-and O2-,and eight open shell systems with non-convergent perturbation energies,C,N,O,F,NH,OH,CH2 and NH2,are selected to study.It is found numerically that there exists a minimum perturbation order with respect to the Feenberg transformation parameter from a small continuous region of 0 to 1 for each system,at which the perturbation series become convergent.