New Quantum Chemistry Methods Based On The Renormalization Group

In the past decades, quantum chemistry has achieved great progresses in the treat-ment of large systems and in the improvement of computational accuracy. However, it is still difficult to extend the application of ab initio quantum chemistry (QC) meth-ods to very complicated electronic structure problems (e.g. systems with large sizes or system with strong electron correlations), and accordingly the development of ad-vance QC methods is nowadays an important and active research area. Meanwhile, the numerical renormalization group (NRG) and density-matrix renormalization group (DMRG) achieved great successes in solid state physics for solving large systems with weak interaction and strong interaction system, separately. Therefore, in this thesis, we extended the applications of these RG-based methods to the field of quantum chemistry by virtue of further developing the renormalized excitonic method (for calculating the excitation of molecular aggregates) and the multi-level DMRG strategy (for solving large active space with60～80active orbitals). The concreted study result as fol-lowed:The idea behind renormalized excitonic method (REM) is that the general ex-cited state can be approximated as an assembly of various block excitations with the suitable account of the interactions between adjoined blocks. When concretely imple-menting, the whole system is divided into many blocks, and the interactions between adjoined blocks are taken into account through Bloch’s effective Hamiltonian theory. Since the block canonical molecular orbitals (BCMOs) are more suitable than the lo-calized molecular orbitals (LMOs) for the description of excitation, we proposed two new strategies, which are REM based on BCMOs and REM based on symmetrical-orthogonalized BCMOs (SYM-BCMOs), and the combination of these REM methods with many QC approaches (e.g. HF/CIS, SAC/SAC-CI, and DFT/TDDFT) were al-so presented. The computational scaling of these methods is Ne3(in BCMOs, Ne3is the number of total electrons) or even lower (in SYM-BCMOs). Such scaling is very promising because it is much lower than that of whole system’s calculation.We applied these REM methods to the descriptions of various molecular aggre-gates when finishing the detailed tests on the factors which may affect the accuracy. These aggregates include one dimensional (1-D) H2O molecular chains, ring crystals (H2O rings and C2H4rings),2-D benzene aggregates, as well as aqueous systems with polar and non-polar solutes (benzene+(H2O)n and acetone+(H2O)n). The results show that these methods are effective in reproducing the electronic excitation energies of low-lying excited states affected by static, hydrogen-bonded, van-der Waals, and π-π stacking intermolecular interaction:the typical deviations are0.01～0.1eV. Besides that, the analyses of the the simple1-D H2O molecular chain show that REM also provides a qualitative picture where the excitation locates.DMRG is regarded as an efficient alternative to full configuration interaction (FCI) in quantum chemical descriptions, it can handle up to40active orbitals. Considering the particularly important issue of orbital choosing and orbital ordering in ab initio DMRG, we investigated the influence of various natural orbitals (NOs) as the basis of large active DMRG-CASCI calculations, and found:to general systems (e.g. N2and Cr2), the normal multi-reference methods can provide reliable NOs; to strong cor-related systems (e.g.2-D hydrogens in dissociation condition), only the preliminary DMRG-CI can provide reliable NOs. Further investigation show that using DMRG-CASCI with reliable NOs, one can get results very close to that of DMRG-CASSCF calculation. Based on the above analysis, we proposed that DMRG-CASCI calcula-tion in a basis of carefully chosen NOs can provide a less expensive alternative to the standard DMRG-CASSCF calculation and avoid the convergence difficulties of orbital optimization for large active spaces.Based on the analysis of various orbital bases, we further proposed the ML-DMRG strategy, in which the whole orbital spaces are divided into many fine-sorted or-bital levels via orbital’s different contribution in electron correlation, and each level has its specific precision-control scheme. With this strategy one can give efficient descrip-tions of larger active orbitals (60～80) than CAS (up to17) and standard DMRG (up to 40), which may offer a potential tool in the description of multi-core transition metal systems. Besides that, we propose DMRG-multi-level active space self-consistent-field theory (DMRG-MASSCF) via combining ML-DMRG and Multi-configuration SCF (MCSCF), and made preliminary tests on the simple N2molecule.