New Dmrg Methods And Code Implementation For Quantum Chemistry

In the past decades,the single-reference quantum chemistry methods based on the mean-field approximation have been successfully applied to general molecules with dozens or even hundreds of atoms for the accurate calculations of structures,energies,and properties.But in strongly correlated systems,such as conjugated molecules and transition metal complexes,there are a large amount of near-degenerateπ,d or f or-bitals,which,as well as the electrons in these orbitals,constitute the active space.The computational efforts to exactly diagonalize the active space increase exponentially with the extension of systems,which leads to the failure of the applications of the tra-ditional multi-configuration and multi-reference methods to the molecules with more than 18 active orbitals.The density matrix renormalization group（DMRG）method uses the matrix product state（MPS）ansatz to efficiently compress the wave function of one-dimensional systems and can be used to calculate the static electronic correlations of dozens of active orbitals with high precision.However,for the accurate quantitative characterization of the electronic structure of strongly correlated systems,it is necessary to perform high-precision post-DMRG dynamic electronic correlation calculations in hundreds or even more inactive orbitals.Currently,the widely-used post-DMRG meth-ods based on internal contraction approximation are subject to the expensive costs of computing and saving high-order reduced density matrices,and inapplicable for dy-namic electronic correlation calculations for systems with more than 30 active orbitals.To address the above challenges,we proposed a method of transforming the DMRG wave function to a multi-configurational wave function by using the genetic algorithm corporating with orbital entanglement entropies.Then we developed a new DMRG-MRCI implementation based on the selected configuration interaction（Selected CI）method and external contraction approximation.This method broke through the limit of 30 active orbitals in dynamic correlation calculations and proved to be an effective theoretical tool for high-precision calculations of strongly correlated molecules.The works are listed below in detail,1.We proposed an efficient scheme to transform the ab-initio quantum chemistry amiltonian to compact matrix product operator（MPO）tensors.For N active or- bitals,the number of operator terms in the Hamiltonian could be N⁴（e.g.several hundreds of thousands for dozens of active orbitals）,the size of the MPO tensors constructed using our method is generally only thousands.Besides,we imple- mented a new MPS-based ab-initio quantum chemistry DMRG software,and then we combined DMRG with the second-order complete active space self-consistent field（CASSCF）method to implement a new DMRG-CASSCF program.Compared with the implementation of the DMRG-CASSCF method in Molcas,our program can significantly reduce the number of macro iterations during orbital optimization and avoid lots of repetitive and expensive DMRG single-point calculations.2.By introducing orbital entanglement entropy into the genetic algorithm,we pro- posed the entanglement-driven genetic algorithm（EDGA）to efficiently construct a CI-type multi-configurational wave function from the MPS state generated by the DMRG method.The benchmarks against conjugated molecules and transition metal systems proved that the EDGA program could construct an accurate approx- imation of the exact CASCI wave function while traversing only a tiny part of the whole configuration space.The EDGA program can be used to analyze the ex- citation modes,configuration weights,and other properties of an MPS state and construct the reference wave function for subsequent multi-reference calculations.3.Based on the approximated CASCI wave function constructed by the EDGA pro- gram,we combined the Selected CI method and the external contraction approxima- tion and proposed a new DMRG-MRCI implementation.Unlike the usual internally contracted methods,the externally contracted DMRG-MRCI method avoids com- puting and saving the complete high-order reduced density matrices in the active space,which makes it practical for dynamic correlation evaluations of the systems with even more than 40 active orbitals.We tested the externally contracted DMRG-MRCI method by computing the dissociation curve of Cr₂,the energy gap between the singlet and triplet states of the polyacene molecules as well as the ground state energy of the europium complex Eu-BTBP（NO₃）₃and the results proved the effec-tiveness of this method.