A Reduced Scaling Approach to Obtaining Embedding Orbital Coefficients: Benchmarking DMET-CCSD(T) Relative Energies in Water Clusters

We present a method to significantly reduce the computational scaling of the post-Hartree- Fock (post-HF) component in Density Matrix Embedding Theory (DMET) calculations by exploiting the exponential decay properties of both the mean-field density matrix and the or- bital transformation matrix. Additionally, we extend this reduced-scaling approach to calculate the coupled-cluster CCSD(T) density matrix, facilitating DMET-CCSD(T) energy evaluations through a back-transformed energy formula. The accuracy of relative electronic energies is benchmarked using the all-electron solver, Lowdin-partitioned fragments, and fragments de- rived from Intrinsic Atomic Orbital and Projected Atomic Orbital (IAO+PAO) partitioning schemes. Our results demonstrate that, with appropriate utilization of the decay of one particle density matrix (1-PDM), the evaluation of the post-HF energy can achieve asymptotically linear scaling. Furthermore, for relative electronic energies calculations, Lowdin partitioning 1 performs well in weakly interacting systems, such as water clusters. This study underscores the potential of reduced-scaling techniques to improve computational efficiency and the efficacy of CCSD(T) solvers in delivering accurate thermochemical predictions in weakly interacting systems.