Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference

The many-body expansion (MBE) is an efficient tool which has a long history of use for calculating interaction energies, binding lattice and so on. In the past, applications MBE to correlation energy have been unfeasible large systems, but recent improvements computing resources sparked renewed interest in capturing using generalized $n$-th order Bethe-Goldstone equation. this work, we extend approach, originally proposed Slater determinant, tensor product state (TPS) based wavefunction. By partitioning active space into smaller orbital clusters, our approach starts from cluster mean field reference TPS configuration includes contribution excited TPSs expansion. This method, named (cMBE), improves convergence at lower orders compared directly doing block RHF reference. We present numerical results strongly correlated systems such as one- two-dimensional Hubbard models chromium dimer. performance cMBE method also tested by extended $\pi$ several $\pi$-conjugated including graphene nano-sheet with very 114 electrons orbitals, would require $10^{66}$ determinants exact FCI solution.