Construction of downfolded Hamiltonians from projective transcorrelation

Abstract: Projective transcorrelation recovers the short-range electron correlation by a similarity transformation with a geminal function $f(r_{12})$, at the cost of an effective Hamiltonian containing a 3-body term. We replace the term by an effective operator of rank at most two, obtained from the two-body cumulant (2C) approximation to the three-particle reduced density matrix. The 2C 3-body energy is written without cumulants, and the effective one- and two-body interactions are derived as its partial derivatives with respect to the reduced density matrices. The truncation is assessed on the atomization and reaction energies of the HEAT set with CCSD(T), and on the CAS-pTC model, whose downfolded Hamiltonian is held on a qubit register with the number of Pauli strings reduced from the sixth power of the orbital count to the fourth.