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We introduce a novel three-body correlation factor that is designed to vanishin the core region around each nucleus and approach a universal two-bodycorrelation factor for valence electrons. The Transcorrelated Hamiltonian isused to optimize the orbitals of a single Slater determinant within abiorthonormal framework. The Slater-Jastrow wave function is optimized on a setof atomic and molecular systems containing both second-row elements and $3d$transition metal elements. The optimization of the correlation factor and theorbitals, along with increasing the basis set, results in a systematic loweringof the Variational Monte Carlo energy for all systems tested. Importantly, theoptimal parameters of the correlation factor obtained for atomic systems aretransferable to molecules. Additionally, the present correlation factor iscomputationally efficient, using a mixed analytical-numerical integrationscheme that reduces the costly numerical integration from $\mathbb{R}^6$ to$\mathbb{R}^3$.

Bi-orthonormal orbital optimization with a cheap core-electron free three-body correlation factor for Quantum Monte Carlo and Transcorrelation