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We explore the applicability of the transcorrelated method to the elements in the second row of the periodic table. We use transcorrelated Hamiltonians in conjunction with full configuration interaction quantum Monte Carlo and coupled cluster techniques to obtain total energies and ionisation potentials, investigating their dependence on the nature and size of the basis sets used. Transcorrelation accelerates convergence to the complete basis set limit relative to conventional approaches, and chemically accurate results can generally be obtained with the cc-pVTZ basis, even with a frozen Ne core in the post-Hartree--Fock treatment., Comment: 11 pages, 5 figures

An efficient implementation for approximate inclusion of the three-body operator arising in transcorrelated methods via exclusion of explicit three-body components (xTC) is presented and tested against results in the "HEAT" benchmark set [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)]. Using relatively modest basis sets and computationally simple methods, total, atomization, and formation energies within near-chemical accuracy from HEAT results were obtained. The xTC ansatz reduces the nominal scaling of the three-body part of transcorrelation by two orders of magnitude to O(N^5) and can readily be used with almost any quantum chemical correlation method.

We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at the level of singles and doubles excitations. Our results show that already with the cc-pVTZ basis the transcorrelated distinguishable cluster method gets close to complete basis limit and near full configuration interaction quality values for relative energies of over thirty atoms and molecules. To gauge the performance in different correlation regimes we also investigate the breaking of the nitrogen molecule with transcorrelated coupled cluster methods. Numerical evidence is presented to further justify an efficient way to incorporate the major effects coming from the three-body integrals without explicitly introducing them into the amplitude equations., Comment: peer-reviewed and accepted manuscript (J. Chem. Phys.)

We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians, and show applications in \emph{ab initio} molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron-electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by some recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem; but this is currently limited to treating the ground state, and has lower efficiency than the time-independent DMRG (TI-DMRG), due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. Accelerated basis set convergence rate is also observed, as expected, within the TC framework.