Orbital optimisation in xTC transcorrelated methods.

We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Additionally, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.

Two determinant distinguishable cluster.

A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.

xTC: An efficient treatment of three-body interactions in transcorrelated methods.

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 [Tajti et al., J. Chem. Phys. 121, 011599 (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(N5) and can readily be used with almost any quantum chemical correlation method.

Transcorrelated coupled cluster methods. II. Molecular systems.

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 the 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.

Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in Molecules.

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 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 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. An accelerated basis set convergence rate is also observed, as expected, within the TC framework.

Transcorrelated coupled cluster methods.

Transcorrelated coupled cluster and distinguishable cluster methods are presented. The Hamiltonian is similarity transformed with a Jastrow factor in the first quantization, which results in up to three-body integrals. The coupled cluster with singles and doubles equations on this transformed Hamiltonian are formulated and implemented. It is demonstrated that the resulting methods have a superior basis set convergence and accuracy to the corresponding conventional and explicitly correlated methods. Additionally, approximations for three-body integrals are suggested and tested.

Accuracy of the distinguishable cluster approximation for triple excitations for open-shell molecules and excited states.

The distinguishable cluster approximation for triple excitations has been applied to calculate thermochemical properties and excited states involving closed-shell and open-shell species, such as small molecules, 3d transition metal atoms, ozone, and an iron-porphyrin model. Excitation energies have been computed using the ΔCC approach by directly optimizing the excited states. A fixed-reference technique has been introduced to target selected spin-states for open-shell molecular systems. The distinguishable cluster approximation consistently improves coupled cluster with singles doubles and triples results for absolute and relative energies. For excited states dominated by a single configuration state function, the fixed-reference approach combined with high-level coupled-cluster methods has a comparable accuracy to the corresponding equation-of-motion coupled-cluster methods with a negligible amount of spin contamination.