Transcorrelated coupled cluster methods. II. Molecular systems

Abstract

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.

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

“…To do this, we chose what might be considered “minimal” test systems. However, as has been done on “conventional” hardware, ,,,,, in future work, we will extend the application of TC approach to larger molecular systems than studied here. Additionally, we will develop new methodologies to obtain not only energy estimates, but also properties in the form of unbiased density matrices, and consequently, combine the TC approach with self-consistent orbital optimization. − /embedding, − spin-conserving schemes, − as well as adaptive quantum circuit Ansätze. − …”

“…It has been found that when optimizing the Jastrow factor by minimizing the variance of the TC reference energy, as done in this work, the results usually converge to the CBS limit from above. Additionally, in this and all recent studies using the TC approach (combined with a variety of methods and applied to different types of problems), 48,49,[55][56][57]78,86 the amount by which the TC results falls below the CBS limit is in all cases small enough to be safely ignored in practice.…”

“…The applicability of these types of approximations must be carefully considered for each studied system. However, the N 4 -scaling method introduced in ref ( 78 ) has recently been applied to the entire “HEAT” benchmark set 98 and the N 5 scaling approximation has been used in ref ( 59 ) for all first-row atoms, as well as the molecular systems CH 2 , FH and H 2 O, and in ref ( 55 ) for relative energies of molecular systems.…”

“…In the TC approach, ,,,− a correlated Ansatz–exactly incorporating the cusp condition–is applied and used to perform a similarity transformation of the electronic Hamiltonian, H ̂, describing the ab initio chemical system. The undisputed benefit of the TC method is that it yields highly accurate results with very small basis set expansions ,, and thus reduces the number of required qubits as well as the circuit depth on a quantum computer.…”

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

“…Motivated by the inherent advantages of such an approach, including the precise description of dynamic correlation and the consequential ability to employ a significantly reduced one-electron basis set size for accurate calculations, various strategies have been proposed to mitigate the complexity of the ansatz while retaining its benefits: examples are variational Hylleraas-configuration interaction (Hylleraas-CI), − usage of explicitly correlated Gaussian (ECG) wave functions, − or transcorrelated (TC) approaches. − These methods are generally linked with significant computational costs, limiting their applicability to small system sizes. Nevertheless, the growing interest in the advancement of TC methods has recently resulted in several promising approaches that enable highly accurate calculations. − …”