Coupled clusters and coulomb correlations

Jacob Townsend, Konstantinos D. Vogiatzis

Solving the coupled-cluster (CC) equations is a cost-prohibitive process that exhibits poor scaling with system size. These equations are solved by determining the set of amplitudes ( t ) that minimize the system energy with respect to the coupled-cluster equations at the selected level of truncation. Here, a novel approach to predict the converged coupled-cluster singles and doubles (CCSD) amplitudes, thus the coupled-cluster wave function, is explored by using machine learning and electronic structure properties inherent to the MP2 level. Features are collected from quantum chemical data, such as orbital energies, one-electron Hamiltonian, Coulomb, and exchange terms. The data-driven CCSD (DDCCSD) is not an alchemical method because the actual iterative coupled-cluster equations are solved. However, accurate energetics can also be obtained by bypassing solving the CC equations entirely. Our preliminary data show that it is possible to achieve remarkable speedups in solving the CCSD equations, especially when the correct physics are encoded and used for training of machine learning models.

Josef Paldus

Artur Nowak, Örs Legeza, Katharina Bogusławski

Wave functions based on electron-pair states provide inexpensive and reliable models to describe quantum many-body problems containing strongly correlated electrons, given that broken-pair states have been appropriately accounted for by, for instance, a posteriori corrections. In this article, we analyze the performance of electron-pair methods in predicting orbital-based correlation spectra. We focus on the (orbital-optimized) pair-coupled cluster doubles (pCCD) ansatz with a linearized coupled-cluster (LCC) correction. Specifically, we scrutinize how orbital-based entanglement and correlation measures can be determined from a pCCD-tailored CC wave function. Furthermore, we employ the single-orbital entropy, the orbital-pair mutual information, and the eigenvalue spectra of the two-orbital reduced density matrices to benchmark the performance of the LCC correction for the one-dimensional Hubbard model with the periodic boundary condition as well as the N2 and F2 molecules against density matrix renormalization group reference calculations. Our study indicates that pCCD-LCC accurately reproduces the orbital-pair correlation patterns in the weak correlation limit and for molecules close to their equilibrium structure. Hence, we can conclude that pCCD-LCC predicts reliable wave functions in this regime.

Werner Kutzelnigg

Isaiah Shavitt, Rodney J. Bartlett

Ramón Alain Miranda‐Quintana, Rugwed A. Lokhande, Carlos E. V. de Moura +2 more

We introduce a novel class of coupled cluster (CC) methods that leverage the seniority concept to enhance efficiency and accuracy in electronic structure calculations. While existing approaches, such as the pair coupled cluster doubles (pCCD) method, are limited to seniority-zero (Ω = 0) wavefunctions,1 we propose a more flexible framework: seniority-restricted coupled cluster (sr-CC). This new methodology selectively constrains the seniority sectors accessible through excitation operators in the cluster expansion, enabling a more systematic exploration of electron correlation effects. By balancing computational cost and accuracy, sr-CC provides a promising pathway for advancing electronic structure theory, particularly in strongly correlated systems.