Related papers: Richardson-Gaudin geminal wavefunctions in a Slate…
This chapter gives an overview of Richardson-Gaudin states which represent weakly correlated pairs of electrons. They are parametrized by sets of numbers obtained from non-linear equations. The best method to solve these equations is…
Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly-interacting pairs of…
Richardson-Gaudin (RG) states are employed as a variational wavefunction ansatz for strongly correlated isomers of H$_4$ and H$_{10}$. In each case a single RG state describes the seniority-zero sector quite well. Simple natural orbital…
Geminal wavefunctions, introduced in the late 1950s, have long been recognized for their ability to compactly capture strong electron correlation. Despite their promise, they were historically overshadowed by more computationally efficient…
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes, to the promise of serving as building blocks of quantitative descriptions of the electronic…
We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of…
Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analogue of Wick's theorem for fermions or bosons. This expression is in general…
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction Ansatz for strongly-correlated electronic systems. These states are geminal products whose coefficients…
We develop a bivariational principle for an antisymmetric product of nonorthogonal geminals. Special cases reduce to the antisymmetric product of strongly-orthogonal geminals (APSG), the generalized valence bond-perfect pairing (GVB-PP),…
Wavefunction forms based on products of electron pairs are usually constructed as closed-shell singlets, which is insufficient when the molecular state has a nonzero spin or when the chemistry is determined by $d$- or $f-$electrons. A set…
Strongly correlated systems are well described as a configuration interaction of Slater determinants classified by their number of unpaired electrons. This treatment is however unfeasible. In this manuscript, it is demonstrated that single…
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this…
We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an Antisymmetrized Geminal Power (AGP), based upon singlet pairs between electrons, is particularly suited for describing the electronic…
Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally capture static correlation in…
Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson-Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical…
Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost…
We introduce a simple generalization of the well known geminal wavefunction already applied in Quantum Chemistry to atoms and small molecules. The main feature of the proposed wavefunction is the presence of the antisymmetric geminal part…
We analyze wave functions constructed as a sum of product of two-electron functions, or as a polynomial of geminals, to investigate their ability to represent the ground state of a strongly correlated few-body system. The known difficulty…
Strong pairing correlations are responsible for superconductivity and off-diagonal long range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that…
Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a…