Richardson-Gaudin geminal wavefunctions in a Slater determinant basis
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Richardson‑Gaudin geminal wavefunctions in a Slater determinant basis Charles‑Émile Fecteau1 · Frédéric Berthiaume1 · Meriem Khalfoun1 · Paul Andrew Johnson1 Received: 17 September 2020 / Accepted: 16 November 2020 © Springer Nature Switzerland AG 2020
Abstract Geminal wavefunctions have been employed to model strongly-correlated electrons. These wavefunctions represent products of weakly-correlated pairs of electrons and reasonable approximations are computable with polynomial cost. In particular, Richardson-Gaudin states have recently been employed as a variational ansatz. This contribution serves to explain the Richardson-Gaudin wavefunctions in the conventional language of quantum chemistry. Keywords Geminal wavefunctions · Strong electron correlation · RichardsonGaudin wavefunctions
1 Introduction Strong electron correlation remains an unsolved problem in quantum chemistry. In such systems the orbital picture breaks down and thus methods built upon a meanfield of electrons such as Hartree-Fock (HF) or Kohn-Sham Density Functional Theory are not sufficiently accurate. In such cases, it is often more productive to employ wavefunctions built from weakly-interacting pairs of electrons, i.e. geminals. Geminals were considered early in quantum chemistry [1–3], though long before the availability of commercial software. Recently, there has been a strong renewed interest in these types of wavefunctions [4–20]. In particular, the antisymmetric product of 1-reference orbital geminals (AP1roG), or equivalently pair coupled-cluster doubles (pCCD), has been found to describe the energetics of many bond-breaking processes quite well. The physical wavefunction is however not always clean in terms of geminals: if more than one pairing-scheme is required, then inter-geminal correlation will be strong and the wavefunction expression in terms of geminals is complicated. * Paul Andrew Johnson [email protected] 1
Département de chimie, Université Laval, 1045 avenue de la Médecine, Québec, Québec G1V 0A6, Canada
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Journal of Mathematical Chemistry
Recently we have employed another geminal wavefunction, the RichardsonGaudin (RG) states [21–24], as a variational ansatz for strongly-correlated electrons [25]. The results were promising though there remain issues to be addressed before it could be considered a black-box approach. These wavefunctions are also being employed in nuclear structure theory [26] as well as condensed matter physics [27]. The advantage of RG states is that they are eigenvectors of model Hamiltonians. See refs [28, 29] for a large variety of model Hamiltonians possible. Thus we have not a single wavefunction, but a complete set with which to construct perturbation theories and Green’s functions in an analogous fashion to many-body theories built upon Hartree-Fock. Indeed this is our intention. The intermediate developments are tricky, but the final expressions are simple [30]. Along similar lines, the group of Scuseria has built a mean-field theory based on the antisymm
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