Seniority-zero wavefunction parameterizations

Wave function methods tailored to seniority-zero Hamiltonians have emerged as practical tools for describing strong (static) electron correlation while retaining computational tractability. The seniority quantum number counts unpaired electrons; setting it to zero restricts the wave function to doubly occupied or empty spatial orbitals, yielding geminal-based ansätze and a Hilbert space that scales as the square root of the full configuration space. This structure enables inexpensive evaluation of reduced density matrices—up to fourth order—facilitating post-geminal treatments of dynamic correlation. We review the main families of seniority-zero (pair-preserving) wave functions, from the antisymmetric product of geminals (APG) and its interacting (APIG) and strongly orthogonal (APSG) reductions, through generalized valence bond/perfect pairing (GVB-PP), to modern mean-field–cost approaches such as AP1roG (equivalent to pair coupled cluster). For each, we summarize formal properties (size consistency/extensivity), computational scaling, typical accuracy, and common add-ons for recovering missing dynamic correlation (perturbation theory, density functionals, multireference coupled cluster). We close by outlining opportunities for future development.