  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 structure of complex molecules and materials. However,
traditionally, two-electron wavefunctions (geminals), have not enjoyed the
popularity and widespread use of the more standard single-particle methods.
This has changed recently, with a renewed interest in the development of
geminal wavefunctions as an alternative to describing strongly-correlated
phenomena. Hence, there is a need to find geminal methods that are accurate,
computationally-tractable, and do not demand significant input from the user
(particularly, via cumbersome and often ill-behaved orbital optimization
steps). Here we propose new families of geminal wavefunctions, inspired by the
pair Coupled Cluster (pCCD) ansatz. We present a new hierarchy of two-electron
wavefunctions that extend the one-reference orbital idea to other geminals.
Moreover, we show how to incorporate single-like excitations in this framework,
without leaving the quasiparticle picture. We explore the role of imposing
seniority restrictions on these wavefunctions, and benchmark these new methods
on model strongly-correlated systems.
