  In chemistry and condensed matter physics the solution of simple paradigm
systems, such as the hydrogen atom and the uniform electron gas, plays a
critical role in understanding electron behaviors and developing electronic
structure methods. The H$_2$ molecule is a paradigm system for strong
correlation with a spin-singlet ground state that localizes the two electrons
onto opposite protons at dissociation. We extend H$_2$ to a new paradigm system
by using fractional nuclear charges to break the left-right nuclear symmetry,
thereby enabling the competition between strong correlation and charge transfer
that drives the exotic properties of many materials. This modification lays a
foundation for improving practical electronic structure theories and provides
an extendable playground for analyzing how the competition appears and evolves.
