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 H2 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 H2 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.