  Understanding many-electron phenomena with competing near-degenerate
electronic states is of fundamental importance to chemistry and condensed
matter physics. One of the most significant challenges for exploring such
many-electron phenomena is the necessity for large system sizes in order to
realize competing states, far beyond those practical for first-principles
methods. Here, we show how allowing non-integer nuclear charges expands the
space of computationally tractable electron systems that host competing
electronic states. The emergence of competing electronic states from
non-integer nuclear charges is exemplified in the simple 2-electron H_{2}
molecule and used to examine the microscopic structure of doped quasi-1D
cuprate chains, showing how non-integer nuclear charges can open a window for
first-principles calculations of difficult many-electron phenomena.
