  Neural wave functions accomplished unprecedented accuracies in approximating
the ground state of many-electron systems, though at a high computational cost.
Recent works proposed amortizing the cost by learning generalized wave
functions across different structures and compounds instead of solving each
problem independently. Enforcing the permutation antisymmetry of electrons in
such generalized neural wave functions remained challenging as existing methods
require discrete orbital selection via non-learnable hand-crafted algorithms.
This work tackles the problem by defining overparametrized, fully learnable
neural wave functions suitable for generalization across molecules. We achieve
this by relying on Pfaffians rather than Slater determinants. The Pfaffian
allows us to enforce the antisymmetry on arbitrary electronic systems without
any constraint on electronic spin configurations or molecular structure. Our
empirical evaluation finds that a single neural Pfaffian calculates the ground
state and ionization energies with chemical accuracy across various systems. On
the TinyMol dataset, we outperform the `gold-standard' CCSD(T) CBS reference
energies by 1.9m$E_h$ and reduce energy errors compared to previous generalized
neural wave functions by up to an order of magnitude.
