Gauge symmetry, chirality and parity violation in four-particle systems:   Coulomb's law as a universal molecular function
  Following recent work in search of a universal function (Van Hooydonk, Eur J Inorg Chem, 1999, 1617), we test symmetric potentials for reproducing molecular potential energy curves (PECs). For a bond, a four-particle system, charge inversion is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms. The analytical perturbed Coulomb function scales attractive and repulsive branches of 13 PECs (HH, HF, LiH, KH, AuH, LiLi, LiF, KLi, NaCs, RbRb,RbCs, CsCs and II) in a single straight line. Turning points are reproduced with a deviation of 0.3 % (0.007 angstrom). At the repulsive side, the deviation is 0.2 % (0.003 angstrom). The ab initio zero molecular parameter function gives PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting energy levels. The theory may be tested with femtochemistry. Reactions between hydrogen and anti-hydrogen, feasible in the near future, will probably produce normal HH. 
G. Van Hooydonk