  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.
