Gauge symmetry, chirality and parity effects in four-particle systems: Coulomb's law as a universal function for diatomic molecules

• Published in: Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy Molecular and biomolecular spectroscopy, 2000-11, Vol.56 (12), p.2273-2331
• Main Author: Van Hooydonk, G.
• Format: Article
• Language: English
• Subjects: Antimatter; Cesium - chemistry; Chemical Phenomena; Chemistry, Physical; Chiral symmetry; Gauge symmetry; Heitler–London theory; Hydrogen - chemistry; Hydrogen-antihydrogen four particle systems; Inorganic Chemicals - chemistry; Lithium Compounds - chemistry; Models, Chemical; Potential energy curves; Static Electricity
• ISSN: 1386-1425
• DOI: 10.1016/S1386-1425(00)00298-5

Following recent work in search for a universal function (Van Hooydonk, Eur. J. Inorg. Chem., (1999), 1617), we test four symmetric ± a n R n potentials for reproducing molecular potential energy curves (PECs). Classical gauge symmetry for 1/ R-potentials results in generic left–right asymmetric PECs. A pair of symmetric perturbed Coulomb potentials is quantitatively in accordance with observed PECs. For a bond, a four-particle system, charge inversion (a parity effect, atom chirality) is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms and to a soluble Bohr-like formula, a Kratzer (1− R e/ R) 2 potential. The result is similar to the combined action of spin and wave function symmetry upon the Hamiltonian in Heitler–London theory. Analytical perturbed Coulomb functions varying with (1− R e/ R) scale attractive and repulsive branches of PECs for 13 bonds H 2, HF, LiH, KH, AuH, Li 2, LiF, KLi, NaCs, Rb 2, RbCs, Cs 2 and I 2 in a single straight line. The 400 turning points for 13 bonds are reproduced with a deviation of 0.007 Å at both branches. For 230 points at the repulsive side, the deviation is 0.003 Å. The perturbed electrostatic Coulomb law is a universal molecular function. Ab initio zero molecular parameter functions give PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting levels and gives a first principle's comparison of short- and long-range interactions, important for the study of cold atoms. Wave-packet dynamics, femto-chemistry applied to the crossing of covalent and ionic curves, can provide evidence for this theory. We anticipate this scale/shape invariant scheme applies to smaller scales in nuclear and high-energy particle physics. For larger gravitational scales (Newton 1/ R potentials), problems with super-unification are discussed. Reactions between hydrogen and antihydrogen, feasible in the near future, will probably produce normal H 2.