The 4-particle hydrogen-anti-hydrogen system revisited. Twofold molecular Hamiltonian symmetry and natural atom anti-hydrogen

The historical importance of the original quantum mechanical bond theory proposed by Heitler and London in 1927 as well as its pitfalls are reviewed. Modern ab initio treatments of H-H-bar systems are inconsistent with the logic behind algebraic Hamiltonians H± = H0 ± ΔH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H2 and HH-bar. Their eigenvalues are exactly those of 1927 Heitler-London (HL) theory. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H2. A wrong choice leads to problems with anti-atom H-bar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H2. Their theory explains the stability of attractive system H2 with a repulsive Hamiltonian H0 + ΔH instead of with the attractive one H0 - ΔH, representative for charge-asymmetrical system HH-bar. A new second order symmetry effect is detected in this attractive Hamiltonian, which leads to a 3-dimensional structure for the 4-particle system. Repulsive HL Hamiltonian H+ applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H- takes over and leads to bond H2 but in reality, HH-bar, for which we give an analytical proof. This analysis confirms and generalizes an earlier critique of the wrong long range behavior of HL-theory by Bingel, Preuss and Schmidtke and by Herring. Another wrong asymptote choice in the past also applies for atomic anti-hydrogen H-bar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic H-bar and molecular HH-bar, including the problem with antimatter in the Universe. (author)