The 4-particle hydrogen-antihydrogen system revisited

Abstract.

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-$\bar {\rm H}$ systems are inconsistent with the logic behind algebraic Hamiltonians H± =H 0 ± ΔH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H2 and H$\bar {\rm H}$. Their eigenvalues E± =E 0± β 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 antiatom $\bar {\rm H}$. 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 H$\bar {\rm H}$. 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, H$\bar {\rm H}$, 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 antihydrogen $\bar {\rm H}$, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic $\bar {\rm H}$ and molecular H$\bar {\rm H}$, including the problem with antimatter in the Universe.