It has been given in a book and on Wikipedia that:
hard bases have highest-occupied molecular orbitals (HOMO) of low energy, and hard acids have lowest-unoccupied molecular orbitals (LUMO) of high energy.
soft bases have HOMO of higher energy than hard bases, and soft acids have LUMO of lower energy than hard acids. (However the soft-base HOMO energies are still lower than the soft-acid LUMO energies.)
Let us consider the energy difference between HOMO and LUMO is given by $\Delta E$. Thus, $$\Delta E (S-S)<\Delta E(H-S) < \Delta E (H-H)$$
Hence the hard-hard interaction should have been weaker than hard-soft, which is not the case. Please explain.
P.S.: I went through the reference (Meissler and Tarr) and this question but could not find a satisfying explanation.