I'm trying to explain the 3c-2e bridge-bonds in Diborane using L.C.A.O. method, to construct M.O. and show that the situation is bonding.
Now,for simplicity let us try to explain only one of the bridge-bonds in diborane.
I am considering 2 sp3 hybrid orbitals from the two boron atoms, and the s-orbital of hydrogen- involving a total of 3 atomic orbitals. We are to fill these with two electrons.
I understand that number of atomic orbitals combining should give the same number of molecular orbitals, right? That means I should get three molecular orbitals.
Now- I can-not get three MOs by LCAO. I'm getting 4.
One of them is bonding - which is formed by in-phase overlap of all three orbitals.
Two of them are non-bonding- each one being formed by in-phase overlap of the s-orbital and one sp3 orbital but out-of-phase overlap of the other sp3 orbital.
One of them is anti-bonding - which is formed by out of phase overlap of both the sp3 hybrid orbitals with the s-orbital of hydrogen.
Where am I going wrong? What should be the proper combination?