I'm considering a molecule made by three atoms, each a vertex of an equilateral triangle. Each atom has a covalent bond with its neighbours, sharing their only valence electron. I must estimate the energy gain when creating the molecule, using tight binding theory.
How much is the energy gain when the molecule is created?
The Attempt at a Solution
I used tight binding theory and named each atom's orbital |1>,|2> and |3>. Assuming that [tex] <i|H|j>=-t (hopping) [/tex] if [tex] i\neq j [/tex] and [tex] <i|H|j>= \epsilon _0 [/tex] if [tex] i=j [/tex]. I wrote my 3x3 matrix and calculated the eigenvalues which are-2t, t and t. The solutions tell that the energy gain is -2t-2t+t = -3t and I don't understand why.