Electronic band structure in one-dimension: A primer

Everything begins with directional wavefunction overlap in the context of tight-binding (Hückel theory) invoking the Born-Oppenheimer approximation.

Schrödinger Equation:

Of course y is the wavefunction, m is the electron mass and U is the potential

The calculation is exact and analytic if we use a H2+ion.

Ebonding < Eantibonding

Bonding orbitals occur when symmetric solution is used yH(r) + yH(r + R)

Anti-bonding orbitals occur when asymmetric solution is used yH(r) - yH(r + R)