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### The Equations for the Orbitals

The orbitals are the solution of a Schrodinger-like equation
 (31)
where  is the orbital energy, F is the hamiltonian (in the molecular orbital approximation). If we substitute the MO-LCAO expression we get
 (32)
Multiply on the left  and integrate to give
 (33)
where we have introduced the notation
 (34) (35)
We can therefore write the equations
 (36)
or
 (37)
These are of course the secular equations and they have been written in an eigenvector notation.

Next: Valence-Bond Theory Up: Contents - Previous: The Molecular Orbital Wavefunction

Nicholas Handy

1998-09-23