How would you interpret the partial charges if the basis functions are orthonormal? See Szabo Eq (3.196) and (3.197).
if orthonormal basis then overlap matrix S_ij = integral{dr phi^*_i(r) phi_j} = delta_ij = Identity, so we can use 3.196/3.197 and get the same result...
3.196) q_atom = z_atom - sum_{mu in A}(PS)_(mu mu) = z_atom -(tr(P) - P_{mu mu not in A} )so we just take the diagonal elements of density matrix for wavefunctions center on the atom we want and subtract the sum of those from the nuclear charge
3.197)q_atom = z_atom - sum_{mu in A}(S^{alpha}P S^{alpha -1})_{mu mu} but S^alpha = I^alpha = I^(alpha -1) = I
so q_atom = z_atom - sum_{mu in A}( I P I)_{mu mu} = z_atom - sum_{mu in A} P_{mu mu} which is same as above written a little differently
no?
(is there any way to use latex formatting ? )
Jason,
this was generated with TTH (see http://hutchinson.belmont.ma.us/tth/)
Other alternatives are LaTeX2HTML and maybe Hyperlatex.
TTH creates HTML, which might be better than generating images. To generate the formula above, I used this link http://hutchinson.belmont.ma.us/tth/tthform.html and copy-and-paste into the forum. If an image needs to be used, it can be inserted by using "Insert Media" button. The inline image below was generated with Word (type in the formula, save as html, and use the saved PNG image).