Ideas of Quantum Chemistry P44 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 396 8. Electronic Motion in the Mean Field Atoms and Molecules LOCALIZATION OF MOLECULAR ORBITALS WITHIN THE RHF METHOD The canonical MOs derived from the RHF method are usually delocalized over the whole molecule . their amplitudes are significant for all atoms in the molecule. This applies however mainly to high energy MOs which exhibit a similar AO amplitude for most atoms. Yet the canonical MOs of the inner shells are usually very well localized. The canonical MOs are occupied as usual by putting two electrons on each low lying orbital the Pauli exclusion principle . The picture obtained is in contrast to chemical intuition which indicates that the electron pairs are localized within the chemical bonds free electron pairs and inner atomic shells. The picture which agrees with intuition may be obtained after the localization of the MOs. The localization is based on making new orbitals as linear combinations of the canonical MOs a fully legal procedure see p. 338 . Then the determinantal wave function as shown on p. 338 expressed in the new spinorbitals takes the form f det A . For obvious reasons the total energy will not change in this case. If linear transformation applied is an orthogonal transformation . ATA 1 or a unitary one A A 1 then the new MOs preserve orthonormality like the canonical ones as shown on p. 339. We emphasize that we can make any nonsingular109 linear transformation A not only orthogonal or unitary ones. This means something important namely the solution in the Hartree-Fock method depends on the space spanned by the occupied orbitals . on the set of all linear combinations which can be formed from the occupied MOs and not on the orbitals only. The new orbitals do not satisfy the Fock equations these are satisfied by canonical orbitals only. The localized orbitals being some other orthonormal basis set in the space spanned by the canonical orbitals satisfy the Fock equation with the off-diagonal Lagrange multipliers.
