Orbital magnetic, orthogonal

The difference in magnetic properties between the manganese and copper complexes was explained by the difference of their magnetic orbitals of metal ions d y, dy, d z, dx2.y2, d dz2 for Mn(II) ion and dx2-yi for Cu(II) ion. In the former, some of the d- orbitals containing the unpaired elelctron can overlap with the JT-obital of the ligand, while, in the latter, the dx2 y2 orbital is orthogonal to the ligand Ji-obital. 

Assuming orthogonality of AOs centered at different atoms, and orthonormal basis functions centered at one particular atom, we finally obtain the following expression for the d-orbital contribution to the orbital magnetic moment < fif > ... 

Let us now proceed to E2- and M 1-transitions. Formulas of the sort (30.7) hold for 2-transitions, too. The magnetic dipole transition operator Omi has no radial part. Since the orthogonal radial orbitals are used in calculations, the operators and do not contribute to the... 

In Section 1.4, we discussed the history and foundations of MO theory by comparison with VB theory. One of the important principles mentioned was the orthogonality of molecular wave functions. For a given system, we can write down the Hamiltonian H as the sum of several terms, one for each of the interactions which will determine the energy E of the system the kinetic energies of the electrons, the electron-nucleus attraction, the electron-electron and nucleus-nucleus repulsion, plus sundry terms like spin-orbit coupling and, where appropriate, other perturbations such as an applied external magnetic or electric field. We now seek a set of wave functions P, W2,... which satisfy the Schrodinger equation ... 

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