Multiphoton transitions for the harmonic oscillator

2- and 3-photon electric dipole transitions for the harmonic oscillator are shown to have zero intensity. This is extended to the general cases of Δv?=?n and Δv?=?n???2 for n-photon transitions. Although not proved in general, it seems likely that all multiphoton transition moments vanish. This suggests that electric dipole multiphoton transition intensity is due to anharmonicity.     

Evidence for d orbital aromaticity in square planar coinage metal clusters

Quantitative evidence for the existence of aromaticity involving the d orbitals of transition metals is provided for the first time. The doubly bridged square planar (D(4)(h)()) coinage metal clusters (M(4)Li(2), M = Cu (1), Ag (2), and Au (3)) are characterized as aromatic by their substantial nucleus independent chemical shifts (NICS) values in the centers (-14.5, -14.1, and -18.6, respectively). Nevertheless, the participation of p orbitals in the bonding (and cyclic electron delocalization) of 1-3 is negligible. Instead, these clusters benefit strongly from the delocalization of d and to some extent s orbitals. The same conclusion applies to Tsipis and Tsipis' H-bridged D(4)(h)() Cu(4)H(4) ring (4). Canonical MO-NICS analysis of structures 1-3 shows the total diatropic d orbital contributions to the total NICS to be substantial, although the individual contributions of the five sets of filled d orbitals vary. The d orbital aromaticity of Cu(4)Li(2) also is indicated by its atomization energy, 243.2 kcal/mol, which is larger than Boldyrev's doubly (sigma and pi) aromatic Al(4)Li(2) (215.9 kcal/mol).