Coulomb energy transition metal complexes

Cr(C6Hii)4 is tetrahedral and a triplet however, square-planar discriminating factor. Another factor at work in these molecules is the spin pairing energies. As indicated previously, 3d valence orbitals are considerably more contracted that 4d and 5d thus the Coulomb repulsion integrals are much larger for first-row transition metal complexes and high-spin states are more favored than is the case for second and third row complexes. 

Such a balance between the one- and two-electron terms in the energy play important roles in several places in chemistry. For example the relative stability of high spin (large P/A ) and low spin (small P/A ) octahedral transition metal complexes is set by a similar ratio. Here P is the pairing energy associated with a pair of electrons (a combination of exchange and coulomb terms) and A the ej splitting. In fact there are observations from molecular coordination chemistry which are of use to... 

In 1933 Herzberg and Teller demonstrated that certain electronic transitions which are forbidden in the fixed nuclei approximation may attain a non-zero transition probability through the interaction of electronic and nuclear motions. What they essentially did was to note that in every molecule there exist asymmetric nuclear displacements which yield a non-zero expectation value for the gradient of the nuclear-electronic coulombic energy terms. To illustrate their mode of thought we shall here give a pictorial outline of the calculation of such vibronic intensities in two systems of current interest aromatic compounds and transition metal complexes. For the sake of clarity we shall limit our discussion to the exemplary molecular systems of benzene and potassium titanium hexafluoride (KjTiFg). 

In the earliest implementation applied to molecular problems, K. Johnson [39] used scattered-plane waves as a basis and the exchange-correlation energy was represented by (13). This SW-Xa method employed in addition an (muffin-tin) approximation to the Coulomb potential of (17) in which Vc is replaced by a sum of spherical potentials around each atom. This approximation is well suited for solids for which the SW-Xa method originally was developed [40]. However, it is less appropriate in molecules where the potential around each atom might be far from spherical. The SW-Xa method is computationally expedient compared to standard ab initio techniques and has been used with considerable success [41] to elucidate the electronic structure in complexes and clusters of transition metals. However, the use of the muffin-tin approximation precludes accurate calculations of total energies. The method has for this reason not been successful in studies involving molecular structures and bond energies [42]. 

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