Bond distance offset

We may now check the quality of the bond distance offsets between the 5f and the states by calculating the band shape of the absorption and/or emission bands. It is well known that the shape of an absorption or emission band between different electronic states is mainly controlled by the equilibrium distance offset on the totally symmetric vibrational coordinate and by its vibrational frequency in the initial and final states. This is often used for the... 

In summary, the comparison with the spectroscopical measurements available on the 5f 6d(t2g) manifold of U -doped Cs2NaYCl6 reveals that the predicted electronic origins are reliable, with positive deviations from experiment lower than 600 cm, the absorption bands are complex bands built on several electronic origins, the set of observed bands correspond to the states of the J ( H4)x5c (t2g) (Fgg) and 5/ ( H4)xdc((t2g) (F7g) configurations, and the calculated vibrational frequencies and bond distance offsets are also reliable in this material. 

Identical Ni-S and Cu-S bond distances are observed in these two structures, and the expected reduction of the ionic radius of copper is not reflected in a shorter Cu-S bond. Two possible reasons for this result are (1) a concomitant increase of the ionic radii of the sulfur donors offsets the effect of a shorter Cu(III) radius, and (2) there exists significant covalency in the Cu—S bonds. 

A possible explanation for the small change in bond distance is that, with increasing oxidation state of the metal, the d orbitals contract. This contraction may cause overlap of d orbitals in tt bonding to become less effective. Thus, as 8 electrons are removed, the tt interactions become weaker the two factors (increase in bond order and increase in oxidation state of Re) very nearly offset each other. 

In fig. 6 a clear discontinuity is seen in Ln OHj bond distances of curve A between Nd and Tb with an offset value of 0.045 A. This value agrees with the analysis of Sinha (1976) who calculated a 0.047 A decrease in the effective La radius per unit decrease in the coordination number. In the solid heptahydrate (La Pr) and hexa-hydrates (Nd-Lu), the offset value in the Ln OHj distances between the heavy and the light lanthanides is only 0.039 A. The smaller value was attributed to the differences in the structures of the heptahydrate and hexahydrales (the former form dimers with chloride bridging). 

Of course, with these alkane spacers rotation is possible about any number ofo-bonds and the convergent conformation is only one of many available to the molecule. This flexibility permits variable distances between opposing carboxyl functions. The price paid for this adjustability is the relatively low probability of any single conformation. The advantage of fine-tuning then, is somewhat offset by the entropic... 

To estimate the dispersion interaction contribution to the overall interaction between stacked rings we studied, in parallel with the role of electrostatics in Section 27.3.2, the interaction between monosubstituted benzenes Ph-X (X = H, F, NH2, Cl, CH3, OH, CN, COOH, CHO, N02) and pyridine, a simpler case with only one H-bond accepting site [58], and cytosine (with two H-bond accepting sites). An offset parallel geometry was chosen, keeping the X group and the N atom of pyridine at maximal distance, the level used being MP2/6-31G (0.25)//MP2/6-31G with BSSE correction [68]. 

Each term in (1) is represented by a simple mathematical expression as exemplified in (2), where the k are appropriate force constants, 0 are bond angles, r are torsion angles, n is the torsional periodicity parameter, is the torsion offset, p are partial atomic charge, s is the dielectric constant, A and are Lennard-Jones vdW parameters, and the summations run over bonded atom pairs (ij), angle triples (ijk) and torsional quadruples (ijkl). The nonbonded terms are summed over the distances, d,j, between unique atom pairs excluding bonded pairs and the atoms at either end of an angle triple. For the atoms at the ends of a torsion quadruple, the nonbonded term may be omitted or scaled. 

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