Normal coordinates complex

More formally, the general solution can be expressed in terms of N complex normal coordinates Q( ) by the following transformation ... 

By definition (2.53) the normal coordinates Q( ) are complex quantities. For many applications and, in particular, for effecting the transition to quantum mechanics, it is more convenient to re-express the complex normal coordinates in terms of r al normal coordinates [2.2,6]. The most obvious way of expressing Q(S) in terms of real normal coordinates is as follows ... 

Some principles of normal coordinate analysis of transition metal complexes. N. Mohan, S. J. Cyvin and A. Muller, Coord. Chem. Rev., 1976, 21, 221-260 (91). 

The cocondensation of nickel atoms and CS2 at 12 K resulted in the formation of three binary, mononuclear, nickel/CS complexes, NKCSjln, n = 1-3 (145). Mixed CS2/ CS2 isotopes were used to identify the lowest stoichiometry species. An interpretation of the IR and UV-visible spectra, as well as normal-coordinate analyses (144), suggested that these species are best considered as normal 7r-complexes, with the nickel atom coordinated to the C=S bond in a manner analogous to C=C bond coordination (123). 

Warwel, S., Sojka, M., and Rusch, M. Synthesis of Dicarboxylic Acids by Transition-Metal Catalyzed Oxidative Cleavage of Terminal-Unsaturated Fatty Acids. 164, 79-98 (1993). Wexle.r, D., Zink, J. I., and Reber, C. Spectroscopic Manifestations of Potential Surface Coupling Along Normal Coordinates in Transition Metal Complexes. 171,173-204 (1994). Willett, P., see Artymiuk, P. J. 174, 73-104 (1995). 

Wexler, D., Zink, J. I., and Reber, C. Spectroscopic Manifestations of Potential Surface Coupling Along Normal Coordinates in Transition Metal Complexes. 171,173-204 (1994). 

DFT calculations were performed on Mo dinitrogen, hydra-zido(2-) and hydrazidium complexes. The calculations are based on available X-ray crystal structures, simplifying the phosphine ligands by PH3 groups. Vibrational spectroscopic data were then evaluated with a quantum chemistry-assisted normal coordinate analysis (QCA-NCA) which involves calculation of the / matrix by DFT and subsequent fitting of important force constants to match selected experimentally observed frequencies, in particular v(NN), v(MN), and 8(MNN) (M = Mo, W). Furthermore time-dependent (TD-) DFT was employed to calculate electronic transitions, which were then compared to experimental UVATs absorption spectra (16). As a result, a close check of the quality of the quantum chemical calculations was obtained. This allowed us to employ these calculations as well as to understand the chemical reactivity of the intermediates of N2 fixation (cf. Section III). 

The N-N and metal-N force constants resulting from normal coordinate analysis of the N2-, NNH-, NNH2-, and NNH3-complexes l ppe, 2 ppeF, 34ppeF, and 4 epeF as well as the nitrido and imido complexes 5, Ns and 6 pe C1 are graphically represented in Fig. 4 (15-17). Upon protonation of l pe to the NNH complex 2 peF, the N-N force constant decreases from... 

There is a small complication in that the frequency to is different for the reduced and oxidized states so that one has to take an average frequency. Marcus has suggested taking u>av = 2woxu>red/(wox + a>reci)-When several inner-sphere modes are reorganized, one simply sums over the various contributions. The matter becomes complicated if the complex is severely distorted during the reaction, and the two states have different normal coordinates. While the theory can be suitably modified to account for this case, the mathematics are cumbersome. 

Sakurai et al. have observed that vanadyl complexes with coordination modes such as VO(S4) (103) can normalize blood glucose levels (515) and are effective for normalizing both serum glucose and free fatty acid levels in streptozotocin rats and are orally active (516). Bis(picolinato)oxovanadium(IV) is also orally active against the diabe-... 

The functions hf,[q(t) were dependent on the geometry of the complex and were related to the local symmetry-distorting motions by a set of normal coordinates, q(t) = [q (t),..., qN(t)], through the Taylor expansion ... 

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