Normal coordinate analysis complexes

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). 

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... 

The normal coordinate analysis also allowed the authors to quantify the relative weakness of the metal-carbon force constant in comparison with other metal-ethylene complexes (0.33 vs 0.58 mdyneA ) . 

The complexes [Cr(S2CNMe2)3], [Cr S2P(OEt)2 3] and [Cr(S2COEt)3] have Pfeiffer CD activity but this develops only when there is a large ratio of optically active environment compound to the racemate.1021 A normal coordinate analysis of the IR spectra of [Cr(S2CNR2)3] (where R = Me, Et, Pr or Bun) has shown that the alkyl substituent affects the thioureide band at ca. 1550 cm"1 through kinematic as well as electronic effects.1022... 

Very little IR or Raman spectroscopy of copper(III) complexes have been reported,297 but recently the spectra of [Cuu,11I(biuret)] have been examined by normal coordinate analysis,1349 and the biuret ligand undergoes little change on oxidation from copper(II) to copper(III), with a general increase in the frequency of the modes of vibration. 

The complexes ML2-nH20 (M = Zn or Cd H2L = diformyl- or diacetyl-hydrazine) have also been synthesized, and are dimeric or polymeric with the quadridentate hydrazine acting as a bridging ligand.158 159 A normal coordinate analysis of diformylhydrazine and its zinc complex with deprotonated ligand has been reported.160... 

A complete IR and normal coordinate analysis (including metal isotope data) have been carried out on the thiocarbonato complexes A2M(CS3)2M(CS3)2 (M = Ni or Zn A = PPh4, NMe, or AsPhJ).872... 

In contrast to the results described above, experiments with palladium atoms and SiO lead to a different behavior. It is clear that PdSiO is formed, but compared with monomeric SiO the corresponding stretching vibration of PdSiO is shifted to higher wavenumbers (1246 cm-1 in solid argon)118. With the aid of a normal coordinate analysis involving different isotopomers, a linear structure of PdSiO is deduced. Bonding in PdSiO is similar to that in typical transition metal carbonyl complexes. 

Raman and UV-visible spectroscopy, but no precise characterization was made. A report was made in 1981 where the IR spectrum of Cu atoms deposited with C02 at 80 K was interpreted in terms of the formation of a -coordinated complex between C02 and zerovalent copper [32]. Almond et al. [33] prepared a (C02) M(CO)5 molecule (M = Cr, W), that led to the formation of CO and oxometal carbonyl under UV irradiation. The first complete study of the reactivity of C02 with the first row of transition metals was made by Mascetti et al. [34, 35]. Here, it was shown that the late transition metal atoms (Fe, Co, Ni, and Cu) formed one-to-one M(C02) complexes, where C02 was bonded in a side-on (Ni), end-on (Cu), or C-coordinated (Fe, Co) manner, while the earlier metal atoms (Ti, V, and Cr) spontaneously inserted into a CO bond to yield oxocarbonyl species OM(CO) or 0M(C0)(C02). Normal coordinate analysis showed that the force constants of CO bonds were significantly decreased by 50%, compared to free C02, and that the OCO angle was bent between 120 and 150°. 

The average Mo=0 bond distance of the (MPT)Mo(0)2(S-eys) cofactor of sulfite oxidase is 1.68 A by EXAFS (Figure 14). The RR results are consistent with bis(oxido) coordination of MoVI and the two expected Mo=0 stretching modes are found at 903 and 881 cm-1 [119,139], Upon reduction and reoxidation in the presence of H2180 the Mo=0 bands shift to 890 and 848 cm-1, respectively [119,139], The difference in the 180 isotopic shifts for the symmetric and asymmetric bands is consistent with labeling of only one of the oxido ligands. This observation has precedent in the labeling of bis(oxido) model complexes and is supported by normal coordinate analysis [140],... 

Kramers idea was to give a more realistic description of the dynamics in the reaction coordinate by including dynamical effects of the solvent. Instead of giving a deterministic description, which is only possible in a large-scale molecular dynamics simulation, he proposed to give a stochastic description of the motion similar to that of the Brownian motion of a heavy particle in a solvent. From the normal coordinate analysis of the activated complex, a reduced mass pi has been associated with the motion in the reaction coordinate, so the proposal is to describe the motion in that coordinate as that of a Brownian particle of mass g in the solvent. 

As shown in Section 1.3, force constants of diatomic molecules can be calculated by using Eq. (1-20). In the case of polyatomic molecules, force constants can be calculated via normal coordinate analysis (NCA), which is much more involved than simple application of Eq. (1-20). Its complete description requires complex and lengthy mathematical treatments that are beyond the scope of this book. Here, we give only the outline of NCA using the H20 molecule as an example. For complete description of NCA, the reader should consult references (63-65) and general reference books cited at the end of this chapter. 

The function used to calculate the energy associated with deformation of a valence angle is given in Eq. 3.7. A first approximation to the force constant, k, can again be derived from the infrared spectrum, though in the case of bond angles it is necessary to carry out a full normal-coordinate analysis in order to obtain accurate values. However, there are relatively few normal-coordinate analyses of metal complexes[ 131]. 

The relative frequencies of the M—S stretching modes in tris(dithiolene) complexes can be assessed based on IR and Raman studies and normal coordinate analysis of the NbS6 unit in the structurally characterized tris(etha-nedithiolate) Nb(V) complex, [Nb(S2C2H4)3]1- (27). The complex has D3... 

The early work of Miyazawa [109] described the normal modes of vibration for a polypeptide backbone in terms of the normal modes of 77-methyl acetamide (NMA). This established the basis for understanding these complex spectra in terms of normal coordinate analysis (NCA) f 7/0]. A detailed review of the development of this methodology is given by Krimm [7/7]. The foundation for the use of NCA resides in the useful approximation that the atomic displacements in many of the vibrational modes of a large molecule are concentrated in the motions of atoms in small chemical groups, and that these localized modes are transferrable to other molecules. This concept of transferability is the basic principle for the use of spectroscopic techniques for studying problems associated with peptide structure [777],... 

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