Coordination analysis

In general, two related techniques may be used principal component analysis (PCA) and principal coordinate analysis (PCoorA). Both methods start from the n X m data matrix M, which holds the m coordinates defining n conformations in an m-dimensional space. That is, each matrix element Mg is equal to q, the jth coordinate of the /th conformation. From this starting point PCA and PCoorA follow different routes. 

Principal coordinate analysis (PCoorA) [37], on the other hand, operates on the square n X n matrix, reflecting the relationships between the conformations. The... 

Figure 4 The energy landscape of the pnon protein (Pi P) (residues 124-226) in vacuum, obtained by principal coordinate analysis followed by the minimal energy envelope procedure. Two large basins are seen. One basin is associated with the native Pi P conformation the other is associated with partially unfolded conformations.

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). 

Work has also been conducted that involved the investigation, via infrared spectroscopy, of matrix-isolated, plutonium oxides (40), with the appropriate precautions being taken because of the toxicity of plutonium and its compounds. A sputtering technique was used to vaporize the metal. The IR spectra of PuO and PUO2 in both Ar and Kr matrices were identified, with the observed frequencies for the latter (794.25 and 786.80 cm", respectively) assigned to the stretchingmode of Pu 02. Normal-coordinate analysis of the PUO2 isotopomers, Pu 02, Pu 02, and Pu 0 0 in Ar showed that the molecule is linear. The PuO molecule was observed in multiple sites in Ar matrices, but not in Kr, with Pu 0 at 822.28 cm" in the most stable, Ar site, and at 817.27 cm" in Kr. No evidence for PuOa was observed. 

After the first unsuccessful attempts to record a matrix IR spectrum of the methyl radical, reliable data were obtained by the use of the vacuum pyrolysis method. IR spectra of the radicals CH3 and CD3 frozen in neon matrices were measured among the products of dissociation of CH3I, (CH3)2Hg and CD3I (Snelson, 1970a). The spectra contained three absorptions at 3162 (1 3), 1396 V2) and 617 cm (I l) belonging to the radical CH3 and three bands 2381, 1026 and 463 cm assigned to the radical CD3. Normal coordinate analysis of these intermediates was performed and a valence force field calculated. In accordance with the calculations, methyl radical is a planar species having symmetry >31,. 

IR absorptions of these species were assigned to fundamental modes by comparison with the spectra of stable perfluoroorganic compounds. Normal coordinate analysis of the perfluoroethyl radical was performed and the valence force field of C2F5 was calculated (Snelson et al., 1981). 

Normal coordinate analysis of the radical has been carried out and excellent agreement of experimental and calculated frequency values was obtained for the trans structure of HOCO. 

The allyl radical [115] trapped in an argon matrix can be photolytically (A = 410 nm) converted into the cyclopropyl radical [116] (Holtzhauer er a/., 1990). Dicyclopropane and cyclopropane were formed when the photolysed matrix was warmed from 18 to 35 K. The intermediate [116] was shown to be a cr-type (Cs symmetry) and not a rr-type symmetry) radical. Normal coordinate analysis of the radical [116] has been carried out and the IR band at 3118 cm has been assigned to the stretching vibration of the C—H bond at the radical centre. 

Principal coordinates analysis 31.6.1 Distances defined from data... 

Principal coordinates analysis (PCoA) is applied to distance tables rather than to original data tables, as is the case with principal components analysis (PCA). 

Using D as input we apply principal coordinates analysis (PCoA) which we discussed in the previous section. This produces the nxn factor score matrix S. The next step is to define a variable point along they th coordinate axis, by means of the coefficient kj and to compute its distance d kj) from all n row-points ... 

Yoshizawa, K., Shiota, Y., Yamabe, T., 1999, Intrinsic Reaction Coordinate Analysis of the Conversion of Methane to Methanol by an Iron-Oxo Species A Study of Crossing Seams of Potential Energy Surfaces , J. Chem. Phys., Ill, 538. 

For polyatomic molecules, the stretching force constant for a particular bond cannot in general be obtained in an unambiguous manner because any given vibrational mode generally involves movements of more than two of the atoms, which prevent the expression of the observed frequency in terms of the force constant for just one bond. The vibrational modes of a polyatomic molecule can be analyzed by a method known a normal coordinate analysis to... 

Saito, S. and Tasumi, M. 1983. Normal-coordinate analysis of P-carotene isomers and assignments of the Raman and infrared bands. J. Raman Spectrosc. 14 310-321. 

With the aid of a normal coordinate analysis involving different isotopomers a linear structure of the Pd-Si-0 molecule is deduced. The results of ab initio MP2 calculations (Tab. 4) confirm the experimentally obtained IR spectra and their interpretation. The Pd-C bond in PdCO is similar to the Pd-Si bond in PdSiO which means, that the donor bond is strengthened by x acceptor components. This conclusion is in line with the high value of the Pd-Si force constant (exp. f(PdSi) = 2.69, f(SiO) = 8.92 mdyn/A) as well as with the energy of PdSiO (Pd + SiO —> PdSiO + 182 kJ/mol for comparison Pd + CO —> PdCO + 162 kJ/mol, MP2 level of theory). 

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... 

It is also possible to deduce pathways in a more adventurous way by noting which modes are enhanced, doing the normal coordinate analysis to find out where those modes have their maximum amplitudes, and arguing that this describes the pathway for the electron going through the molecule. An example is shown in Fig. 11, also from Troisi s work [108]. 

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