Cluster modes

Mode (D2 symmetry) Oxidized cluster Reduced cluster Mode (C2 symmetry)... 

For systems comprised of nonlinear molecules, the heat capacity of the cluster ion of size n is taken to be 6(n - 1) (in units of the Boltzmann constant) by considering (only) the cluster modes. The binding energy of a molecule in a cluster ion of size n can be calculated from the equation,... 

Hierarchical cluster analysis (Section 6.4)—with the result represented by a dendrogram—is a complementary, nonlinear, and widely used method for cluster analysis. The distance measure used was dTANi (Equation 6.5), and the cluster mode was average linkage. The dendrogram in Figure 6.6 (without the chemical structures) was obtained from the descriptor matrix X by... 

The effective-mode transformation described here is closely related to earlier works which led to the construction of so-called interaction modes [75, 76] or cluster modes [77, 78] in Jahn-Teller systems. The approach of Refs. [54,55,72] generalizes these earlier analyses to the generic form - independent of particular symmetries - of the linear vibronic coupling Hamiltonian Eq. (8). 

Kuduk, S., Schwarz, J., Chen, X.-T., et al. (1998) Synthetic and immunological studies on clustered modes of mucin-related Tn and TF G-linked antigens The preparation of a glycopeptide-based vaccine for clinical trials against prostate cancer. /. Am. Chem. Soc. 120,12474-12485. 

Raman and IR spectra of polyphosphides clearly show the separation of internal and external modes (Figure 25). The external modes are strongly pressure and temperature dependent, whereas the internal cluster modes are nearly... 

Resonance Models Induced by Vibronic Interaction (Cluster Modes).142... 

Probably the most stringent verification so far of the cluster mode description has come from the low temperature near-infrared absorption data in this system73). The analysis of the zero phonon line under uniaxial stress and of the associated broad absorption band led to a consistent set of parameters for a single coupled mode (Ke, ... 

Fig. 11. The motion of the excitation wave-packet (after Toyozawa et al.1S3)). The lower part of the figure exhibits the excitation pathway in the space of the cluster mode coordinate, including the overshooting (once) of the minimum.

A. General Aspects. We shall consider as model systems six-coordinate trigonal dihedral (D3) metal complexes in which the metal ion-donor atom cluster (MLe) has near-octahedral (Ojj) symmetry. Furthermore, we shall restrict our attention to vibronic interactions involving only those vibrational modes which are localized within the MLe cluster (the socalled "cluster modes"). The ML6 cluster has 15 vibrational degrees-of-freedom which, assuming octahedral (Ojj) symmetry, can be described in terms of six normal coordinates Qi(aig), Q2(eg), Q3(tiu), Qq(tiu), Q5(t2g), and Q6(t2u)- For a trigonally distorted (D3) ML6 cluster, ten normal coordinates are required to describe the 15 vibrational degrees-of-freedom. We shall denote the normal coordinates of the... 

A protein may have more than one metal center, each with its own set of electronic transitions, and in favorable cases the RR spectra can be elicited selectively by judicious choice of laser wavelengths. For example, sulfite reductase has an iron-isobacteriochlorin cofactor, siroheme, which is coupled magnetically to a Fe4S4 cluster, probably through a thiolate bridge. The siroheme modes are strongly enhanced in resonance with the isobacteriochlorin Soret or Q bands, but intermediate excitation (457.9-488.0 nm) enhances the Fe4 4 cluster modes (Fig. 11). The protein rubrerythrin has two rubredoxin-like Fe(Cys)4 centers and a (/u.-oxo)di-iron(III) center (similar to those found in hemerythrins and ribonucleotide reductase), each of which can be enhanced selectively by excitation at... 

Fig. 11. Low-temperature (77 K) RR spectra of sulfite reductase hemoprotein obtained with various excitation wavelengths and structural drawing of a proposed model for the active site. The Fe4S4 cluster modes are selectively enhanced with 457.9 or 488.0 nm excitation (correlated with dashed lines), whereas the siroheme modes are enhanced with 406.7 (Soret band) or 568.2 nm (Q band) excitation. ...

Schuyler, A.D., Chirikjian, G.S. Normal mode analysis of proteins a comparison of rigid cluster modes with Cq. coarse graining. Journal of Molecular Graphics and Modelling 2004, 22,183. 

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