Coordinates local symmetry

The eigenvectors of polypeptide chain modes, as in the case of NMA, can be described by PEDs in terms of symmetry coordinates, which in turn are related to internal coordinates. A list of the internal coordinates for (Ala) is given in Table IV, and the local symmetry coordinates are given in Table V (Moore and Krimm, 1976b). These serve as the general local symmetry coordinates for most polypeptide chain structures [for the particular set for (Gly) I, see Dwivedi and Krimm (1982a)]. 

To eliminate the correlations between the linear force constants, an explicit relationship between them can be used. The energy is expressed once as a Taylor series in local symmetry coordinates, As, ... 

Since the local symmetry coordinates normally used obey Sy c y = 0 it follows from Eq. [32] that... 

For the above reason, researchers felt the need to describe normal modes in terms of group coordinates (or local symmetry coordinates) which can be defined by an orthogonal transformation... 

In the GVFF there is no inherent limit to the number of FyS that are included. There is only the restraint that the number of Fs should not exceed the number of observable frequencies in fact, it should generally be much smaller so as to overdetermine the force field. Since an independent set of coordinates can be chosen, e.g., local symmetry coordinates, and the redundancy conditions explicitly given, there is no need to include linear terms in F, and Eq. (5-1) is the most general representation of the force field. Our discussion will focus on applications of the GVFF. 

X-ray or neutron diffraction IR and Raman spectroscopies, MNR EXAFS X-ray photoelectron spectroscopy (XPS) X-ray reflectometry Radial distribution and/or crystal phase Local symmetry, coordination Local symmetry, radial distribution, coordination Surfece arrangement (Section 5.8) Surface arrangement (Section 5.8)... 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

When we look in the local segment coordinate system, the symmetry of the equation seen in the global coordinate system is lost, and we will see azimuthal variations. We wish to express the equation for the segment surface in its local coordinate system... 

In the framework of the chain migratory insertion mechanism (Scheme 1.3), the stereospecific behavior of the model sites depends on the relationship between the two situations obtained by exchanging, in the coordination step, the relative positions of the growing chain and the incoming monomer. Depending on the local symmetry of the coordinated bridged n-ligand, these two situations can be as follows ... 

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 ... 

The key to get a diabatic electronic state is a strict constraint i.e. keep local symmetry elements invariant. For ethylene, let us start from the cis con-former case. The nuclear geometry of the attractor must be on the (y,z)-plane according to Fig.l. The reaction coordinate must be the dis-rotatory displacement. Due to the nature of the LCAO-MO model in quantum computing chemistry, the closed shell filling of the HOMO must change into a closed shell of the LUMO beyond 0=n/4. The symmetry of the diabatic wave function is hence respected. Mutatis mutandis, the trans conformer wave function before n/4 corresponds to a double filling of the LUMO beyond the n/4 point on fills the HOMO twice. At n/4 there is the diradical singlet and triplet base wavefunctions. 

The following is a summary of the local group molecular orbitals from which one may select the primary building blocks for interaction diagrams. The orbitals are classified according to the coordination number of the central atom. The local symmetry properties and relative energies are independent of the atomic number of the central atom itself. 

The lone pair MO of the free amine and phosphine possesses at symmetry in Cjt, local symmetry. As anticipated, this MO undergoes considerable stabilization as coordination to the metal occurs. The lone pair stabilization energies of amines have been found to be greater than those of phosphines with respect to main group acceptors such as BH3, O, and S (32, 113, 210). The sulfide ligands feature two MOs with significant lone pair character. 

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