Charge-mass-permutation

We will now explain the meaning of the word identical used above. Physically, it is meant for particles that possess the same intrinsic attributes, namely, static mass, charge, and spin. If such particles possess the same intrinsic attributes (as many as we know so far), then we refer to them as physically identical. There is also another kind of identity, which is commonly refeiTed to as chemical identity [56]. As discussed in the next paragraph, this is an important concept that must be steessed when discussing the permutational properties of nuclei in molecules. 

This model is a polar cross-/ structure with a left-handed twist that complies with the mass-per-unit-length data moreover, it readily accommodates sequence randomization because like residues are still stacked over like residues, regardless of their order, and sequence permutation does not increase the number of charged residues or prolines which would be most likely to destabilize structures of this kind (Fig. 10). The configuration of strands and turns allows some variation without putting charged residues inside the core structure. We envision that structural variations of this kind offer a plausible explanation for the phenomenon of prion variants, as discussed in Section VIII. 

Thereby the matrix 11(F) denotes a K-dimensional permutation matrix and F (F) a 3 by 3 orthogonal matrix. The form of this representation follows from the fact that each isometric transformation maps the NC Xk, Zk, Mk onto a NC which by definition has the same set of distances, i.e. is isometric to NC Xk, Zk, Mk. Expressed alternatively, the nuclear configurations NC Xk( ), Zk, Mk and NC Xk(F 1 ( )), Zk, Mk are properly or improperly congruent up to permutations of nuclei with equal charge and mass for any F G ( ). The set of matrices Eq. (2.12) forms a representation of J d) by linear transformations and will furtheron be denoted by... 

Apart from the endoergic dissociation reactions mentioned above, a variety of other reactions can also be accessed in tandem mass spectrometry. In many such reactions, collectively termed charge-permutation reactions, there is a change in the charge of the colliding species during the collision-activation step. Some of the reactions are discussed here. For further reading, an excellent review on the subject can be consulted [32]. 

M. He and S. A. McLuckey, Charge permutation reactions in tandem mass spectrometry, 7. Mass Spectrom. 39, 1231-1259 (2004). 

Isomerization of ionic structures is frequently observed. Several mass spectrometry techniques have been developed to identify the structure of the ion formed initially or its isomerized form. These methods are based on determination of the heat of formation, study of metastable ion spectra and CID spectra, experiments involving kinetic-energy-release measurements, isotope labeling, charge-permutation reactions, ion-molecule reactions, field ionization kinetics, and ab initio calculations. 

It is easily established that the Coulomb Hamiltonian is invariant imder the coordinate transformations that correspond to imiform translations, rotation-reflections, and permutations of particles with identical masses and charges. Because of the symmetry of the Coulomb Hamiltonian its eigenfunctions will be basis functions for irreducible representations (irreps) of the translation group in three dimensions, the orthogonal group in three dimensions, and for the various symmetric groups corresponding to the sets of identical particles. 

Figure 3 (A) Neutralization-reionization NR ) and (B) colli-sionally activated dissociation (CAD) spectra of Li2F. Reprinted with permission of Elsevier from Polce MJ and Wesdemiotis C (1999) Hypermetallic dilithium fluoride, Li2F, and its cation and anion a combined dissociation and charge permutation study. InternationalJournal of Mass Spectrometry S2I S3 45-52.

The full Hamiltonian is invariant under all uniform translations of the variables, under all orthogonal transformations of the variables and under the permutation of all variables that correspond to particles of equal charge and mass. It is the first of these invariances that has the most immediate consequences. It implies that the full Hamiltonian has a completely continuous spectrum arising from the free motion of the whole system (atom, molecule, ion or whatever) through space. Any bound-states corresponding... 

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