Center of interaction

Depending on the analyses of structure-activity relationships and electrochemical studies [158,162], the indole nucleus is the reactive center of interaction with oxidants due to its high resonance stability and very low activation energy wall towards the free-radical reactions. However, the methoxy and amide side chains are also important for indole s antioxidant capacity [169]. 

Integy moments as distance from the center of mass to the center of interaction with the water probe eight energy levels... 

For homonuclear diatomics, hi = 2, A = 0, the potential is represented by even powers in rj and all terms containing A vanish. On the other hand, for heteronuclears the potential consists of both even and odd powers of rf multiplied by coefficients containing A. This A has been referred to as the displacement of the center of interaction (i, 8) of the molecule from the center of gravity. 

Singh and Thornton (172) and Burley and Petsko (173) investigated the geometry or aromatic interactions in protein environments using the Brook-haven Protein Data Bank. The preferred distance between aromatic ring centers of interacting aryl rings was about 4.6 A, with the planes of the... 

Instimte of Macromolecular Chemistry, Freiburg Materials Research Center, FMF, and Freiburg Center of Interactive Materials and Bioinspired Technologies, FIT, of the University Freiburg, Stefan-Meier-Strasse 31, 79104 Freiburg, Germany e-mail rolfmuelhaupt web.de... 

The molecules behave hke point centers of interaction with a spherical potential field. The total interaction potential energy of... 

We will see in Section V.B that De Boer s quantum theory is valid only if the center of interaction of the molecule coincides with its center of mass. When this condition is not fulfilled, two additional parameters must be introduced besides A in order to determine the quantum effects. 

In Section V it will be shown that in the case where the center of interaction of the molecule does not coincide with its center of mass, (I-ll) must be replaced by... 

Consider a system of N diatomic molecules. We assume that the interaction potential of the system depends only on the positions of the centers of interaction of the N molecules ... 

In the case of a heteronuclear molecule, the position of the center of interaction will, in general, not coincide with the position of the center of mass. One has the relation... 

Figure V-1. Heteronuclear diatomic molecules. 1, light nucleus h, heavy nucleus I, center of interaction C, point situated halfway between land h G, center of mass a, distance between I and G d, distance between I and C. In Figure V-la, dis negative, it is positive in Figure V-lb. d has the same value for all isotopic species of a given chemical compound, whereas a depends on the distribution of the total molecular mass among the constituent atoms. When both atoms of the diatomic molecule belong to the same element, I and C coincide (d = 0).

The influence of the separation between the center of mass and the center of interaction on equilibrium properties has been studied recently by Babloyantz. This author has shown that, in the... 

Two systems of coordinates can be used in the expression of the kinetic and potential energy operators (a) the coordinates of the centers of mass and the polar angles (b) the coordinates of the centers of interaction and the same polar angles as in system (a). System (a) leads to a simpler expression of the kinetic energy while (b) is more convenient for the potential energy. 

Using coordinates of the centers of interaction and polar angles [system (b)] it has been shown that assumes the form... 

If the center of interaction and the center of mass coincide (a = 0), the coupling terms in (V-11) vanish. The Schroedinger equation can then be separated into a rotational part and a translational part so that the energy eigenvalues may be written as a sum of a rotational, volume-independent part and a translational, volume-dependent part ... 

In our opinion, (V-20) and (V-21) present only a purely formal interest in dealing with equilibrium properties of systems of diatomic molecules belonging to different chemical species. When quantum effects are small [which is the condition under which (V-20) and (V-21) are valid] they will indeed be masked by other effects which we did not take into account, notably by supposing that the reduced two-body potential is a universal function of the reduced distance between the centers of interaction and also by supposing that the interaction potential is angle-independent. 

Equations (V-20) and (V-21), or more generally, (V-18) and (V-19) will be especially interesting when comparing systems of isotopic molecules. In the latter case, we may admit (cf. Section I) that the interaction potential, expressed in terms of the positions of the centers of interaction, is the same for aU isotopic species of a given chemical compound. It follows that, in the approximation of... 

We note that from (V-18a) and (V-20a) it can be seen that, when the distance between the center of interaction and the center of mass goes to zero, the effective molecular mass goes over into the total molecular mass and Agg transforms into A. 

The effect resulting from the separation of the center of mass from the center of interaction only represents 2% of the effect due to the total molecular mass (1-4). 

Vext can be expressed as a function of the three spatial coordinates of the center of interaction, the orientational coordinates of the molecular axes in space and the intramolecular... 

The uses of NMR spectroscopy to study H-bonding appears to be a superior method to optical frequency-shift measurements in the infrared since it is possible to measure shifts for protons in a molecule which are several bonds removed from the center of interaction. It is also possible to obtain the lifetime of the hydrogen-bonded state by using NMR spectroscopy. 

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