Intermolecular scalar

In a computer simulation of fluoride ions in water, possible intermolecular scalar relaxation coupling mechanism was studied, modulated by water dynamics (exchange of water molecules in the first hydration sphere) due to modulation of the J coupling [81]. 

It is of interest to note that in this model the anisotropy in the attractive energy is determined by the same parameter, 7, as that controlling the anisotropy in the repulsive energy. In these expressions for the contact distance and the well depth their angular variation is contained in the three scalar products Uj Uj, Uj f and uj f which are simply the cosines of the angle between the symmetry axes of the two molecules and the angles between each molecule and the intermolecular vector. 

In this work a property hypersurface was constructed by calculating the Jqf and Jhf intermolecular spin-spin coupling constants quantum mechanically for a large number of spatial F - H2O configurations and fitting them to an analytical three dimensional function in the principal coordinate system of water. The scalar couplings were assumed to be additive when the total coupling was calculated from the closest water molecules. 

A. Laaksonen, J. Kowalewski, and B. Jdnsson, Intermolecular nuclear spin-spin coupling and scalar relaxation. A quantum-mechanical and statistical-mechanical study for the aqueous fluoride ion, Chem. Phys. Lett., 89 (1982), 412. 

All intermolecular interactions can be adequately described, at least in principle, by multidimensional scalar and vector fields representing the energetics of a molecular system as functions of both intermolecular distances and orientations as well as intramolecular structure data. The visualization of these fields, however, has to be based on a three-dimensional picture or a two-dimensional projection because human pattern recognition ability is strongly related to the two- and three-dimensional world. Consequently, the multidimensional field has to be reduced to a two- or three-dimensional representation. In molecular science this can be done in many different ways. 

In many applications, it is more computationally convenient to express the S functions in terms of the scalar products between the unit local axis vectors (xj, yi, and X2, ya, i) and the unit intermolecular vector R. This set of variables is highly redundant, but easily calculated from the local axis vector information in most simulations. As an illustration. Table 1 gives the S functions that are important in describing the anisotropy of the atom-atom repulsion between an N atom in pyridine and a hydrogen-bonding proton of methanol. 

These are expressed in terms of scalar products between the unit axis system vectors on sites 1 and 2 (on different molecules) and the unit vector 6. from site 1 to 2. The S functions that can have nonzero coefficients in the intermolecular potential depend on the symmetry of the site. This table includes the first few terms that would appear in the expansion of the atom-atom potential for linear molecules. The second set illustrate the types of additional functions that can occur for sites with other than symmetry. These additional terms happen to be those required to describe the anisotropy of the repulsion between the N atom in pyridine (with Zj in the direction of the conventional lone pair on the nitrogen and yj perpendicular to the ring) and the H atom in methanol (with Z2 along the O—H bond and X2 in the COH plane, with C in the direction of positive X2). The important S functions reflect the different symmetries of the two molecules.Note that coefficients of S functions with values of k of opposite sign are always related so that purely real combinations of S functions appear in the intermolecular potential. 

To conclude this review, several important aspects should be highhghted. The nitrogen atoms of the purine skeleton are the centers for the intermolecular interactions between the purine molecule and its environment. The changes in the electron distribution induced by these interactions are reflected in changes of several NMR parameters which can be obtained from the samples at natural and " N abundance, namely the C and " N NMR chemical shifts and the and scalar coupling constants. All these... 

In the same way we can define the equatorial angle

scalar product between the unit vectors perpendicular to two planes the zy-plane defined by two different intramolecular C-Cl vectors and the plane defined by the z-axis and the intermolecular C-C vector ... 

When there is unpaired electron density produced at the nucleus being studied, a so-called scalar interaction between the electron and the nucleus can occur. This unpaired electron density is transmitted from the free radical to the nucleus by a similar mechanism to that giving rise to the nuclear hyperfine structure in normal e.s.r. spectra. Since the unpaired electron and the nucleus are usually in different molecules, the rapid molecular motion means that the scalar interaction, which of necessity can only occur when the unpaired electron and the nucleus are close to one another, will be varying rapidly. This rapid switching on and off of the scalar interaction means that although any intermolecular nuclear hyperfine structure in the e.s.r. signal is averaged to zero, the scalar interactions may now provide an efficient... 

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