Internuclear distances, and

The collision diameter is at the value of s(r) equal to zero, and die maximum interaction of the molecules is where s(r) is a minimum. The interaction of molecules is thus a balance between a rapidly-varying repulsive interaction at small internuclear distances, and a more slowly varying attractive interaction as a function of r (Figure 3.7). 

While the rate of change of dipolar interaction depends on t its magnitude depends only on the internuclear distance and is independent of t,. Thus the dipole-dipole relaxation depends on the molecular correlation time T the internuclear distance r, and the gyromagnetic ratios of the two nuclei, y and js -... 

With regard to the results obtained for the ground state system N (ls ) -i- He, all the crossings are shifted towards shorter internuclear distances and have a lower height. The main remark concerns, however, the presence of an avoided crossing between the entry... 

In general three position variables will be needed to specify the potential energy of the reaction system. These may be the X-Y, Y-Z, and X-Z internuclear distances or two internuclear distances and the included angle. Even in this relatively simple case, four dimensions would be required for generation of the potential energy surface. However, if we restrict our attention to linear configurations of these atoms, it is possible... 

We next consider the expression for k in the classical formalism. According to the Franck-Condon principle, internuclear distances and nuclear velocities do not change during the actual electron transfer. This requirement is incorporated into the classical electron-transfer theories by postulating that the electron transfer occurs at the intersection of two potential energy surfaces, one for the reactants... 

The matrix elements of r and r, which in the case of a diatomic molecule are the internuclear distance and its square, can easily be obtained using relationship (66) ... 

Nonadiabatic Variational Energies for 15 States of the H2 Molecule with Zero Total Angular Momentum (the Ground Rotational States) Obtained with 3000 Basis Functions for Each State and Expectation Values of the Internuclear Distance and the Square of the Internuclear... 

According to Fig. 5 the maximum and minimum in the NACME to the first excited state produce a minimum and maximum in the corresponding contribution to the electronic contribution to the vibrational g factor. The extrema are at the same internuclear distances and have positions near the extrema in the total electronic contribution to g R), but are not as steep. The contributions from the second, third, and up to the fifth excited states modify slightly the position and the form of the extrema but introduce no fundamental modification. We, therefore, conclude that the extrema in the vibrational g factor reflect extrema in the first-order NACME to the first excited state, and not in the energy of the excited state. The exact position of the minimum in the vibrational g factor is, however, influenced by more highly excited states. 

The internuclear distances and bond angles used in this study are the usual experimental equilibrium geometries. The details are given in Table 2. 

A The p values for the molecules B2, C2, N2, 02 and F2 are calculated from the internuclear distances and the Slater values for the effective nuclear charges of the respective atoms ... 

Figure 5. Architecture of the [Cr2(CO)io(M2-H)] monoanion of crystallographic Q-I symmetry showing the approximate D4/, geometry of the metal carbonyl framework and the two centrosym-metrically related (half-weighted) sites of the bridging hydrogen atom in the bent Cr-H-Cr molecular fragment. Internuclear distances and bond angles are given with their estimated standard deviations.

Here k is the force constant, De the equilibrium internuclear distance, and an and values determined by the nature of the bonded atoms, as given in Table 7-7. 

Figure 23-2 The potential energy of the hydrogen molecule as a function of internuclear distance, and the position of its vibrational energy levels. AE values are energy differences between successive levels v designates vibrational quantum numbers. Adapted from Calvert and Pitts,2 p. 135.

For exoergic channels, there is often no accessible avoided crossing, in which case the trajectory assumptions underlying the LZS theory are violated. The nonadiabatic coupling region may extend over a considerable range of internuclear distance, and semiclassical methods using exact classical trajectories represent the minimal necessary improvement over LZS. 

Transitions from the A 2 potential become optically allowed for small internuclear distances and give rise to the well-known Hopfield continuum and the 600-A emission and absorption bands.86 The inner attractive parts of the potentials have been determined quite accurately from analysis of the optical spectrum. Information on the long-range parts, however, has been only semiquantitative at best. 

The main contribution to the FC factor comes from the overlap region at small internuclear distances and hence the frequencies and equilibrium positions correspond to this region. 

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