Spacing between neighboring energy

A plot of the spacing between neighboring energy levels versus vj should be linear for values of vj where the harmonic and first overtone terms dominate. The slope of such a plot is expected to be -2h( x)j and the small -vj intercept should be h[ j - 2( x)j], Such a plot of experimental data, which clearly can be used to determine the j and ( x)j parameter of the vibrational mode of study, is shown in the figure below. 

Since the energy E is restricted to match the state-to-state energy differences E = Ei - Ef, the integral over dE in Eq. (46) can be replaced by a sum over accessible final-state Ef values multiplied by the spacing between neighboring such states (dEf = Ef-Ef i) ... 

In (2.1), e, is again taken to be the average spacing between neighboring ((>/ levels at the energy of is again the decay rate of the zeroth order level, , which in isolated molecules is due to infrared emission and has typical values on the order of 10 -10 s . In the small molecule limit the condition (2.2) is obeyed, and the states of the system are characterized... 

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

GR conceives gravity not as a force between masses but as a change in the geometry of spacetime due to neighboring energy. Consider Euclidean space which may be written in the familiar forms... 

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