Anharmonic potential energy shape

MAIN FEATURES OF IR SPECTRA RELATED TO THE ANHARMONIC POTENTIAL ENERGY SHAPE... 

Let us come back to the problem of anharmonicity and its relationship with the hydrogen bond strength and hence the potential energy shape for the proton motion. 

Here r, r, and are the atomic distance, equilibrium bond length, and potential-well depth, respectively. Further, h is Planck s constant and c is the light velocity in vacuum. The potential-curve shapes depend on the parameters and D. By analytically solving the Schrodinger equation with the anharmonic potential (Equation 2.3), one can obtain the vibrational energy levels ofthe Morse molecular oscillator ... 

Overtone spectra are due to deviations from harmonic vibrational motion and, compared to the fundamental ones, give valuable information on the harmonic frequencies coe, the anharmonicities Xe, the shape of the potential curve and hence on the dissociation energy, which is related to the former by... 

Now let us consider an anharmonic oscillator, the potential energy for which is plotted by the curve in Figure 1.15(b). We can clearly see that this shape of curve allows for the breaking of the link. However, we can also see that if the temperature increases, the average position of the end of the spring follows a curve that inclines to the right, thus showing an expansion. We can demonstrate this numerically. 

Because the transition at vq dominates the spectrum, the harmonic oscillator seems to be a valid approximation for diatomic molecules, but it is clear from Fig. 3.3.3 that anharmonic effects will have to be included if we wish to reproduce observed spectra in detail. In all diatomic molecules the deviation of their potential energy curve from a strictly parabolic shape causes the departure from harmonicity. The curve for HCl in Fig. 3.2.1 is only approximately parabolic near minimum and deviates more so at large nuclear displacements. Indeed, a parabola carmot describe the actual curve as the nuclear separation is increased indefinitely the molecule... 

The ground-state adiabatic potential curves in Fig. 27.3 are constructed by adding accurate anharmonic zero-point energies for the stretch and bend modes to V]y[gp. On the reactant side the shapes of Vmep and are very similar with the adiabatic potential being shifted up by approximately the zero-point energy for the FI2 stretch vibrations, 6.2 kcal mokk Near the saddle point this contribution decreases markedly for the FI -1- H2 reaction, to 2.9 kcal mokh causing the adia-... 

There exist additional factors that can influence the v(OH) of isolated (non-H-bonded) hydroxyls. One of them is the anharmonicity of the O—H bond, which is related to the shape of the Morse potential that is overlaid with the harmonic potential. The harmonic frequencies are higher than the measured ones in general, an increase of the anharmonicity of a particular vibration lowers the O—H stretching frequency. For Morse potentials of equal shape, the anharmonicity decreases with decreasing wavenumber, because the zero-point energy of O—H bonds characterized by low frequencies hes closer to the bottom of the Morse potential curve, where the deviations from the harmonic oscillator model are smaller. However, the factors affecting the anharmonicity are far from being completely... 

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