Morse potential/ curve

FIGURE 6.2 Hannonic, cubic, and Morse potential curves used to describe the energy due to bond stretching in molecular mechanics force fields. 

Determine v (v ) from your spectrum and then r" - from this expression. Compare the resultant value of r with the literature value of 0.3025 nm obtained by analysis of the rotational structure of the electronic spectrum. Include the Morse potential curve for the upper state on your plot for the X state and comment on the differences in the various parameters determined for the two states. 

Aside from the assumptions not open to direct test [e.g., equations (1) and (2)], there is a serious we2ikness in the assumption of constant A—H distance. Experiment shows that a H bond of over-all length 2.5 A would have an O—H bond length near 1.07 A (see Fig. 9-1). Because equation (2) is extremely sensitive to a change in r(A—H), this raises the estimate of the amount of covalent character to 22 percent, double the value obtained by Coulson and Danielsson. Since this is in fair agreement with a second estimate (based on a Morse potential curve) by Coulson and Danielsson, it would seem that the appropriate conclusion of this paper should not be that the H bond is essentially ionic but rather that the covalent contribution is quite important for... 

Since the ELT to CCI4 leads to the concerted C—Cl bond cleavage, contribution of the bond breaking should be considered. The dissociative ELT model, in which the Morse potential curve is employed, has been developed to describe... 

The data for F6 indicate a positive vertical and adiabatic electron affinity for the ground state. The presence of a low-lying excited state was observed in other experiments with a vertical electron affinity of —0.4 eV [71]. The higher-energy resonances also result from excited states. These data do not provide direct estimates of the adiabatic electron affinity of a molecule, but have been used to calculate pseudo-two-dimensional Morse potential curves for the molecular anions using data from various sources including the ECD [72]. 

All the curves discussed in this chapter have been assigned to the general Herschbach ionic Morse potential curves classification. While many of these curves are speculative, they reflect the data. As stated by Robert Sanderson Mulliken in offering curves for I2 in 1971, While the curves shown cannot possibly be quantitatively correct, they should be useful as forming a sort of zeroth approximation to the true curves. [128]. 

FIGURE 2 The behavior of an ion along the axis under the influence of only a Morse potential. Curve (a) is the potential, (b) the first derivative, and (c) the second derivative. 

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... 

Figure 2.48 Schematic representation the Morse potential curve of OH and OD bonds.

No transition other than B-X has yet been seen in the afterglow spectrum of BrCl, and it would seem that direct population of the B state from Br + Cl proceeds without an appreciable activation barrier. (Morse potential curves for BrO are shown in Figure 9.)... 

Fig. 4.1 Calculation of van der Waals distances from the Morse potential curve...

The kinetic (T) and potential V) energies of the and u states for H2 as a function of intemuclear distance. The addition of the Tg and 7, energies leads to the typical Morse potential curve, while the addition of the T and V energies leads to a function that is always repulsive. Adapted from course notes by W. A. Goddard III, "Nature of the Chemical Bond."... 

Since the real energy of the system is T plus V, we must add the T and V curves for both the g and u states. Upon addition for the g state, you find there are certain intemuclear distances that the T term dominates, causing a bond to form. At shorter distances the V term dominates, giving the typical shape found for a Morse potential curve (see Sections 2.1.4 and 8.1.2). For all intemuclear distances, the T term dominates in the u state, and this state is always repulsive. This is the origin of the repulsion between atoms that arises when populating an antibonding orbital with electrons. 

Fig. 3. Morse potential curves representing interaction potential between Ar and hydroxyl radicals in the A and X states as a function of Ar to OH (center-of-mass) distance.

Figure 2.3 Morse potential curve and vibrational energy levels.

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