Morse Potential Energy Curves Bonding

Figure 2.2 Morse potential energy curves for the neutral and negative-ion states of anthracene. The vertical electron affinity VEa, adiabatic electron affinity AEa, and activation energy for thermal electron attachment E are shown. The two Ea are 0.68 eV and 0.53 eV observed in ECD data. There will be nine other negative ion curves, yielding a total of thirteen anion curves, four each for the different C—H bonds and a polarization curve. Some of these will be accidentally degenerate.

With the Ea of the molecules and radicals, bond dissociation energies, and electron impact data, the Morse potential energy curves for the C6F5X compounds can be calculated. They are shown in Figures 11.7 and 11.8. There are two curves dissociating to each of the complementary limits C6F5 + X(—) and C6F5(-) + X. The... 

However, one of the limitations of the Morse potential energy is that, in contrast to the experimental" curve, the value of the energy at J = 0 (corresponding to nuclear fusion) is finite, rather than infinite. The minimum in the Morse potential energy curve occurs at / = which represents the equilibrium bond length. 

The r(X ) = f(E) dependence being the same for molecular and crystalline halides, the radii of non-isoelectronic ions can be determined, provided the bond energies are known. The ionic radii for MX molecules and crystals are listed in Table 1.15, from which it follows that cationic and anionic radii change with to a similar degree. The radii of F (1.21 A), Cr (1.63 A), Br (1.71 A), and 1 (1.90 A) have been calculated from the Morse potential energy curves (calculated from the spectroscopic data) for the dissociation of molecular ions, X2 X +X,... 

Figure 2.3 shows the potential energy curve for a diatomic molecule, often referred to as a Morse curve, which models the way in which the potential energy of the molecule changes with its bond length. 

The shapes of the absorption band associated with the intensities of vibrational transitions, are sensitive functions of the equilibrium bond length, about which approximately harmonic vibrational oscillations occur. Potential energy curves for a diatomic molecule (Figure 4.2), are commonly represented by Morse equation,... 

The potential energy curve corresponding to the bonding state is often well described by a Morse potential ... 

Figure 5.8 Experimental Morse curve for CH3-NH2 and multiple-bond potential-energy curves obtained from the Morse curve by screening the in-temuclear repulsion [144]-...

Figure 28-7 In force field calculations, different levels of approximations are used to reproduce the stretching and compression of chemical bonds The plot shows a Morse potential energy function siipenmposed with various power series approximations (quadratic, cubic, and quartic functions) Note that the bottoms of the curves, representing the bond length for most chemical bonds of interest to medicinal chemists, almost overlap exactly. This nearly perfect fit in the bonding region is the reason simple harmonic functions can be used to calculate tx>nd lengths for unstrained molecular structures in the force lield method.

Inorganic chemistry concerns molecules of all the atoms. The electron affinities of atoms, small molecules, and radicals and their relationship with the Periodic Table, electronegativities of elements, Morse curves of diatomic anions, and the energies of ion molecule reactions and bond energies are inorganic problems we have considered. Ionic radii can be estimated using potential energy curves. 

For strong hydrogen bonds a second potential minimum appears, and that leads to a substantial modification of the potential energy curve. The simplest solution of the problem was the application of the double Morse function [8], shown in the form... 

In MM3, this problem of trying to compute as efficiently as possible has been corrected by adding a quartic term. In this way, the possibility of having the potential energy curve invert is eliminated. Moreover, the new curve is a better approximation to a Morse potential over a longer distance. Accordingly, MM3 has one additional term to describe bond stretching as shown in Eq. [4]. 

To explore the true reaction coordinate, assumed to be represented simply by C-OR bond breaking, the authors proposed a way to relate the data to a standard potential energy curve. The requirement that such a curve has an approximately linear region on the dissociation side of the energy minimum, is fulfilled by the Morse function ... 

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