Morse potential energy

The hot bond fracture stress [Pg.383]

Fig. 18. The Morse potential energy of a bond under equilibrium ( — ) and in the presence of an applied force equal to 0.6 fb (-)...

Figure 3.6 shows the Morse potential energy curves for two hypothetical electronic states of a diatomic molecule, the vibrational energy levels for each, and the shape of the vibrational wavefunctions (i//) within... 

Fig. 55. The probability that a pair of iodine atoms remain unreacted at a time f after they were formed with an initial separation of 0.7 nm. The encounter distance is 0.37 nm. A Morse potential energy getween the iodine atoms is imposed and the temperature was chosen as 300 K. The diffusion coefficient is 5 X 10 9 m2 s1 and iodine atom has a mass of 0.127 kg mol . Monte Carlo techniques were used to calculate the survival probability, with-----, toe — 2xl013s 1, cjc = 1013s l --------,...

There have been several studies of the iodine-atom recombination reaction which have used numerical techniques, normally based on the Langevin equation. Bunker and Jacobson [534] made a Monte Carlo trajectory study to two iodine atoms in a cubical box of dimension 1.6 nm containing 26 carbon tetrachloride molecules (approximated as spheres). The iodine atom and carbon tetrachloride molecules interact with a Lennard—Jones potential and the iodine atoms can recombine on a Morse potential energy surface. The trajectives were followed for several picoseconds. When the atoms were formed about 0.5—0.7 nm apart initially, they took only a few picoseconds to migrate together and react. They noted that the motion of both iodine atoms never had time to develop a characteristic diffusive form before reaction occurred. The dominance of the cage effect over such short times was considerable. 

Now let us idealize the intersection region of the overlapping Morse potential energy curves as shown in Figure 2.15. In the nonequilibrium situation, we arbitrarily define a and b so that the change in barrier height for the reverse reaction is... 

A simple case is the portrayal of the ground state of the OH radical, see Figure 2.14. For simplicity, we show a part of the Morse potential energy curve with the highest bound and quasibound vibrational levels indicated by solid lines and dashed line, respectively, Figure 2.14a. The spectral density is... 

Activated Complex Theory The effect of the operating potential on the rate constants [Eqs. (1.18) and (1.19)] can be understood in terms of the free-energy barrier. Figure 1.8 shows a typical Morse potential energy... 

The Frank-Condon principle is based on the fact that the time of an electronic transition (of the order of 10 s) is shorter than that of a vibration (of the order of 10 s). This means that during an electronic transition the nuclei do not change their positions. This phenomenon can be illustrated using the Morse potential energy curves for diatomic molecules (Figure 2.17). The series of horizontal lines... 

The principles of photoluminescence applied to solid oxide surfaces can be most easily understood by assuming some simplifications. For example, we can start by considering the Morse potential energy curves (Fig. 1) related to an ion pair such as M-+0-, taken as a harmonic oscillator to represent an oxide, typically an alkaline earth oxide. The absorption of light close to the fundamental absorption edge of this oxide leads to the excitation of an electron in the oxide ion followed by a charge-transfer process to create an exciton (an electron-hole pair), which is essentially... 

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.

Figure 2.1 Morse potential energy curves for the neutral and negative-ion states of F2. The vertical electron affinity VEa, adiabatic electron affinity AEa, activation energy for thermal electron attachment E, Err — AEa — VEa, EDEA — Ea(F) — D(FF), and dissociation energy of the anion Ez are shown.

Figure 2.3 Morse potential energy curves for the neutral and negative-ion states of CC14. The new quantity illustrated in this figure is photodetachment energy. It is larger than AEa and is the peak in the photodetachment spectmm. Thermal electron attachment is exothermic, that is, EDEA = a positive quantity. Two other states dissociating to Cl + CC13(—) and the polarization curve are not shown.

HERSCHBACH IONIC MORSE POTENTIAL ENERGY CURVES... 

Figure 2.4 Classification of negative-ion Morse potential energy curves originally presented by Herschbach in 1966. The curves are calculated from actual data. The empty spaces are impossible combinations. These classifications have been modified so that they are symmetrical and all combinations are possible [34, 36].

NEGATIVE-ION MASS SPECTROMETRY AND MORSE POTENTIAL ENERGY CURVES, 1980 TO 1990... 

Figure 4.9 Morse potential energy curves for chloromethane and its ions. The curves are calculated using the activation energy determined from data in Figure 4.8. The high-temperature data is for unimolecular dissociation via the curve crossing on the approach side of the molecule. Only the VEa is negative and dissociation occurs in the Franck Condon transition. The thermal energy dissociation occurs through the thermal activation of the molecule, as is the case for all DEC(l) molecules.

In 1963 negative-ion Morse parameters for the ground-state anions of Br2 and I2 were obtained by estimating D, re, and v from the VEa measured from charge transfer spectra and properties of the excited states of the neutral. Multiple excited states of I2(—) were characterized by D. R. Herschbach in 1966. He presented general forms for ionic Morse potential energy curves (HIMPEC). Nine total groups... 

Figure 7.11 Original Hershbach ionic morse potential energy curves and the modified HIMPEC [2, 3], The curves are calculated for the current best available data. The multiple curves for 02(—) and I2( ) are given to illustrate the relative positions of the curves. The specific example is the curve that is solid.

Figure 7.12 Historical Morse potential energy curves for H2 and its anions, dating back to 1936 [25], 1956 for the excited state [26], 1967 for the polarization ground state [27], and 1981 for the valence excited state [28].

Figure 7.13 Current best Morse potential energy curves for H2 and its anions, from [30-32],...

Figure 7.15 Current best Morse potential energy curves for I2 and its anions. The X axis is the reduced intemuclear distance 5=1 — reJ r, where r is the intemuclear distance and re is the equilibrium intemuclear distance. The data are taken from [18]. The 12 curves were predicted in [23].

Figure 7.18 Current best Morse potential energy curves for naphthalene and its anions. There are four additional antibonding curves that are not shown, giving a total of eight valence-state curves. The adiabatic electron affinity corresponds to the valence state with an Ea of 0.16 eV. The polarization curve has an Ea of about zero.

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