Morse Chemical

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Morse, P. M. Producers brace for MTBE Phaseout, Chemical and Engineering News, April 12, 1999, p. 26. 

It is difficult to point to the basic reason why the average-potential model is not better applicable to metallic solutions. Shimoji60 believes that a Lennard-Jones 6-12 potential is not adequate for metals and that a Morse potential would give better results when incorporated in the same kind of model. On the other hand, it is possible that the main trouble is that metal solutions do not obey a theorem of corresponding states. More specifically, the interaction eAB(r) may not be expressible by the same function as for the pure components because the solute is so strongly modified by the solvent. This point of view is supported by considerations of the electronic models of metal solutions.46 The idea that the solvent strongly modifies the solute metal is reached also through a consideration of the quasi-chemical theory applied to dilute solutions. This is the topic that we consider next. 

In 1936, de Boer formulated his theory of a stressed bond which, despite its simplicity, still constitutes the basis for most models of chemical reactivity under stress [92], In order to fracture an unstressed bond which, in the absence of any vibration, is approximated by the Morse potential of Fig. 18, an energy D must be supplied. If, however, the bond is under tension due to a constant force feitt pulling on either end, the bond rupture activation energy will be decreased by an amount equivalent to the work performed by the mechanical force over the stretching distance from the equilibrium position. The bond potential energy in the presence of stress is given by ... 

Bishea, G.A. and Morse, M.D. (1991) Spectroscopic studies of jet-cooled AgAu and Au2. Journal of Chemical Physics, 95, 5646-5659. 

Morse, M.D., Hopkins, J.B., Langridge-Smifh, P.R.R. and Smalley, R.E. (1983) Spectroscopic studies of the jet-cooled copper trimer./oitmai of Chemical Physics, 79, 5316-5328. 

Roth, K.M., Zhou, Y., Yang, W. and Morse, D.E. (2005) Bifunctional small molecules are biomimetic catalysts for silica synthesis at neutral pH. Journal of the American Chemical Society, 127, 325-330. 

Vibrational levels are often analyzed in terms of an harmonic model, but in practice this is not a good approximation for real chemical bonds. An empirical expression that provides a more realistic description of a stretched bond, is the Morse function... 

Equation (9.19) is a chemical version of Hooke s law, and only applies where the Morse curve is parabolic, i.e. near the bottom of the curve where molecular vibrations are of low energy. 

FIGURE 3.1. Morse curve modeling of the contribution of bond breaking to the dynamics of dissociative electron transfer. Adapted from Figure 1 of reference 6a, with permission from the American Chemical Society. 

FIGURE 3.2. Variation of the rate constants of dissociative electron transfer from aromatic anion radicals to butyl and benzyl halides as a function of steric hindrance. Data points from reference 10. Solid lines, best-fit parabola dashed lines, prediction of the Morse curve model, logAf-1 s-1). Adapted from Figure 3 of reference 6b, with permission from the American Chemical Society. 

FIGURE 3.25. Potential energy profiles (from B3LYP/6-13G calculations) for the clevage of 3- and 4-nitrobenzyl chloride anion radicals (a and b, respectively) in the gas phase (top) and in a solvent (middle and bottom) (from COSMO solvation calculations with a dielectric constant of 36.6 and 78.4, respectively). Dotted and solid lines best-fitting Morse and dissociative Morse curves, respectively. Adapted from Figure 3 of reference 43, with permission from the American Chemical Society. 

FIGURE 3.30. Reaction of iron(0) and iron(I) pophyrins with n-, s-, and r-butyl bromides. The chart shows the various porphyrins and their symbolic designations. iron porphyrins, aromatic anion radical, lines best-fitting parabolas through the aromatic anion radicals data. Dashed lines outer-sphere curves obtained by use of the Morse curve model (Section 3.2.2). Adapted from Figure 4 in reference 47b, with permission from the American Chemical Society. 

In the stepwise case, the intermediate ion radical cleaves in a second step. Adaptation of the Morse curve model to the dynamics of ion radical cleavages, viewed as intramolecular dissociative electron transfers. Besides the prediction of the cleavage rate constants, this adaptation opens the possibility of predicting the rate constants for the reverse reaction (i.e., the reaction of radicals with nucleophiles). The latter is the key step of SrnI chemistry, in which electrons (e.g., electrons from an electrode) may be used as catalysts of a chemical reaction. A final section of the chapter deals... 

Walter and Morse (1984) were able to document the relative importance of microstructure for the dissolution of biogenic carbonates. Biogenic magnesian calcites are structurally disordered and chemically heterogeneous. Both these factors play a role in the reactivity of these minerals in natural systems. 

The above data have been analyzed theoretically within the same model as described for the chemical shift tensor (5iso In order to understand the chemical shift observed within the KDP family, we concentrate here on the polarizability modified double-well potential of the protons, which has been modelled by two back-to-back Morse potentials (see Chap. 1 in this volume). The separation between the protons and the centre of the left (/) or right (r) PO4 shell... 

David C. Morse, Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. S.E., Minneapolis, MN... 

Fig. 9.30. Morse curves for the reactants and products at zero driving force (v, elongation of the R-X distance from the equilibrium B = iz (2jt2p /Drx)1/2 uq, vibration frequency p, reduced mass Dm, bond dissociation energy). (Reprinted with permission of J. M. Saveant, J. Am. Chem. Soc. 109 6788 copyright 1992 American Chemical Society.)...

The harmonic oscillator model does not take into account the real nature of chemical bonds, which are not perfect springs. The force constant k decreases if the atoms are pulled apart and increases significantly if they are pushed close together. The vibrational levels, instead of being represented by a parabolic function as in equation (10.3), are contained in an envelope. This envelope can be described by the Morse equation (Fig. 10.5) ... 

The Lennard-Jones potential is a rather crude representation of an actual intermolecular potential, chosen more often for computational simplicity than chemical accuracy. More accurate for many chemical purposes is the Morse potential... 

The potential maximum could not be fitted by a parabola as in the singlet case a rA functional dependence was found to be more adequate. The deep chemical well at 1.045 A was represented by a Morse function, which reproduced Ginter s spectroscopic results.160... 

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