Morse curve for

The kinetics of the electron transfer reaction leading to the homolytically dissociating primary radical is also a question of interest. It may be modeled using the Morse curve for the reactant and the Morse curve shown in Fig. 10 representing the homolytic dissociation of the primary radical. This point will be discussed in detail in Section 5. 

Figure 2.3 A Morse curve for a diatomic molecule, showing the quantised vibrational energy levels. The minimum on the curve represents the equilibrium bond distance, re...

Since all photochemical reactions require the absorption of a photon, the result is that the reactant molecule is raised to a higher energy level. The outcome of this process depends on the nature of the upper and lower electronic states of the molecule. Four types of absorption behaviour are possible and we will first illustrate these by referring to Morse curves for the simple, diatomic, molecules. Although the potential energy of a complex molecule as a function of its molecular geometry is not a simple two-dimensional curve but a complex multidimensional surface, the conclusions arrived at by the use of Morse curves are instructive. 

Figure 2.11 Morse curve for an excited molecule. The energy required for excitation (A) is lost as the molecule returns to the ground state but only the energy lost between states (C) may be emitted as radiation. Energy losses due to internal rearrangements (B and D) are non-radiative.

Figure 12 Morse curves for the reactants and products at zero driving force (y, elongation of the R-X distance from the equilibrium ...

Figure 3.7 Morse curves for H2+ (black line) and H2 (red line)...

Suppose that a potential difference is applied across the interface. How does this affect the barrier obtained if one linearizes the Morse curves for the electrodic reaction... 

The vertical shift has arisen from the application of an absolute potential difference of d to a hypothetical interface, initially with zero potential difference across it, i.e., zhj) = 0. But the argument is valid for any change of potential across the interface. Thus, if the double-layer potential is initially Atye (i.e., the interface is at equilibrium) and then the potential is change to zf< ), the Morse curve for the initial state is shifted vertically through an energy F(Aty — Atye), or Ft],... 

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.)...

Objectives Reproduce approximately a Morse curve for a molecule in the gaseous state... 

Figure 4.19 Morse curve for anharmonic vibration (the broken curve is a parabola corresponding to harmonic vibration)...

Point a corresponds to X at large distances from YZ. Interaction energy between X and YZ is virtually zero, and the side view of the model shows the typical Morse PE curve for the diatomic molecule YZ. Point d represents products, giving the PE for molecule XY with Z at a large distance, the side view giving the Morse curve for XY. 

Morse curves for electron ionization. A vertical transition is observed if the interatomic distances have no time to adjust. The opposite is represented by the oblique line. Ionization can also lead to higher energies, including the excited electronic state. 

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]-...

Fig. 6. Morse curves for transitions from the molecule to different electronic states of the molecular ion.

Calculate the harmonic force constant 4 and the Morse parameter j8 for the two states. Using the known r J value (0.2666 nm), plot the Morse curve for the ground electronic state of I2. Compare this with the harmonic potential calcnlated from k. ... 

As early as the 1960s D. R. Herschbach calculated six Morse curves for I2(—). The data used to calculate these curves were described as follows ... 

The Morse curves for SF5(—) shown in Figure 9.27 are drawn with positive Ea. The ground-state curve is M 3) and has a large activation energy. The first excited... 

Figure 1 Two-dimensional potential energy diagram for Equation (6) formed from combined Morse curves for the elementary processes A + C A-C and A-B... 

Figure 1 Example of a Morse curve for a dissociation process (D = b =, = 1)...

A o becomes positive because the tangent m2 approaches zero. For the exothermic case AEq becomes negative and the tangent m tends towards zero this is due to the cross-over point approaching the minimum of the Morse curve for dissociation of the reactant. 

The problem is to formulate these relationships quantitatively. One approach, called the interacting state model (ISM) uses the Morse curves for the C-H and H-X bonds as the starting point and describes the TSs in terms of the length of the C-H and C-X bonds at the The total bond order is taken to be 1.0 unless one of the... 

Fig. 1. Morse curve for the dissociation of the bond C-H indicating zero-point energies for C-H and C-D.

The elastic modulus of a material arises from the relation between an applied force and the resultant change in the average separation distance of the atoms which form the structure of that material. If we consider the Condon-Morse curve for force, F, as a function of atomic separation distance, r, we can write an expression of the form ... 

Figure 7. Approximate configuration and scheme of reaction complex terms of discharge step of hydrogen evolution reaction. The equilibrium Hg-H bond length is taken as measured in gas phase (0.18 nm) rn H = 0.105 nm. The final state term (dashed line 4) has been plotted as the basis of Morse curve for //ads (curve 2) and H3O decay curve (curve 3). Electron tunneling length is taken to be 0.45 nm. Curve 1 is the HaO" term.

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