Diatomic molecule, Morse curve

Figure 1.6 Potential energy as a function of interatomic distance in a diatomic molecule (Morse curve) showing vibrational energy levels for molecules containing the heavier (H) and lighter (L) of the two isotopes considered. The dissociation energies Do for these two types of molecules are also indicated.

This time period is too short for a change in geometry to occur (molecular vibrations are much slower). Hence the initially formed excited state must have the same geometry as the ground state. This is illustrated in Figure 1.2 for a simple diatomic molecule. The curves shown in this figure are called Morse curves and represent the relative energy of the diatomic system as a... 

Figure 9.12 Morse curve of the diatomic molecule X2 in the ground state...

Another way of looking at the Morse curve in Figure 9.12 is to say it represents the energy E (as y ) of the two atoms of X as a function of their bond length r (as V). The two atoms of X form a simple diatomic molecule in its ground state, i.e. before it absorbs a photon of light. 

Figure 9.15 Morse curve of a diatomic molecule X2 showing vibrational fine structure...

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. 

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 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... 

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,... 

Fig. VII-1.—A curve representing the electronic energy of a diatomic molecule as a function of the distance between the nuclei. The zero for energy is the energy of the separated atoms. The minimum of the curve corresponds to the equilibrium value of the internuclear distance. The curve shown, which approximates closely the observed electronic energy curves for many states of diatomic molecules, corresponds to the Morse function.

A. simple function that gives a close approximation to the electronic energy curve for many states of diatomic molecules is the Morse function. This function is... 

An understanding of what is implied by a Morse curve is necessary here, in order to understand the following point. A diatomic molecule has one normal mode of vibration. If the vibration behaves as a harmonic oscillator, the PE is proportional to the square of the displacement from the equilibrium internuclear distance. The... 

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. 

Figure 1.1 Morse curve characterizing the energy of the molecule as a function of the distance R that separates the atoms of a diatomic molecule such as hydrogen. At a distance equal to Re, which corresponds to point 0, the molecule is in its most stable position, and so its energy is called the molecular equilibrium energy and expressed as Ee. Stretching or compressing the bond yields an increase in energy. The number of bound levels is finite. Dq is the dissociation energy and De the dissociation minimum energy. The horizontal lines correspond to the vibrational levels.

Figure 1-6 Potential energy curve for a diatomic molecule. Solid line indicates a Morse potential that approximates the actual potential. Broken line is a parabolic potential for a harmonic oscillator. De and D0 are the theoretical and spectroscopic dissociation energies, respectively.

The two cases which arise in diatomic molecules are rotational predissociation and electronic predissociation the latter case applies only to excited electronic states. We deal first with rotational predissociation, with can arise for either ground or excited states. The potential energy curve shown for a Morse oscillator in section 6.8 is for a rotationless (./ = 0) molecule. For a rotating molecule, however, we must add a centrifugal term to the potential,... 

If this Morse function is used to represent any single bond, not necessarily of a diatomic molecule, the constant a calculated from the harmonic force constant may not be entirely appropriate, and especially not over the entire range of r. Before deriving multiple-bond properties from the single-bond curve it is therefore useful to optimize the Morse constant empirically to improve the match between calculated and observed single-bond values of De and re. 

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... 

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. 

The homonuclear diatomic molecules are the simplest closed set of molecules. Many of the electron affinities of the main group diatomic molecules have been measured by anion photoelectron spectroscopy (PES), but only a few have been confirmed. These Ea can be examined by their systematic variation in the Periodic Table. Calculating Morse potential energy curves for the anions and comparing them with curves for isoelectronic species confirm experimental values. The homo-nuclear diatomic anions of Group IA, IB, VI, VII, and 3d elements and NO are examined first. 

Fig. 6.44. Morse curve (Equation 6.5) calculated by using constants Z), = 38.8 kcal mol and p = 13.87 A derived (least-squares method see text) to fit the bond length reactivity data in the way suggested by Figure 6.43. The dashed curve shows the shallower potential function calculated for the gas-phase dissociation into the component atoms of a diatomic molecule joined by a bond with similar properties to that of the C-OR bond of a 2-alkoxytetrahydropyran derived from an alcohol ROH of 15.5...

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