Potential-energy curve

Figure Al.5.1 Potential energy curve for NeF based on ab initio calculations of Archibong et al...

An example of a potential energy fiinction based on all these ideas is provided by the 10-parameter fiinction used [88] as a representation of ab initio potential energy curves for Fle-F and Ne-F ... 

Morgan J D III and Simon B 1980 Behavior of molecular potential energy curves for large nuclear separations/nf. J. Quantum Chem. 17 1143... 

Figure Al.6.13. (a) Potential energy curves for two electronic states. The vibrational wavefunctions of the excited electronic state and for the lowest level of the ground electronic state are shown superimposed, (b) Stick spectrum representing the Franck-Condon factors (the square of overlap integral) between the vibrational wavefiinction of the ground electronic state and the vibrational wavefiinctions of the excited electronic state (adapted from [3]).

Figure A3.12.5. A model reaction coordinate potential energy curve for a fluxional molecule. (Adapted from [30].)...

Figure Bl.2.3. Comparison of the hannonic oscillator potential energy curve and energy levels (dashed lines) with those for an anliannonic oscillator. The hannonic oscillator is a fair representation of the tnie potential energy curve at the bottom of the well. Note that the energy levels become closer together with increasing vibrational energy for the anliannonic oscillator. The aidiannonicity has been greatly exaggerated.

Figure Bl.26.21. Potential energy curves for an electron near a metal surface. Image potential curve no applied field. Total potential curve applied external field = -E. ...

To compare the relative populations of vibrational levels, the intensities of vibrational transitions out of these levels are compared. Figure B2.3.10 displays typical potential energy curves of the ground and an excited electronic state of a diatomic molecule. The intensity of a (v, v ) vibrational transition can be written as... 

Tellinghuisen J A 1974 A fast quadrature method for computing diatomic RKR potential energy curves Comput. Phys. Commun. 6 221-8... 

Kolos W and Wolniewicz L 1965 Potential energy curves for the X H. and Cn states of the hydrogen molecule J. Chem. Phys. 43 2429-41... 

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

Figure C3.2.1. A slice tlirough tlie intersecting potential energy curves associated witli tlie K-l-Br2 electron transfer reaction. At tlie crossing point between tlie curves (Afy, electron transfer occurs, tlius Tiarjiooning tlie species,...

L1948. Steric Effects. I. Van der Waals Potential Energy Curves. Journal of Chemical Physics 16 399-04. 

The fact that the separated-atom and united-atom limits involve several crossings in the OCD can be used to explain barriers in the potential energy curves of such diatomic molecules which occur at short intemuclear distances. It should be noted that the Silicon... 

A transition structure is the molecular species that corresponds to the top of the potential energy curve in a simple, one-dimensional, reaction coordinate diagram. The energy of this species is needed in order to determine the energy barrier to reaction and thus the reaction rate. A general rule of thumb is that reactions with a barrier of 21 kcal/mol or less will proceed readily at room temperature. The geometry of a transition structure is also an important piece of information for describing the reaction mechanism. 

FIGURE 17.2 Illustration of the reaction coordinate for a reaction with a change in the electronic state, (a) Potential energy curves for the two electronic states of the system. (A) Avoided crossing that can be seen in single-detenninant calculations. 

If the system can only be modeled feasibly by molecular mechanics, use the potential energy curve-crossing technique or a force held with transition-structure atom types. 

The reason that does not change with isotopic substitution is that it refers to the bond length at the minimum of the potential energy curve (see Figure 1.13), and this curve, whether it refers to the harmonic oscillator approximation (Section 1.3.6) or an anharmonic oscillator (to be discussed in Section 6.1.3.2), does not change with isotopic substitution. Flowever, the vibrational energy levels within the potential energy curve, and therefore tq, are affected by isotopic substitution this is illustrated by the mass-dependence of the vibration frequency demonstrated by Equation (1.68). 

Figure 6.4 Potential energy curve and energy levels for a diatomic molecule behaving as an anharmonic oscillator compared with those for a harmonic oscillator (dashed curve)...

The dissociation energy is unaffected by isotopic substitution because the potential energy curve, and therefore the force constant, is not affected by the number of neutrons in the nucleus. However, the vibrational energy levels are changed by the mass dependence of 03 (proportional to where /r is the reduced mass) resulting in Dq being isotope-... 

The potential energy curve in Figure 6.4 is a two-dimensional plot, one dimension for the potential energy V and a second for the vibrational coordinate r. For a polyatomic molecule, with 3N — 6 (non-linear) or 3iV — 5 (linear) normal vibrations, it requires a [(3N — 6) - - 1]-or [(3A 5) -F 1]-dimensional surface to illustrate the variation of V with all the normal coordinates. Such a surface is known as a hypersurface and clearly cannot be illustrated in diagrammatic form. What we can do is take a section of the surface in two dimensions, corresponding to V and each of the normal coordinates in turn, thereby producing a potential energy curve for each normal coordinate. 

Figure 6.38 General shapes of the potential energy curves for the vibrations (a) v- and (b) V3 of CO2...

It might be supposed that, since the potential energy curve for V2 is of a similar shape to that in Figure 6.38(a), if we excite the molecule with sufficiently high energy it will eventually dissociate, losing six hydrogen atoms in the process ... 

Figure 6.40 Potential energy curve for the inversion vibration V2 of NH3...

Figure 6.41 Potential energy curves and vibrational energy levels for an inversion vibration when the barrier to planarity is (a) infinite, (b) moderately low and (c) zero...

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