Energy curves

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 A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

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,...

Fig. 5. Total energy curve with finite basis correction (due to Francis and Payne [18]). (lhartree = 627kcal/mol or 2624kJ/mol).

Example For two atoms having point charges of 0.616 and -0.504 e and a constant dielectric function, the energy curve shows a switching function turned on (Ron) at a nonbonded distance of 10. A and off (R(,rr) al a distance of 14 A. Compare the switched poieniial with the abruptly inincaied poteiiiial. 

Caution C omparing the shifted constant dielectric to a constant dielectric function without a cutoff shows that the sh ifted dielectric, iin like a switch in g fun ction, perturbs the en tire electrostatic energy curve, not only the region near the cnioff. 

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

---