Potential energy curve for

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.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. ...

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 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. 

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 7.1 7 Potential energy curves for the ground and several excited states of C2. (Reproduced, with permission, from Ballik, E. A. and Ramsay, D. A., Astrophys. J., 137, 84, 1963 published by the University of Chicago Press Copyright 1963 The American Astronomical Society)...

Sketch potential energy curves for the following states of CdH, Br/ and CH, given their intemuclear distances r, and suggest qualitative intensity distributions in the v" = 0 progressions for transitions between the states observed in absorption ... 

Figure 9.41 Potential energy curves for the two lowest electronic states of Nal showing avoided level crossing and the effect of excitation with a femtosecond laser pulse. (Reproduced, with permission, from Rose, T. S., Rosker, M. J. and Zewail, A. H., J. Chem. Phys., 91, 7415, 1989)...

An example of an investigation of vibrational motion in a bound (excited) electronic state is in the B state of I2 (see Section 73.2). Figure 9.44 shows potential energy curves for three electronic state of I2, the ground state the first excited state B IIq+ and a higher... 

Fig. 4. Potential energy curves for R-900 Titanium Dioxide/Tamol 850 (T-850) dispersant mixtures. Tamol is a trademark of Rohm and Haas Co. Numbers on curves indicate the 2eta potential in mV. The fluidity point = 0.21% T-850 = —52 mV.

Fig. 13.6. Energy diagram showing potential energy curves for interconversion of ground-state (5 o) and first and second singlet (,Sj and S2) and first triplet (7"]) excited states. The angle is the C—C—C bond angle at C-2 and C-3. [From D. Grimbert, G. Segal, and A.

Figure S-1. Form of a potential energy curve for diatomic molecule AB. VfrAa) is the potential energy, Tab is the intemuclear distance, is the equilibrium intemuclear distance, and D is the bond dissociation energy. (The zero point energy is neglected in the figure.)...

What are the energies for each species Plot the general shape of the potential energy curve for this reaction. 

Figure 1.22 Potential energy curve for rotation about C-C bond of ethane...

Figure 3.2 Potential energy curve for hydrogen molecule-ion...

At the other end of the spectrum are the ab initio ( from first principles ) methods, such as the calculations already discussed for H2 in Chapter 4. I am not trying to imply that these calculations are correct in any strict sense, although we would hope that the results would bear some relation to reality. An ab initio HF calculation of the potential energy curve for a diatomic Aj will generally give incorrect dissociation products, and so cannot possibly be right in the absolute sense. The phrase ab initio simply means that we have started with a certain Hamiltonian and a set of basis functions, and then done all the intermediate calculations with full rigour and no appeal to experiment. 

Potential energy curves for a reaction proceeding homogenously (full curve) or on a surface (dotted line). 

Sketch the qualitative molecular potential energy curves for the N—N bond on one graph for N2H4, N2, and N,. ... 

Figure 6. Various potential energy curves for the interaction between 02+-02 A = U(r) given by Equation 13 B = the inverse (12-6) power potential shown for comparison C = U(r) given by Equation 15 D = U(r) given by Equation 2. The most probable distance r and the potential at this distance U(r )...

Fig. 5.—Potential energy curves for alkali halide molecules.

Fig. 6.—Potential energy curves for hydrogen molecules. The electron-pair halide molecules. bond structures H F , etc., are...

Fig. 7.—Potential energy curves for the carbon monoxide molecule.

A computational method which is suitable for studies of this nature should fulfill certain basic requirements (a) it should be sufficiently economical to allow computation of full potential-energy curves for comparatively large number of states, (b) the calculated potential curves for bound states should give rise to vibrational and rotational constants which are in reasonable agreement with experiment when a comparison is possible, (c) the calculated total energies of all the states should be of comparable accuracy, and (d) the ordering of the states should be correct. 

Figure 61. Adiabatic potential energy curves for the atomic hydrogen transmission through the five-membered ring in the case of center approach. Taken from Ref. [47].

Figure 6. Calculated potential energy curves for sextet states of FeO. The ground electronic Slate and excited states accessible by allowed electronic transitions from the ground state are shown. Points are calculated using TD-DFT at the B3LYP/6-311G(d,p) level. Sohd hnes are S states and dashed lines are II states, the vertical dashed hne indicates for the ground state. The experimental value of the dissociation energy is also diown for reference.

Figure 6.34 shows potential energy curves for a hypothetical diatomic molecule X2, which approaches a surface, coming from the right-hand side of the diagram. First... 

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