Potential energy curves for two electronic states

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]).

Fig. 1 Configurati(ni coordinate diagram showing the potential energy curves for two electronic states a and b. The ordinate is energy and the abscissa is the configuration coordinate, which in one dimension can be thought of as a change in bond distance. Equilibrium (minimum) values of potential energy are identified by the 0 subscript...

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

The determining feature by which laser action can be efficiently obtained from this type of active medium is the fact that the atoms that form the dimmer are only bound in the excited state. Figure 2.9 shows a schematic diagram of the laser energy levels in a molecule of excimer. The laser transition is produced between two molecular electronic levels in which the potential energy curve for the fundamental state is repulsive. This ensures the population inversion. 

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... 

FIGURE 3.8 Potential energy curves for the ground state and two electronically excited states in a hypothetical diatomic molecule. Predissociation may occur when the molecule is excited into higher vibrational levels of the state E and crosses over to repulsive state R at the point C (from Okabe, 1978). 

Figure 5 Potential energy curves for an electron-transfer reaction p(A+- -B) — s A- -B+), showing vibrational quantization, assuming the same vibrational frequency v in precursor and successor states. Some of the vibrational wavefunctions are indicated. The dotted arrows refer to electron transfer below the energy of the crossing of the two curves...

The electronic spectra of rare gas dimers have been a subject of interest for many years, mainly because these dimers are model systems for studying van der Waals interactions, and because of their potential as media for VUV and XUV lasers. Yet very little is known about the excited states of these dimers. Two experimental techniques were combined in our laboratory for this investigation four-wave summixing (4-WSM) and a pulsed supersonic jet to produce rotationally and vibrationally cold dimer molecules. In this way it was possible to resolve rovibronic structures in several isotopic band systems of Xe2, Kr2 and Ar2, in the region 150 to 104 nm, to determine the relevant molecular constants, and to calculate potential energy curves for the ground states and the three lowest (stable) excited states, for all three dimers [41,42,43]. 

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. 

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)...

Fig. 1. (a) HI absorption curves from the work of Romand3. The solid portion of curve 1 is the experimental absorption curve the broken portion is the proposed continuum curve at lower wavelength. Curves 2 and 3 are the component curves (calculated) corresponding to two different electronic transitions (b) Potential energy curves for the low-lying electronic states of HI. ... 

FIGURE 3.7 Potential energy curves for a hypothetical diatomic molecule showing electronic transitions to two repulsive excited states having no minima. A is an electronically excited atom. 

Figure 8.51. Potential energy curves for the a 3n and a 3S+ excited electronic states of CO, showing the near-coincidence of the v = 4 and u = 0 vibrational levels of the two respective electronic states [168].

Figure 3. (a) Valence bond representation of the electronic structure of the (HON)-CH-(NOH) radical, a prototype of nitronyl nitroxide. (b) Potential energy curve for the interaction of two (HON)-CH-(NOH) radicals placed one on top of the other (the coordinates differing by a displacement along the vertical coordinate z). Each fragment is a doublet state, and the curve was computed for the triplet state at the UB3LYP/6-31+G(d) level. 

Figure 2.2 Morse potential energy curves for the neutral and negative-ion states of anthracene. The vertical electron affinity VEa, adiabatic electron affinity AEa, and activation energy for thermal electron attachment E are shown. The two Ea are 0.68 eV and 0.53 eV observed in ECD data. There will be nine other negative ion curves, yielding a total of thirteen anion curves, four each for the different C—H bonds and a polarization curve. Some of these will be accidentally degenerate.

Figure 2.3 Morse potential energy curves for the neutral and negative-ion states of CC14. The new quantity illustrated in this figure is photodetachment energy. It is larger than AEa and is the peak in the photodetachment spectmm. Thermal electron attachment is exothermic, that is, EDEA = a positive quantity. Two other states dissociating to Cl + CC13(—) and the polarization curve are not shown.

The electron affinities of several triatomic molecules and the azide radical have been evaluated and are supported by the CURES-EC method. The molecules that are linear in the neutral and bent in the anion have been emphasized. The ECD data support two negative-ion states. Morse potential energy curves for N20 and CS2 have been constmcted for the linear and bent ions. The relative energies of the anion and neutrals for C02, COS, CS2, and N20 were presented to explain the electron attachment data. The electron affinities of the SF molecules n = 1 to 6 were evaluated and the largest values assigned to the ground state. 

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