Potential energy curves state

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]).

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... 

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. 

Potential energy curves in excited electronic states... 

For each excited electronic state of a diatomic molecule there is a potential energy curve and, for most states, the curve appears qualitatively similar to that in Figure 6.4. 

As an example of such excited state potential energy curves Figure 7.17 shows curves for several excited states and also for the ground state of the short-lived C2 molecule. The ground electron configuration is... 

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... 

A kinetic scheme and a potential energy curve picture ia the ground state and the first excited state have been developed to explain photochemical trans—cis isomerization (80). Further iavestigations have concluded that the activation energy of photoisomerization amounts to about 20 kj / mol (4.8 kcal/mol) or less, and the potential barrier of the reaction back to the most stable trans-isomer is about 50—60 kJ/mol (3). 

Such diagrams make clear the difference between an intermediate and a transition state. An intermediate lies in a depression on the potential energy curve. Thus, it will have a finite lifetime. The actual lifetime will depend on the depth of the depression. A shallow depression implies a low activation energy for the subsequent step, and therefore a short lifetime. The deeper the depression, the longer is the lifetime of the intermediate. The situation at a transition state is quite different. It has only fleeting existence and represents an energy maximum on the reaction path. 

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.

Finally we have to remember to add on the nuclear repulsion and, if we repeat the calculation for a range of values of the internuclear separation, we arrive at the potential energy curves shown in Figure 4.3 for the ground-state (singlet)... 

If e is now decreased, with the chain in the extended state, the dumbbell nevertheless stays in the stretched state where the potential is the lowest. The transition back to the coiled state occurs only when there is a single minimum on the potential energy curve, i.e. at et = 0.15. Since the critical strain-rate for the stretch-to-coil transition (esc) is much below the corresponding value for the coil-to-stretch transition (eca), the chain stretching phenomenon shows hysteresis (Fig. 11). 

Fig. 9. Sketch of potential energy curves of a segment of conducting polymers in the ground state and in the ionized state Eip, is the vertical ionization energy, E ] the relaxation energy gained in the ionized state, Eip d the ionization energy of the distorted molecule, and Ej, the geometrical distortion energy in the ground state...

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. 

The potential energy curves (Fig. 1), the non-adiabatic coupling, transition dipole moments and other system parameters are same as those used in our previous work (18,19,23,27). The excited states 1 B(0 ) and 2 B( rio) are non-adiabatically coupled and their potential energy curves cross at R = 6.08 a.u. The ground 0 X( Eo) state is optically coupled to both the and the 2 R( nJ) states with the transition dipole moment /ioi = 0.25/xo2-The results to be presented are for the cw field e(t) = A Yll=o cos (w - u pfi)t described earlier. However, for IBr, we have shown (18) that similar selectivity and yield may be obtained using Gaussian pulses too. 

Figure 1.3. Real-time femtosecond spectroscopy of molecules can be described in terms of optical transitions excited by ultrafast laser pulses between potential energy curves which indicate how different energy states of a molecule vary with interatomic distances. The example shown here is for the dissociation of iodine bromide (IBr). An initial pump laser excites a vertical transition from the potential curve of the lowest (ground) electronic state Vg to an excited state Vj. The fragmentation of IBr to form I + Br is described by quantum theory in terms of a wavepacket which either oscillates between the extremes of or crosses over onto the steeply repulsive potential V[ leading to dissociation, as indicated by the two arrows. These motions are monitored in the time domain by simultaneous absorption of two probe-pulse photons which, in this case, ionise the dissociating molecule.

An initial, ultrafast pump pulse promotes IBr to the potential energy curve Vj, where the electrostatic nuclear and electronic forces within the incipient excited IBr molecule act to force the I and Br atoms apart. contains a minimum, however, so as the atoms begin to separate the molecule remains trapped in the excited state unless it can cross over onto the repulsive potential VJ, which intersects the bound curve at an extended... 

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