Potential energy curves electronic excitation

Potential energy curves in excited electronic states... 

The potential energy curves of excited electronic states need not have potential energy minima, such as those shown in Fig. 3.6. Thus Fig. 3.7 shows two hypothetical cases of repulsive states where no minima are present. Dissociation occurs immediately following light absorption, giving rise to a spectrum with a structureless continuum. Transition a represents the case where dissociation of the molecule AB produces the atoms A and B in their ground states, and transition b the situation where dissociation produces one of the atoms in an electronically excited state, designated A. ... 

Fig. AIII.2. Potential energy curves, electronic orbitals, and vibrational levels are schematically depicted for the electronic ground state and an excited electronic state of a homonuclear diatomic molecule such as Hg. The molecular c-axis is assumed to be perpendicular to the...

Fig. 3. Potential energy curves for excited states of a bichromophoric system with negligible (a), weak (b), and strong (c) electronic coupling. In (b) and (c) the dashed curves represent zero-order 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]).

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... 

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 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... 

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... 

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.

Considering again the case of a structureless continuum, we have that 8j3 arises from excitation of a superposition of continuum states, hence from coupling within PHmP [69]. The simplest model of this class of problems, depicted schematically in Fig. 5b, is that of dissociation of a diatomic molecule subject to two coupled electronic dissociative potential energy curves. Here the channel phase can be expressed as... 

Hydroxyl radical (OH) is a key reactive intermediate in combustion and atmospheric chemistry, and it also serves as a prototypic open-shell diatomic system for investigating photodissociation involving multiple potential energy curves and nonadiabatic interactions. Previous theoretical and experimental studies have focused on electronic structures and spectroscopy of OH, especially the A2T,+-X2n band system and the predissociation of rovibrational levels of the M2S+ state,84-93 while there was no experimental work on the photodissociation dynamics to characterize the atomic products. The M2S+ state [asymptotically correlating with the excited-state products 0(1 D) + H(2S)] crosses with three repulsive states [4>J, 2E-, and 4n, correlating with the ground-state fragments 0(3Pj) + H(2S)[ in... 

The photolysis experiments have also received theoretical attention, with electronic structure methods used to calculate the nature of the excited states (44), as well as the potential energy curves for loss of CO (45). Theoretical models for the excited-state dynamics leading to dissociation have also been proposed (46). 

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. 

Fig. 2.2. Electron ionization can be represented by a vertical line in this diagram. Thus, ions are formed in a vibrationaUy excited state if the intemuclear distance of the excited state is longer than in the ground state. Ions having internal energies below the dissociation energy D remain stable, whereas fragmentation will occur above. In few cases, ions are unstable, i.e., there is no minimum on their potential energy curve. The lower part schematically shows the distribution of Franck-Condon factors, fyc, for various transitions.

The wave function of Eqs. (14) and (15) was widely used to obtain BO potential energy curves and adiabatic corrections for the ground state (Kolos et al., 1986 Kotos and Rychlewski 1993, Wolniewicz 1993, 1995a) and electronically excited... 

FIGURE 3.6 Potential energy curves for the ground state and an electronically excited state of a hypothetical diatomic molecule. Right-hand side shows relative intensities expected for absorption bands (from Calvert and Pitts, 1966). 

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