Term with electronic transitions

The advent of the laser has stimulated new research in collisional physics. The term laser-assisted collision was coined to describe the various research activities that have evolved. These studies are concerned with electronic transitions in supermolecules and will be briefly considered here. Similarities between laser-assisted collisions (LAC) and collision-induced absorption (CIA) exist, both in the types of phenomena considered and in the calculations of the spectra [208]. 

Optical excitations quite often generate considerable changes in fixed partial charges, usually described in terms of the difference solute dipole Amo ( 0 refers here to the solute). Chromophores with high magnitudes of the ratio Amo/Rl, where Rq is the effective solute radius, are often used as optical probes of the local solvent structure and solvation power. High polarizability changes are also quite common for optical chromophores, as is illustrated in Table 2. Naturally, the theory of ET reactions and optical transitions needs extension for the case when the dipole moment and polarizability both vary with electronic transition ... 

In the ultraviolet and visible spectrum, the energy of protons associated with electronic transitions lies in the range 147 to 630 kJ/mol. This energy (A ) can be expressed in terms of the principal parameters that define electromagnetic radiation, i.e. frequency V (Hz), wavelength X (nm), and wave-number v (cm )... 

In most cases of interest to us we will be dealing with electronic transitions, i. e., transitions between orthogonal electronic states ipi and Therefore (i j) = 0, so that the second term in the parenthesis of Eq. (17 ) vanishes. Eq. (17 ) now becomes,... 

Fig. 35. The n molecular orbitals according to Huckel MO calculations (kfi), energy level diagram (center) and term diagram of benzene with electronic transitions indicated (right). Quoted from [6]. Copyright John Wiley and Sons, Ltd. Reproduced with permission. The other parts are taken from Chang R (1971) Basic principles of spectroscopy. McGraw-Hill Kogakushi, Ltd, Tokyo. Reproduced with permission of the McGraw-Hill Companies...

Interestingly, this approximation yields an exponential term with a transition factor of a = 1/2 which would correspond to a slope for the Tafel equation of 120 mV per current decade. There are certainly many redox systems with which this slope has nearly been verified (a 0.4—0.5). On the other hand, one would expect a deviation from a linear log j—rj plot for redox couples with a reorganization energy of A < 1 eV. This is, however, difficult to prove because small A values lead to large exchange currents (Eq. (7.16)). Since then the electron transfer process is... 

Since we are dealing with electronic transitions j i), the second term on the RHS of the previous equation is null due to the orthogonality of the electronic wave-functions, so that... 

Projecting the nuclear solutions Xt( ) oti the Hilbert space of the electronic states (r, R) and working in the projected Hilbert space of the nuclear coordinates R. The equation of motion (the nuclear Schrddinger equation) is shown in Eq. (91) and the Lagrangean in Eq. (96). In either expression, the terms with represent couplings between the nuclear wave functions X (K) and X (R). that is, (virtual) transitions (or admixtures) between the nuclear states. (These may represent transitions also for the electronic states, which would get expressed in finite electionic lifetimes.) The expression for the transition matrix is not elementaiy, since the coupling terms are of a derivative type. 

We note that three spin-allowed electronic transitions should be observed in the d-d spectrum in each case. We have, thus, arrived at the same point established in Section 3.5. This time, however, we have used the so-called weak-field approach. Recall that the adjectives strong-field and weak-field refer to the magnitude of the crystal-field effect compared with the interelectron repulsion energies represented by the Coulomb term in the crystal-field Hamiltonian,... 

Before dealing further with the non Bom-Oppenheimer case, it is useful to recall how one can cast other rate expressions, such as the rate of photon absorption (7) accompanying an electronic transition in a molecule, in terms of a... 

Emission of light due to an allowed electronic transition between excited and ground states having the same spin multiplicity, usually singlet. Lifetimes for such transitions are typically around 10 s. Originally it was believed that the onset of fluorescence was instantaneous (within 10 to lO-" s) with the onset of radiation but the discovery of delayed fluorescence (16), which arises from thermal excitation from the lowest triplet state to the first excited singlet state and has a lifetime comparable to that for phosphorescence, makes this an invalid criterion. Specialized terms such as photoluminescence, cathodoluminescence, anodoluminescence, radioluminescence, and Xray fluorescence sometimes are used to indicate the type of exciting radiation. 

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.

---