Absorption photon

The photochemical reaction of a material starts with photon absorption. In other words, only the photons absorbed by the molecule can bring about photochemical reactions. This is the first law of photochemistry, also called the Grotthuss-Draper law. The second law of photochemistry is one molecule is activated when one photon is absorbed. This is called the Stark-Einstein photochemical equivalence law. Generally, a particular group in an irradiated molecule absorbs a photon with an appropriate wavelength. When photoabsorption occurs, the molecule in the ground state is 

TABLE 24.1 Homolysis Energy of Some Chemical Bonds and the Corresponding Photon Wavelength [2, 4] 

Photoexcitation does not occur for all molecules with the same probability. This is because photoabsorption depends on the chemical structure of the chromophore group. As the Lambert-Beer equation describes 

Energy and wavelength values are estimated based on the cited references. 

FIGURE 24.2 Electron transitions between molecular orbitals. Note The distance between orbitals is drawn equally for better comprehensibility. 

---

We will now look at two-photon processes. We will concentrate on Raman scattering although two-photon absorption can be handled using the same approach. In Raman scattering, absorption of an incident photon of frequency coj carries... 

One very important aspect of two-photon absorption is that the selection ndes for atoms or synnnetrical molecules are different from one-photon selection ndes. In particular, for molecules with a centre of synnnetry, two-photon absorption is allowed oidy for g g or u u transitions, while one-photon absorption requires g-f u transitions. Therefore, a whole different set of electronic states becomes allowed for two-photon spectroscopy. The group-theoretical selection ndes for two-photon spectra are obtained from the synnnetries... 

Three-photon absorption has also been observed by multiphoton ionization, giving Rydberg states of atoms or molecules [36]. Such states usually require vacuum ultraviolet teclmiques for one-photon spectra, but can be done with a visible or near-ultraviolet laser by tluee-photon absorption. 

Monson P R and McClain W M 1970 Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene J. Chem. Rhys. 53 29-37... 

Strickler S J, Gilbert J V and McClanaham J E 1984 Two-photon absorption spectroscopy of molecules Lasers and Applications eds H D Bist and J S Goela (New Delhi Tata McGraw-Hill) pp 351-61... 

All nonlinear (electric field) spectroscopies are to be found in all temis of equation (B 1.3.1) except for the first. The latter exclusively accounts for the standard linear spectroscopies—one-photon absorption and emission (Class I) and linear dispersion (Class II). For example, the temi at third order contains by far the majority of the modem Raman spectroscopies (table B 1.3.1 and tableBl.3.2). 

Lee D and Albrecht A C 1985 A unified view of Raman, resonance Raman, and fluorescence spectroscopy (and their analogues in two-photon absorption) Advances in Infrared and Raman Spectroscopy vo 12, ed R J H Clark and R E Hester (New York Wiley) pp 179-213... 

Figure Bl.18.14. Schematic representation of the increase of absorption with photon density for two- and tliree-photon absorption.

Lindek St, Cremer Chr and Stelzer E H K 1996 Confocal theta fluorescence microscopy using two-photon absorption and annular apertures Optik 02 131-4... 

Figure Bl.22.7. Left resonant seeond-hannonie generation (SHG) speetnimfrom rhodamine 6G. The inset displays the resonant eleetronie transition indueed by tire two-photon absorption proeess at a wavelength of approximately 350 mn. Right spatially resolved image of a laser-ablated hole in a rhodamine 6G dye monolayer on fiised quartz, mapped by reeording the SHG signal as a fiinetion of position in the film [55], SHG ean be used not only for the eharaeterization of eleetronie transitions within a given substanee, but also as a mieroseopy tool.

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

Plakhotnik T, Walser D, Pirotta M, Renn A and Wild U P 1996 Nonlinear spectroscopy on a single quantum system two-photon absorption of a single molecule Science 271 1703-5... 

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

Returning to the kinetie equations that govern the time evolution of the populations of two levels eonneeted by photon absorption and emission, and adding in the term needed for spontaneous emission, one finds (with the initial level being of the lower energy) ... 

Beyond sueh eleetronie symmetry analysis, it is also possible to derive vibrational and rotational seleetion rules for eleetronie transitions that are El allowed. As was done in the vibrational speetroseopy ease, it is eonventional to expand if (R) in a power series about the equilibrium geometry of the initial eleetronie state (sinee this geometry is more eharaeteristie of the moleeular strueture prior to photon absorption) ... 

If this expression is then multiplied by the equilibrium probability pi that the moleeule is found in the state i and summed over all sueh initial states and summed over all final states f that ean be reaehed from i with photons of energy h co, the equilibrium averaged rate of photon absorption by the moleeular sample is obtained ... 

If cof i is positive (i.e., in the photon absorption ease), the above expression will yield a non-zero eontribution when multiplied by exp(-i cot) and integrated over positive covalues. If cOf j is negative (as for stimulated photon emission), this expression will eontribute, again when multiplied by exp(-i cot), for negative co-values. In the latter situation, pi is the equilibrium probability of finding the moleeule in the (exeited) state from whieh emission will oeeur this probability ean be related to that of the lower state pf by... 

The absorption and emission eases ean be eombined into a single net expression for the rate of photon absorption by reeognizing that the latter proeess leads to photon produetion, and thus must be entered with a negative sign. The resultant expression for the net rate of decrease of photons is ... 

To summarize, the line shape function I(co) produces the net rate of photon absorption... 

For all of the eases eonsidered earlier, a C(t) funetion is subjeeted to Fourier transformation to obtain a speetral lineshape funetion I(co), whieh then provides the essential ingredient for eomputing the net rate of photon absorption. In this Fourier transform proeess, the variable co is assumed to be the frequeney of the eleetromagnetie field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to I(co) is ... 

The similarity between a two-photon absorption and a Raman scattering process is even closer. Figure 9.27(a) shows that a Raman transition between states 1 and 2 is really a two-photon process. The first photon is absorbed at a wavenumber to take the molecule from state 1 to the virtual state V and the second photon is emitted at a wavenumber Vj,. 

In a two-photon absorption process the first photon takes the molecule from the initial state 1 to a virtual state V and the second takes it from V to 2. As in Raman spectroscopy, the state V is not an eigenstate of the molecule. The two photons absorbed may be of equal or unequal energies, as shown in Figures 9.27(b) and 9.27(c). It is possible that more than two photons may be absorbed in going from state 1 to 2. Figure 9.27(d) illustrates three-photon absorption. 

Two-photon absorption has been observed in the microwave region with an intense klystron source but in the infrared, visible and ultraviolet regions laser sources are necessary. 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

Fig. 20. Proposed photochemical mechanisms for the generation of acid from sulfonium salt photolysis. Shown ate examples illustrating photon absorption by the onium salt (direct irradiation) as well as electron transfer sensitization, initiated by irradiation of an aromatic hydrocarbon.

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules ia a gas at low pressure can be taken to be isolated for the short time between coUisions. Unimolecular reactions such as photodissociation or isomerization iaduced by photon absorption can sometimes be studied between coUisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity ia one direction and almost zero velocity ia perpendicular directions. Not only does this reduce coUisions, it also aUows bimolecular iateractions to be studied ia intersecting beams and iacreases the detail with which unimolecular processes that can be studied, because beams facUitate dozens of refined measurement techniques. (J) Means have been found to trap molecules, isolate them, and keep them motionless at a predetermined position ia space (11). Thus far, effort has been directed toward just manipulating the molecules, but the future is bright for exploiting the isolated molecules for kinetic and dynamic studies. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

---