R

branch

Lower electronic state v" = 1

FIGURE 3.5 Schematic of some possible rotational and vibrational transitions involved during an electronic transition of a diatomic molecule from the ground electronic state.

Intensity

Internuclear distance, r

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).

Internuclear distance, r

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).

each vibrational energy level. At room temperature, most molecules will originate in v" = 0; the vertical line is at the midpoint of v" =0 since the probability of finding the molecule at r = rc is a maximum here.

The probability of a particular transition from v" = 0 to an upper vibrational level v' is determined largely by the product of the wavefunctions for the two states, i//,,.i//r». A qualitative examination of the wavefunctions in the upper state, i/jt.,, in Fig. 3.6 shows that if/v,, and hence the product !/>,,<!/>,.», is a maximum around v' = 4; thus the vibrational transition corresponding to v" = 0 -> v' = 4 is expected to be the most intense. On the other hand, the wavefunction at v' = 0 is very small; hence the v" = 0 -» v' = 0 transition should be weak. The right side of Fig. 3.6 shows the corresponding intensities expected for the various absorption lines in this electronic transition.

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*.

Some molecules may have a number of excited electronic states, some of which have potential minima, as

FIGURE 3.7 Potential energy curves for a hypothetical diatomic molecule showing electronic transitions to two repulsive excited states having no minima. A4 is an electronically excited atom.

in Fig. 3.6, and some of which are wholly repulsive, as in Fig. 3.7. In this case, depending on the wavelength absorbed (i.e., the electronically excited state reached), the molecule may dissociate or undergo one of the photophysical processes described below.

A simplified, hypothetical example of this situation is shown in Fig. 3.8. If the molecule absorbs light corresponding to energies insufficient to produce vibrational energy levels above v' = 2 in the excited state E, a structured absorption (and emission) spectrum is observed. However, if the photon energy is greater than that required to produce A + B, that is, greater than the bond dissociation energy, then the molecule may be excited either into the repulsive state R, from which it immediately dissociates into ground-state atoms A + B, or alternatively into vibrational levels v' > 2 of excited state E. In the latter case, the excited molecule may undergo one of the photophysical processes discussed below (fluorescence, deactivation, etc.) or it may cross over from state E into the repulsive state R (point C in Fig. 3.8) and dissociate. This phenomenon is known as predissociation. In a case such as that in Fig. 3.8, the absorption spectrum would be expected to show well-defined rotational and vibrational structure up to a certain energy corresponding to the transition v" = 0 -» v' = 2. For transitions to higher vibrational levels, the rotational structure becomes blurred, and a predissociation spectrum is observed. 12 is an example of a molecule with both a low-lying repulsive electronically excited state and bound excited states; excitation from the ground 'S

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 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).

state into the repulsive 'if state results in dissociation into the ground state iodine atoms. On the other hand, excitation into the B3I1 state below the dissociation limit gives electronically excited I2, which returns to the ground state via light emission or crosses into the repulsive 1 n state and predissociates (Okabe, 1978).

Finally, if the incident photon is sufficiently energetic and the appropriate selection rules are obeyed, the excited molecule may be produced in vibrational levels of state E that are sufficiently high that the molecule immediately dissociates into A + B*, where B* is an electronically excited state.

b. Polyatomic Molecules

The principles discussed for diatomic molecules generally apply to polyatomic molecules, but their spectra are much more complex. For example, instead of considering rotation only about an axis perpendicular to the internuclear axis and passing through the center of mass, for nonlinear molecules, one must think of rotation about three mutually perpendicular axes as shown in Fig. 3.11^ Hence we have three rotational constants A, B, and C with respect to these three principal axes.

Furthermore, polyatomic molecules consisting of n atoms have 3n — 6 vibrational degrees of freedom (or 3n — 5 in the special case of a linear polyatomic molecule), instead of just one as in the case of a diatomic molecule. Some or all of these may absorb infrared radiation, leading to more than one infrared absorption band. In addition, overtone bands (At; > 1)

3. SPECTROSCOPY AND PHOTOCHEMISTRY: FUNDAMENTALS

and combination bands (absorptions corresponding to the sum of two or more of the fundamental vibrations) are much more common.

An atmospherically relevant example of just how complex infrared spectra of polyatomic molecules can be is water vapor. A multitude of observed transitions occurs in the regions ~ 1300-2000 cm~' and 3000-4000 cm-1. This, combined with the relatively high, and often rapidly changing, concentrations of water vapor, makes long-path-length infrared spectroscopic determination of trace atmospheric species in ambient air very difficult in these wavelength regions. Similarly, absorption of C02 renders the region from ~ 2230 to ~ 2390 cm~' unusable for ambient air studies.

2. Fates of Electronically Excited Molecules

Once a molecule is excited into an electronically excited state by absorption of a photon, it can undergo a number of different primary processes. Photochemical processes are those in which the excited species dissociates, isomerizes, rearranges, or reacts with another molecule. Photophysical processes include radiative transitions in which the excited molecule emits light in the form of fluorescence or phosphorescence and returns to the ground state and nonradiative transitions in which some or all of the energy of the absorbed photon is ultimately converted to heat.

a. Photophysical Processes

Photophysical processes are often displayed in the form of the Jablonski-type energy level diagram shown in Fig. 3.9. The common convention is that singlet states are labeled S0, S,, S2, and so on and the triplets are labeled T,, T2, T3, and so on, in order of increasing energy. Vibrational and rotational states are shown as being approximately equally spaced only for clarity of presentation. Radiative transitions, for example, fluorescence (F) and phosphorescence (P), are shown as solid lines, and nonradiative transitions as wavy lines. Vertical distances between the vibrational-rotational levels of the singlet ground state, S(), and the two electronically excited states, the first excited singlet, S,, and its triplet, T,, correspond to their energy gaps.

Fluorescence is defined as the emission of light due to a transition between states of like multiplicity, for example, S, —> S() + hv. This is an allowed transition, and hence the lifetime of the upper state with respect to fluorescence is usually short, typically 10~h-10~9 s. For example, the fluorescence lifetime of OH in the electronically excited A2X+ state is ~ 0.7 /as (McDer-

1 st excited singlet St

1st triplet T1

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