Energy Levels of Excited Molecules

In the case of organic molecules, for instance dyes, several oxidation states generally exist. Each electron transfer step can be correlated qualitatively with the energy of molecular orbitals as illustrated in Fig. 10.2 (triplets are neglected here). A reduction of a molecule M can only occur by electron transfer from an electron donor to an unoccupied level of M. On the other hand, an oxidation of M is only possible by an electron transfer from the lower lying occupied state to a suitable acceptor molecule. These two processes must be described by two different redox potentials, which cannot be 

10 Electron Transfer Processes - Excited Molecules and Semiconductor Electrodes 

It is well known that an excited molecule is more easily reduced or oxidized because the excitation energy AE is stored in the molecule. Possible reactions are 

This is immediately clear from the molecular orbital scheme in Fig. 10.2b. Here, an electron transfer is possible from a higher level to an acceptor, or from a donor to a level of M which is only half-filled. 

In Sections 3.2.4 and 6.2.1 the energy states of a redox couple in the dark were derived in terms of a Fermi level, Ep.redox (redox potential) and of occupied and empty states ( red ox)- According to the molecular energy scheme, one would expect that the standard redox potentials, Fredox(M M ) and Fredox(M/M )- corresponding in the first case to the oxidation and in the second to the reduction of the dye molecule M in the dark, should differ by about AE (see Fig. 10.2a), i.e. 

The stored energy is given by the 0-0 transition (between the lowest vibrational levels in the ground and excited states) in the electron spectra, i.e., AF = AEo-o The excited state may be either a singlet or triplet state (see below). It is now possible to estimate the redox potentials of excited molecules by adding or subtracting AEo-o from the redox potential for the molecules in the ground state. One obtains 

The situation can be very well illustrated taking M = Ru(II)(bipy)3 as an example. This compound is very stable and the ruthenium can exist in various oxidation states (+3 to -2) and most standard potentials in the ground state are known, i.e., Ef(Ru /Ru ) = 1.26 eV, Ef(Ru /Ru ) = -1.28 eV, and AEo o(Ru ) = 2.12 The calculated Ef s are given 

Semiconductor Electrochemistiy, Zweite Auflage. Rudiger Memming. 

Using the normal electrochemical scale, j (M/M ) occurs at more positive potentials than Equation (10.3) has been verified by measure- 

This result suggests that the reorganization energy must be nearly equal for all 

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Fig. 1. Schematic of the vibrational energy levels of a molecule where (-) indicate the changes effected by the excitation photon, and (—) those of...

Efficient Calculation of Highly Excited Vibrational Energy Levels of Floppy Molecules The Band Origins of Hj up to 35000 cm-1. 

As pointed out before kuni is a pseudo first order rate constant. Since kuni/[M] is independent of [M], kuni/[M] is a second order rate constant at low pressure. It is significant and important for consideration of isotope effects that this second order rate constant for unimolecular reactions depends only on the energy levels of reactant molecules A and excited molecules A, and on the minimum energy Eo required for reaction. It does not depend on the energy levels of the transition state. There will be further discussion of this point in the following section. 

S0 is the unperturbed vapour phase energy level of the molecule in the ground state, in solution it is depressed by an amount proportional to R0. On excitation, the molecule is promoted to the Franck-Condon excited te (FC). In the excited state, the dipole moment may not only have a... 

The development of a new form of spectroscopy based on the exploitation of the time evolution of the coherence associated with the rotational motion of an excited molecule. Conventional spectroscopies depend on the measurement of differences between the energy levels of a molecule, which become more and more difficult to measure and to interpret as the size of the molecule increases. In contrast, the intervals between recurrences in the coherent rotational motions of large molecules are directly related to the moments of inertia of the molecules and can be used to determine their structures. 

Figure 13.2 Jablonski diagram. Energy levels of excited states of a polyatomic molecule.

In Section B we have discussed how the basic quantities of line emission and absorption, the excitation temperature Tex and optical depth r can be determined from observations. Energies required for rotational excitation are generally low enough (< 200 cm-1) so that the rotational levels are expected to be populated even at the very low kinetic temperatures of the interstellar molecular clouds. On the other hand, with a few exceptions such as H20 and NH3, one may assume that only the lowest energy levels of interstellar molecules are populated. Under these conditions the observable fractional column density Nx may not deviate appreciably from the total column density N of a molecule, which can be computed by means of Eq. (17) on the assumption of LTE. 

The absorption of light by a substance causes the formation of excited-state molecules. This excitation is followed by various elementary transformations which eventually lead to the deactivation or to the disappearance of those excited molecules. The absorption of light as well as each one of the elementary transformations of the original molecule in an excited state is a primary step. Specifically, a primary step may be (a) a transformation of the excited molecule into a different chemical species, as in steps 24, 15, and 14 of Figure 1, or (b) a radiative or nonradiative transition between different energy levels of the molecule, e.g., steps 02, 21, 22, 23, 13, 11, and 16 of Figure 1. Those corresponding to (a) are photochemical primary steps, while those of (b) are photophysical primary steps. 

Somewhat complicated values for the ground state (v = 0) and succeeding excited states are obtained upon solving the equation. A simplified version of these levels may be written for the energy levels of diatomic molecules,... 

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