Energy and Electronic States

Perspectives on Structure and Mechanism in Organic Chemistry, Second Edition By Felix A. Carroll Copyright 2010 John Wiley Sons, Inc. 

Frequencies, radiation types, spectroscopic regions, energies, and wavelengths of electromagnetic radiation of interest to chemists. (Note that the vertical scale is logarithmic. Based on data in reference 3.) 

A generalized set of energy levels for an organic molecule. (Adapted from reference 4). 

Photochemistry is inherently related to photophysics, the study of those radiative and nonradiative processes that convert one electronic state into another electronic state without chemical change. Central to both photochemistry and photophysics is the classification of UV-vis radiation in terms of its energy. Because electromagnetic radiation is quantized, it has properties like those of a particle, and a mole of photons is called an einstein. Electromagnetic radiation also has the properties of a wave, and equation 12.1 gives the relationship between the energy of UV-vis radiation in kcal/mol and its wavelength in run.  

TABLE 12.1 Energy Content of Different Wavelengths of UV-vis Radiation  

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In order to calculate q (Q) all possible quantum states are needed. It is usually assumed that the energy of a molecule can be approximated as a sum of terms involving translational, rotational, vibrational and electronical states. Except for a few cases this is a good approximation. For linear, floppy (soft bending potential), molecules the separation of the rotational and vibrational modes may be problematic. If two energy surfaces come close together (avoided crossing), the separability of the electronic and vibrational modes may be a poor approximation (breakdown of the Bom-Oppenheimer approximation. Section 3.1). 

Figure 9. Determination of the first electron affinity, and the first and higher ionization potentials of formyl radical from the SCF orbital energies and electronic repulsion integrals, and K,j (cf. eqs. (90), (92), and (93)). The experimental value (112), 9.88 eV, for the first ionization potential corresponds to the theoretical value I . All entries are given in eV. With A and I a lower index stands for MO the upper one indicates the state multiplicity after ionization.

Both energy and electron transfer quenchers have been employed to show that the quenching rates of the fullerene triplet state are decreased as a function of the size of the dendrimer shell [36]. These results further demonstrate that fullerene is an excellent functional group to probe the accessibility of a dendrimer core by external molecules. 

The mobility is one of the more significant and readily measurable properties of the electron in a medium. Since it is sensitive to the energy and the state of the electron, a detailed study of mobility can be used as a tool for their evaluation. Knowledge of mobility can be applied to dosimeters and ionization chambers togther with a measurement of induced conductivity and free-ion yield (see Eq. 10.2). The subject of electron mobility is vast. In this chapter, we will limit ourselves to electron mobility in liquid hydrocarbons with occasional reference to other liquids. Also, the treatment will be mainly descriptive. The subject matter has been reviewed by Munoz (1991). 

When the two reservoirs are connected a steady state is soon established as energy and electrons flow along the wire under the influence of the driving terms T2 — 7 and /i2 — /ij. As energy and particles flow the joint entropy of the reservoirs increases at a rate given by (9) and (10) as... 

Using the fact that the energy is linear with respect to the number of electrons and Janak s theorem [31], the orbital energies of the N—n and N+n electron system become equal to the exact ground state vertical ionization energy and electron affinity, respectively ... 

The electronic states of the molecule and their relative energies. Singlet electronic states are denoted by S0, Si, S2, etc. and triplet... 

The potential energy curves of the species AB, AB+, and AB- are used in figure 4.1 to summarize the definitions of the adiabatic ionization energy and electron affinity of AB. Note that the arrows start and end at vibrational ground states (vibrational quantum number v = 0). 

For many ionization energies and electron affinities, diagonal selfenergy approximations are inappropriate. Methods with nondiagonal self-energies allow Dyson orbitals to be written as linear combinations of reference-state orbitals. In most of these approximations, combinations of canonical, Hartree-Fock orbitals are used for this purpose, i.e. 

Optical charge transfer (CT) is commonly observed in un-symmetrical molecules or molecular complexes in which there are sites of distinctly different ionization energies and electron affinities. The origin and properties of optical charge transfer transitions provide the basis for this account. A convenient place to begin chemically is with mixed-valence compounds and two examples are shown below (1-3). In the first (eq 1), the sites of different oxidation states are held in close... 

The visible and near-infrared LID results for NO/Pt were discussed in terms of hot electrons combined with a charge transfer mechanism. For the 193 nm LID result considered here, the photon energy is above the substrate work function, thereby providing a direct source of electrons to bathe the adsorbed NO species. Comparison of translational energy and vibrational state distributions for NO/Pt(lll), NO/Pt(foil), and N0/Ni(100)-0 suggests that the mechanisms driving the desorption processes in these systems might be related. However, the details of the specific interaction potentials must be substantially different to account for the disparate spin-orbit and rotational population distributions. 

Ionization in Cl is the result of one or several competing chemical reactions. Therefore, the sensitivity in Cl strongly depends on the conditions of the experiment. In addition to primary electron energy and electron current, the reagent gas, the reagent gas pressure, and the ion source temperature have to be stated with the sensitivity data to make a comparison. Modem magnetic sector instmments are specified to have a sensitivity of about 4 x 10" C pg for the [Mh-H] quasi-molecular ion of methylstearate, m/z 299, at / = 1000 in positive-ion Cl mode. This is approximately one order of magnitude less than for El. 

The fact that surface structure, in particular steps and coordinatively unsaturated sites, has an influence on the state and reactivity of carbon monoxide is entirely in keeping with the empirical correlation (Fig. 6) between heat of adsorption, electron binding energies, and molecular state. Elegant studies by Mason, Somorjai, and their colleagues (32, 33) have established that with Pt(lll) surfaces, dissociation occurs at the step sites only, and once these are filled carbon monoxide is adsorbed molecularly (Fig. 7). The implications of the facile dissociation of carbon monoxide by such metals as iron, molybdenum, and tungsten for the conversion of carbon monoxide into hydrocarbons (the Fischer-Tropsch process) have been emphasized and discussed by a number of people (32,34). 

An approximate quantum mechanical expressions- that allows one to calculate the electrostatic surface potential around atoms, radicals, ions, and molecules by assuming that the ground-state electron density uniquely specifies the Hamiltonian of the system and thereby all the properties of the ground state. This approach greatly facilitates computational schemes for exact calculation of the ground-state energy and electron density of orbitals. 

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