Adiabatic ionization energies

Figures 8.7 and 8.8 illustrate the point that there are two ways in which we can define the ionization energy. One is the adiabatic ionization energy which is defined as the energy of the v = 0 — v" = 0 ionization. This quantity can be subject to appreciable uncertainty if the...

The proton affinity of a carbene can be derived by means of Eq. 9 (M = RR C ) if AHf of the carbene and of the corresponding carbocation have been estimated independently (Table 7). Appearance potentials (AP) are convenient, although sometimes inaccurate, sources of AHf (RR CH+).129 Adiabatic ionization energies (IEa) of free radicals, in combination with dissociation enthalpies... 

Tab. 4.4 Vertical and adiabatic ionization energies (kcal mol-1) for a set of furocoumarins and related compounds, in vacuum and in bulk water solvent. 1 eV=23.06 kcal mol-1.

The adiabatic ionization energy of any molecule AB (mono-, di-, or polyatomic), represented by ) (AB), is the minimum energy required to remove an electron from the isolated molecule at 0 K ... 

In short, the adiabatic ionization energy is the standard internal energy or the standard enthalpy of reaction 4.1, at 0 K ... 

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). 

Figure 4.2 Potential energy curves for the molecules AB and AB+ showing the vertical and the adiabatic ionization energies of AB. r is the A-B bond length, and v represents the vibrational quantum number.

Note that the standard enthalpy of this reaction, Aacid77°(AH), is equal to the proton affinity of the anion, PA(A ). As shown in figure 4.5, this quantity can be related to PA(A) by using the adiabatic ionization energy of AH and the adiabatic electron affinity of A. The result is also expressed by equation 4.28 (derived from equations 4.4 and4.9), where A = (TT g - o)ah+ ( 298 o)ah and A = ( 298 o )a- - ( 298— o )a These thermal corrections are often smaller than the usual experimental uncertainties of proton affinity data (ca. 4 kJ mol-1). 

Figure 4.5 Thermochemical cycle (T = 298.15 K), showing how the proton affinities of A and A- are related. Fj(AH) is the adiabatic ionization energy of AH, and fea(A) is the adiabatic electron affinity of A. A, A, and X are thermal corrections (see text).

Transition energies between cations and neutral species were calculated by two procedures. In the first one, the vertical ionization energy of the neutral molecule was determined with the P3 method. These values were compared with experimental adiabatic ionization energies of the neutral molecules, which were adjusted according to... 

The probability of a particular vertical transition from the neutral to a certain vibrational level of the ion is expressed by its Franck-Condon factor. The distribution of Franck-Condon factors, /pc, describes the distribution of vibrational states for an excited ion. [33] The larger ri compared to ro, the more probable will be the generation of ions excited even well above dissociation energy. Photoelectron spectroscopy allows for both the determination of adiabatic ionization energies and of Franck-Condon factors (Chap. 2.10.1). 

In Fig. 14 the magnified central part of the spectrum shown in Fig. 13 is presented together with the positions of the Rydberg peaks of two series calculated using Eq. (6). The assignment of the series limits leads to accurate values of the lowest adiabatic ionization energy of the benzene (C6D6> molecule and the rotational constants of its cation [89]. 

Tamm-Dancoff Green s function results relative intensities given in parentheses. c Adiabatic ionization energies. 

One further consideration is that the measured IE may not be the adiabatic ionization energy. If the ion structure differs significantly from that of the neutral, the measured IE may exceed the adiabatic value. In this situation, substituting the measured IE in eqn. (20) will tend to make the calculated critical energy [eqn. (20)] too small. Examples of molecules with which the adiabatic IE has not been clearly observed are (C2HS)+from (C2H5) [16] and [(CH3)3CH]t from (CH3)3CH [794]. 

Heats of formation of carbocations, which are the basis data for these scales have been derived from the heats of formation of the neutral precursors (e.g., radicals) and the adiabatic ionization energies [ = ionization potentials, Eq. (2)] [20]. 

Interestingly, the energy of the HOMO of bicyclobutane was found to be higher than that of ethylene The first electronic transition in bicyclobutane, namely the n-n (HOMO-LUMO) transition, is lower in energy than in ethylene" The position of the onset of the first band in its photoelectron spectrum suggests an adiabatic ionization energy of 8.70... 

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