Ionization adiabatic

The principles of ion themiochemistry are the same as those for neutral systems however, there are several important quantities pertinent only to ions. For positive ions, the most fiindamental quantity is the adiabatic ionization potential (IP), defined as the energy required at 0 K to remove an electron from a neutral molecule [JT7, JT8and 1191. 

Adiabatic ionization. A process whereby an electron is removed from the ground state of an atom or molecule, producing an ion in its ground state. 

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...

Figure 7. The photoelectron spectrum of formaldehyde with the data on adiabatic ionization potentials. The fourth potential can be determined only at higher resolutions. [From (103) by permission of D. W. Turner and the publishing house].

Even the photoelectron spectroscopy of closed-shell molecules is valuable for the physical chemistry of radicals because a difference between the nth and the first adiabatic ionization potentials determines the excitation energy in a radical cation for a transition from the ground doublet state to the (n — 1) excited doublet state. 

Distances Ce are in A, dissociation energies in eV (calculated values are not corrected for the 2ero-point vibrational energy, harmonic frequencies Oe in cm , and adiabatic ionization potentials AEip and electron affinities AEea in eV. Experimental values are from Refs. [94, 159-162]. 

The physical nature of the ZEKE states has been the subject of intense experimental and theoretical investigation in the past several years. In the well-studied case of NO,14,21 we know from the 3 cm-1 red shift of the ZEKE-PFI threshold band relative to the true adiabatic ionization potential (extrapolated from highly accurate measurements of Rydberg series) that the ZEKE states have principal quantum number n 200 and lifetime of 2 (is or longer. Recent work has found ZEKE states with lifetimes as long as 20 ps.22... 

The adiabatic ionization potential (1A) of a molecule, as shown in Figure 4.1, equals the energy difference between the lowest vibrational level of the ground electronic state of the positive ion and that of the molecule. In practice, few cases would correspond to adiabatic ionization except those determined spectroscopically or obtained in a threshold process. Near threshold, there is a real difference between the photoabsorption and photoionization cross sections, meaning that much of the photoabsorption does not lead to ionization, but instead results in dissociation into neutral fragments. 

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 band gap, determined as the onset of the absorption band in thin films is 2.95 eV (425 nm). Janietz et al. [252] used the onset of the redox waves in CV experiments to estimate the /P and Ea energies of the dialkyl-PFs (Figure 2.11). The gap between the obtained energy levels (5.8 eV for 7P and 2.12 eV for EA) IP—EA 3.8 eV is substantially higher than the optical band gap. Although optical absorption and electrochemistry test two physically different processes (vertical electron excitation and adiabatic ionization) and are not expected to be the same,... 

First of all, quantum calculations allow one to predict basicity scales in agreement with experiment provided that the calculations are performed on the preferred conformation of the isolated molecule. If this is not done, a given term within a consistent series may jump from one rank to another as a function of the conformation used for the calculations. The determinant role of preferred conformation on any property (barrier to internal rotation and inversion, dipole moment, first adiabatic ionization potential, acidity and basicity in the gas phase, energy of complexation to BF3, etc.) was clearly demonstrated. We further show the importance of the role of preferred conformation in explaining some of the anomalies in Drago s systematics. 

Fig. 2.6-9. The calculated adiabatic ionization potentials of P clusters with n = 2-11 [8].

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... 

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ signihcantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable. As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent efifect, due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

Fig. 9a, b. A portion of a photoelectron spectrum (idealized) showing (a) the identification of adiabatic and vertical ionization potentials with resolved (1) and unresolved (2) vibrational structures, (b) the identification of a higher adiabatic ionization potential with a break . 

Fio. 12. Fhotoelectron spectrum of methanol vapour using the helium resonance line (21-21 e.v.). Ionization energy increases from left to right. The adiabatic ionization potentials measured (Al-Jobomy and Turner, 1964) are indicated by vertical arrows, and can be compared with (probably) vertical I.P. values derived from electron impact appearance potentials by Collin (1961) (dotted arrows). 

Fio. 19. Comparison of the two lowest adiabatic ionization potentials in benzene with the three lowest in pyrrole and furan. The values arranged as an energy level diagram were obtained by photoelectron spectroscopy. (T, N. Badwan and D. W. Turner, unpublished work.)... 

Fig. 23. Adiabatic ionization potentials for methane, ethane, propane, and butane arranged as an energy level diagram.

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). 

The counterpart of the vertical ionization is a process where ionization of the neutral in its vibrational ground state would yield the radical ion also in its vibrational ground state, i.e., the (0 <— 0) transition. This is termed adiabatic ionization and should be represented by a diagonal line in the diagram. The difference lEvert -lEad can lead to errors in ionization energies in the order of 0.1-0.7 eV. [7]... 

---