Adiabatic electron affinities

We saw previously that hydrated electrons react very rapidly with the conjugated 1,3-butadiene (k = 8 x 109 M-1 s 1). In less polar solvents the attachment of an electron to 1,3-butadiene (with adiabatic electron affinity of —0.62 eV20) will be slower. The... 

The enthalpy of reaction 2.45 cannot be determined directly. As shown in figure 2.5, it is calculated by using several experimental quantities the standard enthalpy of formation of the solid alkoxide, the standard sublimation enthalpy and the ionization energy of lithium, and the standard enthalpy of formation and the adiabatic electron affinity of gaseous methoxy radical (equation 2.47). 

The last two terms in equation 2.47, the ionization energy of Li and the adiabatic electron affinity of CH30, respectively, will be discussed in section 4.1. For now, it is enough to note that both processes are referred to T = 0 and that 2.5RT in figure 2.5 is an approximate correction to 298.15 K. Notice also that this correction cancels out in equation 2.47. 

All of the previous discussion applies, with minor changes, to the second important concept we wish to address the adiabatic electron affinity, Eea. For any molecule AB (mono-, di-, or polyatomic), ea( AB) is the minimum energy required to remove an electron from the isolated anion at 0 K. In other words, /i ea(AB) is the standard enthalpy of reaction 4.7 at T = 0. 

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).

Transitions between anions and neutral species were also calculated with two procedures. In the first, we calculated the vertical P3 electron affinities of neutral species. The experimental adiabatic electron affinities of the neutral molecules were shifted according to... 

This sequence of calculations was applied to neutral and ionic molecular species from the G2 test set. Experimental adiabatic electron affinities and ionization energies were taken from Refs. 53 - 74. 

The theoretical interest in the LiH has increased since the electron affinity of LiH and its deuterated counterpart, LiD, were measured with the use of the photoelectron spectroscopy by Bowen and co-workers [126]. The adiabatic electron affinities of LiH and LiD determined in that experiment were 0.342 0.012 eV for the former and 0.337 0.012 eV for the latter system. The appearance of these data posed a challenge for theory to reproduce those values in rigorous calculations based on the first principles. Since the two systems are small, it has been particularly interesting to see if the experimental EAs can be reproduced in calculations where the BO approximation is not assumed [123]. 

Since the time that Bowen s and co-workers article was published, the theory based on the BO approximation, except for one very recent multireference configuration interaction (MRCI) calculation by Chang et al. [127], has been unable to produce a value of the LiH adiabatic electron affinity that... 

Experimental adiabatic electron affinities from Ref. [90], The uncertainty is shown in parentheses. 

Values of electron affinities of the neutral clusters are also an indication of the stability of the corresponding anionic clusters. In fact, it is important to check if the neutral system is able to attach an extra electron to form a stable species. The adiabatic electron affinity is given by the difference between the energy of the neutral system Lin, at its most stable geometry, and of the anionic Lin"... 

Adiabatic electron affinities (EAt) (kcal/mol) of the small neutral lithium clusters. 

From the ET spectra vertical electron affinities are obtained. However, for several reasons it would be interesting to know the adiabatic electron affinities, particularly since there might be a large difference between the vertical and the adiabatic electron affinities in these cycloalkynes. Therefore, electrochemical investigations were carried out to find additional evidence for the increased electron affinity. 

Figure 20-3. Electron binding energies for molecule M in anionic state are defined pictorially in a representation of the potential energy surfaces of the neutral molecule (M) and anion radical (M ) with the lowest vibration energy level shown for each. During a vertical process, the geometry remains unchanged but for the adiabatic process structural relaxation occurs. Thus the VDE (vertical detachment energy) and VEA (vertical electron affinity) represent the upper and lower bounds to the adiabatic electron affinity (AEA)...

While adiabatic EAs of U and T are known from experiment to be 0 =b 0.1 eV, the uncertainty in the values for the purines A and G is much greater. A and G clearly have negative adiabatic electron affinities which DFT theory suggests to be ca. —0.35 eV (A) and —0.5 to —0.75 eV (G) with their vertical electron affinities... 

Table 20-9. Adiabatic electron affinities (AEAs) of T, C, U, G and AT base pair in solution using different methods and basis set...

Table 21-2. Relative electronic energies and free energies (AE and AG) calculated with respect to the aHX(AT) or aHX(AT)-SPT anion together with the adiabatic electron affinities (AEAG) and electron vertical detachment energies (VDE) for the anionic HX(AT) complexes predicted at the B3LYP/6-31+G" level. AE and AG in kcal/mol AEAG and VDE in eV...

Opposite to rebound reactions is the reaction Na + Ch — NaCl + Cl which proceeds via the spectator stripping mechanism. In this case, the crossing between the nonreactive covalent Na-Cl2 curve and the Na+Cl ion-pair curve, which promotes the reaction, occurs at a large distance [Re = 5.22 A, when using the chlorine adiabatic electron affinity in Magee s equation). This distance increases to 22.3 A when sodium is excited to the 3p P level. One would expect an increased reaction cross-section, but this is not observed because electron transfers at such large distance are inefficient. The overlap between the sodium HOMO and the CI2 LUMO is very small at these distances. As a result, when the crossing radius increases substantially, there is only a small effect on the dynamics of the reaction [164, 165]. 

Hexacyano[3]radialene (50) is a very powerful electron acceptor according to both experiment and MNDO calculations of LUMO energy and adiabatic electron affinity. The easy reduction to the stable species 50 and 50 by KBr and Nal, respectively, has already been mentioned. Similarly, the hexaester 51 is reduced to 51 by Lil. Most [3]radialenes with two or three quinoid substituents are reduced in two subsequent, well-separated, reversible one-electron steps. As an exception, an apparent two-electron reduction occurs for 46 . The reduction potentials of some [3]radialenes of this type, as determined by cyclic voltammetry, are collected in Table i. Due to the occurrence of the first reduction step at relatively high potential, all these radialenes... 

Figure 2.1 Morse potential energy curves for the neutral and negative-ion states of F2. The vertical electron affinity VEa, adiabatic electron affinity AEa, activation energy for thermal electron attachment E, Err — AEa — VEa, EDEA — Ea(F) — D(FF), and dissociation energy of the anion Ez are shown.

The general least-squares procedures can now be implemented in spreadsheets programmed with macros. Adjustments once impossible are now trivial. The classification of molecules to obtain electron affinities from half-wave reduction potentials is an example of a linear least-squares adjustment. The determination of the adiabatic electron affinity for acetophenone is an example of a nonlinear two-parameter least-squares procedure. The nonlinear least-squares adjustment of ECD to the expanded kinetic model is one of the major advances of the 1990s. 

The theoretical calculation of the electron affinities of aromatic hydrocarbons was advanced by the development of the MINDO/3, MNDO, AMI, and PM3 semi-empirical techniques. These procedures gave the adiabatic electron affinities of molecules obtained from the ECD and from half-wave reduction potentials that agreed with the experimental values to within the experimental error. A different semi-empirical procedure yielded consistently lower values than the experimental values partially because they were adjusted to the lower values [67-69]. 

Sometimes, the donor and acceptor are nearly equal in strength and a b. For the strengths, one must not use the adiabatic ionization potential and (adiabatic) electron affinity (AEa) corresponding to the passage of D with its natural skeleton to D with its natural skeleton or from A with its natural shape to A(—) in its natural shape instead, one must take the so-called vertical values of IP (VIP) and Ea (VEa) corresponding to no change in skeleton. Moreover, one must take VIP and VEa for such deformed... 

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