Electron affinity calculation

Electron Affinities Calculated Using Equation 34.23, with the aug-cc-pVTZ and cc-pVTZ Basis Sets, and Equation 34.36, with the aug-cc-pVTZ Basis, Compared to the Experimental Affinity, A0... 

FIGURE 34.3 Correlation of the vertical electron affinity, calculated using Equation 34.36 at the PBE/aug-cc-pVTZ level, with experimental values. All values are in eV data are taken from Table 34.3. (Reprinted from De Proft, F., Sablon, N., Tozer, D.J., and Geerlings, P., Faraday Discuss., 135, 151, 2007. With permission.)... 

Third-order results for closed-shell molecules have average absolute errors of 0.6 - 0.7 eV [31]. Transformed integrals with four virtual indices and OV4 contractions for each value of E are required for the U intermediate, which is needed for ionization energy as well as electron affinity calculations. 

Doublet reference states. Some patterns emerge from the calculations with doublet reference states. Table 5.9 presents a summary of all cases involving transitions between singlets and doublets. Ionization energy calculations perform well when a doublet reference state is used. However, electron affinity calculations are advisable only when the doublet reference state is cationic. Even here, it is preferable to reverse the roles of initial and final states by choosing the closed-shell neutral as the reference state in an ionization energy calculation. The P3 method is not suitable for attachment of an electron to a neutral doublet reference state to form a closed-shell anion. It is preferable to choose the anion as the reference state for a P3 calculation of an electron detachment energy. Results for triplets are unpredictable at best. 

The results of our calculations for the energy are shown in Table VI. In Table VII we show the values of the LiH and LiD electron affinities calculated as the difference of the energies of the anion and the neutral system for all lengths of the basis set for which the total energies are reported. A question can be raised whether it is appropriate to use the total energies obtained with the same length of the basis set for LiH and LiH (or LiD and LiD) in the electron affinity calculation. Since LiH has one more electron than LiH, it should require more basis functions for LiH than for LiH to achieve a similar level of... 

Thus the ionization potential corresponding to removal of the electron from occupied is just the negative of that MO s energy. This observation is known as Koopmans theorem. One can similarly show that the energy of the lowest unoccupied MO is an estimate of the electron affinity of the molecule. In fact, ionization potentials estimated by Koopmans theorem are fairly accurate, but the electron affinities calculated this way are much less so. 

The values of the ionization potentials and electron affinities calculated by the open-shell method are given in parentheses. 

Additionally, electron-affinity calculations confirm these findings. Especially with respect to the oPPV and oPPE molecular wires, local affinity mappings as... 

Baetzold used extended Hiickel and complete neglect of differential overlap (CNDO) procedures for computing electronic properties of Pd clusters (102, 103). It appeared that Pd aggregates up to 10 atoms have electronic properties that are different than those of bulk palladium. d-Holes are present in small-size clusters such as Pd2 (atomic configuration 4dw) because the diffuse s atomic orbitals overlap strongly and form a low-energy symmetric orbital. In consequence, electrons occupy this molecular orbital, leaving a vacant d orbital. For a catalytic chemist the most important aspect of these theoretical studies is that the electron affinity calculated for a 10-atom Pd cluster is 8.1 eV. This value, compared to the experimental work function of bulk Pd (4.5 eV), means that small Pd clusters would be better than bulk metal as electron acceptors. 

A similar structure ofthe energy landscape can be expected for the process of excess electron transfer on the basis ofthe redox potential data available in the literature, see e.g. [10]. However, now the traps have to be pyrimidine deoxynucleobases stacked on the same strand (e.g. TT dimers orTTT triplets), the intermediate states should be associated with the anions T" and/or C", while bridging states will correspond to G and/or A bases (see Fig. 1C). This conclusion directly follows from the hierarchy of the measured reduction potentials, which decrease in the order C T A > G [10]. Electron affinities calculated both for individual nucleobases and for their different trimers exhibit the same trend [11]. 

The electron affinities calculated with the extended, optimized basis sets are shown in Table 13. First of all, the results clearly show that at the Hartree-Fock level (ROHF or UHF) the SF6 molecule is destabilized after the addition of an electron. All calculated values of electron affinity decrease systematically with the expansion of basis set. Furthermore, the combination of the most recent functionals (DF4) gives a value of EA =... 

This value of electron affinity, calculated from the bottom of the potential energy well, must be corrected for the zero-point energy (ZPE) effects. It may be expected that the normal modes of the anion will be softer than in SF6 and the ZPE correction will increase the computed value of electron affinity. In order to establish the magnitude of ZPE and determine the character of the stationary point for the anion, harmonic vibrational analysis was performed. Due to limited computer resources, only the DF1 calculations were done using the extended, (3dl/, 3dlf) polarized basis set. Zero-point energies were found to be 0.51 eV and 0.32 eV for SF6 and SFg, respectively the ZPE correction to the computed value of electron affinity is thus about 0.2 eV, and the ZPE-corrected value of electron affinity is 1.6 eV. 

Figure 10. Electron affinity calculated using atomic electronegativities vs. measured flatband potentials for labeled semiconductors corrected to their respective pzzp s. The solid line is expected from Eq. (29). ° ...

TABLE 3.9 The Hartree-Fock, B3LYP, SVWN, and BP86/6-31G Chemical Hardness Computations for the [CHjO]" Molecule by Using Orbital Energies and Vertical Total Energies for Ionization Potential and Electron Affinity Calculation, Respectively IRHT=intemaUy resolved hardness tensor, H/L=HOMO/LUMO (Putz et al., 2004)... 

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