Vertical ionization potentials states

The ionization being accompanied by a vibrational excitation, the fine structure of bands can be exploited for determination of vibrational levels of an ionized system in the ground and excited states. Of course, the first (0-0) and the strongest vibrational bands are the most important because they determine adiabatic and vertical ionization potentials of radicals. 

FIGURE 4.1 Illustration of adiabatic and vertical ionization potentials. Adiabatic I.P. refers to the energy difference between the lowest quantum states of the molecule and its positive ion. Often, Franck-Condon (vertical) transitions lead to a higher value, the vertical ionization potential. 

Table 3. Vertical ionization potentials for CO in eV. (5s4p2d//2s2p) Basis Set. Ground State Energy. SCF = -112.7798 a.u. 

The vertical ionization potentials of the (lt2) and (2ai) ionic states are indicated in Fig. 2, while that of the (lai) ionic state is far away from the range in Fig. 2. Kameta et al. examined their photoabsorption cross sections c in terms of the TKR sum rule for the oscillator-strength distribution dfjdE, Eq. (3), following the conversion of a to dfjdE,... 

Figure 2 The photoabsorption (c), photoionization (o-,-), and photodissociation (cr

Figure 5 Ionization potentials of the valence electrons of CH4, C2H6, C3H8, and W-C4H10 [8,9, 10,11], which are the vertical ionization potentials of the ionic states produced with the removal of an electron from each valence orbital. The point groups for the molecules are also shown as well as the notation of the orbitals based on them. (From Ref [7]. Reprinted with permission from Elsevier Science.)...

Fig. 3. (a) Ionization potentials for bands E, e2 and e3 in dependence of the excitation energy. Full symbols refer to measurements with 207nm ionization pulse, open symbols to 200nm ionization pulse. The sum of the energy from excitation and ionization pulse is shown as black line. Stars denote the four lowest vertical ionization potentials of 8.4, 8.75, 9.3 and 9.3eV [6], (b) Normalized excitation spectrum showing near degeneracy for the nn states corresponding to bands S and e3. 

An SCF MO calculation gives the following energies for the occupied H20 MOs (Section 1.20) la, 2a]t 1 b2, 3av 1 bx —20.56, —1.28, — 0.62, —0.47, -0.40 hartrees, respectively. For the He 1 PES of H20, answer the following questions, (a) Give the band locations, (b) For each band, state whether or not the adiabatic and vertical ionization potentials will coincide, (c) For each band, state whether the vibrational frequencies of the upper state should be less than, about the same as, or greater than those in the lower state. 

A related topic is the computation of valence-shell ionization potentials (VSIP). The calculation of vertical ionization potentials via Koopmans theorem28 leads in many cases to serious errors, and a version of the ASCF method has been used to compute VSIP for several small molecules, including CH4.29 All the valence hole states of the molecule were computed. Agreement with experiment was substantially better than in the calculations using Koopmans theorem. 

An approximate quantification of the energy change associated with the ionization reaction of Equation 6.37) is offered by Koopmans theorem, which states that the vertical ionization potential (IP) of an electron in the one-electron MO wavefunction (J), as HF solution for the neutral molecular species (cf. Equation 6.18 and Equation 6.22) is equal to the negative of its orbital energy , ... 

The adiabatic and vertical ionization potentials for Lis are very similar, both being approximately 3.95 eV. This results because of the similar geometries for the 82 state of LisCCsv) and the Ai state of Li3" (D3h). It must be noted, however, that the vertical ionization process for the removal of an electron from linear Lis to give linear Lis leads to the higher ionization potential, 4.39 eV. If both Csv and forms are present in an experiment, a complicated threshold dependence for the ionization process will be observed (j4). The results for Lis exemplify that the fluxional nature of a small metal cluster may complicate the experimental determination of electron affinities and ionization potentials. 

At the equilibrium geometries of the neutrals, the symmetry assignments of these cationic doublet states, ordered by ascending vertical ionization potentials, are as follows. The obvious notations Bz+, E-Bz+, 1,2, 1,3, 1,4 and 1,2,3 correspond to the benzene, mono-fluorobenzene, ortho-, meta-, para-difluorobenzene isomers and 1,2,3-trifluorobenzene, respectively. (The numbers refer to the position of the... 

For molecules with closed-shell ground states, the vertical ionization potentials —< f predicted by the LCAO MO method are generally too high relative to experiment. When the SCF energy of the ion is calculated, the correction AEt decreases the theoretical value of P<, but the agreement with experiment is lost if the change in correlation energy (Et — Eg) is taken into account in an approximate way (see Table 7). 

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