Vertical ionization energies, neutral

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 vertical ionization energy and vertical electron affinity are (here ZPEs have not been taken into account, as they should nearly cancel in any case the significance of a calculated ZPE for the cation or anion at the geometry of the neutral is questionable, since the two vertical species are not stationary points) ... 

For closer elaboration of the numerous radical cation states of molecules on energy and time scales (Figure 2a and c), photoelectron (PES)3,5,16 and electron spin resonance (ESR/ENDOR)10,25 spectroscopic techniques have complementary time ranges Vertical ionization energy patterns are measured with a time resolution of less than 10 15 s (Figure 2c) without any vibrational structural changes on electron ejection and can therefore be correlated to the eigenvalues calculated for the neutral molecule by... 

A neutral Fsc center gives rise to an impurity level in the gap which is about 3 eV above the top of the valence band. F+ centers give rise to states closer to the valence band (for a terrace F+s the level is about 1 eV above the 0 2p states). The vertical ionization energy of a neutral Fsc defect is 3.4eV that of an F+sc center 5.6 eV. Similar IPs (Ionization Potential) are found for F centers located at a corner site The IPs of Fsc and F+sc centers are 3.4 and 6.6 eV, respectively [61], showing that not only electrons trapped at low-coordinated sites may exist but they are also more strongly bound than at the corresponding terrace sites. 

The SCF molecular orbitals of the neutral species, V, > give rise to the ground state wavefunction, 4>(P) = 11//,, while the SCF orbitals of the positive ion for the core-hole state produce a doublet state wavefunction, 2 (P+) = 1i//(. Koopmans Theorem6 assumes that there is no change in the molecular orbitals of the ground state and ionized species, xjsj = xp j, and that a vertical ionization energy can be obtained by the following expression ... 

Table 13.3 Vertical ionization energies (eV) by various methods. Numbers in parentheses are deviations from experimental and numbers in brackets are AMI Koopmans minus 0.6 (see text). Regarding the three Calculated columns MP2/6-31G refers to the difference in energy of the radical cation (at the geometry of the neutral) and the neutral at the MP2/6-31G level, AMI Koopmans refers to the negative of the HOMO energy from an AMI calculation on the MP2/6-31G geometry, and MP2 Koopmans refers to the negative of the HOMO energy from an MP2/6-31G //MP2/6-31G calculation (MP2/6-31G energy at the MP2/6-31G geometry)...

Vertical excitation energies and harmonic vibrational frequencies at D3h and C2V symmetries, as well as adiabatic and vertical ionization energies of the neutral molecules, are reported. Good to excellent agreement with a multitude of experimental values was found. 

Fig. 5.6. One-dimensional cuts of the PESs of the ground states of Ag, Ags, and Ag along Qr = — (Qx) + QyY for fixed values of the polar angle a = arctan(Qx/Qy) = 120° and Qs = 2.81 A(by courtesy of M. Hartmann, taken from [136]). Qs, Qx, and Qy correspond to the symmetric stretching, the bending, and the antisymmetric stretching coordinate of the AgJ cation, respectively. The chosen Qs value is that of the neutral s equilibrium nuclear configuration. The vertical electron detachment energy is 2.45 eV, the vertical ionization energy for the linear transition state and the equilibrium geometry of the neutral are 6.67 eV and 5.73 eV, respectively. The dashed line is the first excited electronic state of Ags...

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). 

---