Vertical ionisation energy

The OVGF function method provides a quantitative account of ionisation phenomena when the independent-particle picture of ionisation holds and as such is most applicable in the treatment of outer-valence orbitals. It provides an average absolute error for vertical ionisation energies below 20 eV of 0.25 eV for closed shell molecules. The TDA and ADC(3) methods allow for the breakdown of one particle picture of ionisation and so enable the calculation of the shake up spectra. The ADC(3) is correct up to 3rd order, is size consistent and includes correlation effects in both the initial and final states. 

Fig. 12. Vertical ionisation energies, Fermi (E.) and vacuum levels (V. L.) for gaseous (1), condensed and chemisorbed phases of (a) benzene, (b) acetylene and (c) ethylene, all plotted relative to cr-orbital ionisation potentials (I. P.) for the gas phase. Relaxation shifts are given by the vacuum level shifts while bonding shifts are given by relevant jr-orbital shifts. [Reproduced with permission from J. E. Demuth and D. E. Eastman, Phys. Rev. Letters 32, 1123 (1974)]...

IE,IP) ionisation potential. Compare with adiabatic ionisation energy, vertical ionisation energy, electronegativity, and electron affinity. The energy needed to remove an electron from a gaseous atom or ion. 

Choose the orbitals to have particularly convenient energetics. We have seen that the diagonalisation of e generates the most useful form for the orbital energies approximations to the vertical ionisation energies of the molecule. 

This estimate of the ionisation energy obtained hg subtracting the total energies of the two species at the same geometry, vnth the same orbital basis is, at best, an approximation to the vertical ionisation energy no allowance is made for molecular relaxation although the electrons have been allowed to attain self-consistency in each separate case. 

Figure 4.5 Oeometty of peroxy at the (OOt) MgO surface quantum mechanical cluster used in the calculations (top left) and details of the optimised structure (bottom left - larger circles are otg gens, smaller ones - magnesiums) vertical ionisation energy diagram (right) shows position of the top of the valence band and peroxy defect with respect to the vacuum level...

The vertical ionisation energy is the energy required to form the positive ion with the same geometry as the ground state molecule. In the adiabatic ionisation energy, the positive ion is formed in its thermally-relaxed vibrational ground state (see Fig. 1.23)... 

Fig. 1.15 Electronic energy levels of singlet and triplet states of benzene, with absolute values relative to the vacuum level (the Fermi limit) obtained from photoelectron spectra and relative values (with reference to the ground state) obtained experimentally from UV/Vis absorption and photoluminescence spectra. The absolute values are based on Koopmans theorem [41], that the energy of the highest occupied molecular orbital (HOMO) is the first vertical ionisation energy of a molecule. The energy of the HOMO level is obtained from the vertical ionisation energy of benzene in Ref. [42] and the energies of the excited states are fl om Ref. [43]. Assignment of the symmetry of the S2 ( Bju) state is from Ref. [44]...

The smaller cluster ions 83", 84" and 85 + have been examined by Zakrzewski and von Niessen at the HF/6-3H-G level [82]. The lowest cationic states are predicted to be 82, and A" for 83 (Cyv), 84 (I>4h) and (Cs), respectively. The ionisation processes may result in significant structural relaxation leading to the sequence of states different from that of the vertical states. The calculated lowest adiabatic ionisation energies, using the GI method with a very large ANO basis set, are 9.53, 8.05, and 8.20 eV for 83, 84 and 85 , respectively. 

Table 1. Vertical ionisation potentials and nj -> n transition energies (eV) of diazenes1)...

Table 6. Comparison between measured vertical ionisation potentials/v,j and calculated orbital energies of trithiapentalene and analogous compounds. The calculations have been carried out on the unsubstituted compounds except for the ab initio calculation on IVh. All values in eV...

The greatest improvement of the DFT-SAPT method over the original SAPT is the acceleration of the calculations by one order of magnitude. The intramolecular treatment is conducted using the DPT and therefore suffers from inaccurate energies of the virtual orbitals. This drawback is corrected for in advance of the actual SAPT treatment by a gradient-controlled shift procedure, which uses the difference between the exact vertical ionisation potential (IP) and the energy of the (HOMO) [24]. In this work, PBEO/aug-cc-pVTZ and PBEO/aug-cc-pVDZ calculations were carried out to obtain the IP respective HOMO values and intermolecular terms were described by aug-cc-pVDZ and aug-cc-pVTZ basis sets. Bromine and iodine atoms were treated by pseudopotentials to describe relativistic effects of inner-core electrons correctly. 

Figure 1.3. Real-time femtosecond spectroscopy of molecules can be described in terms of optical transitions excited by ultrafast laser pulses between potential energy curves which indicate how different energy states of a molecule vary with interatomic distances. The example shown here is for the dissociation of iodine bromide (IBr). An initial pump laser excites a vertical transition from the potential curve of the lowest (ground) electronic state Vg to an excited state Vj. The fragmentation of IBr to form I + Br is described by quantum theory in terms of a wavepacket which either oscillates between the extremes of or crosses over onto the steeply repulsive potential V[ leading to dissociation, as indicated by the two arrows. These motions are monitored in the time domain by simultaneous absorption of two probe-pulse photons which, in this case, ionise the dissociating molecule.

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