Virtual transitions/excitations

The other mechanism involves atomic-size roughness (i.e., single adatoms or small adatom clusters), and is caused by electronic transitions between the metal and the adsorbate. One of the possible mechanisms, photoassisted metal to adsorbate charge transfer, is illustrated in Fig. 15.4. It depends on the presence of a vacant, broadened adsorbate orbital above the Fermi level of the metal (cf. Chapter 3). In this process the incident photon of frequency cjq excites an electron in the metal, which subsequently undergoes a virtual transition to the adsorbate orbital, where it excites a molecular vibration of frequency lj. When the electron returns to the Fermi level of the metal, a photon of frequency (u>o — us) is emitted. The presence of the metal adatoms enhances the metal-adsorbate interaction, and hence increases the cross... 

The sequence of events depicted by Fig. 5(al, for example, is as follows center A first absorbs a real photon of wave vector k and polarization e, and thereby undergoes a virtual transition to. n intermediate excited state r> a virtual photon of wave vector x, polarization e, and frequency — c x ... 

Initially, the calculated results for finite phenylene vinylene, which is A in Fig. 2, are shown. The first virtual transition of the sequence is from ground to Bu state. This transition is mainly composed of that from the highest occupied molecular orbital to the lowest unoccupied orbital, where a Jt-electron which is distributed on C=C double bonds and their alternating bonds, moves into another orbital which is distributed mainly on the other alternating bonds. This type of transition occurs not only for this finite phenylene vinylene but also for all of the molecules we have calculated in Fig 2. The next virtual transition in the sequence is from By to Ag excited state. This mainly comprises three orbital transitions, because the Ag excited states of this energy area are expressed mainly as a linear combination of three configurations according to the result of Cl. The three orbital transitions are HOMO-1 to HOMO, HOMO to LUMO and LUMO to LUMO+1, as shown in Fig. 3, where HOMO-1 represents the otbital level just below HOMO, and LUMO+1 represents the level above LUMO. 

The two-photon absorption normally involves virtual transitions, with associated energy level shifts. This systematic effect has been studied experimentally by Bjorkholm and Liao, using two different laser fields, enabling them to investigate the effect of a resonant intermediate level, also studied theoretically by Salomaa and Sten-holm. Naturally occurring three-level systems, with a resonant intermediate level, are rare, but they have been found in the Na molecule, where detunings as small as 34 MHz, far smaller than the Doppler width, resulted in a TPA, comparable in size to one photon stepwise excitations. 

Because, in principle, transitions can occur on light absorption to any of the many possible energy levels of the excited state from any one of the many possible energy levels of the ground state, the absorption spectmm of a chromogen at room temperature or above is virtually continuous. 

What we want to do is to find an Ajg orbital within the transition list the symmetry of the virtual orbital into which it is excited will give us the symmetry for that excited state. Orbital 7 has Ajg symmetry, and for the first excited state, the first entry is ... 

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

Figure 2.52 Schematic representation of the transitions giving rise to the Raman effect. GS = ground electronic state, ES = excited electronic state, VS = virtual electronic stale, R = Rayleigh scattering, S = transitions giving rise to Stokes lines, AS = transitions giving rise to Anti-Stokes lines, RRS = transitions giving rise to resonance Raman.

The Raman effect arises when a photon is incident on a molecule and interacts with the electric dipole of the molecule. In classical terms, the interaction can be viewed as a perturbation of the molecule s electric field. In quantum mechanics the scattering is described as an excitation to a virtual state lower in energy than a real electronic transition with nearly coincident de-excitation and a change in vibrational energy. The scattering event occurs in 10 14 seconds or less. The virtual state description of scattering is shown in Figure 1. 

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