HOMO states

Spiropyran merocyanine specffa shift markedly to the blue as the solvent polarity increases [4,25], as shown in Fig. 7a for 6,8-dinitro-BIPS merocyanine. This is generally accepted to imply that they have a zwitterionic character caused by the donation of electron density from the indoline nitrogen to the phenolic C9 oxygen [4,25]. The rational behind this assignment to the zwitterion is based simply on the fact that if the zwitterion is in the highest occupied molecular orbital (HOMO) state, then the corresponding quinoidal resonant form is in the lowest unoccupied molecular orbital (LUMO) state and changing the solvent to a more polar one... 

Si skeleton. The electronic properties are instead less affected by the addition of Si-O-Si bridges this is due to the HOMO state that, as already said, maintains its hydrogenated like character. The Eg is reduced, but not as in the Si=0 bond cases. Also when the addition of O atoms implies the substitution of some atoms of the Si core, miming the attack of O towards the inner structure, the reduction is still of the order of a few tenths of eV. The addition of both types of bonds on the same structure (Sii3Hi6>0=0) produces a final Eg value strongly red-shifted, very close to the corresponding results for the double-bond case (Sii3Hi8=0). This means that the electronic, and consequently the optical, behavior of the clusters is mainly characterized by the double bonded O. 

Interfacial electron transfer between a metal and an excited sensitizer, A -L- B where B represents a metal electrode, may be reductive, whereby the electron transfers from the conduction band of the metal to the singly occupied HOMO state of the excited adsorbed molecules, thus resulting in A -L-B and a cathodic photocurrent at the electrode. Alternatively, it may be an oxidative process, wherein the electron is transferred from the adsorbate to the metal, so resulting in A+-L-B and an anodic photocurrent at the electrode. 

Electrical conduction will occur by the hopping of either electrons or holes within these distributions of energy levels. Charge transport can be either of holes by transfer between the LUMO states or of electrons between the HOMO states. These correspond to the formation of either a radical cation by the removal of an electron to an adjacent electrode or an anion by the injection of an electron. The nature of the majority carriers will, therefore, be determined by the ionisation potentials and electron affinities of the conjugated moieties. A low ionisation potential will favour hole transport while a high electron affinity will favour electron transport. Most of the conductive polymers reported in the literature have low ionisation potentials and are hole, conductors. ... 

Both, EH and LMTO calculations yield band structures with band overlap at the Fermi level meaning that a metallic conduction is expected. This is displayed in Fig. 3e and 3f. Indeed, Ca7Mg7j5Sii4 shows metallic conductivity. Thus, there are no localized spins but the HOMO states form a conduction band which, according to LMTO-band structure calculations, is exclusively due to x-orbital overlapping between adjacent ecliptically arranged Si 2 moieties along the stacking direction. 

When discussing the electronic structure of molecules and solids, one-electron descriptions, such as the molecular orbitals of Equation 8.1, are quite intuitive. It is common to talk about individual electrons occupying particular states. For example, reactions often occur by the mixing of the highest occupied molecular orbital (HOMO) of one species and the lowest unoccupied molecular orbital (LUMO) of another. In such a reaction the electrons in the HOMO state move into the new mixed orbital, lowering their energy. The HOMO and LUMO states are each pairs of one-electron molecular orbitals, since in the simplest case an orbital giving the spahal distribution for a spin up electron has an identical partner for spin down. Mulh-electron wavefunctions that describe the whole electronic structure in this picture are constructed from the one-electron states. So, for example, in a four-electron system in which all the electronic states are doubly occupied (spin up and spin down), based on Hartree-Fock theory we can write ... 

Skeleton-side-chain interaction due to TT-like coupling results in a-7T band mixing between the skeleton Si Sp and side-chain phenyl HOMO states. The symmetric tt HOMO can mix with the delocalized a valence band. This mixing results in the formation of two delocalized a bands. The asymmetry of the other tt HOMO states cancels this a-7T mixing effect. The resulting state remains strongly localized in the individual phenyl side chains. 

We saw in Section 3.3.2 that the molecular-orbital states of linear chains are eigenstates of the inversion operator, i. The ground state is constructed by occupying each of the valence molecular-orbital states with two electrons. Thus, the overall inversion symmetry of the ground state must be even (or Ag for a many-body state). Now, because the molecular orbital states alternate in symmetry, the highest occupied molecular orbital (HOMO) state will be either even or odd, while the lowest unoccupied molecular orbital (LUMO) state will be either odd or even. In fact, using eqns (3.19) and (3.20), with [3 = 7r/2a replacing k, the HOMO is... 

Solute ability to accept or donate hydrogen in a hydrogen bond Highest Occupied Molecular Orbital Lowest Unoccupied Molecular Orbital Electronegativity of HOMO state for ELH (hydrogen)... 

Fig. 6.13. Convergence of energies and forces versus grid-spacing. E is the total energy, F the absolute value of total force on a H atom, ei the Kohn-Sham eigenvalue of the HOMO-1 state, and 2,3,4 the Kohn-Sham eigenvalue of the HOMO state (which is triply degenerate). For the sake of clarity, we plot the difference between these quantities and their converged vaiues...

FIGURE 3.14 The orbital structures for working anthocyanidins in HOMO states (Putz et al, 2008). 

FIGURE 4.1 The potential contour maps for the molecules under discussion on their HOMO state. A higher density of contours indicates that the site is susceptible for electrophilic attack either for positive (green) or negative (in cyan) molecular electrostatic potential (Putz et al., 2010). 

FIGURE 7.1 Energies of the electronic levels of Al,3, Al , and AI13H. For AI13 the energies for spin-up and spin-down electrons are shown in different columns. The HOMO state is indicated as Ep. The labeled molecular levels of AI13H have a sizable H-ls contribution. 

Actual comparison with /+(r) and / (r) obtained from Equations 7.14 and 7.15 shows that the approximations by Plumo ( ) and Phomo is very reasonable [43]. In the even- clusters AU4, Aug, Aug, and Aujo, the HOMO state is doubly occupied with one spin up electron and one spin down electron, and an energy gap exists between... 

The second step accompanies the first one through the electrophilicity (co) by putting in act the charge transfer by tunneling of L-R barrier for one electron of the HOMO level passing to the LUMO and then down to the HOMO state by means of the LLR mechanism, see Figure 3.9(b) the minimization principle for electrophilicity, Eq. (3.169), further allows the relaxation of the transferred electron from the HOMOj to HOMOj level ... 

Adding more C atoms results in more states near both the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) states shown. Because each C atom brings in, on average, half filled states, the molecular structure fills all of the orbitals for which bonding dominates without filling any of the orbitals with primarily antibonding character as in other semiconductors. Thus,... 

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