Absolute energy scale

Figure 2.7 The absolute energy scale of orbitals must be referred to the energy of an isolated electron in a vacuum...

The band bending eVbb at n-type semiconductors is expected to decrease EB and additional changes of are related to changes of the electron affinity x (fig 1). As the band bending can possible be reserved by illumination a light induced opposite shift of the spectrum equivalent to a photopotential (Uph) is expected. The relation between the electrochemical energy scale Ered/ox vs NHE and the absolute energy scale E vs vacuum level is made by the relation ... 

In an absolute energy scale, the position of the conduction band with respect to the vacuum level is given by the electron affinity Ea (Fig. 1). The distance of the valence band with respect to the vacuum level is given by the ionization potential I, and that of the Fermi level is the work function . Values of these quantities are usually determined by surface spectroscopic methods [21]. 

As mentioned above, the electrochemical potential of a redox couple is usually given with respect to the Normal Hydrogen Electrode (NHE). Using an absolute energy scale with the vacuum level as a reference, the energy of a redox couple is given by... 

The redox potential is generally referred to the standard hydrogen potential (SHE), which has an exactly defined energy, E y, relative to the energy of the free electron in vacuum or at infinity. Thus, electrode potentials of redox couples can be expressed on the absolute energy scale according to... 

Here all the conduction band-edge , and valence-edges , are put into an absolute energy scale. It is clearly shown in the matrix elements of (28) that 3/2, 3/2) heavy-hole (HH) band-edges are shifted by SE =-P -Q and 13/2, 1/2) light-hole (LH) band-edges are shifted by SE =-P +Q, and conduction band-edges are shifted by SE =P from their previous unstrained positions. The corrections to the Kane inteiband matrix element/ on both in-plane and perpendicular directions are trivial. 

As explained in Appendix lA, the absolute energy scale is related to the redox potential Uredox on the SFIE scale by... 

Thus in considering ordinary everyday kinds of changes and chemical reactions, we will continue to deal with energy changes only, never with how much energy is in any particular equilibrium state. This is entirely sufficient for our needs, but it does introduce some complications that would be avoided if we had a useM absolute energy scale. 

The electrons at the Fermi level of the metal in a normal hydrogen electrode (NHE) have an exactly defined energy, Ereu relative to the energy of the free electron in vacuum. Taking a redox system as an example, then the absolute energy scale of a redox system is only shifted against the conventional scale by the free energy, Er d, i-e.. 

Fig. 3. The dihedral angle dependences of the two-center terms in absolute energy scale for the vicinal H H (a), H 0 (b) and 0 0 (c) interactions. .e. the interaction between the circled atoms in each figure). Note that the abscissa is cj) defined by the 0—C—C—0 bond sequence.

Fig. 10 displays our results for the quasi-particle band-structure in Si for two symmetry directions in an absolute energy scale. The full lines give our HF results. The HF approximation gives a direct gap of 6.8 (eV) compared to 3.3-3.4 (eV) in optical experiments, and a valence-bani gWidth of 13.5 (eV) compared to 12-13 (eV) in photoemission data (see also Table II). The dashed lines (TDSHF) are the dynamically correlated bands, where the two-particle Green s function contains both RPA (including local-field effects) and e-h attraction effects. The direct gap is reduced to... 

The energy of the conduction band and that of the valence band of crystalline BP were determined on the absolute energy scale with an experimental accuracy of 0.05 eV that is, versus vacuum ... 

If this is done suitably, then the (squared) bond valences can also - as demonstrated [25,26] - be linked to the absolute energy scale in static ways such as predicting energy thresholds in sohd electrolytes cf. [6], predicting NMR chemical shifts [36] or other spectroscopic properties, but also in dynamic ways as an effective atomistic forcefield. 

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