Gap energies

The study of small energy gaps in matter using the optical spectral region (say the near-IR, visible and UV) offers many advantages over direct one-photon spectroscopies in the IR, far IR or even the microwave. First,... 

Bechstedt F 1992 Quasiparticle corrections for energy gaps in semiconductors Adv. Solid State Phys. 32 161... 

The electrochemical features of the next higher fullerene, namely, [70]fullerene, resemble the prediction of a doubly degenerate LUMO and a LUMO + 1 which are separated by a small energy gap. Specifically, six reversible one-electron reduction steps are noticed with, however, a larger splitting between the fourth and fifth reduction waves. It is important to note that the first reduction potential is less negative than that of [60]fullerene [31]. 

Semiconductors are a class of materials whose conductivity, while highly pure, varies witli temperature as exp (-Ag//cg7), where is tlie size of a forbidden energy gap. The conductivity of semiconductors can be made to vary over orders of magnitude by doping, tlie intentional introduction of appropriate impurities. The range in which tlie conductivity of Si can be made to vary is compared to tliat of typical insulators and metals in figure C2.16.1. 

In an intrinsic semiconductor, tlie conductivity is limited by tlie tlieniial excitation of electrons from a filled valence band (VB) into an empty conduction band (CB), across a forbidden energy gap of widtli E. The process... 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

Figure C2.16.4. A plot of the energy gap and lattice constant for large-gap nitrides. These materials have wairtzite stmcture.

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

Figure C3.5.6 compares the result of this ansatz to the numerical result from the Wiener-Kliintchine theorem. They agree well and the ansatz exliibits the expected exponential energy-gap law (VER rate decreases exponentially with Q). The ansatz was used to detennine the VER rate with no quantum correction Q= 1), with the Bader-Beme hannonic correction [61] and with a correction based [83, M] on Egelstaff s method [62]. The Egelstaff corrected results were within a factor of five of experiment, whereas other corrections were off by orders of magnitude. This calculation represents the present state of the art in computing VER rates in such difficult systems, inasmuch as the authors used only a model potential and no adjustable parameters. However the ansatz procedure is clearly not extendible to polyatomic molecules or to diatomic molecules in polyatomic solvents.

Nitzan A, Mukamei S and Jortner J 1975 Energy gap iaw for vibrationai reiaxation of a moieouie in a dense medium J. Chem. Phys. 63 200-7... 

The motivation comes from the early work of Landau [208], Zener [209], and Stueckelberg [210]. The Landau-Zener model is for a classical particle moving on two coupled ID PES. If the diabatic states cross so that the energy gap is linear with time, and the velocity of the particle is constant through the non-adiabatic region, then the probability of changing adiabatic states is... 

Stueckelberg derived a similar fomiula, but assumed that the energy gap is quadratic. As a result, electronic coherence effects enter the picture, and the transition probability oscillates (known as Stueckelberg oscillations) as the particle passes through the non-adiabatic region (see [204] for details). 

Not all Iterative semi-empirical or ah iniiio calculations converge for all cases. For SCF calculation s of electronic stnictiire. system s with a small energy gap between the highest occupied orbital and the lowest unoccupied orbital may not converge or may converge slowly. (They are generally poorly described by the Ilartree-Foch method.)... 

Quantum mechanical descriptors (e.g. HOMO-LUMO energy gap) 3D structure See Section 2.7.4... 

What is tlie sum of all the energy gaps as determined from the vibrational speetrum... 

The energy "gap" between the a and a orbitals at R = depends on the eleetronegativity differenee between the groups X and Y. If this gap is small, it is expeeted that the behavior of this (slightly) heteronuelear system should approaeh that of the homonuelear X2 and Y2 systems. Sueh similarities are demonstrated in the next seetion. 

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