Relaxation, electronic

Strains can also be relieved by changing the oxidation states of cations that can adopt more than one oxidation state. Cations in stretched layers can accommodate themselves to longer bonds by reducing their oxidation state, since this will lower the valences of their bonds. Similarly cations that are in compressed layers will tend to increase their oxidation state so as to increase the bond valence and shorten the bonds. This is a mechanism that can be used to stabilize unusual oxidation states. 

The addition of 0.18 interstitial ions to the formula unit of La2Ni04 requires that the oxidation state of Ni be increased to +2.36. Given that the equatorial Ni-O bonds have a length of 194 pm and therefore a bond valence of 0.46 vu, this increase in the oxidation state of Ni allows the axial bond valences to be increased from 0.08 to 0.26 vu reducing the length of the Ni-Oa iai bonds from 259 pm to the more acceptable value of 215 pm. This in turn reduces the valence required for the axial La-O bond by 0.18 vu which, together with the extra valence contributed by the interstitial 0 , reduces the distortion around La to an acceptable level. It is difficult to calculate the BSI and GII for this compound since one needs to know how the interstitial 0 ions are ordered within the LaO double layer, but clearly the BSI will be considerably reduced from the value 0.29 vu that it had before the introduction of the defect and subsequent electronic relaxation. This form of the structure is stable and is the form normally found when the material is prepared in air. 

The relaxation of La2Ni04 to La2Ni04,i8 illustrates a couple of important points. Firstly, the defect and electronic modes of relaxation necessarily work together since the change in oxidation state of NP+ is directly related to the amount of interstitial present. This simultaneous relaxation of both the stretched and the compressed layers is a feature found in many, if not all, of the observed mechanisms for relaxing lattice-induced strain. Secondly, the lattice-induced strain is directly responsible for the crystallization of a stable compound with a fixed, but irrational, composition, involving a fixed, but nonintegral, oxidation state for nickel. 

La2Cu04 has a structure and crystal chemistry virtually identical to that of La2Ni04 with a couple of important exceptions. Firstly, all octahedrally coordinated Cu compounds show a spontaneous electronic distortion (the Jahn-Teller distortion described in Section 8.3.1) by which the two axial bonds become longer and the four equatorial bonds become shorter. The distortion observed in La2Cu04 is usually attributed to this effect, but the observation of the same distortion in La2Ni04 shows that the driving force in both compounds 

The second difference between the nickel and copper compounds is that La2Cu04 is a superconductor, being the first of the Cu02 layer compounds in which superconductivity was observed. The lattice-induced strain is a necessary condition for superconductivity since it stabilizes the higher oxidation state needed to provide the superconducting carriers as discussed in Section 13.3.2. 

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Hyperfine Interaction (dipolar and scalar) 2,0 Electron relaxation, may be complicated Paramagnetic systems and Impurities [17-191... 

Figure Bl.13.3. The inversion-recovery experiment. (Reproduced by pennission of VCFI from Banci L, Bertini I and Luchinat C 1991 Nuclear and Electron Relaxation (Weinlieim VCFI).)...

Band L, Bertini I and Luchinat C 1991 Nuclear and Electron Relaxation (Weinheim VCH)... 

Niv M Y, Krylov A I and Gerber R B 1997 Photodissociation, electronic relaxation and recombination of HCI in Ar-n(HCI) clusters—non-adiabatic molecular dynamics simulations Faraday Discuss. Chem. Soc. 108 243-54... 

An alternative mechanism of excess energy release when electron relaxation occurs is through x-ray fluorescence. In fact, x-ray fluorescence favorably competes with Auger electron emission for atoms with large atomic numbers. Figure 16 shows a plot of the relative yields of these two processes as a function of atomic number for atoms with initial K level holes. The cross-over point between the two processes generally occurs at an atomic number of 30. Thus, aes has much greater sensitivity to low Z elements than x-ray fluorescence. 

The fact is that the molecular orbitals describing the resulting cation may well be quite different from those of the parent molecule. We speak of electron relaxation, and so we need to examine the problem of calculating accurate HF wavefunctions for open-shell systems. 

In this particular example, the Xa orbital energies resemble those produced from a conventional HF-LCAO calculation. It often happens that the Xa ionization energies come in a different order than HF-LCAO Koopmans-theorem ones, due to electron relaxation. 

During the photoelectron emission event there are electronic relaxation effects occurring, which are usually divided into intra- and inter-molecular relaxation effects. These effects can be rationalized in a classical picture as follows. An elec-... 

Electron relaxation times are important parameters that allow us to predict whether high-resolution NMR is feasible. The two most im-... 

For all known cases of iron-sulfur proteins, J > 0, meaning that the system is antiferromagnetically coupled through the Fe-S-Fe moiety. Equation (4) produces a series of levels, each characterized by a total spin S, with an associated energy, which are populated according to the Boltzmann distribution. Note that for each S level there is in principle an electron relaxation time. For most purposes it is convenient to refer to an effective relaxation time for the whole cluster. 

The [Fe4S4p clusters contain four equivalent irons and give relatively narrow signals (3, 7, 62, 63) (Fig. 2E). The electron relaxation time is evaluated around 5 X 10 s (Table I), which is somewhat smaller than that of the Fe(II) monomer. Also, the signals of [Fe4S4l (15, 64-68) (Fig. 2D) and [Fe4S4fi+ (8, 13, 69-71) (Fig. 2F) systems are sharp. 

The symmetry-breaking of the HF function occurs when the resonance between the two localized VB form A+...A and A...A+ is weaker than the electronic relaxation which one obtains by optimizing the core function in a strong static field instead of keeping it in a weak symmetrical field. If one considers for instance binding MOs between A and A they do not feel any field in the SA case and a strong one in the SB solution. The orbitals around A concentrate, those around A become more diffuse than the compromise orbitals of A+ 2 and these optimisations lower the energy of the A. A form. As a... 

Fig. 5.6 Changes in the shape of the valence contribution due to geometric and electronic relaxation in [FeF4]" . Full line [FeF4] at its equilibrium geometry, dashed line [FeF4] at its equilibrium geometry. The square of the valence orbital that mainly contributes to p(0) along the Fe-F bond (distances are in units of the Bohr radius) is also drawn (from [19])...

Ullrich S, Schultz T, Zgierski MZ, Stolow A (2004) Direct observation of electronic relaxation dynamics in adenine via time-resolved photoelectron spectroscopy. J Am Chem Soc 126 2262... 

Schwalb NK, Temps F (2007) Ultrafast electronic relaxation in guanosine is promoted by hydrogen bonding with cytidine. J Am Chem Soc 129 9272... 

In general, intramolecular isomerization in coordinatively unsaturated species would be expected to occur much faster than bimolecular processes. Some isomerizations, like those occurring with W(CO)4CS (47) are anticipated to be very fast, because they are associated with electronic relaxation. Assuming reasonable values for activation energies and A-factors, one predicts that, in solution, many isomerizations will have half-lives at room temperature in the range 10 7 to 10 6 seconds. The principal means of identifying transients in uv-visible flash photolysis is decay kinetics and their variation with reaction conditions. Such identification will be difficult if not impossible with unimolecular isomerization, particularly since uv-visible absorptions are not very sensitive to structural changes (see Section I,B). These restrictions do not apply to time-resolved IR measurements, which should have wide applications in this area. 

It is clear from the above equations that numerous parameters (proton exchange rate, kcx = l/rm rotational correlation time, tr electronic relaxation times, 1 /rlj2e Gd proton distance, rGdH hydration number, q) all influence the inner-sphere proton relaxivity. Simulated proton relaxivity curves, like that in Figure 3, are often used to visualize better the effect of the... 

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