HT approximation

This description accounts for transition dipole moments induced by displacements along the normal modes during the electronic transition, that is, a simultaneous excitation of vibrational modes. This approximation is also denoted as double-harmonic. For electric dipole forbidden transitions, the first term in Eq. [24] vanishes and the resulting expression is denoted as the Herzberg-Teller (HT) approximation. 

Tao and Frank [4S] presented data consistent with the FF model without any reference to fitting the exp—(at+ ht ) approximation. We tested this by simulation thus, Tao and Frank s data were simulated with the same amplitude as shown in thdr paper, from their published parameters, and with Gaussian noise added. When our simulated curves were analysed with our FF fitting program, they gave chi-squared values of 1.00 0.05. They were subsequently fitted to Equation (15). The values from the FF fit were then subtracted from the x values from the fit to give a measure of the difference in the quality of the fit These results are presented in Table 15.2, along with parameters extracted from the paper. 

If the HT approximation is considered, an additional quantity is stored, Hci, which gives an upperbound estimation of the square of the pure HT contribution for a given mode k and the corresponding transition (0 6 +... 

The B3Hg ion (p. 166) is a triangular cluster of Cj (rather than C2 ) symmetry (see Fig. 6.15a) the bridging atoms are essentially in the B3 plane with Ht above and below. While it has been conventional to represent the cluster bonding in terms of two BHB and one B-B bond (Fig. 6.15b), recent high-level computations suggest the presence of a 3-centre BBB bond, as depicted approximately in Fig. 6.15c. 

Size No. Designation Approximate Number/Ft We ht, Lb/Ft Free Gas Space... 

The difference in behavior reported by Von Stackelberg is not thought to be an essential one. Whether decomposition of a hydrate containing two solutes by removal of its vapor through pumping will be a univariant process depends on the number and compositions of the phases formed. In the system of Fig. 10, for instance, a mixed HtS-propane hydrate will exhibit a constant decomposition pressure on pumping at — 3°C if it contains HaS and propane in the azeotropic" ratio of approximately 3 1. 

From Fig. 6.14 it becomes clear why one must heat filaments to very high temperatures to see electron emission in electron guns. Only the part of the electron distribution that has obtained energies above 0 can be utilized. The occupation number at the vacuum level can be approximated by e hT leading to the well known Richardson-Dushman formula, which describes the fluxj of electrons evaporating from a surface with work function 0 at temperature T ... 

Of course, cholinergic neurons are not the only ones with axon terminals in the cortex and if their degeneration does originate in the cortex then other afferants and their neurons could also be affected. This contention is supported by reported reductions in the number of NA neurons in the locus coeruleus, and 5-HT neurons in dorsal raphe but these are less marked (approximately 50%) than the loss of cholinergic neurons. Accompanying reductions in cortical NA and 5-HT are also seen but are again lower than those for ChAT but 5-HT2 receptors are reduced (43%). 

A final experiment demonstrating the distinetion between the acute and neurotoxic effects of MDMA is shown in figure 12. In this case, the 5-HT uptake inhibitor fluoxetine was administered at various times after MDMA, with all animals being saerifieed 1 week later. The results are shown as a pereentage of eontrol eortieal 5-HT eoneentrations. Simultaneous administration of an uptake inhibitor with MDMA completely blocked the decrease in 5-HT concentrations measured 1 week later. However, administration of the inhibitor 3 hours after MDMA still resulted in complete protection from the neurotoxicity. Approximately 50 percent of the depletion could still be blocked 6 hours after MDMA by 12 hours, the administration of fluoxetine no longer had any effect. Blockade of the neurotoxicity by an uptake inhibitor 3 hours after MDMA clearly differentiates the acute and long-term effects of MDMA, since at this point the acute depletion of 5-HT is already at a maximum. The administration of fluoxetine to MDMA-treated animals... 

A stagnant diffusion layer is often assumed to approximate the effect of aqueous transport resistance. Figure 4 shows a membrane with a diffusion layer on each side. The bulk solutions are assumed to be well mixed and therefore of uniform concentrations cM and cb2. Adjacent to the membrane is a stagnant diffusion layer in which a concentration gradient of the solute may exist between the well-mixed bulk solution and the membrane surface the concentrations change from Cm to c,i for solution 1 and from cb2 to cs2 for solution 2. The membrane surface concentrations are cml and cm2. The membrane has thickness hm, and the aqueous diffusion layers have thickness ht and h2. 

Figure 12.2 is a plot of the effectiveness factor r] versus the Thiele modulus hT. For low values of hT (slow reaction, rapid diffusion), the effectiveness factor approaches unity. For values of the Thiele modulus above 2.0, tanh hT 1 and the effectiveness factor may be approximated by... 

For situations where the reaction is very slow relative to diffusion, the effectiveness factor for the poisoned catalyst will be unity, and the apparent activation energy of the reaction will be the true activation energy for the intrinsic chemical reaction. As the temperature increases, however, the reaction rate increases much faster than the diffusion rate and one may enter a regime where hT( 1 — a) is larger than 2, so the apparent activation energy will drop to that given by equation 12.3.85 (approximately half the value for the intrinsic reaction). As the temperature increases further, the Thiele modulus [hT( 1 — a)] continues to increase with a concomitant decrease in the effectiveness with which the catalyst surface area is used and in the depth to which the reactants are capable of... 

Scheme V. Representation of the catalytic p-type Si photocathode for Ht evolution prepared by derivatizing the surface first with Reagent III followed by deposition of approximately an equimolar amount of Pd(0) by electrochemical deposition. The Auger/depth profile analysis for Pd, Si, C, and O is typical of such interfaces (49) for coverages of approximately 10 8 mol PQ2 /cm2.

Serotonergic neurons contain the enzyme L-tryptophan-5-monooxygenase (EC 1.14.16.4), more commonly termed tryptophan hydroxylase, which converts tryptophan to 5-hydroxytryptophan (5-HTP) (Fig. 13-5). Tryptophan hydroxylase contains 444 amino acids, corresponding to a molecular weight of about 51 Da. This enzyme is synthesized in serotonergic cell bodies of the raphe nuclei and is found only in cells that synthesize 5-HT. Therefore its distribution in brain is similar to that of 5-HT itself. The Km of tryptophan hydroxylase for tryptophan is approximately 30-60 pmol/1, a concentration comparable to that of tryptophan in brain. If the concentration of tryptophan in serotonergic neurons is assumed to be comparable to that in whole brain, the enzyme would not be saturated with substrate, and the formation of 5-HT in brain would be expected to rise as the brain concentration of tryptophan increases. This has been found to occur in response to raising the dietary intake of tryptophan specifically. 

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