Golden

Femii s Golden Rule expresses the rate of transitions between b and a as... 

Note that if we identify the sum over 8-fimctions with the density of states, then equation (A1.6.88) is just Femii s Golden Rule, which we employed in section A 1.6.1. This is consistent with the interpretation of the absorption spectmm as the transition rate from state to state n. 

Molina M J, Molina L T and Golden D M 1996 Environmental chemistry (gas and gas-solid interactions) the role of physical chemistry J. Phys. Chem. 100 12 888... 

It should be noted that in the cases where y"j[,q ) > 0, the centroid variable becomes irrelevant to the quantum activated dynamics as defined by (A3.8.Id) and the instanton approach [37] to evaluate based on the steepest descent approximation to the path integral becomes the approach one may take. Alternatively, one may seek a more generalized saddle point coordinate about which to evaluate A3.8.14. This approach has also been used to provide a unified solution for the thennal rate constant in systems influenced by non-adiabatic effects, i.e. to bridge the adiabatic and non-adiabatic (Golden Rule) limits of such reactions. 

Golden D M and Benson S W 1975 Physicai Chemistry. An Advanced Treatise vol VII (New York Academic) p 57... 

In equation (bl. 15.7) p(co) is tlie frequeney distribution of the MW radiation. This result obtained with explieit evaluation of the transition matrix elements oeeurring for simple EPR is just a speeial ease of a imieh more general result, Femii s golden mle, whieh is the basis for the ealeulation of transition rates in general ... 

Deiamarche E, Michei B, Biebuyck FI A and Gerber C 1996 Golden interfaces the surface of self-assembled monolayers Adv. Mater. 8 719-29... 

Cate J FI, Gooding A R, Podell E, Zhou K, Golden B L, Kundrot C E, Cech T R and Doudna J A 1996 Crystal structure of a group i ribozyme domain principles of RNA packing Science 273 1678-85... 

Many experimental techniques now provide details of dynamical events on short timescales. Time-dependent theory, such as END, offer the capabilities to obtain information about the details of the transition from initial-to-final states in reactive processes. The assumptions of time-dependent perturbation theory coupled with Fermi s Golden Rule, namely, that there are well-defined (unperturbed) initial and final states and that these are occupied for times, which are long compared to the transition time, no longer necessarily apply. Therefore, truly dynamical methods become very appealing and the results from such theoretical methods can be shown as movies or time lapse photography. 

The simplest theoretical description of the photon capture cross-section is given by Fermi s Golden Rule... 

The solid has a layer structure (p. 434). Lead(ir) iodide, like lead(Il) chloride, is soluble in hot water but on cooling, appears in the form of glistening golden spangles . This reaction is used as a test for lead(II) ions in solution. 

D. Rumelhart, R. Durbin, R. Golden, Y. Chauvin, Backpropagfition The Basic Theory in Mathematical Perspectives on Neural Networks, P. Smolensky, M. C. Mozer, D. E. Rumelhart (Eds.), Lawrence Earlbaum Assoc, Hillsdale, NJ, 1996, pp. 533-566. 

Fig. 41(A) and (b), p. 65) into which the ethereal extract is allowed to run from a dropping-funnel at approximately the rate at which the solvent is distilling. When the ether has been removed, fit a capillary tube and thermometer, and continue the distillation at water-pump pressure. The diethyl ester of collidine-3,5-dicarboxylic acid (II) distils as a pale golden oil, b.p. i76 178°/i4 mm. Yield, 5 g. from 6 g. of the ester (I). 

In a 500 ml. Pyrex round-bottomed flask, provided with a reflux condenser, place a mixture of 40 g. of freshly-distUled phenylhydrazine (Section IV.89) and 14 g. of urea (previously dried for 3 hours at 100°). Immerse the flask in an oil bath at 155°. After about 10 minutes the urea commences to dissolve accompanied by foaming due to evolution of ammonia the gas evolution slackens after about 1 hour. Remove the flask from the oil bath after 135 minutes, allow it to cool for 3 minutes, and then add 250 ml. of rectified spirit to the hot golden-yellow oil some diphenylcarbazide will crystallise out. Heat under reflux for about 15 minutes to dissolve the diphenylcarbazide, filter through a hot water funnel or a pre-heated Buchner fuimel, and cool the alcoholic solution rapidly in a bath of ice and salt. After 30 minutes, filter the white crystals at the pump, drain well, and wash twice with a little ether. Dry upon filter paper in the air. The yield of diphenylcarbazide, m.p. 171 °, is 34 g. A further 7 g. may be obtained by concentrating the filtrate under reduced pressure. The compound may be recrystallised from alcohol or from glacial acetic acid. 

First-Order Fermi-Wentzel "Golden Rule"... 

This expresses the widely used El approximation to the Fermi-Wentzel golden rule. 

The first-order El "golden-rule" expression for the rates of photon-induced transitions can be recast into a form in which certain specific physical models are easily introduced and insights are easily gained. Moreover, by using so-called equilibrium averaged time correlation functions, it is possible to obtain rate expressions appropriate to a... 

So, the final result is the order golden rule expression ... 

A simple method for predicting electronic state crossing transitions is Fermi s golden rule. It is based on the electromagnetic interaction between states and is derived from perturbation theory. Fermi s golden rule states that the reaction rate can be computed from the first-order transition matrix and the density of states at the transition frequency p as follows ... 

The golden rule is a reasonable prediction of state-crossing transition rates when those rates are slow. Crossings with fast rates are predicted poorly due to the breakdown of the perturbation theory assumption of a small interaction. 

In a plastic container the chemist dissolves her golden yellow freebase oil into some DCM, ether or ethanol. The chemist then starts a steady dripping of the sulfuric acid into the HCl/salt and white, puffy HCI gas will start to exit the glass rod or pipette which is at the end of the hose. That tip is then plunged into the sol-vent/freebase solution to bubble the gas through the solvent. 

As the solution cools a big old mass of unreacted ammonium chloride will form. The chemist removes this by vacuum filtration and saves the crystals for reuse at another time. The golden colored filtrate is placed back in the flask and distilled (with vacuum now ) to reduce its volume by about a third. Temperature is not so much a problem now as the chemist will let the stuff distill over at whatever temperature is necessary. Sometimes the reducing solution is so concentrated that the remaining ammonium chloride crystals... 

I give you the end of a golden string, Only wind it into a ball It will lead you in at Heaven s gate, Built in Jerusalem s wall. 

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