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The measurement of the efficiency of Förster long-range resonance energy transfer between donor (D) and acceptor (A) luminophores attached to the same macromolecular substrate can be used to estimate the D-A separation, R. If the D and A transition dipoles sample all orientations with respect to the substrate (the isotropic condition) in a time short compared with the transfer time (the dynamic averaging condition), the average orientation factor less than K2 greater than is 2/3. If the isotropic condition is not satisfied but the dynamic averaging condition is, upper and lower bounds for less than K2 greater than, and thus R, may be obtained from observed D and A depolarizations, and these limits may be further narrowed if the transfer depolarization is also known. This paper offers experimental protocols for obtaining this reorientational information and presents contour plots of less than K2 greater than min and less than K2 greater than max as functions of generally observable depolarizations. This permits an uncertainty to be assigned to the determined value of R. The details of the D and A reoreintational process need not be known, but the orientational distributions are assumed to have at least approximate axial symmetry with respect to a stationary substrate. Average depolarization factors are derived for various orientational distribution functions that demonstrate the effects of various mechanisms for reorientation of the luminophores. It is shown that in general the static averaging regime does not lend itself to determinations of R.

X-ray absorption spectra near the Kx edge have been measured in various iron grou compounds using the intense synchrotron radiation available at the Stanford Synchrotron Research Project. In the cubic compounds KMF3 where M = Mn+2, Fe+2, Co+2, Ni+2, and Zn+2, well resolved lines were observed and assigned to the Is --.3d, Is -4s, and Is -4p transitions. The observed energies agreed rather well with the spectroscopic energy levels of the Z + 1 ion and the intensities are shown to agree with those expected on the basis of one electron transitions of the form Z ls2dn(LS) -. (Z + 1)Is2dnn'1(I",S). The energies of the intense Is-4p transition increase by about 5 V going from KFeF3 to K2NaFeF6, but only by about 1 V from K4Fe(CN)e to K3Fe(CNM. The transitions confirm that upon oxidation of the hexacyanides the iron electronic structure barely changes. In the iron sulfur protein rubredoxin, where the iron is bound to a tetrahedron of sulfurs, the Is-3d transition was about seven times more intense than the same transition in an octahedrally coordinated compound. These intensities parallel those observed in the d-d transitions of optical spectra,bcause in both types of spectra the intensities depend upon 4p admixture. In the heme protein cytochrome c, upon oxidation the Is-s4p transition shifts only about I V to higher energies, similar to the iron hexacyanides. These results are discussed in terms of covalent bonding. The absorption spectrum of x-rays near the K edge has traditionally been divided into a low energy region-the so-called absorption edge-in which the transitions are to bound states (1), and a higher energy region-the so-called extended x-ray absorption fine structure (EXAFS) spectrum-where the transitions are to free electron states (2-6). Recently, synchrotron sources of x-rays have become available whose intensities are about 105 times higher than were previously available. This results in improved signal to noise ratios, which allow meaningful measurements to be made on dilute systems (4-6).In this paper we present measurements, made with synchrotron radiation, of the x-ray absorption spectrum of iron proteins, and of some model compounds in the region of the absorption edge. (Fig. 1). We note that the first indications of absorption, in both compounds, are weak peaks which have been enlarged to facilitate comparison. The K2NaFeF6 peak is shifted about 1.3 V to higher energies from the analogous peak in KFeF3. The K2NaFeF6 peak stands by itself and is composed of a barely resolved doublet. The KFeF3 peak is less clearly separated from the base of the strong absorption, with the suggestion of a weaker peak about 2 V to higher energy.About 16 V to higher energies in the ferrous compound, and 19 V to higher energy in the ferric compound, there is an intense peak whose position depends upon the oxidation state of the iron. At somewhat lower energies, there are shoulders on this intense peak of varying degrees of resolution.We measured the absorption spectra of a series of perovskite cubic fluoride...

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