Atomic f values

Natural uranium consists almost entirely of the oi emitters " U and As " - U decays more than six times fastet than (Fig. 31.1) the proportion of is very slowly hut inexorably decreasing with time. Prioi to 1972, all analyses of naturally occurring uranium had shown this proportion to be notably constant at 0.7202 O.OOObfr. In that year, however, workers at the French Atomic F.ncrgy laboratories in Pierrelatte [terformiiig routine mass speetroinctiie analyses recorded a value of 0.7171%. The difference was small but significant. 

Consider electrons of mass m and velocity v, and atoms of mass M and velocity V we have mjM 1. The distribution function for the electrons will be denoted by /(v,<) (we assume no space dependence) that for the atoms, F( V), assumed Maxwellian as usual, in the collision integral, unprimed quantities refer to values before collision, while primed quantities are the values after collision. In general, we would have three Boltzmann equations (one each for the electrons, ions, and neutrals), each containing three collision terms (one for self-collisions, and one each for collisions with the other two species). We are interested only in the equation for the electron distribution function by the assumption of slight ionization, we neglect the electron-electron... 

For a given molecule and a given intemuclear separation a would have a definite value, such as to make the energy level for P+ lie as low as possible. If a happens to be nearly 1 for the equilibrium state of the molecule, it would be convenient to say that the bond is an electron-pair bond if a is nearly zero, it could be called an ionic bond. This definition is somewhat unsatisfactory in that it does not depend on easily observable quantities. For example, a compound which is ionic by the above definition might dissociate adiabatically into neutral atoms, the value of a changing from nearly zero to unity as the nuclei separate, and it would do this in case the electron affinity of X were less than the ionization potential of M. HF is an example of such a compound. There is evidence, given bdow, that the normal molecule approximates an ionic compound yet it would dissociate adiabatically into neutral F and H.13... 

The values in Table VI were obtained in the following way. Values for C, Si, Ge, and Sn are the same as in Table III, for the tetrahedral configuration is the normal one for these atoms. Radii for F, Cl, Br, and I were taken as one-half the band-spectral values for the equilibrium separation in the diatomic molecules of these substances. Inasmuch as these radii for F and Cl are numerically the same as the tetrahedral radii for these atoms, the values for N, 0, P, and S given in Table III were also accepted as normal-valence radii for these atoms. The differences of 0.03 A between the normal-valence radius and the tetrahedral radius for Br and... 

These F-values are not so reliable as those calculated by Hartree s method. On the other hand, they are obtained with much less labor, Hartree s calculations having so far been carried out for only a small number of atoms. In figure 10 F-curves are shown for Li+, Na+, K+, and Rb+ as obtained by the method described in this paper, by Hartree s method and by the Thomas-Fermi method. It is seen that for all... 

Fluorine is, of course, the most electronegative atom on the periodic table. ap and F values (the pure field inductive effect) provide... 

For the photodiagnostic use of these compounds, a high quantum yield of fluorescence, r, is desirable. The metal complexes of the common first-row transition metals are not suitable, because they show very low 4>f values. On the other hand, porphyrin complexes of d° and d10 elements show appreciable fluorescence, although generally less than that of the metal-free compounds, presumably because of the heavy-atom effect (e.g., TPP ZnTPP, Table 5). The further operation of the heavy-atom effect, which increases the rate of intersystem crossing (/cisc) by... 

Isotope effects on equilibria have been formulated earlier in this chapter in terms of ratios of (s2/si)f values, referred to as reduced isotopic partition function ratios. From Equation 4.80, we recognize that the true value of the isotope effect is found by multiplying the ratio of reduced isotopic partition function ratios by ratios of s2/si values. Using Equation 4.116 one now knows how to calculate s2/si from ratios of factorials. Note well that symmetry numbers only enter when a molecule contains two or more identical atoms. Also note that at high temperature (s2/si)f approaches unity so that the high temperature equilibrium constant is the symmetry number factor. 

From the intensity, the value for the observed F is obtained. This is substituted into the electron density equation for locating the atoms that determine the structure of the protein. Through an iterative process, the observed and calculated F values are compared to determine the goodness of fit and hence the quality of the structure. 

The 4/(H-F) values are usually lower when atoms other than nitrogen separate the two nuclei <1985 8 1966,30 1968 45 t969 62and84) as for example in ... 

It is clear that some information is lost as a result of our approximation, specifically regarding the individual bonds formed by sp carbon atoms, but the total of the F values in a molecule is expected to be generally reasonably accurate. The salient feature of ethylenic double bonds, namely, the inward displacement of tt orbital centroids on the C=C axis revealed by direct calculations, and its important role in energy calculations, can now be put in a clear perspective and efficiently tested for large collections of molecules. 

As for radical substitutions in compounds XV, XVII, XXV, and some other compounds, the F values (hence also Ar and Sr values, cf. section V, A) correctly predict the experimental reactivity order. The calculated and experimental orders disagree in the case of compounds XXI and, particularly, XVI the latter case (radical phenylation of quinoline) represents a serious failure of the theory, for the experimental study was very thorough.160 It is worth noting that in the compounds which have no meso-position the center of radical reactivity is the position adjacent to the nitrogen atom (with the exception of the just mentioned phenylation of quinoline). 

The enormous f0 and values reflect the ability of the electron pair on O to stabilise, selectively, the transition states for o- and p-attack (cf. p. 154), while the f value of < 1 reflects the destabilisation (compared with attack on benzene) of the transition state for m-attack by the electron-withdrawing inductive (polar) effect of the oxygen atom. 

We have selected the most appropriate lines suitable for use for the ions observed in SN 1987A, and they are listed in Table 1 together with the relevant atomic data for the transitions and the observed absorption depths. The f-values have been taken from the sources referenced. 

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