Constant screening

Later methods, especially that of Gordy (1955), and later Allred and Rochow (1958) make use of screening constants of the electron strucmre for the nuclear charge of each atom. This determines die attraction between the nucleus of the atom and an electron outside the normal electron complement, and is die effective nuclear charge. The empirical equation for the values of electronegativity obtained in this manner by Allred and Rochow is... 

Various other sets of screening constants have been proposed, for example those by Pauling and Sherman (1932). 

Atomic Screening Constants from SCF Functions E. Clementi and D. L. Raimondi The Journal of Chemical Physics 38 (1963) 2686-2689... 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

Eckart, C, Phys. Rev. 36, 878, "Theory and calculation of screening constants." Open shell idea discussed, b. 

A similar model for many-electron atoms has been developed,6 by considering each electron to be hydrogen-like, but under the influence of an effective nuclear charge (Z — Ss)e, in which Ss is called the size-screening constant. It is found that atoms and ions containing only 5 electrons (with the quantum number l equal to zero) and completed sub-groups of... 

For an ion of nuclear charge Ze, the size-screening constant for a given electron is... 

The agreement is satisfactory, except in the cases where there are deviations from additivity. This fact is a verification of our treatment and of the correctness of our screening constants, for the arbitrary selection of only one ionic radius in a series of salts showing additivity in inter-atomic distances is permitted, and our screening constants fixed four radii independently. 

It is customary to express the empirical data concerning term values in the X-ray region by introducing an effective nuclear charge Zeff e in the place of the true nuclear charge Ze in an equation theoretically applicable only to a hydrogen-like atom. Often a screening constant S is used, defined by the equation... 

This equation, including succeeding terms, was obtained originally by Sommerfeld from relativistic considerations with the old quantum theory the first term, except for the screening constant sQ> has now been derived by Heisenberg and Jordan] with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. 

We shall now predict values of SE for ions for which z4/Z is small, i.e., for Z large. If this screening constant is constant, and does not depend on Z, these values hold for all atoms and ions with the structures considered. The nature of the agreement between the theoretical and the experimental values of R or of SE will show to what extent this is true. 

For the mole refraction screening constant we accordingly have... 

We are now led to introduce a second empirical correction into our calculations. The theoretical values for the rubidium, caesium, bromide, and iodide ions in Table III resulted from the assumption that SE is independent of Z, which is known not to be true for these structures, on account of the difference between SE<1 and SEw. The solution values of R, which we may assume to hold also for gaseous ions in these cases, also show that the screening constant for the negative ions should be larger and for the positive ions smaller than that used that is, as Z increases SE decreases, presumably approaching our theoretical values for Z large. We shall assume that SE is a linear function of Z in this region, and evaluate the parameters of the function with the use of the solution values for the bromide and iodide ions. If we write... 

In Table IV are given values of the mole refraction of gaseous ions calculated from equations (24) and (29) with the use of the values found above for SE and ASe. Values for hydrogen-like atoms and ions are also included these are, of course, accurate, since no screening constant is needed. Table IV is... 

Adhering to our general method of treatment, we shall now evaluate a screening constant SM valid in the case of Z large. Taking the time average of r2 in the various regions traversed, we write... 

The molal diamagnetic susceptibilities of rare gas atoms and a number of monatomic ions obtained by the use of equation (34) are given in Table IV. The values for the hydrogen-like atoms and ions are accurate, since here the screening constant is zero. It was found necessary to take into consideration in all cases except the neon (and helium) structure not only the outermost electron shell but also the next inner shell, whose contribution is for argon 5 per cent., for krypton 12 per cent., and for xenon 20 per cent, of the total. 

The value of the size screening constant SSoo is accordingly given by equation (26), r/t being replaced by 2. 

As before, we may expect the values of Ss calculated for Z large to be valid for actual ions with the helium and neon structures. For the other structures we introduce the empirical corrections based upon those used for the mole refraction screening constant, with the aid of the principle of the constancy of the ratios of corresponding screening defects, already used for the diamagnetism screening constant. In this way the values of SSo and ASs given in Table VIII are obtained. An equation similar to equation (29) is to be used to find individual values of Ss. 

Screening Constants for Many-electron Atoms. The Calculation and Interpretation of X-ray Term Values, and the Calculation of Atomic Scattering... 

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