M. Salim Banna Vanderbilt University, Nashville, TN 37235
The imoortance of relativitv to chemists is now well estahlished 11-3). but the conclusions of sprcial relativity hnve not vet been fulls incorporated in undergraduate textbooks, to knowledge. In this note I would like to summarize the contents of the lecture I give to my freshman class on relativistic effects in chemistry. The lecture is based primarily on the articles by Pitzer (I) and hy l'yykii and Dt.sclaux (21 as well as my own research in photoelectron spectroscopy. I start by giving the well-known ;elation between the massof an object and its speed u ,
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X.' -where mn"~~ is the rest mass and c is the speed of liaht. ~~.~ - Now, for electrons in atoms or molecules, u increases with the atomic number Z. which means that relativisticeffectsaremoreimportant foi heavier elements. As a result of increased mass, the relativistic average radius for s and p electrons will be smaller than the non-relativistic one, since i t is inversely proportional to the mass. This results in a relativistic contraction of s and p electrons. On the other hand, d and f electrons tend to stay away from the nucleus and will expand radially since the s and p electrons screen the nuclear attraction more efficiently. This also means that they are energetically destabilized (1,2) due t o this indirect effect. Photoelectron spectroscopy of core levels (4) provides a direct verification of these conclusions, since ionization energies for a number of core levels in atomic species have recentlv been measured 6-23), In the figure I compare experimekal atomic hinding energies (ionizaiioneneryiesof core and nonlevels) with those calculated relativistically (5,9), relati;istically (10). Note that the contraction of s a n d p orbitals is manifested by an increase in the energy i t takes to ionize electrons from these orbitals while thr expansion of the d's and f's results in lower hinding energies. The relativistic calcula&ons yield two p , d , or f levels, as observed experimentally. (This point is not crucial in this context since this is a separate relativistic effect from the one discussed here, so it is best to consider the weighted mean of the two components in each case, where the relative weights are in the ratio of 4:2 f o r p levels, 6:4 for d levels, and 8:6 for f levels.) As expected, the relativistic calculations are in better accord with experiment. The agreement is not perfect in every case, but this is due to a deficiencv in the calculations not related to relativity {namely, the failure to account for "correlation enerw"). The data in the fieure show that relativistic eflects are present even in light elements, but as expected they become more significant for heavier elements like mercury. These simple results can now he used to help explain a variety of physical and chemical properties (1,2). For example, the colors of silver and gold differ primarily because the 5d 6s transition in cold requires less energy than the 4d 5s transition in silver resulting in a smaller d - s gap (see Fig. 1 in Ref. ( 2 ) ) Thus . gold absorbs in the blue region and appears yellow while silver absorbs in the ultraviolet and appears "silvery." Many other chemical facts can be explained with the aid of relativity. For example, the smaller size of gold compared to silver is usually attributed to the lanthanide contraction, but i t is partly due to the greater effect of relativity on the 6s or-
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Comparison between non-relativistic(NR) and relativistic calculations (Rel)of atomic core ionization energies end experiment. The data for Mg. Zn, and Cd are taken fromref.(9).The experimentalvalues forHg are from ref. ( 8 ) and Vls theoretical values are from ref. ( 14 (NR) and this wwk (Rel).All relativistic calculations were performed using the program of Desclaux ( 127.
bit& of gold compared t o its effect on the 5s orbitals of silver (1,2). 1 Other interesting observations amenable to explanation by relativity include the well-known "inert-pair" effect which in thallium for example is due to the contraction of the filled 6s2 shell. This contraction also helps explain why mercury is a liquid at room temperature while cadmium is a solid. The reader is referred to refs. (I) and (2) for additional explanations of chemical facts based on relativity; and, for a lucid quantum mechanical treatment of relativity a t the undergraduate level as well as a summary of its effect on chemical properties, see the recent work of McKelvey in THIS JOURNAL (11 ). Literature Cited (I) P i h r , K. S..Ace. Cham. Re&, 12,271 (1979). (2) Pyykkb P..and Dsschux,J.-P.,Ace. Chem Rea..
12,276(1979).
'
Pitzer (Ref. ( 1)) discusses some very elegant calculations which make it possible to decoupie the effectof relativity from the effect of the 4fshell on the radii of the elements following the lanthanides (Hf to Bi). His results show that the relativistic contribution gains over the 4f contribution in reducing the radius. Pitzer also gives calculations which show that the lanthanide contraction is itself partly a relativistic effect. Volume 62 Number 3 March 1985
197
(3) Malli, G. L.. (Editor), Relativistic Effeeta in Atoms, Molecules. and Solids; NATO AS1 Series B.vol.87, Plenum Press. New York, 1983. ( B Ellison, F. 0..and White, M. G.. J. CHBM.EDUC., 53,430 (1976). 15) Mehlhom, W., Bmuckmann, B., and Hauaamann, D.,Phrs. S c r , 16,177 (1977). 16) Banna,M.S.. W a l l b a n k , B . , h t , D.C.,McDodl.C. A..andPerers, J.S.H.Q.. J Chsm. Phys, 68,5459 11978).
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Journal of Chemical Education
17) Banns, M. S., Fmnt, D. C., MeDmvell, C. A..and Wallbank. B.. J. Chem. Phva..68.696 .. . (1978). (8) Svenmon. S.. MBmnwn, N.. Basilier, E., Malmqubt, P. A, Geliua, U..and Sippbahn, K.. J Electron Smcfroar. 9.51 11976). 19) Key,R. J.. Banns. M. %.and ~ l s i gC. , S., J . EleclmnSpoctmsc..24,173 (1981) (10) Bmwhton, J. Q., and Bsgus, P. S., J. Elertmn Spectroac., 20,127 11980). (11) M ~ vey, K D ~, R~ , ~ , c ~ ~ , ~112 (1983), 112) Desclaux, J.-P.,Comput. Phys Comm.,9,31 (1975).
