Joel F. Liebman
Princeton University Princeton, New Jersey 08540
Comments and a Warning about Isoelectronic Systems
The notion of isoelectronic systems is easy to apply as a predictive and explanatory principle for molecular structure. Unfortunately, like most simple ideas, the conditions under which it map be applied have not yet been well defined. Therefore, its use often appears artificial or designed only for "simple" and/or 'lnormal" systems. The standard, textbook definition of the isoelect.ronicprinciple is well stated by Bent ( 1 ) : "R'lolecules that have the same number of electrons and the same number of heavy atoms have similar electronic structures and similar heavy-atom geometries." As Coulson (3)additionally points out, the user should be concerned with the total number of valence electrons rather than the total number of electrons. This allows congener substituted compounds (e.g., S for 0 in relating COS and CS2 to COz) to be considered isoelectronic. This injunction also implies that the two molecules to be related must be in the same electronic state. However, identical summetry is not required-e.g., C02 and NzO are isoelectronic even though the former has D,* while the latter has only C,, symmetry. Moreover, the ground and excited states of a molecule are not isoelectronic. Furthermore, the o-bond heavy atom framework of the two molecules must be the same for them to be considered isoelectronic. For example, ozone and propene are isoelectronic, cyclopropane and propene are not. Alternatively, two molecules may be considered isoelectronic if they have the same electronic structure and if they can be coupled by applying the following
procedural transformation or rules. The first rule allows the substitution of an element by its congener. (Hydrogen is not considered to have a congener.) The second rule allows the increase or decrease of the nuclear charge by 1 and a concomitaut molecular charge of +1 or - 1. The third rule allom protonation or deprotonation with a concomitant change of molecular charge of +i or -1 (see the figure). For example, CzHaand CH,S are isoelectronic. Let us apply the procedural transformation or rules in t,he figure to show the relation between the two molecules. Equation (1) shows one mental relation. The number
over the arrow means one should apply mentally the transformation equivalent to that number. There are other orders in which this could have been accomplished, although this is the only one in which all the compounds are known. An alternative mental relation is shown in eqn. (2).
I submit that the following additional rule must also be obeyed: two compounds are isoelectronic only if the major resonance structures would be considered isoelectronic by the previous procedural transformations or rules. The need for this additional rule is demonstrated when one tries to apply the isoelectronic principle to rare gas compounds. Note that many Xe and I compounds are isoelectronic. This has been fruitfully exploited with respect to structural and synthetic considerations.' How ~velldoes similar logic apply to the lower rare gas compounds? Procedural transformotionr or rules for determining :f Wo molecules o r e so. electronir. Z 'I the otomar nmber. 2' ir the otom'c n m b e r of the congener of the element wtth atomic number Z ano the orrow means ?he two oortml structures ore iroelestronicolly related. The Rmt rule ollow~the substitution of on element by its congener. (Hydrogen is not considered to hove a congener) The second rule ollows the increase or decrease of the nuclear The third charge by 1 and concomitont molecular charge of +1 or -1. rule allows pmtonation or deprotonotion with a concomitont chonge of rnoleculm charge of + 1 or -1.
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J ~ u r n o of l Chemical Education
We wish to acknowledge support from the Power Branch, Office of Naval Research, Contract Number N00014-67-A-01510016. XeBr? was synthesized by radioactive decay of IBrl and studied by hlossbauer spectrometry of the excited nuclear state of Xe. Likewise, XeCb and XeCI, have been investigated (5).
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Comparison of Rare Gas Compounds and Analogs
ra
(A, exp.) HFa HeFtb.s
Fzd
NeFt" HFz-~ HeR
.92
1.44 1.13
ra t i , calc.)
D. (keal, exp.)
D. (keal, cdc.)
.92 1.33
141
101 33 0 30 73 0
37
m
1.65 1.16
58
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CADS,P., A N D HUO,W., J. Chem. Phys., 47, 614 (1967). hy BUCHIN, V. P., IleFt was observed mass speet~rometrleelly Z ~ ~ u x r N. n . V.. AND KAPYSHER. V. K.. Hioh Enerm Chemiatrv. 1 . 159 (lb671 (tiandated from ~ h i m v a ' ~ v & k i k~h& o i i , 1, 18i (i967)): There is no experimental datrtbn NeFt or-HkFz, although G. C. Pimentel and R . l]. SpraLley ( J . Arner. Chem. Soc., 85, 826 (1963)) have suggested several syntheses for HeFt and reasons for ~ossihlestabilitv. See reference 14). See reference (5).
In the table, a comparison is made of the rare gas compounds HeF+, NeF+, and HeF%and their isoelectronic analogs HF, F%,and HeF2-. Normal chemical intuition correctly predicts H F is more stable than F2 because of the greater ionic resonance contributions in the former. However, HeF+ is predicted on similar grounds to be less stable than NeF+ because He has a higher ionization potential than Ne. The usual application of the isoelectronic principle would couple HeF+ with HF, NeF+ with F2. Isoelectronic arguments would thus predict that HeF+ would be much more stable than NeF+. Our calculations2 predict that they have about equal stability (4). Let us compare HeFz and HF,- (5). The latter has the strongest existent hydrogen bond (58 kcal/mole) and the residual H-F bond in it and the separated species H F and F- is also very strong. In contrast, HeF2 is calculated to be unbound. Quantitative valence bond calculations shorn- the major resonance structure for HeF2is (F He F ) , while for HFz- they are (F- H + F-) and (F. H . F-). Any term involving H- or He2+ has a negligible contribution compared to that of He or H+. For example, (F+ He F-) has a much larger contribution than (F+ H- F-). Thus note that the major resonance structures for HeF= and HFz- are not isoelectronic. Therefore, it seems inappropriate to consider He& and HF2- isoelectronic. In the above, the need for the proposed additional rule was demonstrated by the use of quantitative Valence Bond calculations. However, one need not do a Valence Bond calculation, or indeed any calculations, in order to apply the new rule. In particular, let us analyze HeF+ and HF. $(HF) = c,p(HtF-)
+ cap(H.F.) + crp(H%+) Likmture Cited
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By a simple application of electronegativity, one sees that c, >> dl, c2 d2 and ca
