edited by: JOHN J. ALEXANDER University of Cincinnati Cincinnati. Ohio 45221
exam quwtion exchange The Abnormally Long C-C Bond in the Oxalate Ion Gongdu Zhou' and Wai-Kee Li The Chinese University of Hong Kong Shatin. N.T.. Hong Kong Chemistry students often equate the appearance of conjugated double bonds with a electron delocalization. Yet there are many examples in which apparent conjugation (as shown in a typicalvalence hond structural formula) does not lead to delocalization a t all, and the oxalate ion is one of the better known cases. This question tests the students' ability in applying group theoretic techniaues and using molecular orbital theorv to obtain qualitativ&y meaningf;l results. I t would he suitable for the upper division undergraduate inorganic course or a first-year graduate inorganic or group theory course. Skills a t the applications level of the Bloom taxonomy are called for. Question T h e oxalate ion, C2042-, with Dzhs metry, has asurprisingly long C-C hond (1.559-1.574 K n seven compounds with a mean of 1.567 A, longer than the normal C-C single hond in aliphatic compounds), despite its planar structure with "conjugated" double bonds.
(1) Deduce the irreducible representations generated by the six 2p orbitals (labelled above) that participate in the a bonding of the anion. I n addition, derive the six linear combinations of atomic orbitals with the svrnmetries vou have just deduced. (2) . . Illustrate oictoriallv the six T molecular orbitals of this anion, and arrange them in the order of increasing energy. (3) Fill in the a electrons and attempt to rationalize the exceedingly long C-C bond.
572
Journal of Chemical Education
Acceptable Answer Let thez axis Lie along the C-C bond and the x axis be perpendicular to the molecular plane. (1) r c = B% + Bau; Po = Bu + Bzs Au + B3u. The MO's generated by Van Vleck's methodzare By:(2)-L"(o - b); B3u:(2)-112 (a + b); B&(c - d + e -fl; By:112(~+ d - e - fl; A,:l/,(c - d - e fl; B&(c d e fl.
+
+ + +
+
(2)
As usual, the energy increases with the number of nodes. It is noted that nonhonding orbitals a, and bu should be of similar energy since the number of nodes is the same. (3) We need todecide bow many of the 34 total electronsto assign to the s orbitals perpendicular to the molecular plane. Each VB structure shows two C-0 r bonds; these contribute a total of four electrons to the perpendicular r system. Each VB structure also shows two O's with single bonds to C each hearing a formal negative charge. Two of the lone pairs on each of these O's will he in s-type orbitals, hut only one of these s orbitals is perpendicular to the molecular olane. Hence. each of these two O's contributes one ekernm pair, iwmg four mke electrons. The vand t
