S tereochemistry of Hydrocarbon Ions Bridged Structure of C2Hi BY J. C. LORQUET Centre de Spectromitrie de Masse, Institut de Chimie Gtntrale, Universitk de Li&ge, Li&ge (Belgium) Received 15th January, 1963 The geometrical structure of A2H6 molecules has been studied by the correlation diagram method. Molecules containing 12 valency electrons (B2H6, C2Hg+) should belong to theD2h group, and assume the bridged configuration characteristic of electron-deficient molecules. Molecules containing 14 valency electrons (C2H6) should belong to the D3 group and have an ethane-like structure. The potential energy hypersurface of the C Z H ~ ion (13 valency electrons) in its ground state has probably two shallow minima, corresponding to the D3 and D2h configurations, and separated by a low activation energy.The CzH; ion is thus expected to have an easily deformed structure. This explains the great ease with which the hydrogen atoms are shuffled in the ethane ion, as shown by the mass spectra of the deuterated ethanes. Other alkane ions (particularly C3H,') are also briefly considered. A2H6 molecules can assume two nuclear configurations. First, there is the configuration taken by ethane in its ground state (D3d symmetry) (fig. l), and secondly, the bridged structure characteristic of diborane ( D ~ A or Vd symmetry) (fig. 2). This bridged configuration is known to be characteristic of electron-deficient molecules.1 For each of these forms, several values of the HAH angle are possible. The purpose of this note is to determine, by the correlation diagram method introduced by Walsh,2 the most stable configuration as a function of the number of electrons in the different molecular orbitals.Let us first examine the D3d configuration. D3d CON FI G UR AT I 0 N The molecular orbitals characterizing a H3AAH3 molecule in the D3d configur- ation are most easily obtained by combining those of two AH3 groups. AH3 molecules may assume two configurations : a planar one (D3h) and a pyramidal one (C3J. Walsh has given the form of the molecular orbitals in the two con- figurations.2 From the a1 orbitals of each AH3, we obtain two orbitals of A2Hs which possess the labels alg and azU. When the HAH angle is go", their expression is : a l g - . (z~-Zz,)+(h,+h,+h,+hq+h5+hs), a t , . . . ( Z , + Z B ) + ( l Z i + h z + h g - h h q - h 5 - k 6 ) .When the HAH angle is equal to 120", their expression is : a l g . . . ( S ~ + S g ) + ( h l + h 2 + h 3 + h q + h 5 + t 2 6 ) y a2U. . (S~-~g)+(hl+h2+h3-h4-hS-h6). (SA designates the 2s atomic orbital of atom A; XA, YA, ZA designate respectively, the 2ps, 2p, and 2pz atomic orbitals of A ; hly h 2 . . ., are the 1s orbitals of the hydrogen atoms, 1, 2, . . .). Walsh's first stability criterion indicates that these orbitals become more tightly bound as the HAH angle increases. a384 STEREOCHEMISTRY OF IONS The expression of the two doubly degenerate orbitals is obtained by a similar procedure. It does not depend on the value of the HAH angle. Since these orbitals are antibonding between the H atoms, they become more tightly bound as the HAH angle increases.6 t I 0 , i I 0 * I k f " FIG. 1.-Structure of the D3d configuration. i e Y FIG. 2.-Structure of the D2h configuration. The orbital bonding the A atoms is formed by the in-phase interaction of the lone-pair orbitals of each AH3 group. Its expression is (SA+SB) when the HAH angle is equal to 90", and (ZA-ZB) when this angle has a value of 120". It becomes less and less tightly bound as the HAH angle increases.J. C . LORQUET 85 The order of the energies of these orbitals has been obtained by Hall 3 for ethane (LHCH = 109"). The correlation diagram is given in fig. 3. The ethane molecule has 14 valency electrons. According to the diagram, it should have a HCH angle intermediate between 90 and 120" ; the experimental value is 109".(a 1,>2(a 2u)2(eu)4(e,)4(a1 g)2- 1 l o j 90" I09 120° D3d FIG. 3.-Correlation diagram for the D3d configuration. D2h c o NFI G UR A T I ON The electronic structure of diborane is very similar to that of ethylene.4-5 The form of the molecular orbitals of diborane can thus be obtained by taking sums and differences of the molecular orbitals of two AH2 groups as outlined by Walsh,2 and then adding the adequate symmetry orbital corresponding to the bridge hydrogens hl and h4 (i.e., adding (hl +h4) to a1 orbitals, and (hl - h4) to the b3u orbital). The expression of the alg and the bl, orbitals can be obtained by taking linear combinations of the a1 orbital of each AH2 group. When the HAH angle is 90", their expression is : alg ( Z ~ - Z g ) + ( h 2 + h 3 + h 5 + h 6 ) - ( h i + ~ ~ 4 ) bl, .. . (ZA+Z,)+(h, +h3-h5 - h 6 ) . For an HAH angle of 180" : a l , . . (sA+sg)+(h2+h3+h5+h6)+(hl+h4) b l , . - ( ~ ~ - S g ) + ( h 2 + h 3 - J ~ s - h 6 ) .86 STEREOCHEMISTRY OF IONS According to Walsh's first criterion, these orbitals become more tightly bound as the HAH angle increases. The expression of the bZu and b3g orbitals is obtained similarly from the b2 orbitals of each AH2. Their expression does not depend on the value of the HAH angle. b 2 u - (y*+y,)+(hz-h3+hg-h6) b,, * ' (Y,-Yy,)+(h,-h3-hs+h6). Since they are both antibonding between the H atoms, they become more tightly bound as the HAH angle increases. The expression of the other alg orbital is (SA +sg) + (hl + h4) when the HAH angle is go", and (ZA - ~ g ) - ( h l + h4) when the HAH angle is 180".It becomes less and less tightly bound as the HAH angle in- creases. The bridge orbital is & in type. Its expression is ( x A + x B ) + ( ~ I - ~ ~ ) and it does not depend on the value of the HAH angle. Finally, we shall also con- sider the lowest antibonding orbital. Its expression is ( x A - x ~ ) and it is b2g in type. The order of the energies of the molecular orbitals of ethylene and diborane is about the same, except that the bridge orbital b3u must be strongly stabilized by the two bridge hydrogens.6 Such a stabilization is also expected for the two alg orbitals, although to a smaller extent. We shall thus adopt the following order for diborane : This order agrees with that obtained from s.c.f. calculations for ethylene 7 and di- borane.8 The correlation diagram is given in fig.4. The diborane molecule in its ground state, containing 12 valency electrons, has to have its two outermost electrons in the ag orbital. Its HBH angle is therefore expected to have a value intermediate between 90 and 180" ; this angle is known experimentally to be about 120". In the first excited state of diborane, the orbitals a, and bZg are both singly occupied. One would expect the HBH angle to be intermediate between 120 and 180". (ag)2(b1u)2(b3u)2(b2u)2((b3g)2(a~)2(bZ8)0 STEREOCHEMISTRY OF THE C2Hz ION The occurrence of rearrangement phenomena was mentioned repeatedly in the study of the mass spectra of deuterated ethanes.9 For example, CH3CD3 gives normal fragmentary ions CH: and CD$, but also rearrangement ions CH2D+ and CHD?.It must be admitted that, before the rupture of the C-C bond takes place, the molecule undergoes a complete modification of structure which shuffles the hydrogen atoms. This phenomenon could be explained by the occurrence of a bridged structure for the C2Ht ion. A similar suggestion was already made by Walsh 10 for the C2Ht ion, and by Rosenstock et aZ.11 for the C3H7+ ion. Since this problem implies a comparison of the relative stability of the two configurations D3d and D2h, we must now establish a correlation diagram between these two structures. The intermediate state (fig. 5) belongs to the symmetry group C2h. From the character tables of the groups D3d, D2h and C2ho a one-by-one correspondence between the orbitals in these three forms can be obtained (table 1).We shall now consider each orbital individually, and discuss its binding energy in each configuration. The expression of the lowest alg-ag orbital is similar in both configurations, first, when the HCH angle is equal to go", and secondly, when it is equal to 120" for the D3d configuration, and to 180" for the D2h configuration. However, in order to take into account the stabilization effect due to the bridge hydrogens mentioned before, we have assumed that the binding energy was a little greater in the D2h configuration. This is not the case for the azu-blU orbital;J . C. LORQUET 87 its binding energy will thus be the same in the two configurations, first when the HCH angle is equal to 90", and secondly, when this angle is equal to 120" for the D3d configuration and to 180" for the D2h form.The b3u orbital is strongly stabil- ized with respect to the eu orbital by the two bridge hydrogens. This is not the r' I I Y '2h FIG. 5.-Structure of the transition state (Czh). case for the e,- bzu orbital, whose binding energy will be the same in both config- urations for equal values of the HCH angle. The other component of the e, orbital corresponds to the antibonding bZg orbital of the D2h configuration: its binding energy must be much smaller in the bridged configuration. Finally, the C-C Q orbital (alg) should have the same binding energy in both configurations when the TABLE 1 .-CORRESPONDENCE BETWEEN THE MOLECULAR ORBITALS OF THE D3d, C2h AND D2h CONFIGURATIONS 03.: C7h Dzh U l g .. . "g . . f Clg azU . . . b, . . . bl, . . . a, . . . b2, . . . b , . . . 63, . . . ag . . . h2g . . . bg . . . b j g HCH angle is equal to go", or when it is equal to 120" in the D 3 d configuration, and to 180" in the D2h configuration. However, we shall again assume a slight stabilization for the bridged structure. The two diagrams reproduced on fig. 3 and 4 have been drawn according to the above discussion. They are thus directly comparable. Let us now consider the C2Hz ion (13 valency electrons) in its ground state. If this ion assumes the configuration D3d, the orbital alg is occupied by only one electron. The value of the HCH angle should then be intermediate between 120 and 109". Let us assume about 115". If the ion belongs to the symmetry group D2h, the outermost electron will be in the bzg orbital.The HCH angle should then have the same value (120") as that observed in diborane. Fig. 6 represents a new correlation diagram between the configurations D2h and &d, in which the binding energies of the orbitals for the D2h configuration have been taken in fig. 4 for a value of 120" of the HCH angle, while those of the D3d configuration have been inter- polated in fig. 3 for a value of 115". An " avoided crossing " case occurs for the88 STEREOCHEMISTRY OF IONS /--- _._---- . . . . . . . ;>:. *.* -----_ __ --__ --.- 1 -. I .s eg A 2 M ba other hand, the orbitals eg-ag and alg-bzg, the latter being occupied only cnce. Although the bridged configuration might seem some- what favoured, it is difficult to arrive at a definite conclusion since the curves of the diagram are drawn in a purely qualitative a9 way.The situation is similar to the CH3 b3 radical and the NHf ion which are thought to be pyramida1,z but where the potential APPLICATKON TO HIGHER HYDROCARBON IONS Hydrogen atom migrations are known to occur in practically all ionized hydro- carbons. It is therefore tempting to explain these rearrangements by bridged structures characteristic of electron-deficient molecules. We might expect struc- tures analogous to that of diborane, where one (or more) " normal " hydrogen atoms would be replaced by alkyl groups. For the C3Hg ion, another possibility appears more likely. The compound B4H10. 2NH3 is known to have an ionic structure [BH~(NH~)~]+[B~Hs]-, where B3Hg, which is isoelectronic to CsH$+, exists as an independent entity.12 By analogy with CzH;, we might expect the potential energy hypersurface of the C3HS ion in its ground state to have two shallow minima : m s B 3.a2u 049 assumes an easily deformed configuration. The two forms D3d and D2h have probably similar energies, and are separated by a low potential barrier. When ethane is ionized by electrons of energy approaching that of the threshold, the Franck-Condon principle probably determines the structure assumed by the ion. But when the energy of the biu A \J . C. LORQUET 89 one corresponding to the neutral molecule (with slightly modified internuclear distances and angles), and a cyclic configuration characterized by two three-centre bonds, and analogous to that of B3Hg and C3Hif (fig.7). H H BH2 FIG. 7.ftructure of the B3Hg ion. The consideration of this possibility might help to visualize and to understand the nature of the activated complexes postulated by Kropf et al. in their statistical calculation of the mass spectrum of propane.13 The author is indebted to Prof. L. DOr for his interest in this work. He also wishes to thank the Fonds National de la Recherche Scientifique of Belgium, for a position of Charg6 de Recherches. 1 Longuet-Higgins, Quart. Rev., 1957, 11, 121. 2 Walsh, J. Chern. Soc., 1953, 2260. 3 Hall, Proc. Roy. SOC. A , 1951,205,541. 4 Pitzer, J. Amer. Chem. Soc., 1945, 67, 1126. 5 Mulliken, Chem. Rev., 1947, 41, 207. 6 Longuet-Higgins, Calcul des Fonctions d'Onde Mole'culuire (ed. du C.N.R.S., Paris, 1958), p. 93. 7Berthod, Compt. rend., 1959, 249, 1354; Ann. Chim., 1961, 285. * Yamazaki, J. Chem. Physics, 1957, 27, 1401. 9 Schissler, Thompson and Turkevich, Disc. Faruday SOC., 1951, 10, 46. Quinn and Mohler, J. Res. Nat. Bur. Stand. A, 1961, 65,93. Stief and Ausloos, J. Chem. Physics, 1962, 36, 2904. 10 Walsh, J. Chem. Soc., 1947, 89. 11 Rosenstock, Wahrhaftig and Eyring, The Mass Spectra of Large Molecules, II. The Applica- 12 Peters and Nordman, J. Amer. Chem. SOC., 1960, 82, 57. 13Kropf, Eyring, Wahrhaftig and Eyring, J. Chem. Physics, 1960, 32, 149. Eyring and tion of Absolute Rate Theory (University of Utah, Salt Lake City, 1952), p. 17. Wahrhaftig, J. Chem. Physics, 1961, 34, 23.