N. Colin Baird University of Western Ontario London. Ontario, Canada
I
The Three-Electron Bond
The similarity between one-electron and three-electron bonds is evident from the simple molecular orbital (MO) theory. For a single electron, occupancy of the bonding M O yields a bond order of %. Although a second electron can also occupy the bonding MO,the stabilization it provides is cancelled by the destabilization of the third electron due to its occupancy of the antibonding MO.At the simplest theoretical level, the stabilization of the bonding M O is equal but opposite to the destabilization of the anti-bonding level. Thus the net stabilization energy for such three-electron bonds is predicted nlwavs to be half the streneth of a two-electron bond. The -~equality between the stabilkation of the lower level and the destahilization of the upper holds a t the simple Huckel level even when the levels initially are nondegenerate. Although the simple Huckel method with overlap integrals neglected predicts that a three-electron bond is always stabilizing, this is not true if the overlap is included. The interactions associated with a three-electron bond involving two initially degenerate levels is net destabilizing if the overlap integral exceeds U;for nondegenerate levels the crossover from stabilization to destabilization occurs at even smaller overlaps. The quantum-mechanical origin of this strange hehavior for three-electron bonds is illustrated by the orbital-splitting diagram in Figure 1. The bonding level is stabilized by an amount proportional to 1/(1 S ) , where S is the "overlap integral" between the orbitals. The antibonding level is destabilized in proportion to 1/(1-S). If S > 0,then the antibondine leuel is more destabilized than the bond in^ level is stabilized (see Fig. 1).Since the advantage in magnitude of destabilization over stabilization increases with S, then under some circumstances the destabiliation of a single electron occu~vinrtheantibondine M O will outweinh the total stabilizatio"n o? two electrons occupying the boGding MO.As the eaD in enerev between the initial levels is increased, the nuk r i c a l advantage held hy desrabilization of the antibonding M O over stabilization of the bondina M O increases. In fact, Huckel theory with overlap integralsincluded predicts that a three-electron bond is significantly stabilizing only when the two levels i n i t i i y are of equal or almmt equal energy, and ~~A~
~
~~
+
'Presented, in part, at the VIll InternationalConference on Photochemistry, Edmonton, Alberta, Canada, August 7-13, 1915. Research supported by the National Research Council of Canada.
the overlan between the orbitals is not too h e . Interestingly, the energy match requirement appears also ;n the ~imple;~alence-bond model for three-electron tmnds. In particular, for the two structures shown below for a 3-electron bond between atoms A and B, resonance will occur significantly only if the structures are of almost equal energy A:
B
-
A.
:B
Therrnodvnarnlc Stabllltles of Three-Electron Systems The prototype Lhree-electron bond with initially degenerate levels occurs in the dihelium wsitive ion, He?'. This system is known(1) spectroscopically t o be stable predicted; the dissociation enerev is about 57 kcal mole-' and the bond distance is 1.08 A:~he prototype for a 3-electron bond with initial levels of very different stability is the hydride of helium, HeH. The ground state of this system is dissociative ( 2 ) ,thus confirming the argument that the net effect of this type of three-electron bond is net destabilizing. The most commonly encountered three-electron bond in organic chemistry is that between carbon and oxygen.
as
IF OVERLAP INCLUDED
STABILIZATION IF DESTABILIZATION IF
s$
Figure 1. Orbital splftting diagram.
Volume 54, Number 5, May 1977 / 291
nn* STATES Of
\
HNNH
Figure 2. Threeelecbon bonds in excited states.
-
A B INITIO (4-31G) SURFACE lor HNN' H ' r N2
-m1
0.8
10
1.2
1.4
1.6
-+
H-N DISTANCE
Figure 3. Potential energy surtace for HNN'
2.0
18
2.2
I
the remaining n electron is localized heavily on the oxygen. The most stable electron configuration for the a system has two electrons localized on oxygen and one on carbon. A strong 3-electron hond would result only if a structure of near-equal stability resulted when two a electrons were localized on carbon and onlv one on oxvgen. Since the latter structure corresponds to k-0+, i t cannot compete energetically with the one shown in Figure 2, and the 3-electron a bond is weak. The MO in diimide from which the electron is excited is delocalized over both nitrogens. On a time-averaged basis, both nitrogen atoms are equivalent in their T orbidstahility, thus vieldine a rather strona three-electron a hond. Indeed, recent ob init; C1 ralculation~(6) predict that the vertical excitation from the around state to the lowest triplet in diimide requires about 30 kcal mole-' less energy than does the same transition in formaldehyde. Recent calculations also indicate that the preferred mnlerular getmetry in this I~nvesttriplet state has the molecule twisted YOo rather than planar as in the ground state (7). . .~In the twisted conformation. two equivalent threeelectron honds exist, each formed byintera&ion of a singly occunied D- orbital on one nitroeen and a doubly occupied ' ~ o n e - ~ abibital ir on the other. The existence of stabilizing three-electron bonds also has a profound effect on the bond dissociation enthalpies of the dinitrogen hydrides (and presumably their substituted derivatives). Consider first the hydrazyl radical, H2NNH. Ab initio calculations in this laboratory indicate that, although the optimum nitrogen-nitrogen bond length of 1.39 .&islong and the geometry about the tricoordinate nitrogen is flapped, the barrier to rotate the NH bond of the diwrdinate nitrogen, and thus to destroy the three-electron hond, is 10.0 kcal mole-', twice as large as in the isoelectronic carhon-oxygen sy~tem.~
2.4
(inA1 H'
NI.
The extra stability imparted by the three-electron hond is responsible partially for the rather low N-H hond dissociation energy of 82 kcal mole-' (76 f 5 experimental ( 9 ) )predicted2 for hydrazine compared to 104 kcal mole-' for ammonia. The nredicted enthalnv of dissociation of HzNNH to yield trans-iiimide in 62% oiihat for hydrazine. lncontrast. the C-H bond dissociation enerm for the ethyl free radical, in which there is no significant stakization by ;three-electron bond, is only 40% of that for ethane (5). ~~~
Both theoretical calculations and experimental evidence suggest that the three-electron carbon-oxygen hond is very slightly stabilizing. In the case of formaldehyde, the energy required (3)to excite the molecule from its ground state to the triplet n a * state is 72 kcal mole-'. Since this value is close to the 74 kcal mole-' difference between a double hond and a single hond (estimated using E(C==O) = 165 and E(C-0) = 91 kcal mole-'), i t follows that the comhination of the single hond plus the 3-electron a bond in the 3na* state is only marginally more stable than is a C-0 single hond alone. For the H Z O H free radical. Ha has calculated ( 4 )a rotational harrier for O-H bond tbrsion of about 4 kcalmole-'. Since such twisting destroys the 3-electron hond between the carbon singly occupied 2p, orbital and a lone-pair orbital on oxveen.. the s t r e n a h of this linkage must he small. Further confirmation is by the experimental finding (5)that the hvdroaen-carbon hond dissociation energy in methanol is uniy 6 kGal mole-' smaller than that inethane. Although the disparity in initial orbital stabilities prevents the formation of strong three-electron bonds between carhon and oxygen, this amsideration is removed for the isoelectmnic dinitrogen compounds. Indeed, recent theoretical and experimental work hasshown that %electron nitrogen-nitrogen iinkaees of substantial streneth occur in manv svstems. Consider the n a * states ofdiimide, HNNH, compared to those of formaldehyde (Fig. 2). In the carbon-oxygen system,
--
~~~
~
292 / J m l of Chemical Education
~~
Kinetic Stability of Three-Electron Bonds A three-electron hond between the nitrogens in the HNN' radical reduces the N-H bond dissociation energy of diimide to 61 kcal mole-' (calcd) compared to 104 for NH3. The hond length predicted (10) for the ground state of HNN' is 1.18 A, which lies between that of 1.08 A for N2 and 1.22 A for HN=NH. Although three-electron bonding.in HNN' does stabilize the system, the nitrogen-nitrogen triple hond in the ~ r o d u c is t such a strona linkaae that the dissociation of HNN. H.+N2 is probahly & exothermic process! This is not to say that all HHN' radicals (and their substituted derivatives RNN.) should spontaneously decompose; indeed, theoretical calculations (10) predict an energy harrier of about 23 kcal energy surface generated mole-I to the reaciion. The for this radical decomposition reaction is illustrated in Figure 3. (Although the energy is plotted against only the H--Nz m e s e calculations use Pople's 4-31G basis set (3a)and Rwthaan's restricted open-shellmethod. (8b).In addition, the theoretical result for the N2Ha N2H3.+ H' reaction and for the HNNH HNM + H' reaction have been corrected semiempiricallyfor the correlation energy changes by adding 14.4 kcal mole-' in both cases. This brings the total AH of the reaction N2Ha Nz + 4H' into agreement with the experimental value.
-
-
-
BEND IN X Z PLANE
i T STATES
z
EXCITED STATE dW
HIGHER I: STATE
Figure 4. Decomposition of linear species: HCO'
-
GROUND STATE Of
K
w
+ CO. Figure 6. Electron distribution in bent geometries of HCO.
HCCS
H'+CO
Figure 5. Correlation of linearstates
HCO' distance, the nitrogen-nitrogen distance was reoptimized a t every point shown.) The potential surface for the decomposition of the isoelectronic HCO' free radical is similar to that for HNN, although the former reaction is endothermic rather than exothermic. The origin of the rather substantial harriers to decomposition of such radicals was explained some time ago (11). Consider a linear HCO' species; the "odd" electron could be placed in either one of the two n*co MO's or else in a o * c ~ orbital (see left side of Fig. 4). Dissociation of the C H bond gives an excited state of carbon monoxide if one starts from a state in which the odd electron of linear HCO' occupies a T * orbital-see top of Figure 4. The correlations between states of linear HCO' and CO are shown in Figure 5. The picture developed above for the decomposition of HCO' is artificial since it assumes that the molecule is linear. In fact, in its ground state H C D is distinctly bent. As illustrated in Figure 6, the two states which had a* odd electrons in their linear geometry are nonequivalent in the bent conformation; the A" state which has an odd "d' electron (i.e., in an MO antisymmetric with respect to reflection in the plane of the nuclei) is of higher energy and prefers a linear geometry, whereas the A' state with the odd electron in an in-plane MO prefers a bent geometry. The important consequence of this nonlinearity is that the bent ground state of the HCO has the same svm&etrv (A') as does the unner state which has the odd e l e c t r k in th; b* 'MO. Since t6ese states are of the same symmetry, they do not cross each other as the molecule dissociates, and the state correlation diagram for bent HCO'CO H.is of the type shown in Figure 7. The ground state of HCO' correlates with the ground states of carbon monoxide and hydrogen. In chemical terms, the origin of the upward slope to the decomposition energy surface is the loss of bond
+
W+CO
Figure 7 . Correlation of bem states. energy in the two-electron H-C (or H-N) link as i t is stretched. Once this hond lengthening proceeds beyond a certain point, the most stable bonding structure switches to a three-electron H-C (or H-N) link and a triple rather than a double carhon-oxygen (or nitrogen-nitrogen) hond. The downward slope portion of the energy profile corresponds to the decomposition of the dissociative three-electron HC (or HN) hond. In all cases investigated theoretically so far, the "crossover" point occurs late so that the activation energy is significantly larger than the enthalpy of decomposition, and thus these radicals nossess some kinetic stahilitv even thoueh " they are rather unstable thermodynamically. Exper~mentally this point has been confirmed (12) for the acetyl radical, since the act~vationenergy for decomposition exceeds the endothermicity by 6.0 kcal mole-'. Literature Cited (11 Sw Gilbrt,T. L.,and Wshl, A. C.J. C h m Phyn., 55,5247 (19711and referencneitcd th~rein (2) Henbrg.0.. "MolecularSpeetmand MolcollarSuueture..'D.Vaz NoatrandCo.Inc., Prineefon,N.J.,Vol 1,2ndEd.,1950.p.355. 131 MeClynn. S. P.,Azumi,T..and Kinashits, M.,"Moleeular Speetrmnlpy c,ftheTriplet State," Prentie-Hall, lnc.. Enslowmd Cliffs, N.,J., 0.84. (41 Ha,T-K.,Chrm. Phys Lett., 30.379119751. (5) Kerr,J. A,. Chem Re"., 65,465 (19561.
15) Vasudevsn,K., PeyerimhoffS.D.6uenker.R.J.snd Kammer. W.E..and Hsu.H.. ChwxPhya., 7.157 11975). 17) Baird, N. C.,andSwenson, J. R., Can. J Chem.. 51.5097 119731. 18) la1 Ditchfield. R.. Hehrs, W. J.. end Paple. J. A. J. Chem. Phyx.. Ri.721 119711. lbl RuoUlaan,C. C. J.,RPu. Mod. Phys., 32.179 (19601. I91 Schurath. U..sndSchindkr,R. N., J. Phys Chsm.. 74,5188 (1970). (LO1 6aird.N.C..J. Chem Phys., 62,5C4 (L9761. 1111 Sea Henhew, G.."Molaeular Spectra and Moleeulsr Structure." D.Van Nustrand Co. Inc., Princetan, N.J., 1957,Vul. III.p.458. 1121 walkinn, K.w.,and word. W.w.lnr. J. chem ~ i n r h 6,855 . (19741.
Volume 54. Number 5, May 1977 / 293
