ORBITALS GEORGE H. STEWART and HENRY EYRING University of Utah, Salt Lake City H o w can one explain the presence of hindered rotation in ethane and in ethane-like molecules? How does one explain the trans-effect of Chernyaev; the predominance of chair-form cyclohexanes over boat-form; trans elimination reactions; anomalous bond angles in simple inorganic molecules, "strained" bonding? These and related phenomena that are usually discussed in a purely descriptive way are the subject of this paper. We present here a principle of valency that accounts for these phenomena in a clear and easily understood manner. Modern theories of valence are incomplete in their ability to account for the stereochemical character of many molecules and activated complexes. Our purpose here is to show how the "principle of minimum bending of orbitals" (1) provides a clear and sound theoretical basis for understanding ground and excited state conformation chemistry. We first must explain the theoretical basis of this principle and fit it into the general valence theory and we will find that, after our quantum mechanical analysis, simple statements such as "electrons hate to go around corners" and "molecular orbitals have high surface energies" contain the essence of the matter. GENERAL THEORY
The advent of wave mechanics resulted in the "in principle" (2) solution of all chemical and structural properties of molecules. The small number of problems that are amenable to exact mathematical solution has led to approximation methodswhichhave beenextremely fruitful in providing quantitative results about chemical structure and have given a soend theoretical basis for many of the gross aspects of structure. Both valence-bond and molecular-orbital methods (5, 4) have led to a better understanding of molecular structure in terms of orbitals with directional properties, and the concepts of maximum overlapping (5) and of hybridization (6) have especially aided the interpretation of the directional properties of bonds. The tetrahedral angles of the normal carbon are well understood in terms of spS hybrid orbitals, and the assigning of more or less p or d character to bonds has given some hasis for understanding anomalous bond angles. The arbitrary assignment of variable degrees of hybridization does not explain completely these effects. Much of the valence-bond and molecular-orbital consideration has emphasized the potential energy effect of the nucleus with its inner electron shells, and it is only in the free-electron model (6) that we meet face to face the kinetic energy effect. In the more exact
valence-bond or molecular-orbital methods the wave functions used are very sensitive to the approximations that it is necessary to make and, as Pople (7) has pointed out, these approximations are especially sensitive to the kinetic energy operator. The freeelectron model, or particle-in-a-box, stresses the importance of the dimensions of the box in assigning energy levels. Even here, one is very likely to neglect a secondary effect due to kinetic energy. It is this secondary kinetic energy effectthat we will develop. The "principle of minimum bending of orbitals" is to be found in the close examination of the wave equation. Consider the charge-cloud interpretation (5, 4) of the eigenfunction, $, of the wave equation where $' is a measure of the density of the electron cloud. We find that the cloud is confined to a small region near the nuclei, and $ contours can be dra.~vnsuch that a definite percentage of the charge iiscontained within that, contour. I t has been found that the shapes of these boundary surfaces are very significant in the elucidation of the stereochemistry of molecules This electron cloud behaves very much like a fluid of high surface tension in that it will seek minimum curvature of the boundary surface consistent with minimum potential energy (8). That this is so can be seen by an examination of the Hamiltonian operator. The energy of a. given eigenfunction is found by application of the Hamiltonian operator: H$ = E$. If we examine the kinetic energy portion of the Hamiltonian, we find it is composed of a curvature (second derivative) term for each of the coordinates. In the unidimensional freeelectron model only one second derivative is retained, corresponding to curvature in one dimension, and the energy is minimized by lengthening the path of the electron. A more careful treatment would retain the other second derivatives and we would find energy contributions dependent on the extent of curvature along these other coordinates. Note that, in the separation of variables in the complete wave equation of a system, we tend to lose sight of the fact that the variables are not necessarily separated in the complete Hamiltonian, and operating on the complete wave function leads to unique one-dimensional energy parameters only in the case of Cartesian coordinates. Indeed, the inseparability of so many wave equations points out the generality of this dimensional interaction. With this discussion in mind, then, we are led to the following more complete picture of chemical bonding. We classify the effects that determine the size and shape of orbitals in the order of their significance. (1) Potential and kinetic energy about a single nucleus: brings the electrons in close to the nucleus, an JOURNAL OF CHEMICAL EDUCATION
effect of the order of a few hundred kilocalories as measured by the ionization potentials. (2) Lowering of kinetic euergy by spreading over more than one nucleus. (a) U n i d i m e n s i o n a l : tends to extend the path of electrons by delocalization of the orbital over as many nuclei as possible. This effect can be measured as being of the order of bond energies. (b) Resists curvatnre by minimizing the bendiug of orbitals and by smoothing the surface of the orbital-an effect of the order of a few kilocalories. Effect 2b provides the basis for the "principle of minimum bending of orbitals" and this will lead us to the fluiddrop model of valence when combined with effect 2a. But first we will consider examples that are primarily concerned with bending alone.
ETHANE BARRIER One of the interesting applications of this concept is to the problem of a harrier to free rotation in ethane and ethane-like molecules. The early quantum mechanical analysis of this problem by Eyring (Q),showed that the usual steric factors can account for only about a tenth of the existing barrier. Extension of this work in subsequent years has not resolved the problem (10,11). Approximationsbased on effect 2b do yield results of the correct order of magnitude and indicate that the barriers exist primarily as a result of resistance to the bending of molecular orbitals (12a, 12b). Ethane exists in two conformations, staggered and eclipsed (Figure la), with the staggered conformation being more stable by about three kilocalories. We find that ethane can be considered as being composed of three four-nuclei paths over which electrons delocalize somewhat (Figure l b ) . In the staggered conformation the four nuclei are found to lie in a plane, but in assuming the eclipsed conformation one of the terminal nuclei is rotated sixty degrees out of this plane, resulting in an additional bending of the molecular orbital (Figure lc). An alternative choice of four-center orbitals is illutrated in Figure id in which the staggered conformation provides a rather straight path in comparison with the semicircular path representing the eclipsed conformation, and the curvature difference of the two conformations should he treated as a perturbation. The delocalization of the electrons in ethane can he thought of in terms of Mulliken's hyperconjugation effect (13) with CH,-groups or better, in some cases, in terms of a-hydrogen bonding (14), and is largely brought about by effect 2a. The straighter or smoother paths in the staggered conformation of the ethane-like molecules account for the greater stability of this form and illustrate the idea that electrons hate to go around corners. CYCLOHEXANES
The predominance of the chair conformation of
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Id Figure 1
cyclohexanes over the boat form has been vell established (15). Utilizing the foregoing discussion of ethane we see that the chair-form is composed of the same four-center orbitals as the more stable staggered molecule (Figure 2). The boat-form, holyever, has the less stable, bent, four-center orbitals found in the eclipsed conformation of ethane. Here, again, the electrons prefer the straighter pathways provided by trans conformation of four-center obitals.
CONJUGATED SYSTEMS
A logical extension of these arguments is to the cistrans isomers found in the conjugated dienes. Here v e have the normal delocalization provided by the piorbitals of the double bonds and need not look for hyperconjugative or other resonance effects to provide delocalization over the many-center orbitals. The triene benzene is one of the best examples of conjugated double bonds restricting a molecule to a planar configuration and the advantage of a closed circular pathway provided by the cyclic structure far exceeds any disadvantage from the cis arrangement of the four carbon groupings. The fact that conjugated double bonds restrict a molecule to a planar configuration can be interpreted as the resistance of an orbital tocurvature. Admitting that the restriction of these conjugated systems to a plane is a kinetic effect, effect 2b ,we look for the evidence of this curvature effect within the plane. The illustration of this is found in the comparison of d l r z P = O the s-cis, s-trans isomers of c= C \ conjugated chains such as butadiene, acraldehyde, and F ~ F ~ 3. crotonaldehyde (Figure 3). Mulliken's calculations for butadiene indicate that the s-trans form predominates and is more stable than the s-cis (16, 17). Bradacs and Kahivec (18) come to the same conclusion from Raman spectra as did Shoma-
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The strained angles decrease delocalization with a resultant \ \ \\ loss of stabilization energy C from delocalization. Here O C H I agam we have an effect of the \ \ / \ same order of magnitude as the C= '-6' C=-c ethane harrier and in the case / / / CH, of the smaller molecules the d Irons s trana d cia a trans d trans s cis d cis s cis effect even exceeds that in (Not iound) (Not found) ethane. The small amount of puckering, as in cyclobutane ker and Pauling (19) from electron diffraction studies. (99), represents a balance between the striving for Aston, Szasz, Wooley, and Brickwedde (to), on the planarity to minimize curvature and the relieving of the basis of entropy and specific heat measurements, state strained H-C-C-H orbitals. that the two forms differ in energy by 2.3 kcal. per mole and are separated by a 2.6 kca1.-per-mole barrier-the s-cis being the higher energy form. LuValle and Heats of Combustion per CH2 Unit for Cyclic Alkanes (27, 28) in k cal. Shomaker find the s-trans form predominant in glyoxal and diiethyl glyoxal (91). Mackle and Sutton (92) 5 6 n 3 4 from electron distribution curves find evidence for an 157.4 165.5 158. 7 AH 168.5 s-trans/s-cis ratio between 3/1 and 611. It is also H interesting that they find no evidence for the d-cis \ /" form in either the s-trans or s-cis (Figure 4) form of -\ proton magnetic resonance crotonaldehyde. More about that later. This evi\ shows high electron density H in trans position. dence indicates that the elongated trans form has a lower energy than the semicircular cis form by roughly 2 t o 3 kcal. per mole- about the same as the ethane Fipr. 5 barrier. It also indicates that delocalization across the carbon-carbon single bond occurs more readily in the THE ELUID-DROP ORBITAL MODEL minimum curvature trans form. We wish now to consider examples that illustrate the The nonexistence of d-cis crotonaldehyde is particufluid-drop analogy and contain more of the "surface" larly interesting as one expects the hyperconjugation phenomena of effect 2b and a more active illustration of delocalization from the terminal methyl group of the effect 2a. That is to say that we are concerned with crotonaldehyde to conjugate with the delocalization of more than just the extent of curvature imposed on an the rest of the molecule across the smoother path orbital. The combined kinetic effect produces an provided by the trans conformation. However, it orbital that will try to minimize its surface energy by would be suprising if the hyperconjugative effect were having a smooth surface with a minimum of curvature greater than is the normal diene conjugation and the and that will tend to delocalize that orbital over as complete exclusion of the other isomer is improbable. long a pathway as possible by effect 2a. One of the A supporting piece of evidence is gained from proton best illustrations of this is the hydrogen molecule. nuclear resonance studies (25) which show that in a As two hydrogen atoms approach each other, each styrene molecule (Figure 5) there is a higher electron atom has an electron in the i s orbital. Effect 2a density trans to the benzene moiety than a t the cis tells us that these electrons would like to have longer proton-again supporting the postulated greater depaths. When the two hydrogen atoms come together localization through the straighter trans pathway. their atomic orbitals fuse into a molecular orbital which results in a lowering of the kinetic energy as governed BAEYER STRAIN THEORY by the Wilson-Sommerfeld quantization rule: Xpdg = The first formal recognition of strained chemical nh. Complying with both the quantization rule and bonds was announced in the Baeyer strain theory (94). the exclusion principle, the electrons have found a The tetrahedral bonding of carbon atoms proposed by longer pathway (Figure 6) and retained a smooth van't Hoff and leBel had been most successful in orbital surface closely reexplaining the optical activity of the carbon compounds sembling the fusion of two (95, 26). The perplexing problem of the nontetrahefluid drops. dral angles of cyclopropane and cyclobutane could he We have spoken of manyexplained only through recognition of a strained bendcenter orbitals as a result of ing of the normal tetrahedral bonds. Thermodynamic this kinetic effect producinvestigations subsequently established the existence ing delocalization. In this of an instability energy directly related to the extent section we nil1 show how of bending of the carbon bonds. the orbitals will actually We now understand how the strain energy arises. "flow" into regions of low In the cycloalkanes of five carbons or less and in their potential energy (SO) while heterocyclic analogues there is a definite amount of maintaining a minimum energy which can be related to the extent that the carbon bond angles are deformed from the normal spa surface energy consistent with that potential field. tetrahedral angle (Table 1). rigurn e
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THE TRANS-EFFECT OF CHERNYAEV
This effect was first postulated by Werner (31) to account for the Peyrone and Jorgensen reactions of the isomers of dichlorodiarnrnineplatinum (Figures 7 and 8) and was formulated by Chernyaev as a regularity of the effect of acidic ligands exercising a much greater labiliziug effect on bonds trans to the ligand than do
In like manner, we are led to an interpretation of such phenomena as the higher dissociation constants of the trans forms of compounds such as Pt(NH3)2(OH)2 (36, 37) and [Pt(NH3)2(H20)2]++(38, 39) (Table 2). TABLE 2 Dissociation Constants Pt(NH8)dOHh K, K,
[Pt(NH8)2(H30)2l++ K. K,
In keeping with these arguments, we expect that unsaturated ligands with their readily available delocalized electrons would display an enhanced trans-effect, as indeed, they do. Ligands such as carbon monoxide and olefinsgive a very high trans-effect (40). ORGANIC ELIMINATION REACTIONS
neutral coordinating groups (38). Syrkin (33) has recently developed a reasonable explanation of this effect in terms of hybridization and resonance, but we feel that the principles discussed here provide added clarification of the factors involved. Consider first the Peyrone reaction (34). The labilizing of one of the chlorines prior to entry by the reacting ammonia produces a potential hole in the activated complex into which the chlorine-platinum orbitals will tend to "flow" by the delocalization attributable to the kinetic effect 2a. That the chlorineplatinum orbital will he the one to delocalize is understood if one considers the ortho-para directing character of a chlorine-substituted benzene. Effect 2b, minimum curvature, will allow a greater delocalization if the potential hole is in a trans position than if the orbital must delocalize at right angles to the cis position. This leads to a gfeater stabilization of the trans elmination activated complex and a greater probability of substitution in the trans position. In the Jorgensen reaction (%), the same argument holds where removal of the ligand trans to the chlorine leaves the potential hole in the square-planar activated complex axial to the chlorine-platinum orbital facilitating its delocalization and the stabilization of the activated complex.
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Jowenaen Reaction
VOLUME 35, NO. 10, NOVEMBER, 1958
From the foregoing discussion we have a model by which we can understand the mechanism of the trans eliminations of organic chemistry. Let us discuss the elimination reaction of the 2,3 halobutanes. From the discussion of the ethane barrier it is apparent that in butane the preferred conformation will be staggered with the two terminal methyl groups in trans arrangement. This arrangement is supported by the potential curves of Pitzer (41, 48) (Figure 9). In the 2,3 halobutanes the 2 and 3 carbons will he asymmetric and we have a meso form and a D.L . .vair (Figure . 10). In the meso form, with the CH3- groups trans to one another, the hromiines are also trans to each other.
This is also in accord with the postulate that the preferred orientation of a dihalide molecule is such that the smallest group of an asymmetric carbon atom will lie between the two largest groups on the other asymmetric carbon atom (43). This latter postulate does not seem reasonable for the D,L form as one would expect one of the electron-donating pairs to take a trans conformation for the lowest energy. Of the three possible forms of one of the D,L pair we will choose the one with the bromines trans as this will facilitate the trans elimination. The trans elimination reaction from the mesa form will yield the trans butene while the reaction of the D,L pair will lead to the cis isomer. Examination of the models as the reaction takes place reveals that the elimination in the meso form proceeds with a continual smoothing of the four carbon delocalization path while
a qualitative understanding of the H / structure of simple molecules and C the observed structural trends. We will begin the discussion by constructing a water molecule in such a manner that we can observe each / C\ Br Br / \ effect in its particular role. CH3 The oxygen atom can be expected meso trans dl cis t o have an spa tetrahedral set of Figura 10 valence orbitals with two of the orbitals having only single electrons the D,L t o cis reaction represents an increase in the curvain accord with the Hund rule of maximum multiplicity ture of the four carbon delocalization orbital. This (Figure ila). explains why the elimination reaction of the meso The fluid orbitals with only single electrons mill have isomer proceeds a t a faster rate (43). less curvature minimizing force so that the paired The mechanism of the elimination reaction can be electron orbitals will expand slightly a t their expense understood in the same way as the trans-effect of the (49) and the angle between the two bonding orbitals metal chelates. The removal of an atom such as will he less than the normal 109' 28'. The two hydrobromine leaves a potential hole into which the adjacent gen atoms with an electron in i s orbitals will overlap orbitals will tend to extend. If the bromine on the along the major axis of the one-electron oxygen orbitals adjacent atom is in a position trans to the first, this and fuse into molecular orbitals (Figure llb) in order to extension is enhanced by a straighter path and this provide longer paths for the electrons by virtue of the intermediate complex in the elimination is stabilized for minimization of kinetic energy accomplished, since sufficient time t o eliminate the second bromine. this is not in violation of the exclusion principle as in the Dehalogenation by a two step trans elimination mechacase of the hydrogen molecule discussed earlier. The nism is preferred. secondary kinetic energy effect will smooth the meld It is noted that substitution reactions can be analyzed of the orbitals eliminating the excessive curvature at in an identical manner. the iunction (Figure llc). The potential hole provided by the polarize; the center of of the COMPOUNDS OF THE AND electron distribution in the orbital away from the Before proceeding with the analysisa few introductory oxygen, and the additional potefitial center ''thins" the remarks are in order. The classification of mound orbital bv" urovidine- an. additional nucleus for the state structures of simple compounds into linear and electrons to approach closely. These two effects pull bent configurations on the basis of molecular type and the two no-bond orbitals closer to the oxygen and allow a slight solid angle expansion so that they cover more number of valence electrons has long been recognized angle (44, 45) and the work of Walsh (46) and of Mulliken of the oxygen "surface " (49). The H-0-H (47) has clarified the matter with interpretations based is consequently less than tetrahedral. on the assignment of bonding and antibonding orbitals To understand the difference between the OH? and SH2 molecules we take note of two factors. The and their energy depandence on the angular disposition of these orbitals. The use of equivalent orbitals (48) larger orbitals of sulfur, relative to those of oxygen, fuse with the same hydrogen 1s orbital and the lengthenleads t o a further understanding of the angles in these bent orbitals but, as yet, there is no method of predicting of the orbital is accompanied by a greater relative ing the angles a priori. Neglect of the kinetic energy "thinning" to achieve a "smooth" orbital surface. effects discussed hinders the understanding of the Also, the lower electronegativity of the sulfur atom trends found in these molecules and the details of allows a greater polarization of the electron cloud toward the hydrogen nuclei leaving more of the sulfur their structure. Inclusion of these principles leads to "surface" free to the no-bond orhitals. The greater a qualitative understanding of the relative bending polarization of S-H orbitals also pulls the no-bond of these molecules. orbitals closer to the sulfur so that they cover more of Type AH. the surface. Thus we have an accentuation of the The presentation here is designed to focus attention effects observed in the OH? model and the H-S-H on the role of kinetic energy in determining orbital angle approaches a right angle. We pause here to note that the molecules BeH2 shapes and position. and HgH2 have but four valence electrons and can The application of the principles outlined leads us t o he expected to be linear as noted Polorizotion of by Walsh (46). No-Bond Electrons The NH2 radical has two features to distinguish it from the OH?model presented. The lower electronegativity of the nitrogen atom leads to the Thin polarization effect noted in the SH2molecule, but nitrogen is a -- -- . first period element and the riwre11 size effect will he negligible. H
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Opposing this is the fact that one of the no-bond orbitals contains an unpaired electron. This one-electron nobond orbital will be less effective in commandiug an extra share of the central atom surface. This latler factor will be greater than the electronegativity change, and the H-X-H angle is predicted to be slightly greater than that of the OH, molecule. Present evidence indicates considerable similarity between t,he two. The CH2 radical with only one electron in each nobond orhital and with less electronegativity of the central atom will leave the no-bond orbitals quite ineffective in commanding a share of the central atom surface. Spect,roscopic studies show the radical to have an angle greater than 140' (50). Let us recapitulate two of the factors involved: ( 1 ) Terminal atom electronegativity relative to central atom-draws electrons away from the central atom leaving more "surface" of the central atom available to no-bond orhitals: important as we go dowu a periodic family; i.e., OH*, SHs. (2) The ability of the no-bond orbitals to command more or less of the central atom surface depends on the polarization forces and on the charge density of the orhital: important as we go across a period; i.e. CHI, NH,, OH,. Types AB9 and CAB
So far as is known, all molecules of types AB2 and ABC containing 16 or less valence electrons are linear in their ground state. Walsh (46) has shown through orhital correlation diagrams that this should be ;o. COI, COS, CS,, NzO, ClCN, HgCL, NCO-, Ng-, COz+, NOz+. UOI++. AeC1"- and AuC17- are all linear. One of the first things we notice on considering triatomic molecules of 17, 18, 19, 20 valence electrons, respectively, is that there is a general decrease in the apex angle as we increase the number of valence electrons. If we were considering a series with completed octet terminal atoms, the picture would be completely analogous to the hydrides where me are filling the two no-bond tetrahedral orbitals of the central atom and consequently the orhitals command a greater portion of the central atom surface. As an example of this we observe: NO2 (17 electrons, 132') and NC2(18 electrons, 114"). It is of interest here to quote Walsh (46) : "Thus the fundamental reason why 17 and 18 electron molecules have ground states that are bent is because they have 1 aud 2 electrons, respectively, which are in orbitals more localized on the central than on the end atoms and repel the bond electrons." In the series with electron vacancies in the octet of the terminal atom we have a relative electron deficiency which will aid in the delocalization of the electrons of the central atom. The delocalization of the electrons on the central atom will resist the curvature of the molecule by the principle of minimum bending of orbitals (Table 3). If we consider OFzwe note that the terminal potential hole provided by the fluorines in the two-center orbitals are very deep and the orbitals are polarized and thinned to a great extent and we expect more angle (101'). We should closing of the F-0-F remark here that, by virtue of the extreme electro-
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VOLUME 35, NO. 10, NOVEMBER, 1958
Effect of Incomplete Terminal Octets NO9 132' NO.- 115'
XOC1 116" NOBr 117" OClO 116.5" ClOCl 110"
FOF 101'
negativity of the fluorine, there is little tendency for the terminal outer shell electrons to delocalize. In OCL, on the other hand, the chlorine has a lower electronegativity than fluorine and the polarization will be slightly tomard the oxygen and the oxygen-chlorine two-center orbitals will command slightly more than the tetrahedral angle. One is tempted to postulate a delocalization of electrons from the terminal chlorine atoms, but this effect would be small compared to a delocalization from the central atom which is a pronounced effect only when the terminal atoms have incomplete octets of electrons. If we were to consider atoms in other than the first, and second period we would take more note of the arguments presented by Mulliken (47) that 6-hybridization must be considered. Types AHa and ABI
First noting that the valence electron numbers up through 6 for AH3and through 24 for AB3type molecule result in planar configurations, the arguments set forth in the preceding sections hold for the analogous cases here. The dipole moments of NH3 and NF3, 1.5d and 0.2d respectively, have been of some concern but they ar2 explained on the basis of the directioual properties of the lone pair being quite slrongly opposed by the N-F moment; this is much stronger than the S-H moment (8). Isoelectronio Series
Were a neon atom altered by removing a proton from its nucleus to a hond distance, the electrons mould redistribute themselves to form the hydrogen fluoride molecule. Repeating this process a second and a third time produccs, in turn, the water molecule and the ammonia molecule. The electronic configuration of the neon atom is such as to minimize the potential and kinetic energy about a single nucleus. The exclusion principle is the only factor restricting the electronic configuration. As each new bond is created as one passes down the isoelectronic series Ke, HF, H20, KH3, a pair of electrons is channeled along the nex axis. As directional properties are conferred on each succeeding pair of electrons, the remaining no-bond orbitals hecome correspondingly restricted in direction because of the Pauli principle. In ammonia, with only one no-bond orhital, the unused electron pair must already be channeled to form a tetrahedral hond. I t is not surprising, then, that an extra proton readily adds to KH3since it does not have to do the work of channeling the electron pair it uses, as the other ?;-H bonds have already done this preparatory mork. In fact, the water molecule has sufficiently channeled unused electron pairs so that they bond with a proton to form a hydronium ion, while the lack of channeling of the non-bonding pairs in either the hydrogen fluoride molecule or the neon atom unfits them for bonding a
proton. The Bronsted basicity of this series is thus bound up with the degree of channeling of the prospective coordinating electron pair. Oxygen and ethylene are an interesting pair of isoelectronic molecules. Oxygen, in contrast t o ethylene, has a triplet ground state which is not hard to understand in terms of channeling. I n ethylene the electrons which form the pi bond are channeled by the four hydrogen bonds into a plane passing through the two carbon atoms and bisecting the plane containing the four hydrogen atoms. Thus, their effort to delocalize is naturally fulfilled by forming a pi bond. I n oxygen there is no such channeling of the unpaired electrons into the pi bond. The ability to spread out around the respective oxygen atoms together with the advantage of noninterference with the sigma bond favors the acceptance of the node between oxygen atoms provided by a triplet state.
SUMMARY
We have now a model and a language that are clear and simple and are founded on sound quantum mechanical concepts and are born out by experimental data to fill in one of the shortcomings of valence theory. The presentation here has been broad in scope to show the general nature of the principles but there are many applications yet to be found. We hope that chemists will find this a valuable addition t o their repertoire. We wish to express our appreciation to the National Science Foundation for their support of this work. LITERATURE CITED (1) EYRING,HENRY,GEORGEH. STEW^, AND RICHARDF. Proc. Nall. Aead. Sei. U.S., 44,259 (1958). SMITH, P.A. M.,Pme. Roy.Soe. (Ladon),A123,714 (1929). (2) DIRAC, (3) COULSON,C. A,, "Valence," Clarendan Press, Oxford 10G7
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Planar F i g " .
12.
Chlolin. Rifluolid.
EXCEPTIONAL MOLECULES
Chlorine TrifEuoride. There occur in nature, molecules which take rather exceptional conformations, and the model presented here provides a powerful tool for understanding these. One such molecule is chlorine trifluoride (51). We see that the planar structure with its different C1-F bond lengths and 87" angles (Figure 12) can he accounted for in the following manner. The C1-F orbitals are thinned by the extreme electronegativity of the fluorine molecule leaving considerable surface of the central chlorine for the two pairedelectron orbitals. These two large orbitals pressing down on each side of the plane of the atom will interfere with the two lateral bonds, stretching them and bending them downward as a result of the electronegativity of the fluorines and the demand of these orbitals for chlorine surface. This molecule has, then, a very reasonable structure. Borazole. Borazole (Figure 13) provides a fine example of unused valence electrons delocalizing by virtue of incomplete octets on adjacent atoms. The force constant for twisting is 56y0of the benzene twisting constant indicating that the delocalized orbitals have less resistance in bending than the formal pi orbitals of benzene (52). The lack of symmetry can be shown by different physical properties of substitution compounds depending on the attachment of a group to either the boron or the nitrogen. This indicates that the delocaliatiou is by no means complete.
(4) CARTMELL, E., AND G. W. A. FOWLES,"Valency and Molecular Structure," Butterworth Sci., Pub., London, 1956. (5) PAULING,LINUS, "The Nature of the Chemical Bond," Cornell Univ. Press, N . Y., 1948. N. S., Q z u ~ T Revs., ~ . 6, 319 (1952). (6) BAYLISS, (7) POPLE,J. A,, Proc. Roy. Soc. (London),AZOZ, 323 (1950). H. STEW^, A N D RANSONB. (8) EYRING,HENRY,GEORGE Can. J. Chem., 36, 72 (1958). PARLIN, (9) EYRING,H., J. Am. Chem. Soe., 54,3191 (1932). (10) GORIN,E., J. WALTER,AND H. EYRING,ibid., . 61.. 187G (1939). (11) WILSON,E. B., JR., Pme. Nall. Amd. Sci. U . S., 43, 816 (1957). (12) (a) PAULING, LINUS,PTOC. Natl. Aead. Sci. U. S., 44,211 H., G. H. S T E W ~ T AND , R. P. SMITH, (1958); (b) EYRING, PTOC.Natl. Acad. Sci., U . S., 44, 229 (1958). R. S., CAROLA. RIEKE, AND WELDONG . (13) MULLIKEN, BROWN,J. Am. Chem. Soe., 63, 41 (1941). MAURICE M., AND HENRYEYRING,J. Am. Chem. (14) KREEVOY, Sac., 79, 5121 (1957). Acla. Chem. Scand., 1, 149 (15) HASSEL,O., AND H. VIERVOLL, (1947). J. Chem. P h ~ s .18, , 1338 (16) P ~ RR., G., AND R. S. MULLIKEN, I~ -I - -Q - ,~. (17) MULLIKEN, R. S., Rev. Mod. Phys., 14, 265 (1942). (18) BRADACS,K., AND L. KNIIYEC,Z. physik Chem., B48, 63 (1940). V., AND L. PAULING, J. Am. Cham. Soc., 61, (19) SHOMAKER, 1769 (1939). H. W. WOOLEY, AND F.G. BRICK(20) ASTON,J. G, G. SZASZ, ~ D D E J. . Chem. Phus.. 14. 67 11946). LUVALLE,' J. E., AND f. SHOEMAKER, 3. Am. Chem. Soe., 61, 3521 (1939). MACKLE, H., AND L. E. SUTTON,T7an8. Fa~adaySoe., 47, 691 (1951). CHAUDET, J. H., H. W. PATTON,AND W. D. KENNEDY, A.C.S. SE regional meeting, Nov. 14, 1957. BAEYER,A., Ber., 18, 2269 (1885). YAN'T HOFF,J. H., Bull. soe. Chim ( Z ) , 23, 295 (1875). LEBEL,ibid. (2), 22, 337 (1874).
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(27) R U Z E C KYON ~ , L., AND P. SCHLAPFER, Helo. Chim. Ada, 16, 162 (1933). (28) SPITZER,RALPH,AND HUGHM. HUFFMAN,J. Am. Chem. SOC., 69, 211 (1947). (29) DUNITZ,J. D., AND V. SHOUKER,J. Chem. Phys., 20, 1703 (1952). SMITH, R. P., AND HENRYEYRING,J. Am. Chem. Soe., 74, 229 (1952). WERNER,A., 2. Anwg. allgm. Cham., 3, 267 (1893). CHERNYAEV, I. I., Ann. inst. platine (U.S.S.R.), 5, 109 11927). ~ ~,~ STREIN, Y. K., Bull a d . nei. U.R.S.S. Classe sci chim., 1- O4R. - --,69 - -. PEYRONE, M., Ann., 51, 1 (1845). JORGENBEN, S. M., J . prakl. Chem., 33, 489 (1886). GR~NRERO, A. A., AND D. I. RJABTSCHIKOV, Ada. Phys. Chem. U.S.S.R., 3. 555 (1935). GRUNBERG, A. A,; AND D: I. ~JABTSCHIKOV, C. R. A d . Sei. U.R.S.S.. 4. 259 (1935). (38) ~ A B T S C ~ I K O V , ' D :I., Ann. secteur plotine inst. h i m . gen. (U.S.S.R.), 15, 35 (1938). (39) JENSEN,K. A., Z. anwg. Chem., 242,87 (1939).
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(40) KELLER,R. N., Chem. Reus., 28, 229 (1941). (41) PITZER,K. S., ibid., 27, 39 (1940). (42) DAUBEN,WILLIAMG., AND KENNETH8. PITZER,"St& Effects in Organic Chemistry," Chap. I, N E W ~ NM., S., editor, John Wiley & Sons, Ino., New York, 1956. AND C. D. CORZELL, J. Am. (43) YOUNO,W. G., D. PRESSMAN, Chem. Sm., 61, 1640 (1939). PTOC. ROY. (44) PENNEY,W. G., AND G. B. H. M. SUTHERLAND, Soc. (Ladon), A156, 654 (1936). ibid., A176, 153 (45) SIDGWICK,N. V., AND H. M. POWELL, (1940). (46) WALSH,A. D., J. C h m . Soc., 1953, 2260. (47) MULLIKEN,R. S., J . Am. Chem. Soc., 77, 887 (1955). SIRJOHN,PTOC. R o ~Soc. . (London), AZOZ, (48) LENNARDJONES, 155 (1949). , . (49) MELLISH,C. E., AND J. W. LINNETT,Trans. Famday Soe., 50, 657 (1954). (50) GALLUP.C. A.. J. Chem. Phus.. " , 26. 716 (19571. . . i a j SMITH,D. F.,;bid., 21, 609 (1953). CHANG, ibid., 19, 518 (52) SPURR,ROBERTA.,AND SHIH-CHUAN (1951).
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