March, 1952
LENGTH AND REACTIVITY IN CARBOWHALOGEN BONDS
iodine with IF5 and IF?:must be taken as strong evidence against the high dissociation energy and in favor of 1.98 e.v. For the two possible values of D(IF), either 2.87 or 1.98 e.v., the systematic comparison of force constants and dissociation energies is not very helpful, perhaps slightly favoring the high value. The chemical evidence that IF does not exist in appreciable concentration is, however, strong evidence in favor of the lower value. If we accept the lower value for IF, then by analogy we should favQr the lower values for BrF and CIF. I n the case of ClF the change is not appreciable, but such as it is it would cause a further lowering in the value of D(F2) if we accept a value for this constant based on D(C1F) and the heat of formation of C1F. It may be necessary to make some slight reservations to these conclusions. To begin with, the apparent convergence limits of the vibrational levels of the excited states may not coincide exactly with the dissociation limits if there are potential maxima. It seems quite likely from the work of Brown and Gibson5 that such potential maxima exist. Such maxima are, however, small, a t the most a few hundred cm.-' and would not alter the main conclusions and would only affect the result slightly.
319
We must also take into account the possibility of the correlations between the excited electronic states of the molecules and the atomic products varying from molecule to molecule. For the homonuclear molecules, it seems certain that the excited states are WO+,but for the heteronuclear molecules the excited state might be an ordinary l2+; it is possible that for the heavier molecules containing I we are near Hund's case c coupling and that the upper states are 0' derived from 311, but that for the lighter molecules nearer Hund's case b the transition from 311 to the ground l2+ is forbidden and the upper state for .these molecules is the '2+, Another possible way of getting at the dissociation energy would be by a Birge-Sponer extrapolation for the ground state. Unfortunately the extrapolation is so long that it carries little weight. For IF a very long linear extrapolation would give D(1F) = 3.5 e.v., but it is known6 that these extrapolations tend to come high, especially for heavy molecules, and while the *result probably favors the higher dissociation energy, it carries negligible weight. Further work to confirm the chemical instability of IF seems the most promising way to settle t,he dissociation energies of this group of molecules.
1tELATIONS BETWEEN LENGTH AND REACTIVITY I N SOME CARBONHALOGEN BONDS BYA. GILCHRIST AND L. E. SUTTON Physical Chemistry Laboratory, Oxford University, England Received December $6,1061
In recent discussions of reactivity of carbon-halogen bonds, and in particular of their dissociation energies, emphasis has tended to shift from the unperturbed state to the transition state. It is of interest, therefore, to find that for the methyl halides and acetyl halides there is an inverse linear relation between bond length and dissociation energy; and that an inverse relation between the mean bond energy and the square of the bond length applies to these compounds and several other organic halides.2 Such relations indicate that the characteristics of the transition state are to some extent shown in the unperturbed state. It is unlikely that so simple a state of affairs holds very widely. Other series of halides are in fact found to give dissociation energy/bond length lines parallel t o the original one. An explanation of these facts is offered.
As a result of examining the structures of the relation between the length and the energy content acetyl halides by the electron diffraction method assignable to a particular bond in a molecule when for vapors, Allen and Sutton2 found two relations this latter is formed by simultaneous coalescence of between the lengths of the carbon-halogen bonds all the atoms. It is not an obvious inference, howand bond energy quantities. ever, that there will be any simple relation between First, they showed that the mean bond energies, the length of a bond in a polyatomic molecule and derived using C-C bond energies corrected for bond the energy required to break it, and it alone; belength by a relation of the type proposed by G ~ r d y , ~cause this energy is a function not only of the bond i.e., Ha(X - Y ) = (rZ-2(X - Y ) p, themselves itself but also of the molecule of which it is part, fall on a curve obeying this relation. The points and of the radical which is formed by diss~ciation.~ for the acetyl halides and for a number of fluorides, If the molecule as a whole is stabilized, relative t o chlorides, bromides and iodides all fall, in fact, on a some reference state, e.g., by resoiiance (alias mesomerism or bond delocalization), or is in some way common curve destabilized, then as dissociation proceeds this enH.(C-Hal) = 250 X l-*(C-Hal) - 4 (1) ergy term becomes zero: in the former case it would increase the energy required to break the bond, in Ha being in kcal./mole and 1 in 8. ' This observation shows that there is a simple the latter case it would decrease it. Furthermore, the radical which is formed may be stabilized, ( I ) Pieeeiited a t the Symposium on Bond Strengths, New Yolk, again, e.g., by resonance, or it may be destabilized, PI'. Y . . September, 1S5l.
+
(2) Allen and Sutton, T r a n s . F a r a d a y Soc., 47, 23G (1951). (3) Gordy, J . Chem. Phys., 15, 305 (1947).
(4) Szwarc, {bid., 18, lOG0 (1950); Long and Sorrish, Prnc. R o y . Soc. (London), 8187, 337 (1946).
A. GILCHRIST AND L. E. SUTTON
320
in a way that the molecule itself is not, and this energy would reach its limiting value as dissociation proceeds; so in the first case it would decrease the energy required to break the bond and in the latter case it would increase it. Despite this unfavorable prognostication, Allen and Sutton found that a very simple linear relatioil holds between the length and the dissociation energies6 for the carbon-halogen bonds in three methyl halides (that for the fluoride has not been reported) and the four acetyl halides (see Fig. l),viz. D(C-Hal) = 213
- 76
X Z(C-Hal)
(2)
A relation of the inverse square type used above between Ha and E has also been tried, but the point for acetyl fluoride, which is removed somewhat from the others, fits less well on this than on the linear relation.
r ‘cy
\
3 100 d &
0 CNCl
h
8 80
5 .*8
I
42
-2
w
60
8 40
L
1.5
2.0 Bond length (A.). Fig. 1.-Dissociation energy/bond length curves for carbon-halogen bonds. The abbreviations (e.d.) and (m.w.) mean respectively, from electron diffraction measurements and from micro-wave measurements, The broken line through the points for the allyl compounds is the best one parallel to that for the methyl and acetyl one8, while the dashed line is the best line through t,hem. The circles denote probable error in bond length.
The relations given previously between dissociation energy and other energy quantities may be expressed by the equation D = Do - (R, - R,) (3) wherein D is the observed dissociation energy, R, is the stabilization energy of the radical, R, that of the molecule save for that portion of the stabilization energy which may be regarded as belonging to the bond which is to be broken. Domay thus be regarded as the “intrinsic energy” of this bond, i.e. as the energy which would be needed to break it if the reorganization energy, R, - R,, were zero. As defined above, it includes part of the stabilization or destabilization energy of the whole molecule; therefore it is not a constant characteristic only of the type of bond, e.g., it would not be the same for all C-Br bonds; it depends upon its molecular environment. There might therefore be some connection between this quantity which is a characteristic of the unperturbed bond, and the bond length. ( 5 ) Roberts and Skinner, Tram. Faradav Soc., 45, 339 (1949); Carson and Skinner, J . Chrm. Soo., 936 (1949).
Vol. 5G
From equation (3) it follows, however, that D can be put equal to Doonly if R, = R,. It is difficult to imagine a molecule for which this condition actually holds, or to suggest how we should know if it did hold. Szwarc4 has suggested that the methyl compound might be taken as a standard of reference in such considerations. Rr R m need not be zero for the methyl compounds. It is a t least likely to be small; and if it is not zero, this means merely that the true zero line is displaced vertically and parallel to that for the methyl compounds (vide i n f r a ) , Having tliis in mind, the present authors suggest that the linear relation described above means that the bond length provides a measure of Do of the type Do = K - A1 which is common for the bonds from carbon to all four of the halogens, and that the value of R, - R, for acetyl compounds is accidentally the same as that for methyl compounds.6 The first of these two assumptions embraces the more limited one that Dofor a particular caybonhalogen bond is composed of a constant term and a variable one which represents the effect of, e.g., resonance stabilization on that bond alone, and which is related to the difference between the actual bond length and that of the reference bond to which the constttnt energy term also relates. If these assumptions be granted, it would be predicted that for instances where Rr > R, the points would fall below the curve to equation (2), and conversely. In general, then, carbon-halogen bonds will not fit equation (2): but it might be expected that R, - R,, would be roughly constant for the series of halides of anyone radical, so that all the points for such a series would be displaced vertically by an equal amount from the line to the equation, i.e., will lie on a line parallel to this latter. This is indeed the case for the allyl halides’ and the &butyl halides according to determinations of carbon-halogen bond lengths therein by one of the authors and Mr. H. J. RII. Bowen (see Fig. 1). The displacements correspond to R, - R,, = 1G and G kcal., respectively. The former is somewhat smaller than the radical stabilization ascribed by taking R, - R , = D(CH3-Hal) - D(R-Hal) ; because some allowance has been made in it for the destabilization of the unperturbed carbon-halogen bond in allyl halides relative to methyl halides. It appears that the point for the carbon-chlorine bond in vinyl chloride lies on or very near to the line to equation (2); so here again R, - R, = 0 or, more precisely, is the same as for methyl compounds. If this be true, the greater dissociation energy for this compound is to be regarded as a fuaction of the carbon-halogen bond itself in this compound. The same is true of chlorobenzene. These are unexpected results. The point for cyanogen chloride lies above the line; so in this case R, > R,, according to these arguments, which is prausible because of the possibility of there being two generalized ?r-bonds in the (8) Allen and Sutton (ref. 2) had reached the same conclusion from a different argument. (7) The best straight line through the points for the allyl compound is not quite parallel to that for the methyl compounds, but is inclined R m decreases numerically to it in such a way as to signify that Rr in the order C1, Br, I.
-
c
March, 1952
POTENTIAL .BARRIERS RESTRICTING INVERSION I N "3,
molecule which are not possible in the radical. The same is true for cyanogen iodide. The treatment outlined above may make possible a better assessment of the relative parts played by the bond itself and by effects characteristic of the molecule as a whole or of the radical, in determining dissociation energies. The simplicity of the relation between Do and 1 is surprising: it is unlikely to be accidental. If we assume, as above, that R, - R,, is the same for acetyl compounds as for methyl ones, then some such explanatioii as the following seems to be required. The potential energy/bond length curve for any bond arises by the superimposition of curves showing, respectively, the variation of attraction energy and of repulsion energy with internuclear distance. The latter generally varies with a much higher inverse power of the distance than does the former. If nom we assume (a) that, over the range of internuclear distance which covers all carbon-halogen bonds, there is one linear attraction curve common to aZZ .four halogens, and (b) that the repulsion curves between carbon and the several halogens have the same form and differ merely by their lateral displacement, then the observed relation follonw; for as may be seen from Fig. 2 the minima lie on a straight line (the broken line) parallel to the attraction curve (the inversion is due merely to the different sign conventions for D and V ) . The assumptions are possibly rather more restrictive than is necessary, e.g., it would be sufficient if the repulsion curves were geometrically similar.
ASH^ AND PH,
321
Fig. 2.-Hypothetical potential energy/distance relations for carbon-halogen bonds.
Further, if Rr - R, were not the same for acetyl compounds as for methyl ones, so that the DO values for the carbon-halogen bonds therein really lie off the line for those of the bonds in the methyl compounds, then it might be that the curves of Do against l for the individual halogens do not form a common straight line but lie O H four parallel straight lines: in this case the attraction curves for the several halogens could also form a set of parallel straight lines, which would have to be such that the lateral displacements between them are in the same ratio as those of the repulsion curves. In any case, the degree of regularity in the relations between the energy curves for the different halogen-carbon bonds seems surprisingly high.
A METHOD OF DETERIJIINING THE POTENTIAL BARRIERS RESTRICTING INVERSION IK AMMONIA, PHOSPHINE AND ARSINE FROM VIBRATIONAL FORCE CONSTAKTS
-
BY C. C. COSTAIN AND G. B. B. M. SUTHERLAND
Department of Physics, University of Nichigan, Ann Arbor, Michigan Received December $8, 1061
The height of the potential barrier restricting inversion in' the ammonia molecule has been determined by several investigators using data on the hyperfine splitting of certain lines in the infrared and micro-nave spectra of that molecule. None of these methods can be applied to phosphine and arsine, since no corresponding experimental data are available. Ry assuming that the ammonia molecule can be inverted by gradually increasing the amplitude of the symmetrical deformation vibration, the force constants controlling this vibration can be used to plot a parabolic potential of the form V = A ( A c Y either )~~~ side of the planar configuration. For ammonia, the resulting calculated barrier height agrees very closely with that derived from inversion splittings in the spectrum by the Manning potential function, v i a , 2070 cm.-1 (5.9 kcal./mole). This indicates that a similar method can be applied to phosphine and arsine and when this is done the corresponding barrier heights are computed to be close to 6000 cm.-l (17.1 kcal./mole) and 11,200 cm.-l (32.1 kcal./mole). Such values are consistent with the absence of inversion splittings in the infrared spectra of phosphine and arsine. The implications of these results in the stereochemistry of trivalent derivatives of ammonia, phosphine and arsine are briefly discussed.
Analyses of the infrared spectra of ammonia, phosphine and arsine prove conclusively that these molecules all possess a pyramidal configuration. In the case of ammonia, the dimensions of the pyramid can be deduced with great accuracy from the observed values of the moments of inertia of NH3 and NDa, but in addition a doubling of all the lines in certain of the absorption bands makes it possible to estimate1v2the height of the potential barrier re(1) G. Herzberg, "Infra Red and Rainan Spectra," D. Van Nostrand Co., Inc., New York, N. Y., 1945. (2) D. h1. Dennison and G. I?, UIil~iibwk, PBus. Rea., 41, 313 (IYSZ).
stricting inversion as 2100 50 cm.-l or 6000 f 200 cal./mole. Early analyses of the infrared spectrum of phosphine indicated a similar doubling of the Q branch in an absorption band a t 10 p , from which it was deduced3 that the height of the barrier in phosphine was approximately the same as that in ammonia. No doubling has been observed i n the infrared spectrum of arsine but it can be simi- . larly deduced3 that if the iiiversion potential for arsine i s also ab,out GOO0 cal./mole, the result,ziit (3) G . B. H. AI. Rutlierlarid, E. Lee and C. IC. Wu, Trans. Il'aradau SOL,36, 1373 (lY39).
