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).
C. C. COSTAINAND G. B. B. M., SUTHERLAN'D
322
splitting of the spectral lines would be much too small to be observed. However it has recently been shown4 that the apparent doubling of the 101 Q branch in phosphine is probably spurious, arising from an accidental conglomeration of rotation lines and thus no inversion doubling is observed in either phosphine or arsine. The previous estimates of the barrier heights in phosphine and arsine must therefore be discarded and some other method sought for evaluating the heights of these barriers from spectroscopic data. In the present paper a method is suggested based on vibrational force constants, which is shown to yield excellent results for ammonia and may therefore be assumed to give a reasonable first approximation to the true values in phosphiiie and arsine. The basic assumption underlying this method is that the simplest way for a pyramidal XY, molecule to invert is through the motion associated with the symmetrical deformation vibration, in which the apical angle of the pyramid opens symmetrically, accompanied by a minor symmetrical change in the X Y bond lengths. For such a vibration, the simple valency force field gives as the potential energy V =
3 - I
