Structure, Pseudorotation, and Vibrational Mode Coupling in IF7: An Electron Diffraction Study*

Free vapor-phase molecules of iodine heptafiuoride are pentagonal bipyramids with axial bonds (1.786± 0.007 A esd) shorter than equatorial bonds (1.858±0.004 Al. They are deformed from Doh symmetry on the average by 7.5 ring puckering displacements (e2" symmetry) and 4.5 axial bend displacements (e,' symmetry). The distortion from Doh, interpreted in terms of the points-on-a-sphere variant of the valence-shell electron-pair theory, is compatible with an effective force law between electron pairs of Vij""' r;r" with n in the broad vicinity of 3.5. Expressing forces harder than simple Coulomb repulsions and much softer than conventional atom-atom nonbonded repulsions, the potential-energy law is in a range consistent with Gillespie's bond-bond repulsion theory. The simplest interpretation of the diffraction intensities is that the molecules undergo essentially free pseudorotation along a pathway (predominantly e2" displacement coordinates) connecting 10 equivalent C2 structures via C. intermediates. The observed pseudoradial displacement suggests a value of about 5 cm-l for the pseudoangular rotation constant h/8tr2cI. fI • The appreciable axial bend induced by the ring pucker is correlated in phase with the pucker displacement. This correlation is responsible for introducing a pronounced skewing of the Fax ••• FeQ radial distribution peak (i.e., an "anharmonic shrinkage") and also presumably imparts significant infrared activity to the e2" modes in overtones and combination bands. Furthermore, the axial bend gives the molecule a dipole moment which may explain recent molecular-beam experiments by Klemperer et al.


INTRODUCTION
mentioned analysis of the bond-bond force law.In the initial phase of the present electron-diffraction research,9 it was not clear whether the discrepancies between observed intensities and intensities calculated for D5h were real or were merely an artifact of fluorocarbon contamination.Therefore, a completely independent redetermination was undertaken with a new, pure sample of IF 7 • It resulted in virtually identical intensities and is described in the following.A concurrent structure analysis of ReF 7 is described else- The only seven-coordinated binary compounds known to be stable in the vapor phase are IF7 and ReF7.1,2It is of special interest to investigate their structures, not only because of the rarity of such compounds but also because of the unique opportunity they provide in diagnosing the nature of intramolecular forces.Perhaps the simplest theory of directed valence, in concept and in application, is the Sidgwick-Powell-Gillespie-Nyholm valence-shell electron-pair repulsion where.lIl(VSEPR) theory.3-5It makes definite and, for the most part, quite satisfactory predictions about the geometries of molecules consisting of a central atom (other than a transition metal) containing six or fewer valence-shell electron pairs (bond pairs and lone pairs).The predictions, qualitatively, are independent of the force laws invoked to describe the mutual repulsions between the localized orbitals housing the pairs.The case of seven electron pairs is a different story and a much more illuminating one, since the predicted geometry is sensitive to the effective force law. 5 -7 An experimental determination of the geometry, then, can establish empirically the degree of hardness of the repulsions _.operating between the bonds.This is a significantcstep beyond the information derived from studies of molecular vibrations which usually yield

EXPERIMENTAL PROCEDURE
Iodine heptafluoride of spectroscopic purity was provided by Argonne National Laboratory, Argonne, Illinois, in a Monel storage vessel.The sample introduction system for the diffraction unit, specifically constructed by Argonne National Laboratory for previous XeF 6 experiments,!1 was made of Monel and nickel.All sample introduction surfaces were thoroughly seasoned before use with CIFs and IF7.Diffraction patterns were recorded and processed conventionally as described elsewhere. 12

ANALYSIS OF DATA
only the quadratic potential-energy terms in a Taylor Experimental intensities were corrected for sector series expansion.
imperfections in the manner previously described for Several previous studies of IF7 have been reviewed XeF 6 ,Il Experimental levelled intensity, Io(s) , and in detail in a recent pUblicationS and therefore will not background intensity, IE(s), functions for each camera be discussed here.They are in agreement in concluding distance are available from ASIS,I3 Indices of resoluthat IF7 has a structure deviating, if at all, only tion 14 were 1.10 for the 21-cm (r 2 -sector) camera modestly from D Sh , but they have not led to a suf-distance and 1.03, 0.90, and 1.00 for the 21-, 11-and ficiently complete characterization to permit the afore-6.S-cm (r 3 -sector) camera distances, respectively.4040 Experimental and calculated molecular intensities and radial distribution functions were computed as previously described ll ,14,16 with the usual corrections applied. 1 4--18 Radial distribution functions were calculated using a Degard damping factor [exp( -0.001Os 2 )].Atomic scattering factors used in all phases of the analysis were the partial wave elastic factors of Cox and Bonham 19 and the inelastic factors of Tavard 20 for fluorine and of Pohler and Hansen 21 for iodine.Anharmonicity constants I7 were estimated 22 to be 2.1 A-I for the I-F bonded distance and were taken to be 1.0A -1 for F• .. F nonbonded distances.Corrections for Bastiansen-Morino shrinkage effects,23 estimated roughly from calculations on octahedral fluorides,24 were taken to be 0.0005 A for (Feq• .. F,q)sholt, o.o01A for (Fax .. •Feq), and 0.002 A for (Feq ... Fcq)long and (Fax .. •Fax).The difference in amplitude of vibration between the different I-F bond lengths was estimated roughly to be leql"x=0.002A, using an extension 25 of Badger's rule. 26is difference was included as a constraint in subsequent analyses, since it was not possible to establish independent values of leq and lax from the diffraction intensities.Calculated standard errors took into account the effects of both random and known systematic errors.27 Molecular parameters were derived from geometrically constrained least squares analyses of the molecular intensity for each camera distance and the composite molecular intensity.In final analyses the 21-cm (r 2 -sector) data were not used in constructing the composite molecular intensity and experimental radial distribution function.The neglect of these data has little influence on the derived parameters but has a strong effect on the observed standard deviation between the experimental and calculated intensities.e [(I-Fax) constrained to be /(I-Feq) -0.002 A.
The influence of this range of data on the radial distribution function is to increase the magnitude of the "foot" at the leading edge of the I-F bonded peak.Similar troublesome contributions from small angle scattering data have been encountered in the case of all other molecules we have studied containing bonds between atoms with a great disparity in atomic number.1O,28,29Imperfections m current scattering theory seem to be involved.

General Inferences
A comparison between the experimental radial distribution function of iodine heptafluoride and a calculated distribution function for a DSh symmetry model is shown in Fig. 1.The molecular parameters used in constructing the calculated distribution function were derived from a least squares analysis of the composite molecular intensity and are given in Table 1.The over-all correspondence between peak positions and peak areas in the experimental and calculated distribution functions indicates that the molecule closely approaches D5h symmetry (Fig. 2).The most compelling evidence that the deviation from Dsh. symmetry is small is the open space preceding the final "peak" in the radial distribution function.Among possible sevencoordinate structures, only D6h, with its tight equatorial girdle, corresponds to such a discontinuous spacing of nonbonded distances.Although the misfit in the 2.1-2.7-Aregion suggests that displacements from Doh symmetry are not much larger than common amplitudes of vibration, it also suggests that the deviation is real.Least squares analyses imply that a significant difference exists between axial and equatorial bond lengths in the molecule, the two axial bonds being shorter than the five equatorial bonds by about 0.07 A.
Evidence for this difference is provided by the breadth of the I-F bonded peak and the shape and p08ition of the 3.5-A peak.The conspicuous failure of the first Born approximation,16 which results in the severe splitting of the I-F bonded peak into two unsymmetrical peaks, hinders an analysis of the precise distribution of I-F bond lengths.
The asymmetry and breadth of the experimental peak at 2.5 A indicate that a majority of the Fax ••• Feq nonbonded distances have been shortened while a few have been lengthened relative to the distribution in the D5h model.Such a distribution of internuclear distances cannot arise for a molecule with a DSh equilibrium structure, whatever its amplitudes of vibration may be, if the modes of different symmetry vibrate independently, uncoupled in phase.The implications of this statement are discussed in greater detail in subsequent sections.
In contrast to the 2.5-A peak, the 2.2-A peak, which corresponds to the short Feq'" Feq nonbonded distances, has a very narrow breadth and its center of gravity has been displaced outward.The significance of the misfit in the 2.2 A is not completely unequivocal.Poorly understood deficiencies in scattering theory make somewhat uncertain the interpretation of details in the leading and trailing edges of peaks corr-esponding to scattering pairs of much different atomic number (i.8-A peak in IF7)' In all subsequent models discussed, it is assumed that the bond distances can be grouped into two sets, corresponding to the axial and equatorial bond lengths of the D5h reference model.This assumption should be valid since the displacements from D5h are only the order of magnitude of bending amplitudes of vibration.In addition, mean amplitudes of vibration for the bonded and nonbonded distances are divided into four sets, a single amplitude being associated with the component distances under each peak in the radial distribution function..i'= 1, ",,5, in which 0'0 is a maximulll out-of-plane angular displacement and c/>eq is a phase angle equal to ml" /10 for C, and (21£+ 1) 7r /20 for C2 structures, where n is an integer.

Models of Static Deformation from
Although the puckering away from the equatorial plane significantly improves the fitting of the 2.2-A peak, its effect in first order on the 2.5-A peak is to increase its breadth symmetrically.In order to obtain the skewing of the distribution-for the 2.5-A.peak required to fit the diffraction data, the axial atoms must be displaced away from the reference fivefold axis (by an angle denoted as fJ) in such a way as to shift the majority of the Fax" •Feq distances inward a small amount while shifting a few rather far outward.Two conformations which satisfy this requirement and still preserve C 2 or C s symmetry are shown in Fig. 2.
Results of least squares analyses of the molecular intensities for these two cases are given in Table 1 under their respective headings.The experimental data are fitted equally well by either of the models, with a very significant improvement in the fit compared to that for the D5h model.The derived molecular parameters including bond lengths, skeletal amplitudes of vibration, the puckering displacement (to, and the axial bend fJ, are nearly independent of whether a C2 or C structure is assumed. A least squares fit assuming equal concentrations of the C 2 and C s models gave the same standard deviation as that for the C 2 and the C. fits separately.Comparisons between the experimental and calculated radial distribution functions and composite molecular intensities, sM(s), are made in Figs. 1 and 3, respectively.Although the calculated curves used structure parameters derived in the next section, they are indistinguishable from those calculated for the C2 and C models.A matrix of correlation coefficients based on the least squares fit of the composite molecular intensity using a diagonal weight matrix proportional to the scattering variable s is available from ASIS. 13  Rotation of the displaced axial atoms about the z axis by an amount 6.cpax has little effect on the standard deviation until 6.cpax deviates from its value in the C 2 (or C 8 ) model by more than 40°.Symmetry breaking displacements greater than this value lead to rapidly increasing standard deviations.This is understandable since the effect of increasing 6.cpax by more than 90° is to reverse the direction of the skew of the 2.5-1\ peak.
Several least squares analyses were also made assuming various isomeric concentrations of C2, C, and D5h molecules.Little change in standard deviation was found as the D5h concentration was increased up to 20%.Beyond 20% a rapid increase in standard deviation occurred.Many other types of deformation and combinations of deformations were also tested; none were able to impart the observed skew in the 2.5-A peak.

Model of Dynamic Pseudorotation
The equivalent fits of the diffraction intensities and excellent agreement between the derived parameters for the C 2 and C models suggest the possibility of a dynamic pseudorotation analogous to that observed  in cyclopentane 3 (}-32 and tetrahydrofuran. 33- 35 The description of such a pseudo rotation model may be given in terms of the same variables a O , CPeq, {3, and CPax that were defined in the previous section.
Although pseudorotation involving C2" displacements of the equatorial atoms allows the 2.2-1\ peak to be fitted, the skewed 2.5-A peak cannot be reproduced unless the axial atoms undergo e/ axial bend displacements that are in phase with the equatorial displacements-i.e., unless normal modes of vibration of different symmetry are coupled.The leading anharmonic term responsible for this coupling is of the form F iijS i 2Sj, where Si represents an C2" symmetry coordinate and Sj an CI' coordinate.No other cubic term is capable of accounting for the misfit between the calculated D5h and observed intensities.
The influence of the anharmonic coupling may be shown to be as follows.A ring puckering displacement (aD, cPeq) induces an axial bending displacement ({3, CPax) .For example, if CPeq = 0, the unique atom F. in the ring rises by a O , and both axial atoms bend by {3 from the axis in a direction away from the ring site Fs.Let this direction of axial bend be used to identify the reference orientation CPax= O.As the ring puckering amplitudes progress clockwise around the ring (corresponding to a counterclockwise progression of phase angle CPeq), the axial bend progresses counterclockwise about the axis, andlthe magnitudes of the phases are related by CPax=4c/Jeq such that v(axlbend)=2v(ring'i: pucker) .ring pucker angle at and e/ axial bend angle (3 are defined in the text and are coupled as if by a cubic term F S2(e2") S(eJ').By n=5 the structure has closely approached the limiting C2v form it retains for all higher n (an alternative Csv potential minimum also exists for high n).The experimental structure of IF7 is represented by the point with indicated uncertainties.depicting pseudorotation in ReF 7 .A somewhat similar model was proposed by La Villa and Bauer 36 on the basis of visually estimated electron diffraction intensities.These authors did not, however, derive quantitative deformation parameters, nor did their thermodynamic treatment correspond to free pseudorotation.

Note that one complete pseudo rotation cycle in
The individual nonbonded distances calculated for various pseudorotational phase angles, CPeq, assuming an equatorial puckering of aO= 7.5°, and axial bending of ~=4.5°, depend markedly on the phase angle but the envelope of the distribution function is virtually independent of CPeq.37 Therefore, it cannot be determined by electron diffraction alone whether the molecule is pseudorotating or whether it exists in a single static conformation.On the other hand, the diffraction intensities are sensitive to (CPa;x-CPeq) and to aO and ~.The structural parameters that can be derived and their estimated standard errors are given in Table II.

DISCUSSION
Electron diffraction intensities of gaseous iodine heptafluoride may be accounted for equally well by statically deformed structures with C2 or C. symmetry (or intermediate structures) or by a dynamic pseudorotation description.In any case, the deformations from DSh symmetry are small and characterized by a correlation in phase of displacements along e2" and e/ symmetry coordinates.Although diffraction intensities do not distinguish between the static and dynamic interpretations, physical arguments favor the dynamic pseudorotation model.The atomic displacements required to take the molecule from one C2 configuration to an equivalent one via a C. intermediate are so small (the hindering potential is tenfold) that it is difficult to envision a potential barrier high enough to inhibit pseudorotation.Moreover, there is a striking similarity in geometry and in the magnitude of the displacements involved between the ring of fluorine atoms in the equatorial plane of IF7 and the rings in cyclopentane and tetrahydrofuran which have been found to exhibit essentially free pseudorotation.3 O-3s The possibility of a correlation between the phases of the equatorial puckering and axial bending was suggested by a simple variant of the Gillespie-Nyholm valence-shell electron-pair repulsion theory.s~7Calculations by Thompson and BartelF treated bondbond repUlsions in XY 7 molecules as repulsions between points on a sphere and led to a simple relation between e2" and el' displacements.It was found that the C2 and C. conformations ultimately become more stable than the DSh conformation as the hardness of the bond-bond repulsive potential is increased.For potential functions of the form (rii)-n expressing the i, j interaction, the deformation from DSh becomes spontaneous when n exceeds 2 and the C 2 and C. configurations remain equivalent in energy.The model predicts that, as n increases, the first deformation is an e2" buckling of the equatorial ring.As n is increased further the axial atoms experience an e/ displacement from the fivefold reference axis, and the axial bend {3 is proportional to the square of the ring pucker aO, as shown in Fig. 4. The direction of the bend is just that required to fit the diffraction intensities.Also plotted in Fig. 4 is the point corresponding to IF7 according to the present experiment.Although the observed magnitude of the axial bending is somewhat larger in comparison with the observed ring pucker than given by the simple model, the points-on-a-sphere model shows a pleasing qualitative agreement with experiment for a value of n~3.5 or 4.This result reinforces Gillespie's VSEPR4,s interpretation that molecular geometry is determined by repulsions between occupied bond orbitals imposed by orthogonality requirements and the exclusion principle.If the repUlsions causing the deformation from Doh symmetry had been ligand-ligand steric forces between atoms instead of bond-bond repulsions, a much harder repulsion (n~lO) would have been expected.On the other hand, a combination of Coulombic and steric repUlsions between the negatively charged ligands might also lead to the apparent hardness observed.Moreover, the "experimental" value of n should be viewed with reservation.Electron diffraction vields the distribution of molecular structures of the 'vibrating molecules rather than a direct measure of the structure corresponding to minimum potential energy.A glance at Fig. 2 of Ref. 7 reveals that the potential-energy surface is so flat that large out-of-plane deformations will occur (coupled in phase with axial bends) even for n=2.
The I-F bond lengths in the molecule confirmed another implication of the VSEPR theory.As predicted qualitatively by a bond-bond repulsion mode!, the less crowded axial I-F bonds are 0.072±0.Ol A shorter than the equatorial bonds.The mean I-F bond length, 1.837±0.002A,.is shorter than that observed in IF5,38 1.860±O.003A, despite the increased crowding.Such a trend is found in a large number of inorganic fluorine compounds as fluorine substitution is increased.
The present electron diffraction structural analysis appears to be consistent with results of other experimental techniques, although as yet no other method has provided a detailed resolution of the problem.The infrared and Raman spectra of IF7 vapor 8 ,39 have been interpreted in terms of Doh symmetry.This is not in serious conflict with the present study since the displacements from D5h symmetry found by electron diffraction are the order of magnitude of vibrational amplitudes.According to our analysis, however, the distortion from D5h symmetry will cause the doubly degenerate e/ ' frequency (infrared and Raman in- active) to split into a high (pseudoradial) frequency and a very low (pseudo-angular) frequency, the latter of which should correspond to a pseudoangular rotational constant of Bps= h/87r2Cleff~5 cm-l (where the pseudorotational energy levels are Em = m 2 Bps; see Ref. 10 for details).The strong coupling between e2" and el' should make the e2" overtones and the pseudoradial pseudoangular combination bands appreciably infrared active, with intensity borrowed from the induced el' displacements.4o It is to be hoped that the low frequencies implied by the present analysis will be visible as fine structure of combination bands analogous to that reported for cyclopentane.Such low frequencies might be inferred, alternatively, from a careful measurement of the entropy.It has also been conjectured on the basis of infrared and Raman analyses 8 that IF7 is a relatively rigid molecule compared to ReF 7 , a conclusion that is consistent with electron diffraction analyses of amplitudes of vibration in IF7 and ReF 7 .1O Considerable controversy has arisen over the interpretation of x-ray diffraction data for IF 7 .41,42The debate has been concerned with the observed small deformations from D5h symmetry in the orthorhombic crystal phase and whether they are statistically significant.,42 The present electron diffraction data provide some basis for understanding the difficulty in interpreting the x-ray diffraction data, since the free 1F7 molecule does indeed depart appreciably from D5h symmetry.The ease with which the free molecule can be deformed from one configuration to another along the pseudorotational pathway causes complications when the molecules pack in a crystal.How effective the neighbor-neighbor interactions are in inducing a regular and repeating array of conformations is an interesting problem warranting further research.A somewhat analogous situation arises in the case of cyclopen tane. 43articularly significant observations on IF7 and ReF 7 were made by Klemperer et al. in electrostaticfocussing molecular-beam experiments at -60 0 C. 44 At low temperatures, IF7 molecules behave as if they have electric dipole moments, whereas at room temperature 45 there is no measurable focussing.Whether the dynamic dipole moment implied by the el' axial bend of the present diffraction analysis is sufficient to impart the required Stark effect for focussing has not yet been established quantitatively.Qualitatively, the diffraction results for IF7 and for ReF-,-which exhibits a greater axial bend-are consistent with the molecular beam results, including the fact that ReF7 continues to focus at much higher temperatures than does IF 7 .

CONCLUSIONS
Iodine heptafluoride exhibits several novel features each of which can be understood qualitatively on the basis of the simple valence-shell electron-pair repulsion theory.Consistent with an electron-pair repulsive force law of low to intermediate hardness, the molecule is a pentagonal bipyramid.Repulsions between the crowded equatorial bonds cause the equatorial ring to pucker slightly, presumably giving rise to a very low-frequency pseudorotational mode.The equatorial pucker induces an axial bend in a direction to maximize bond-bond avoidance, which has two striking observable consequences.The interaction couples modes of different symmetry, resulting in a pronounced skewing ("anharmonic shrinkage") of the Fax.' , 'Feq radial distribution peak.This coupling apparently leads to a polar deformation of the molecule of sufficient magnitude to cause it to interact strongly with external electric fields. 44ote added in proof: An extended Huckel molecular orbital calculation has proven illuminating [V.Plato and L. S. Bartell (unpublished work)]' Differing from an earlier calculation by R. L. Oakland and G. H. Duffey [J.Chem.Phys.46, 19 (1967)J primarily in the inclusion of all valence electrons instead of only the (j electrons, it strikingly reproduced the observed behavior and could be decomposed into bonded and nonbonded components.Contrary to the earlier results for which D5h symmetry proved the most stable, a spontaneous deformation along the e2" coordinates was indicated, along with an el', el' coupling in the observed direction.
H is a pleasure to acknowledge the assistance of Mr. Lee Winstrom in processing some of the data.We express our appreciation to the Michigan Computing Center for a generous allowance of computing time.
~ This researc~ was supported by a grant from the National SCIence FoundatIOn.Based on a dissertation by W. J. Adams in partial fulfillmen t of requirements for the degree of Doctor of Philosophy, The University of Michigan, 1969.t Author to whom correspondence concerning reprints should be addressed.
D5h Symmetry Displacements of fluorine atoms away from the equatorial plane to give a better F• .. F avoidance are suggested by the position of the experimental nonbonded peak at 2.2 A. These displacements must be along e/' symmetry coordinates and may be expressed by the individual I-F} angular out-of-plane displacements, O'j.The angular displacements, in turn, can be characterized by two coordinates, 0'0 and c/>cq, associated with the doubly degenerate C2" representation, by the relation:J1I

2 FIG. 4 .
FIG.4.Deformation of seven repelling points on a sphere from DOh structure as a function of n, the exponent in the potentialenergy function V=:E(r-n)ij.The lowest potential-energy e,"

TABLE 1 .
Results• of least squares analyses of the composite molecular intensity for IF,.Equatorial amplitude of puckering.See text for further details.d Axial amplitude of bending.See text for further details. C

TABLE II .
Structural parameters' for pseudorotational model of IF7 and estimated standard errors.bEquatorial amplitude of puckering.See text for further details.e Axial amplitude of bending.See text for further details. d