Vibrational Spectra of PF5 and AsF5: Height of the Barrier to Internal Exchange of Fluorine Nuclei

Vibrational Spectra of PF5 and AsF5: Height of the Barrier to Internal Exchange of Fluorine Nuclei L. C. Hoskins and R. C. Lord Citation: The Journal of Chemical Physics 46, 2402 (1967); doi: 10.1063/1.1841049 View online: http://dx.doi.org/10.1063/1.1841049 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/46/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Fission barrier heights and lifetimes for heavy and superheavy nuclei AIP Conf. Proc. 1175, 231 (2009); 10.1063/1.3258229 Potential function for axial–equatorial fluorine atom exchange in PF5, AsF5, and VF5 J. Chem. Phys. 64, 3228 (1976); 10.1063/1.432662 Vibrational spectra of solid fluorine J. Chem. Phys. 59, 5600 (1973); 10.1063/1.1679912 Raman Spectra of AsF5 and VF5 and Force Constants for PF5, AsF5, and VF5 J. Chem. Phys. 53, 2559 (1970); 10.1063/1.1674369 Internal Barrier Height of Methyl Mercaptan J. Chem. Phys. 23, 1736 (1955); 10.1063/1.1742445 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 http://scitation.aip.org/content/aip/journal/jcp?ver=pdfcov http://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/www.aip.org/pt/adcenter/pdfcover_test/L-37/327320036/x01/AIP-PT/JCP_ArticleDL_101514/PT_SubscriptionAd_1640x440.jpg/47344656396c504a5a37344142416b75?x http://scitation.aip.org/search?value1=L.+C.+Hoskins&option1=author http://scitation.aip.org/search?value1=R.+C.+Lord&option1=author http://scitation.aip.org/content/aip/journal/jcp?ver=pdfcov http://dx.doi.org/10.1063/1.1841049 http://scitation.aip.org/content/aip/journal/jcp/46/6?ver=pdfcov http://scitation.aip.org/content/aip?ver=pdfcov http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3258229?ver=pdfcov http://scitation.aip.org/content/aip/journal/jcp/64/8/10.1063/1.432662?ver=pdfcov http://scitation.aip.org/content/aip/journal/jcp/59/10/10.1063/1.1679912?ver=pdfcov http://scitation.aip.org/content/aip/journal/jcp/53/7/10.1063/1.1674369?ver=pdfcov http://scitation.aip.org/content/aip/journal/jcp/23/9/10.1063/1.1742445?ver=pdfcov THE JOURNAL OF CHEMICAL PHYSICS VOLUME 46, NUMBER 6 15 MARCH 1967 Vibrational Spectra of PF6 and AsF6: Height of the Barrier to Internal Exchange of Fluorine Nuclei * L. c. HOSKINSt AND R. C. LORD Spectroscopy Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts (Received 31 October 1966) The infrared spectra of gaseous PF6 and AsF. have been obtained over the spectrll:l range 30-2000 cm-I , and Raman spectra have been observed for the liquid state. The observed freq~encles for bo!h ~olecules are satisfactorily assigned on the basis of a Dab. st.ructure. A .normal-coordm~te calculatIOn IS. made with the help of a valence-force system and simplIfymg assumptIons about off-dlagon~l elements m t~e potential-energy matrix. An approximate potential diagram for internal exchange of aXIal and equatonal fluorine nuclei is evaluated from the potential constants of species E'. From the calculated exchange rates it is concluded that it is unlikely that the axial-equatorial chemical shifts in the NMR spectra of PF6 and AsF6 will be resolved at low temperatures. I. INTRODUCTION ELECTRON-diffraction st~diesl,2 ?f PF.6 show its molecule to be a trigonal blpyramld (D3h point group) with axial and equatorial distances of 1.577 and 1.534 A, respectively.2 Although no com- parable determination of the structure of the AsF 5 mol~­ cule has as yet been published, it seems likely that It also has the D3h configuration. Despite the fact that the axial fluorine nuclei should have a significantly differe.nt electronic environment from that of the equatorial nuclei in both PF6 and AsF6, NMR studies on gaseous and liquid PF6 by Gutowsky, ~cCall, an? SI~c?te~S and on liquid AsF6 by Muettertles and Phillips Indi- cated that all five nuclei are equivalent. As is well known such apparent equivalence can be observed if the no~equivalent fluorine nuclei are interchanging at a faster rate than the frequency difference of the NMR chemical shifts of the two kindb of nuclei. Berry6 has proposed a mechanism for intramolecular exchange of fluorine atoms i~ PF6• The pathway for ~e exchange is indicated in Fig. 1. In. the top drawI~g PF6 is seen along the threefold aXIS, and the aXIal fluorine atoms 5 and 6 have displacement vectors per- pendicular to that axis, whereas Atoms 2 and 3 move as indicated within the equatorial plane. In the center figure the fluorine atoms 2, 3 have reached positions equivalent to those of Atoms 5 and 6, an? t~e structure has C4• symmetry with the fourfold aXIs In ~he. P-F1 direction. If the fluorines continue to move as Indicated ,. This paper is based on the Ph.D. thesis of L. C. Hoskins, submitted to the Department of Chemistry, Massachusetts Institute of Teclmology, June 1965. . .. t Present address: Department of Chellllstry, Ulllversity of Alaska, College, Alaska 99735. 1 L. O. Brockway and J. Y. Beach, J. Am. Chern. Soc. 60, 1836 (1938). 2 K W Hansen and L. S. Bartell, Inorg. Chern. 4, 1775 (1965). 3 H: S. 'Gutowsky, D. W. McCall, and C. P. Slichter, J. Chern. Phys. 21, 279 (1953). . .. 4 E. L. Muetterties and W. D . .l'hillips, J. Am. Chern. Soc. SI, 1084 (1959). 6 R. S. Berry, J. Chem. Phys. 32, 933 (1960). in the center figure, they will eventually reach the posi- tions shown in the bottom drawing. Here the 2-3 axis has become a threefold axis, and the equatorial fluorines are Atoms 1, 5, and 6; that is, the original axial atoms 5 and 6 have exchanged places with the equatorial atoms 2 and 3. The motion given in the top part of Fig. 1 is a possible normal coordinate of species E' of Dsn. While there is no reason to suppose a priori that the force field of PF5 is such as to provide a normal coordinate exactly of this form, we can still represent the potential e~ergy of such a motion in terms of a single coordinate (Fig. 2). If the motion of Fig. 1 (top) were harmonic, its potential func- tion would be given by the parabolas (dashed lines) in Fig. 2. A more realistic potential, with the he~ght .of the barrier between the two DSh structures arbitrarily placed at about one-half the energy of the point of intersection of the two parabolas, is represented by the solid curve. Passage of the PF6 molecule from one side of this potential diagram to the other side interchanges axial and equatorial fluorines. Quantum-mechanical tunnel- ing is the process for this interchange for molecules occupying vibrational levels below the top of the barrier the tunneling rate increasing very rapidly for the higher levels. Of course for any molecule in a vibra- tional state above the barrier, an interchange occurs during each half of the vibrational cycle. One of the objectives of the present work was to locate in both PF6 and AsF5 the E' frequency which most nearly approximates the coordinate of Fig. 1, and to obtain as much information as possible from the spectra about the form of the potential curve of Fig. 2 for both molecules. II. EXPERIMENTAL The sample of PF6 used in this work was obtained from the Central Research Department, E. I. du Pont de Nemours and Company, through the courtesy of Muetterties. The sample was stated to be 96% PF5, 2402 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 VIBRATIONAL SPECTRA OF PF 6 AND AsF 6 2403 2.5% POFa, and 1 % PFa• It was used without further purification. The sample of AsF5, also obtained from Muetterties, was stated to have been distilled and of high purity. No further purification was attempted. The infrared spectra of PF6 and AsF6 vapor were re- corded from 2000-250 cm-I on a Perkin-Elmer Model 521 spectrophotometer, from 400-200 cm-I on a Beck- man IR-12 spectrophotometer, and from 250-30 cm-I with a small far-infrared spectrophotometer6 and also with a Beckman FS-520 Fourier-transform spectrom- ---------------~~ eter. Both the Model 521 and IR-12 were purged with V(cm- I) dry nitrogen to minimize the effect of water-vapor absorption, while the region from 250-30 cm-I was scanned under vacuum. Under survey scanning condi- tions the achieved resolution was about 1.5 cm-I from 2000-630 cm-I and about 3 cm-I from 630-30 em-I. In all high-resolution spectra above 630 cm-I, the spectral slitwidths were smaller than 0.5 cm-I . The wave- number calibration above 600 cm-1 was carried out with the help of the spectra of NHa, H 20, HeN, and CO2 under high resolution with a scale of 1.25 cm-1 per FIG. 1. Intramo- lecular exchange in XV, molecule of D8Io symmetry. 2 5 3 3 6 8 R. C. Lord and T. K. McCubbin, Jr., J. Opt. Soc. Am. 47, 689 (1957). -7T/12 D3h C4y FIG. 2. Potential-energy diagram for the displacements of Fig. 1 (splitting of lower levels greatly exaggerated). centimeter of chart paper.7 A "pip marker" was em- ployed to ensure that the chart position and the grating position lined up at all times. The reproducibility of the measured band wavenumbers ranged from about ±0.1 cm-1 for the sharp Q branches to about ±1 cm-I for the broad P and R branches. Below 600 cm-I the pure rotational spectrum of water vapor was employed for calibration.7 All spectra were studied with a cell of a lO-cm path length at gas pressures indicated on the figures. In the region 2000-400 em-I, a glass cell equipped with a Teflon needle valve and AgCI windows was used. The windows were sealed to the cell with a 1: 1 mixture of powdered Teflon and Kel-F stopcock grease. A metal cell with polyethylene windows and with an inner lining of Teflon was used to obtain the infrared spectrum of PF6 in the region 400-30 em-I. Because of the high reactivity of AsF5, Teflon windows were required, and only the region from 200-30 em-I could be scanned at high pressures. The cells were filled from a sampling system containing only Teflon needle valves, glass and metal. The gases were injected into the sampling system through a copper tube connected to the stainless-steel tank containing PF5 or AsF6• Both PF5 and AsF5 were found to be stable with respect to AgCI and Teflon, but both molecules slowly 1 (a) Tables of Wavenumbers for the Calibration of Infrared SPectrometers (Butterworths, Inc., Washington, D.C., 1961) i (b) See, for example, K. N. Rao, R. V. de Vore, and E. K. Plyler, J. Res. Natl. Bur. Std. U.S. A67, 351 (1963). This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 2404 L. C. HOSKINS AND R. C. LORD gro=---~9~~~---9~5~O-----94~O-----9~3-0----~9W WAVENUMBER CM-1 FIG. 3. Infrared band due to 1'3 in PF6 (pressure p=2 mm, path length 1= 10 em, approximate spectral slitwidth w=0.5 em-I). attack glass and Kel-F sealant, producing SiF4 and other impurities. The presence of SiF4 was shown by the growth of the SiF4 bands at 1031 and 390 cm-l • Small traces of water vapor were probably responsible for the appearance of HF in the PF6 sample and for a noticeable increase in the amount of POFs. The growth of a broad band at 690 cm-I in AsF. was possibly due to formation of AsOFa, but no HF was observed in any of the AsF. spectra. Polyethylene seemed stable to PF., but AsF. reacted rapidly with both high- and low- density polyethylene. The reaction resulted in the rapid growth of two bands with PQR structure centered at 337 and 263 em-I, which can clearly be assigned as the ~ eo I-z lJJ a: .... e; 60 .... z ~ t: 40 :;; (/) z « a: I- 20 WAVENUMBER CM- 1 8 L. C. Hoskins and R. C. Lord, J. Chern. Phys. 43, 155 (1965). 9 J. E. Griffiths, R. P. Carter, Jr., and R. R. Holmes, J. Chern. Phys. 41,863 (1964). 10 J. K. Wilmshurst and H. J. Bernstein, Can. J. Chern. 35, 911 (1957). V2 and V4 bands of AsFs.8 The reaction also produced a dark-brown liquid on the polyethylene windows. For this reason, it was possible to observe the infrared spec- trum of AsF. using polyethylene windows only if low pressures and fast scanning speeds were used. The Raman spectra of PF. and AsF5 were recorded in the liquid state with a Cary Model 81 Raman spectro- photometer and a low-temperature Raman cell similar to one described by Griffiths et al.9 The wavenumber calibration of the Raman instrument was checked with the accurately known lines of toluene.lO The major bands of the infrared spectra of PF. and AsF. are shown in Figs. 3-7, and the Raman spectrum of AsF5 in Fig. 8. The measured wavenumbers in cm-1 are listed in Tables I and II. The infrared and Raman spectra of PF6 have been reported most recently by Griffiths et al.,9 who summarized the previous work.11·12 Since our Raman results on PF. are in quantitative agreement with those of Griffiths et al.,9 only their Raman results are included in Table 1. However, there are several differences between their infrared results and those of the present study, which are compared in Table 1. Previous infrared and Raman work on AsF6 appears to be restricted to the dissertations of Akers18 and VondrakI4 at Vanderbilt University, which are as yet unpublished. A. Interpretation of the Vibrational Spectra of PF. and AsF. A trigonal bipyramidal XY6 molecule of D8h sym- metry has two At', two A2", three E', and one E" vibra- tional modes. The infrared-active vibrations are of A2" and E' species, and the Raman-active vibrations of At', E', and E" species. Thus the infrared spectrum FIG. 4. Infrared hands of 1'4 and 1'8 in PF5 (p=3 mm, 1= 10 em, w';£!J.7 em-I). 11 H. S. Gutowsky and A. D. Liehr, J. Chern. Phys. 20, 1652 (1953). 12 J. P. Pemsler and W. S. Planet, J. Chern. Phys. 24, 920 (1956). 18 L. K. Akers, Dissertation Ahstr. 15, 1638 (1955). 14 E. A. Vondrak, Dissertation Abstr. 26, 2278 (1965). This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 VIBRATIONAL SPECTRA OF PF 6 AND AsF 6 2405 100r-~-------------r------------~--------------r--------' FIG. 5. Infrared bands due to V7 in PF6 and impurities (see text; p~2 atm, 1=10 em, w~1 em-I). ~ 80 I- Z W U a: w ~ 60 w o Z 2406 L. C. HOSKINS AND R. C. LORD TABLE I. Infrared spectrum of PF6." Obs freq (em-1) 2045 1840.9 1836 1768 1759.9 1757.0 1751 1671.4 1666 1594 1587.4 1582.8 1578.4 1575.5 1576 1062 (1031 SiF4) 1027 1022 (988 POF.) 955 946.6 944.0 941.9 939.3 938 (667 CO,) 585 575.1 565 541 532.5 525 (400 SiF4 ) (390 SiF4 ) (378 SiF4) 300 This work Band type wb ~ } Wol ~ ) wll Q' p g,) wll Q" 0''' P VVW ~ } VS.L g, ) vslI Q" Q'" P i } mil ~ } mol P R Q P Q Raman line 1025 817 640 534 514 " p=poIarized; dp=depolarized; s=strong; m=medium; w-weak.; v=very; b-broad. purities (SiF4, POFa, HF) .15.18 Despite the fact that pressures of PF5 up to 2 atm were studied in a 10-cm cell, the only band found by us in this range that can be unequivocally attributed to PF, is the very weak peak at 300 em-I. Despite its unexpectedly high frequency and vanishingly small intensity, we follow Griffiths18 in assigning it to the degenerate axial bending lI'/ (e') , more from the lack of a suitable alternative than from con- viction. 11 L. C. Hoskins, J. Chem. Phys. 42, 2631 (1965). 11 J. E. Griffiths, J. Chem. Phys. 42, 2632 (1965). Griffiths et al.b •• Obs freqb Band type (em-I) 2030 1830 1764 1755 1665 1593 1584 1573 1457 1355 1346 1335 1271 1198 1061 1034 1026.4 1019.7 989 955.3 944.8 933.8 675 666 652 584.5 575.5 565 548 533 526 397 388 375 300.6 w w R Q w w R w Q w p w vvw R vvw Q vvw p vvw vvw vwb vvw R vs Q vs p vs m R vs Q vs p vs R w Q w p w R m Q m P m R m Q m P m R w Q w R w Assignment and calculated frequency (em-I) 2V6(AI'+ E') Vl+V6(E') va+vs(E') vl+va(E') v6(e') 1', (at") ",(al') ve(e') I's(e") (c) (c) (c) 1'7 (e') (2050) (1842) (1764) (1665) (1587) (1461) (1350) (1202) (1066) b The peaks originally observed by Griffiths el al. (Ref. 9) which were due to HF are not included. • Griffiths (Ref. 16) also assigned these peaks to SiF •. The extremely weak intensity of lI'/(e') can be under- slood a posteriori if one recognizes that during the normal vibration (Fig. 1, top), to a good approximation the two axial fluorines move through a distance r' Af3 (Fig. 9) and the two equatorial fluorines through rt:.a, the fifth fluorine and the phosphorus atom remaining almost stationary. The requirement of zero momentum then gives 2rt:.asina::=2r't:.{3, where a= 120°. Under the special assumptions that the change in molecular dipole moment t:.p. depends only on these four displacements, that r= r', and that identical partial charges 8 are 10- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 VIBRATIONAL SPECTRA OF PF 6 AND AsF, 2407 TABLE II. Infrared and Raman frequencies for AsF6•• Ohs freq (em-I) Band type Raman freq Intensity Polarization Assignment and calculated frequency (cm-I ) 1618 1549 1542.7 1541.5 1530 1520.1 1517.9 1516.0 1513.9 1508 1449 1437 1429.8 1429.0 1427.3 1424.8 1419 819 812.4 811.4 802 798 787.4 786.1 784.8 783.3 781.9 778 407 400.4 392 375 369 132 123 • See Footnote to Table I. ~ l:i Q' P+R Q I Q' ~:' wll Q } wi P+R Q" Q' I ~" wll R Q' Q P 1 "L ~ 1 Q' 8::, vs II Q'" P R Q P R P R Q (liq) (cm-I ) 809 733 642 388 366 100 r----.-----.--:-----,-----,-, .... z '" U II: ~ '" u z ~ .... i CI) Z 2408 L. C. H 0 SKI N SAN DR. C. L 0 KD o .., a: .., ... < (J) 1000 o • FIG. 8. Raman spectrum of liquid AsFi (w~15 cm-l). constants, and inertial parameters. From comparison of their contours with those observed for II.Ce') and 116Ce'), t6 and t8 are, respectively, 0.80±0.10 and 0.30±0.05. Together with the sum-rule value of unity,!7 these give N"-O.lO. The latter implies a P-R separation of about 20 cm-l for 117Ce'), which is in agreement with the observed value given by Griffiths.16 The Raman spectrum of PF. shows two polarized lines at 817 and 640 cm-l . The line at 817 cm-l is intense and can be assigned to the totally symmetric P-F stretching vibration 111 (at') , in which the equatorial and axial fluorines vibrate in phase, while the other line at 640 cm-l is much weaker and is assigned to the totally symmetric stretching 112Ca') ,with axial and equatorial fluorines vibrating out of phase. The line at 514 cm-l z 5 x . 6 FIG. 9. Coordi- nates of the XVi molecule. does not have an infrared counterpart and is therefore assigned to the degenerate bending IIsCe"). For sake of completeness, it may be reported that ra, determined by symmetry and the inertial parameters, is +0.43. The lines at 1025 and 534 cm-l have infrared coincidences and must be assigned to the E' stretching and bending II.Ce') and 116Ce'). No line has been observed in the Raman spectrum which can be attributed to 117C e'). Despite the uncertainty in the assignment of the fre- quency of 117C e'), the infrared and Raman spectra of PF6 can only be understood on the basis of D3h symmetry. 2. SPectrum of AsF6 There are two parallel bands in the infrared spectrum at 787.4 and 400.4 cm-l • The former is assigned to the TABLE III. Symmetry coordinates for an XY. molecule (D3A symmetry). Species Symmetry coordinate AI' Sl =3-112 (Llrt+Ll.r2+Ll.ra) S2 = 2-112 (Ll.r.+Ll.r6) SOl = 3-112 (Lla12+ Lla13 + Lla2a) ==0 redundan t coordinate SO' = 6-112 (Llj31.+Llj316+Llj32.+Llj326+Llj335+ Llj336) ==0 redundant coordinate Ai' S3 = 2-112 (Llro- Ll.ra) S. = 6-112 (Llj315- Llj31a+Llj32.- Llj326+Llj33i- Llj336) E' S6a = 6-112 (2Llr1-Ll.r2- Llr3) S5/>= 2-112 (Ll.r.-Llra) S6a = 6-112 (2Lla2a- Lla12- Lla1a) S~=2-112 (ila13-ila12) S 7a = 12-112 (2Llj31.- ilj32.- ilj336+2ilj316- Llj326- Llj336) S70= i (Llj32.-ilj33.+ Llj326- Llj3a6) E" S8.= 12-112 (2ilj316-Llj326-ilj33i- 2Llj316+Llj328+Llj3S6) S80 = i (Llj326- ilj335- Llj326+Ll.Bas) stretching mode 113Ca2"). The large number of "hot bands" occurring on the low frequency side of the main Q branch almost certainly arise from excited states of the low E' frequency 117 (e') . The other parallel band at 400.4 cm-l is assigned as the equatorial fluorine bending mode 114C~"). The three perpendicular bands are the high-frequency band at 811.4 em-I, which has a PQR structure and is assigned to the degenerate stretching mode lIoCe'); the band at 369 cm-l without PQR structure, which is definitely a perpendicular band and is assigned to the degenerate planar bending 116Ce'); and the degenerate axial bending mode 117 (e') , which occurs as a weak band with a Q branch at about 123 cm-l . The third band showed a minimum transmittance of 60% with 7S0-mm pressure in a 10-em cell. The Raman spectrum of AsF. shows two lines at 733 and 642 em-I, which can be assigned as the totally symmetric in-phase and out-of-phase stretching vibra- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 V I BRA T ION A L SP E C T R A 0 F P F & AND A s F 6 2409 TABLE IV. Elements of the F matrix for PF& and AsF,.·,b Fll =7.468 FI3=3.914 F66=4.966±1.20 Fss=2.082 F22=4.583 F«=2.999 F66 =2.019±0.40 F1F= Fu=O.700 F77= 1. 244±O. 14 F22=4.611 F«=1.930 AsF, F1F= Fll =6.011 FS3=4.305 F66=5.204±O.57 F8S=1.457 F6S= 1. 224±O.16 Fu==fJ F77=O.304±O.04 a P u , F2t, Fu, Faa, and Fi" are in millidynes per angstrom, FM, Fil and Fa; in millidynes and F .. , F .. , F", F" and F .. in millidynes·angstroms. tions I'l(al') and 1'2(al'), respectively. The former is very intense and sharp and has a depolarization ratio of 0.44, while the line at 642 cm-l is much less intense and much broader with a depolarization ratio of about 6/7. There are three depolarized lines at 809, 388, and 366 cm-l • The lines at 809 and 366 cm-1 have corresponding bands in the infrared and must be assigned as 1'6 (e') and 1'6(e') , respectively. The line at 388 cm-1 has no infrared counterpart and is therefore assigned as 1'8(e"). All attempts to observe the 1'7(e') line at 123 cm-1 failed. The infrared and Raman spectra of AsF6 are clearly in good accord with the postulated Dah symmetry. In principle the band contours for the three E' vibra- tions can provide numerical values of the zetas for these vibrations, as described above for PF6. Unfortunately the contours themselves are complicated by the presence of underlying 'hot bands" due to excited states of 1'7 (e'), and there is also considerable overlapping of 1'6(e') by I'a(~") and to a lesser extent of 1'6(e') by 1'4(a2"). Our best estimates are s6=0.24±0.OS and S6= 0.8±0.1. From these values and the zeta sum of unity for the E' species, S{ ...... -0.04, which leads to an esti- mated P-R spacing of 18 cm-l • The rather equivocal contour of 1'7(e') at least shows no contradictory fea- tures to this value of S7. The zeta value for the Raman-active 1'8(e") can be obtained from the molecular geometry and the sum rule: S8= 0.43. B. Force-Constant Calculations for PF5 and AsF. These calculations have been carried out by the standard Wilson FG-matrix method,20 with the sym- metry coordinates listed in Table III, and internal coordinates and G-matrix elements that have appeared several times in the literature.2l ,22 In the calculations on PF. the old P-F bond distancel of l.S7 A, the same for both axial and equatorial bonds, was used. The newer distances2 will make an inappreciable effect on the re- 20 E. B. Wilson, Jr. et al., Molecmar Vibrations (McGraw-Hill Book Co., New York, 1955). 21 L. C. Hoskins, Ph.D. thesis, Massachusetts Institute of Technology, June 1965. 22 P. C. van der Voorn, K. F. Purcell, and R. S. Drago, J. Chern. Phys. 43, 3457 (1965) and Ref. 19 cited therein. b The numbers following the E' force constants are ranges which are de- scribed in the text. suIts obtained. Since no internuclear distances have been reported as yet for AsF6, it was assumed that both As-F bond lengths were equal to 1.74 A from the bond distances in PFa, PF5, and AsFa of 1.S3S, l.S7, and 1.712 A, respectively. The force constants were deter- mined from an iteration procedure2a which uses the Jacobian matrix elements lih= (1/1'.) (Ol'i/oFh) to con- verge on a set of force constants which satisfies the vibrational secular equation. Since the force-constant problem is under determined for all species except E", exact solutions for the calculated force constants were obtained with the help of additional assumptions. The set of force constants always reproduced exactly the input (i.e., observed) frequencies for both PF5 and AsF5• The results are collected in Table IV. In Species At' the constant Fll has the maximum value of 7.468 mdyn/ A and F22 the minimum value 4.S83 when Fl2=0. Within the range F12=±0.8, Fll has values of 7.3S±0.12 and F22 , 4.70±0.12S. For Species A 2" imaginary solutions result unless Fa4 is larger than about 0.7, and for the range 0.7-1.0 in Fa4, Faa=4.30±0.38 and F«=2.79±0.16. An attempt was made to use the Teller zetas of the E' vibrations to impose further restrictions on the E' force constants. Even when the zeta values are in- cluded, the problem is still under determined by one datum, but this would appear preferable to the situation without them. It is well known24 that the zeta values are more sensitive to the off-diagonal than to the diagonal elements of the F matrix, which suggests the possibility that the diagonal elements might be deter- mined in a preliminary way from the frequencies, the off-diagonal elements then obtained from the zetas, and the whole process repeated to suitable self-con- sistency. Unfortunately in the present case we were unsuccess- ful in obtaining a self-consistent solution to the force- constant problem using both frequencies and zetas as 23 J. H. Schachtschneider and R. G. Snyder, Spectrochim. Acta 19, 117 (1963). We are greatly indebted to Schachtschneider and Snyder for giving us their computer program and detailed instructions relating thereto. 24 See, for example, R. C. Lord and I. Nakagawa, J. Chern. Phys. 39,2951 (1963). This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 2410 L. C. HOSKINS AND R. C. LORD input data. The shortage of one datum requires some a priori assumption about one of the off-diagonal ele- ments, and it may well be that the assumed values were incompatible with the requirement of a convergent solution and the observed values of the frequencies and zetas. For lack of a better procedure, we set the off-diagonal element F67 arbitrarily equal to zero and gave various values, not necessarily identical, to Fo6 and F67. When all three constants were equated to zero the diagonal constants have the values listed in Table IV, and the ranges shown are the outside limits to the values of F66, F66, and F77 when the values of F66 and F67 lie in the range +0.4 to -0.4. After the calculations for PF 6 had been completed, a similar set by Van der Voorn et al.22 appeared. The only case considered by them for Species E' was that for which F66=F67=F67=0, and their results for E' as well as the other species agree well with those listed in Table IV. The results for AsF6 shown in Table IV were obtained in the same manner as those for PF6. In Species AI' the constant Fll has a maximum value of 6.01 mdynj A while the minimum value of F22 is 4.61, both at F12 =0. At F12=±0.7, Fll=F22, and both are imaginary at larger values of I F121. Within the range F12=±0.5, Fl1 =S.90±O.lOS, and F22=4.71±0.10S. For Species A 2" imaginary solutions result for Fa4< -0.6. By anal- ogy with PF6, probably Fa4> O. For the range 0-1.0 in Fa4, Faa=4.67±0.37 and F«= 1.86±0.06. The meaning of the ranges given for FQ6, F66, and F77 in Table IV is the same as that described for PF6. C. Form of the Normal Modes of Vibration To determine the form of the normal modes Qi, we have computed the inverse eigenvectors L-1 and also the potential-energy distribution FiiL i),2 for each Q •. The results of the calculations are recorded in Ref. 21. When the assumption is made that F12 =O, the At' normal coordinates Q1 and Q2 are the same as the re- spective symmetry coordinates Sl, the axial symmetri- cal stretching, and S2, the equatorial symmetrical stretching (see Table III), though of course the calcu- lation of Q1 and Q2 from the two observed frequencies cannot determine which frequency belongs to which Qi. It appears from the strong intensity and low de- polarization of the Raman lines at 817 and 733 cm-l in PF6 and AsF6, respectively, that the normal coordinates of these two frequencies have contributions from both Sl and S2 moving in phase. The low intensity and high depolarization of the other AI' lines at 640 and 642 cm-1 suggest that their normal modes involve Sl and S2 moving out of phase. Moreover, since the axial P-F distance is some 0.04-0.05 A longer than the equatorial P-F distance,2 the higher AI' frequency should corre- spond to a normal coordinate containing a larger con- tribution from the equatorial symmetry coordinate. The normal coordinates of the A 2" and E' vibrations in both PF6 and AsF6 are strong mixtures of the corre- sponding symmetry coordinates even though the off- diagonal force constants for the E' vibrations in PF6 and the A 2" and E' vibrations in AsF6 are set equal to zero. In both molecules Qa is the out-of-phase motion of Sa and S4 while Q4 is the in-phase motion. For the E' species Q6 is approximately the in-phase motion of S6 and S6, Q6 the out-of-phase motion of S6 and S6, and Q7 the in-phase motion of S6, S6, and S7. Therefore it is futile to attempt to describe the normal coordinates for the A 2" and E' species as simple stretching or bend- ing motions. The normal coordinates Q6, Q6, and Q7 are of primary importance to the problem of intramolecular fluorine exchange in PF6 and AsF6. The inverse eigenvectors L-I of the simple valence-force approximation, along with the ranges introduced by changing the off-diagonal force constants as stated previously, are, for PF5, Q6= (2.S±0.S) S6+(0.8±0.4) S6+( -0.3±0.3) S7; Q6= (-2.7 ±0.4) S5+(3.0±0.3) S6+( -O.4±O.S) S7; and Q7= (1.3±0.3) S6+(1.6±0.2) S6+(4.6±0.1) S7. For AsF5, the same quantities are Q5= (3.6±0.3) S6+ (0.3± 0.4) S6+( -0.1±0.3) S7; Q6= (-1.4±O.4) S6+(3.8± 0.1) S6+( -0.2±0.2) S7; and Q7= (1.0±O.3) S6+(1.1± 0.2) S6+(S.S±0.0) S7. In view of the assumptions made about the force constants, these results show that the normal coordinates are not sensitive to the off-diagonal force constants, and thus the simple valence-force approximation is reasonably satisfactory for determin- ing the normal coordinates. D. Mechanism and Barrier Height for Intramolecular Exchange of Fluorine Atoms in PF 6 and AsF 5 The normal-coordinate calculations show that none of the normal vibrational modes represent the motion given by Berry" for the intramolecular exchange of fluorines (see Fig. 1). Therefore, a simple normal co- ordinate cannot be used as a basis for quantitative dis- cussion of the exchange process. In other words, the efficiency of fluorine exchange along any actual normal coordinate will be significantly less than that along the exchange coordinate Qex= (2)-1/2(S6a+S7a) where S6a and S7a are the symmetry coordinates for bending two axial and two equatorial P-F bonds, respectively. Berry has estimated the apparent tunneling fre- quency for PF5 at 106 secl by the admittedly crude procedure of placing its logarithm midway between the log of the inverse of the NMR line separation (chemical shifts) of the two types of fluorines and the log of a frequency in the mid-infrared spectrum. The latter limit was chosen because a "normal" infrared spectrum was observed, and therefore, presumably, the lifetime of the vibrational states is long compared with the period of the vibration. No attempt was made by Berry to estimate the height of the barrier for the P7(e') This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 VIBRATIONAL SPECTRA OF PFIj AND AsF Ii 2411 motion. However, he showed that the tunneling fre- quency Vt of an intramolecular motion varies roughly with Zo as where Vt""""exp[ - Zo2J(Zo)], Zo= (!J.Wo/'h) 1/2 R, (1) (2) R is the distance from the potential minimum to the potential maximum, !J. the reduced mass along the tunneling coordinate, and wo the angular vibrational frequency, Wo= 211"vo. The function j(Zo) is slowly vary- ing compared with Z02. Furthermore, it follows from Eq. (2) that if the value of Zo is known for one molecule, the value of Zo for another molecule having a similar tunneling coordinate can be calculated from the ex- pression Zo(A) / Zo(B) = (!J.AVOA/!J.BVOB)1/2(RA/ RB). (3) We have assumed thatj(Zo) is the same function of Zo for NFa, PF5, and AsF5 and have used Eqs. (2) and (3), along with the plot of logvt/vo vs Zo given by Berry5 for a barrier formed by the intersection of two parab- olas, to calculate the tunneling frequencies for PF5 and AsF5• The reduced mass was taken as the mass of a fluorine atom. The results of these calculations are given in Table V. The tunneling frequency for PF5 calculated by this procedure is approximately that estimated earlier by Berry.5 Although an exact calculation of the height of the barrier to intramolecular exchange of fluorine atoms in PF6 and AsF6 is not feasible, it is possible by using an appropriate force constant to set an approximate upper limit to the height of this barrier and to make a crude estimate of its magnitude. The potential energy of the extended v7(e') motion has a double-well form, in which the two potential-energy minima occur in the equilib- rium Dan structures and the maximum of the central barrier occurs at the intermediate C4• structure (see Figs. 1 and 2). The rate of fluorine exchange depends both on the vibrational excitation, as determined by the popUlation of the various levels below the maximum, and on the probability of tunneling from a given vibra- tionallevel. The potential energy of the C4• structure with respect to Dah (barrier height) can be approximated crudely as the potential energy where the two harmonic po- tential wells of each Dah structure intersect. The harmonic potential energy is V = kx2 /2, with k the appropriate force constant and x the displacement from equilibrium (Dah). In order for the molecule to pass from the Dah structure to the C4• structure the fluorine atoms must move through 15° with a displacement of x=rAa, where r is the P-F or As-F bond distance and Aa is equal to 15° or 11"/12 rad. The intersecting barrier height is then given by V=AE=!kr2Aa2=!k'(fi1l")2, (4) TABLE V. Molecular data and tunneling frequencies. R (A) vo (em-I) p. (arou) Zo v, (seCI ) NFa 0.62 505 11.24 5.98 2.3XI0-2 0.42 300 19.0 4.07 3XI0' 0.46 131 19.0 2.91 9X108 where k'=kr2. In terms of kilocalories per mole Eq. (4) can be written as AE in kilocalories per mole= 4.93 k', if k' is expressed in millidyne angstroms per molecule. The only necessary quantity for calculating the height of the barrier AE to this approximation is the force constant k'. Since the motion for the exchange of the fluorine atoms involves the bending of both the axial and equatorial bonds along symmetry coordinates SSG and S7a, respectively (d. Fig. 1), one might expect the maximum value for the force constant for the exchange motion to be set by the larger of the two bending force constants F66 or F77• However, because the true barrier height is expected to be less than the height at the inter- section of the two harmonic potential curves, the true height is probably no more than one-half the intersec- tion value. The lower limit of k' will be set by the smaller of the two bending force constants and again the actual barrier height for the exchange motion is expected to be less than about half the intersection value. Table VI lists the calculated barrier heights for PF5 and AsF5 for the above four cases, along with the Boltzmann factors exp( -1000AE/ RT) at the barrier maximum. The exchange of fluorine atoms in PF5 and AsF5 can occur by two paths: (1) exchange by quantum-me- chanical tunneling as stated previously; (2) exchange by means of a collision process, i.e., by imparting sufficient energy to the molecule by means of molecular motion to "knock" it over the barrier. This process involves exciting the molecule to a vibrational state which lies above the barrier maximum which then passes to the exchanged form during the normal vibration. The mechanism principally responsible for the ex- change will of course be the process with the faster ex- change rate. The tunneling frequency for a given level is independent of temperature while the kinetic process is temperature dependent and can be considered as a rate process with the exchange rate per molecule being given by v(sec1) = (kT/h)exp( -1000AE*/RT)exp(AS*/ R), (5) where k is Boltzmann's constant, h Planck's constant, AE* the barrier height (i.e., AE) in kilocalories per mole, and AS* the entropy difference between the Dah and C4• structures. Since there is a reduction in sym- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07 2412 L. C. HOSKINS AND R. C. LORD TABLE VI. Barrier heights and Boltzmann factors for PF6 and AsF&. Force constant Barrier (AE) used to eval. barrier (kcal/mole) (em-I) PF& F66 9.95 3480 F77 6.14 2145 F66/2 4.99 1745 F77/2 3.06 1070 AsF& F66 6.04 2110 F77 1.50 525 F66/2 3.02 1055 F77/2 0.75 262 metry number on passing from the D3h to the C4v struc- ture, ~S* will presumably be positive and of the order of unity; i.e., the entropy factor will lie in the range of 1-10, but closer to 1. Hence the last factor can be dis- regarded if one is only concerned with an order-of- magnitude estimate. The exchange rates calculated for various barrier heights for PF6 and AsF6 are given in Table VII. T ABLE VII. Exchange frequencies for PF 6 and AsF 6.· v (sec-I) Barrier AE (kcal/mole) T=100oK T=200oK T=300oK PF& 9.95 3.7XI0-IO 5.6X101 3.6XlO& 6.14 8.2XI0--2 8.2XIQ6 2.2XI08 4.99 2.6XI01 1.5XI07 1. 5X 109 3.06 4.3XI0& 1. 9X 109 3.7XI0'o AsF, 6.04 1.4XIQ-I 1.1X106 2.6XIQ8 1.50 1.1XIQ9 9.5XI01O 5.0XIOl1 3.02 S.3XIQ6 2.1XIQ9 4.0XIOlo 0.75 4.8XI01o 6.3XIOl1 1.8XI012 a Calculated on the assumption that exp(AS·/R)rvt. Boltzmann factor T=I00oK T=200oK T=300oK 1.8XI0~ 1.4XIQ-11 5.8Xl~ 4.0XlO-14 2.0XlO-'1 3.5XI0-i 1.3XlO-11 3.6XlO-i 2.3XIQ-"'4 2.1XIQ-'1 4.6XlO-4 6.0XlO-3 6. 6X 10-14 2. 6X 10-'1 4.2XlO-i 5.2XIQ-"'4 2.3XI0--2 8.1XI0-2 2. 6X 10-'1 5. IX 10-4 6.4XI0-3 2.3XlO-2 1.5XlO-1 2.9XIQ-I Comparison of these results with the calculated tunneling frequencies of Table V shows that at T= 2000K (the approximate temperature of liquid PF6 and AsF6) or higher, the exchange rate is probably dominated by the kinetic exchange process. At 100oK, however, the kinetic and tunneling frequencies are about the same, and a choice of exchange mechanism is not possible. Below 1000 K the exchange will probably be dominated by the tunneling process. Observation of the 19F NMR resonance peaks for both axial and equatorial fluorines in PF6 and AsF6 is only possible if the exchange rate v~~vNMR"'-'102-103 sec-I, where ~VNMR is the difference in the resonant frequencies for the two types of fluorine. It is evident from the above discussion that the lower limit of the exchange rate is set by the tunneling frequency Vt. Therefore, since in both PF6 and AsF6 the slowest ex- change rates (the tunneling frequencies) are about 106 and 1010 sec-I, respectively, separation of the two NMR peaks due to the different types of fluorines will not be possible. ACKNOWLEDGMENTS This work was supported in part by NSF Grant GP· 2111. We thank Dr. E. L. Muetterties of the du Pont Company for several samples of PF6 and AsF5• This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.114.34.22 On: Tue, 25 Nov 2014 06:43:07