Physical Chemistry
The Journal of
~~
Q Copyright, 1982, by the American Chemical Society
VOLUME 86, NUMBER 5
MARCH 4,1982
Pseudorotation in Chiorocyclopentane As Determined by Gas-Phase Electron Diffraction Richard L. Hliderbrandt Depertment of Chemlstty, North Dakota State Unhwsiiy, Fargo, North Dakota 58105
and Quang Shen Depertmnt of Chemistry. &/gate Universiiy, Hamilton, New Vork 13346 (Received:Ju& 13, 1981; In Final Form: October 22, 1981)
The structure and pseudorotational potential function for chlorocyclopentane have been determined by gas-phase electron diffraction. The diffraction data at 295 and 387 K indicate the presence of both axial and equatorial conformers with a slight preference for the axial form. The best agreement with the diffraction data is found for a model with a pseudorotational potential function of the form (V1/2)(1 + cos 4) + (V2/2)(1+ cos 24)where 4 is the pseudorotational phase angle. At 295 K the values of Vland V, were found to be 0.45 (15)and 2.0 (1.5)kcal/mol respectively, while at 387 K the best fit values obtained for VI and V, were 0.12 (15)and 1.4 (0.5)kcal/mol. The thermal average puckering amplitudes for the five-membered ring were found to be 0.394 (35)A at 295 K and 0.429 (30)A at 387 K. At both temperatures the best agreement with the experimental data was obtained when the pseudorotational trajectory was assumed to be slightly elliptical. These results are discussed in the context of previous infrared and microwave spectroscopic studies on the molecule.
Introduction Thermodynamic studies by Aston and co-workers1 provided the first experimental evidence for the nonplanarity of the cyclopentane ring. Later calculations by Kilpatrick, Pitzer, and Spitzer2 suggested that the nonplanar ring also underwent a large amplitude motion in which the puckered atom moved freely about the ring from one position to the next. They referred to this motion as pseudorotation since in the third-law entropy calculations it was included as an additional rotational degree of freedom rather than as a vibration. A more detailed treatment of the nature of the pseudorotational motion has been given by Harris et aL3 The motion is most easily visualized in terms of a two-dimensional potential energy surface involving a puckering and (1)J. G.Aston, S. C. Schwann, H. L. Fink, and P. M. Doty, J. Am. Chem. SOC.,63,2029(1941);J. G. Aston, H. L. Fink, and S. C. Schwann, ibid.. 341 (1943). - , 66. (2) J. E. Kilpatrick, K. S. Pitzer, and R. Spitzer, J. Am. Chem. Soc., 80, 6697 (1968);69,2483 (1947). (3)D.0.Harris, G. G. Engerholm, C. A. Tolman, A. C. Luntz, R. A. Keller, H. Kim, and W. D. Gwinn, J . Chem. Phys., SO, 2348 (1969). I
.
~
-
~
~
twisting motion of the planar ring. Owing to the instability of the planar ring to puckering and twisting deformations, both of these motions are found to exhibit double minimum one-dimensional potential functions which are coupled with each other. Transformation of this two-dimensional potential function from rectilinear coordinates into plane polar coordinates results in a definition of two new large amplitude vibrational coordinates: a radial coordinate, q, and a polar coordinate, 4, which is the phase angle for pseudorotation. For cyclopentane the potential energy is readily separable in these new coordinates. The radial motion is characterized by a double minimum quartic potential function with a relatively large barrier at q = 0, while the potential function along the circular pseudorotational trajectory is essentially flat. A number of models have been proposed which relate the instantaneous five-membered ring geometry to the puckering amplitude and pseudorotational phase angle. One such model4 gives the perpendicular displacements
I
0022-3654/82/2086-0587$01.25/0
(4)D. Cremer and J. A. Pople, J . Am. Chem. Soc., 97,1354 (1975). Equation 1 is a minor modification of the equation suggested in ref 2. They differ by a factor of 2 in the phase angle.
0 1982 American Chemical Society
588
Hilderbrandt and Shen
The Journal of Physical Chemistry, Vol. 86, No. 5, 1982
of the atoms, zj, relative to a planar reference confiiation as Z;
= (2/5)'"q
COS
( 4 d j - 1)/5
+ 61
(1)
Between = Oo and C#J = 360" a total of ten equivalent envelope conformations occur at I#I = Oo, 36O, 72O, ..., and ten corresponding twist conformations occur at C#J = 18O, Another model which has been suggested5 54", 90°, gives the torsional angles for the ring in terms of a twisting amplitude T~ and the phase angle 6 as
....
~j
=
T O COS
(4d.j - 1)/5
+ $1
(2)
In this equation T~ is the maximum value of the twist angle found in the C2 twist conformation of the ring. Using various empirical molecular mechanics models, several investigators have found values of T~ ranging from 42 to 48".6-9 A number of ab initio,lOJ ~emiempirical,'~-'~ and molecular mechanics calculationsw have been performed on cyclopentane. In general, all of these techniques agree that the energies of the C2and C, forms are essentially identical. For example, Lifson and WarsheP obtained an energy difference of only 5 cal/mol between the C2 and Cs conformers using a molecular mechanics consistent force field approach. Adams, Geise, and Bartell15have studied the structure and pseudorotation of cyclopentane by gas-phase electron diffraction. Using a model derived from eq 1 they determined a mean value of the puckering amplitude, q, of 0.427 A,and an equilibrium value of 0.437 (73) A. This value is somewhat smaller than the spectroscopic estimates of q which range from 0.47 to 0.48 When one or more substituents are attached to the cyclopentane ring, the pseudorotation becomes restricted, and certain conformers become energetically preferred. Although several possibilities exist, it is generally accepted that monosubstituted cyclopentanes prefer a puckered C, form with the substituent in either the axial or the equatorial position. Empirical force field calculations by Altona and co-w~rkers'~ on monohalogenated cyclopentanes indicate a slight preference for the axial form of the substituted molecule. Monosubstituted cyclopentanes have been extensively studied by infrared and Raman spectroscopy. Liquidphase infrared spectra obtained by Riesse et a1.20on the chloride, bromide, and iodide compounds suggested the presence of a large number of conformers as a result of (5)C. Altona, H. J. Geise, and C. Romers, Tetrahedron, 24,13(1968). (6)K.Pitzer and W. E. Donath, J. Am. Chem. Soc., 81,3213(1959). (7)J. B. Hendrickson, J. Am. Chem. Soc., 83, 4537 (1961). (8)S. Lifson and A. Warshel, J. Chem. Phys., 49,5116 (1968). (9)N. L. Allinger, J. A. Hirsch, M. A. Miller, I. J. Tyminski, and F. A. Van Catledge, J.Am. Chem. Soc., 90,1199(1968);N. L. Allinger, M. T. Tribble, M. A. Miller, and D. W. Wertz, ibid., 93,1637,(1971). (10)J. R. Hoyland, J. Chem. Phys., 50, 2775 (1969). (11)D. Cremer and J. A. Pople, J. Am. Chem. SOC.,97,1358 (1975). (12)R. Hoffman, J. Chem. Phys., 39, 1397 (1963). (13)H.Cambron-Bruderlein and C. Sandorfy, Theor. Chim.Acta, 4, 224 (1966). (14)T. R. Ferfuson and C. L. Beckel, J. Chem. Phys., 59,1905(1973). (15)W. J. Adams, H. J. Geise, and L. S. Bartell, J. Am. Chem. Soc., 92,6013 (1970). (16)J. R. Durig and D. W. Wertz, J. Chem. Phys., 49,2118 (1968). (17)R. Davidson and P. A. Warsop, J. Chem. SOC.,Faraday Trans. 2,68, 1875 (1972). (18)L. A. Carreira, C.J. Tiang, W. B. Person, and J. N. Willis, J. Chem. Phys., 56, 1440 (1972). (19)C. Altona, H. R. Buys, and E. Havinga, Recl. Trau. Chim., Pays-Bas, 85,973 (1966). (20)J . Reisse, L.Naaels. and G. Chirudoalu. - Bull. SOC.Chim.Bela., 74,162 (1965).
pseudorotation. In another study, Buys et a1.21have interpreted the observed C-C1 and C-Br stretching frequencies as evidence for an envelope conformation with the halogen in the axial position. Infrared and Raman phase-dependent studies by Ekejuiba and Hallam22,23 suggested that for the fluoride and chloride both axial and equatorial forms were present while for the bromide and iodide only the axial form was observed. Durig and cow o r k e r investigated ~ ~ ~ ~ ~ ~ the temperature dependence of the infrared and Raman spectra of the ring puckering and C-X stretching modes in cyclopentyl chloride and bromide. They interpreted their results in terms of a mixture of axial and equatorial conformers with a relatively low pseudorotational barrier. They estimated an energy difference between the axial and equatorial conformers of 344 (23) cal/mol for the chloride and 612 (48) cal/mol for the bromide. Loyd, Mathur, and Harmony26have also investigated the microwave spectrum of chlorocyclopentane. The only rotational lines which they observed could be attributed to the axial form of the molecule even though an extensive search was made for evidence of the less stable equatorial conformer. Since the dipole moment of the equatorial form is larger than that of the axial form, it should have a relatively intense spectrum. For this reason they concluded that an equatorial conformer would have been observed if the energy difference between axial and equatorial forms was less than 800 cal/mol. They were also able to assign vibrational satellites up through u = 4 for the pseudorotational quantum number of the axial form. Line intensity measurements indicated an approximate energy level spacing of 150, 150,40, and 40 cm-l. More recently Choe and Harmony2' have also studied the microwave spectrum of cyanocyclopentane. In this molecule both axial and equatorial conformers were observed with an estimated energy difference of aE = 0 (200 ) cal/mol. In the present study results are presented for an electron diffraction investigation of the structure and pseudorotational potential function for chlorocyclopentane. It was hoped that such a study would help to clarify the disagreement between the interpretation of the infrared studies by Durig and c o - w ~ r k e r sand ~ ~ ,the ~ ~ microwave results obtained by Loyd, Mathur, and Harmony.26 Chlorocyclopentaneshould be well suited for such a study. Since chlorine is a strong electron scatterer, it was felt that the conformational-dependent features would be strongly evident in the radial distribution curve for the molecule, and that it would be relatively easy to observe even a small mole fraction of the less stable conformer. Experimental Section A sample chlorocyclopentane obtained from Chemical Procurement Co. (purity, 99%) was used without further purification. Electron diffraction data were collected on the North Dakota State University electron diffraction instrument at nozzle-to-plate distances of 240 and 95 mm. Complete sets of data were obtained at nozzle temperatures of 295 and 387 K. The accelerating voltage used was (21)H. R. Buys, C. Altona, and E. Havinga, Recl. Trau. Chim., Pays-Bas, 87,53 (1968). (22)I. 0.C.Ekejiuba and H. E. Hallam, J.Mol. Strut., 6,341(1970). (23)I. 0.C.Ekeiiuba and H. E. Hallam, Spectrochim. Acta, Part A, 26, 59, 67 (1970). (24)J. R. Durig, J. M. Karriker, and D. W. Wertz, J.Mol. Spectrosc., 31, 237 (1969). (25)W. C . Harris. J. M. Karriker. and J. R. Durig, - J.Mol. Struct., 9. 139 (1971). (26)R.Lovd. S.N. Mathur. and M. D. Harmonv. J. Mol. Soectrosc., 72,359 (1978. (27)J. Choe and M. D. Harmony, J. Mol. Spectrosc., 81,480 (1980).
The Journal of Physical Chemistry, Vol. 86, No. 5, 1982 589
Pseudorotation in Chlorocyclopentane
40 keV, and the background pressure was maintained at
1.0 X torr during exposure. Exposure times for the 0.3-pA beam current were 60 s for the long distance plates and 150 s for the short camera length plates. Kodak 4 X 5 in. electron image photographic plates were used. Approximate voltage/distance calibrations were made with a digital voltmeter and cathetometer, but all final scale calibrations were based on benzene calibrations%[r,(C-C) = 1.397 (4) A] which were obtained under conditions identical with those used for the sample. The photographic plates for each temperature and camera length were used in the analysis. The photographs were traced on the NDSU microcomputer controlled densitometer with data being collected at intervals of 0.150 mm. The data were corrected in the usual manner for emulsion saturation, plate flatness, and sector imperfections after which they were interpolated at integral values of q [(40/X) sin @/a)]for analysis. The data were analyzed by using a least-squares procedure similar to the one employed by Gundersen and HedbergB with elastic scattering factors and phase shifts calculated by Schaffer, Yates, and Bonham.% Anharmonicity corrections were made on the basis of the following assumed Morse anharmonicity arameters: a(C-H) = 2.5 A-l, a(C-C) = a(C-Cl) = 2.0
1-l.
Molecular Mechanics Calculations Molecular mechanics calculations have previously been reported for chlorocyclopentane by Altona and co-worke r ~ They . ~ ~calculated a 5.21 kcal/mol energy difference between the planar form of the ring and the envelope conformer. They also estimated the pseudorotational barrier height to be approximately 1.13 kcal/mol. In order to further screen possible models for the electron diffracion analysis, another series of molecular mechanics calculations were performed on chlorocyclopentane with the program EMIN which has been written in our lab~ratory.~ In~these calculations the entire pseudorotational pathway was explored in order to ascertain the detailed nature of all of the stationary points along the trajectory. The force field used and the results obtained are shown in Table I. Only three stationary points were located along the pseudorotational pathway. The two C, envelope conformations were both found to be minimum energy forms having all positive eigenvalues of their Cartesian force constant matrices. The C2, or twist conformation, was found to be a transition state separating the two C, forms and having only one negative eigenvalue of its force constant matrix. It was also found that the potential energy varied smoothly as a function of the pseudorotational phase angle 6,and that it could be precisely expressed by a two-term Fourier series. The axial C, form was found to be 350 cal/mol more stable than the equatorial form, and the barrier to pseudorotation was estimated to be 1.17 kcal/mol. These results are in surprisingly good agreement with the experimental results of Durig and ~ o - w o r k e r as s ~well ~ as the previous results of Altona et al.19 Vibrational Analysis Although the infrared and Raman spectra of chlorocyclopentane have been studied by several investigators,*% no force field has previously been reported for this molecule. A simplified Urey-Bradley force field for (28)K. Tamagawa,T.Iijima, and M. Kimura, J.Mol. Struct., 30,243 (1976). (29)G.Gundersen and K. Hedberg, J. Chem. Phys., 51, 2500 (1969). (30)L.Schaffer, A. C. Yates,and R. A. Bonham, J . Chem. Phys., 65, 3055 (1971). (31)R. L. Hilderbrandt, Computers Chem., 1, 179 (1977).
TABLE I : Molecular Mechanics Calculations for Chlorocyclopentane Force Field force constant C-C str C-H str C-Cl str CCC bend CCH bend HCH bend CCCl bend HCCl bend -CH,-CH, tors -CH,-CHCltors H-.H C...C C-.C H...Cl C-.Cl
R', a'
value 631 kcal/A 655 kcal/A 524 kcal/A 1 6 3 kcal/rad 94.4 kcal/rad 79.2 kcal/rad 11 8 kcal/rad 1 0 2 kcal /rad 2.60 kcal/rad
1.540 A 1.095 A 1.814 A 109.5" 109.5" 109.5" 109.5' 109.5"
3.20 kcal/rad Nonbonded Terms 2367 exp(-4.00r) - 49.2/r6 13333 exp(-4.00r) - 126/r6 74822 exp(-4.00r) - 325/r6 27314 exp(-3.88r) - 352/r6 153278 exp(-3.88r) - 905/r6 Geometries
c,-c,,A c,-c,, c,-c,,a 2%
C-H, A c-Cl, a L 51 2, deg 1123, deg i234, deg L HCH,, deg LCCH,, deg LCCCl, deg ' 1 1 3 4 3 deg 7 2 3 4 5 , deg 3451 7 deg 5123, deg '45129 deg flap, deg energy, kcal
' '
axial
equatorial
twist
1.535 1.541 1.545 1.095 1.814 103.6 104.9 106.3 110.3 110.0 109.6 -22.2 0.0 22.2 35.9 -35.9 36.2 0.00
1.534 1.541 1.545 1.095 1.814 103.7 104.7 106.4 110.4 110.1 111.7 23.2 0.0 -22.2 -36.0 36.0 36.4 0.35
1.545 1.537 1.534 1.095 1.814 106.5 105.8 104.1 110.4 110.4 110.4 -29.8 37.8 31.4 10.3 12.3 1.17
chlorocyclopentanewas therefore determined by fitting the observed vibrational freuencies assigned by Durig and c o - ~ o r k e r s . ~As~ *a ~starting ~ point in the analysis the Urey-Bradley force constants for alkanes determined by Schachtschneider and Snyder32were used in conjunction with Shimanouchi's33Urey-Bradley force constants for the halogenated portion of the molecule. The force constants were refined by using a least-squares analysis program written in our laboratory. In the course of the refinement, a few minor modifications in the assignments of Durig and co-workers were made. The final force field and calculated vibrational frequencies are shown in Table 11. The overall agreement is about as good as can be expected for a simple Urey-Bradley model, and should be adequate for the calculation of vibrational amplitude and shrinkage corrections. Calculated vibrational amplitudes, lij's, and shrinkage corrections, K,i.'s,for some of the more important internuclear distances in the axial C, conformer are shown in Table 111.
Electron Diffraction Analysis Rigid Model Analysis. The first model investigated for chlorocyclopentane was one involving a weighted mixture of axial and equatorial conformers. In this analysis the following geometrical parameters were used to define the (32)J. H.Schachtschneiderand R. G. Snyder, Spectrochim. Acta, 19, 117 (1963). (33)T.Shimanouchi, J. Chem. Phys., 17, 245,848 (1949).
The Journal of Physlcai Chemistty, Vol. 86, No. 5, 1982
590
Hliderbrandt and Shen
n
TABLE 11: Force Field for Chlorocyclopentane force constanta
value
force constant
Y
value
Fcc 0.260 2.32 FHH 0.046 4.1 0 FCH 0.566 Kcc1 2.24 FCCl 0.493 Hccc 0.554 FH C1 0.681 HCCH 0.317 KcHz -0.012 Hccc1 0.511 "CCl 0.100 CHCl 0.078 Htors 0.101 HHCH 0.51 3 Calculated and Observed Frequencies for Chlorocyclopentane KCC KCH
A' species assignment QCH str
w m str BCH, asym str BCH, sym str YCH, sym str YCH, def BCH, def BCH, wag QCH bend ~ C H twist , YCH, twist YCH, wag ring def ring def BCH, rock breathing YCH, rock C-Cl str ring def C-CI bend pseudorot YCH,
A" species
obsd
calcd
assignment
obsd
calcd
2992 2978 2925 2879 2862 1466 1444 1329 1315 1281 1209 1174 1141 1004 938 888 760 713 588 352 115
3001 2945 2922 2915 2891 1475 1438 1365 1309 1251 1205 1181 1128 987 947 877 780 682 595 345 131
YCH, w m str
2978 2925 2918 2879 1461 1435 1425 1317 1246 1209 1150 1136 1029 908 813 586 320 188
2933 1921 2918 2904 1470 1437 1375 1306 1247 1213 1173 1121 1025 945 786 566 331 197
YCH, sym str B ~ I asym , str BCH, sym str YCH, def BCH, def BCH, wag YCH, wag BCH, twist y cH, twist LYCHbend
ring def YCH, rock ring def YCH, rock ring def C-C1 bend radial mode
a Stretching force constants have units of mdyn A - l , bending and torsional force constants have units of mdyn A , nonbonded Urey-Bradley force constants have units of mdyn and intermolecular tension constants have units of mdyn A. Observed frequency assignments were taken taken from ref 25 with minor modifications where necessary. The quoted assignments are based on the magnitudes of the potential energy distribution values obtained from the normal coordinate calculation.
Fbure 1. The prlnclpal conformations of interest on the pseudorotationai trajectory for chlorocyciopentane. I
I
n
I
OlFF
I
I
I 30
I
c
2 0
I
u0
5Io
Rial
Flgure 2. Radial distribution function for chlorocyclopentaneat 295 K.
I
-
I
TABLE 111: Calculated Parallel and Perpendicular Vibrational Amplitudesa distance
c-c
c...c c-c1 C,...Cl C,...Cl C-H C...H,,, H;..CI a
295 K 387 K Eij x l o 4 Kij x l o 4 lij x l o 4 Kij x l o 4 49 520 529 59 33 67 3 27 711 525 44 505 36 721 21 785 26 1390 8 1570 9 789
189
790
206
1037 1064
133 76
1047 1077
155 85
'yl
i/\
a -
lij parameters are the parallel vibrational amplitudes in
A , and correspond to ( A Z ~ ~ ~ )Kij ~ ' parameters ~ . are the perpendicular vibrational amplitudes in A , and correspond
to
b:
- I
((AXij')
+ (Ayij2))/2rij.
-
--
i 1 t
c
1
2'c
30
--
-
OIFF
1
u0
5'0
Rib1
model: (1)an average C-C bond length for the ring, (2) an average C-H bond length, (3) the C-Cl bond length, (4) the Cz.**C4nonbonded distance, (5) the LClCC valence angle, (6) an average LHCC valence angle, and (7) the flap angle CY formed by C1C2C5and C2C3C4C5planes. In addition the following seven amplitude parameters were also
Figure 3. Radial distribution function for chlorocyclopentaneat 387 K.
varied in the analysis: C-H, C-C, C-C1, C-Cgem,Cz-.C1, C3-Cl, and C-H,,. The conformations of interest are shown in Figure 1.
The Journal of Physicel Chemistry, Vol. 86,No. 5, 1982 591
Pseudorotation In Chlorocyclopentane
TABLE IV: Structural Parameters for Chlorocyclopentane As Determined by Least-Squares Analysisa model I
model I1
387 K parameter 295 K 387 K 1.090 (4) C-H 1.096 (4) 1.090 (5) 1.543 (1) c-c 1.542 (1) c-c 1.542 (1) c-Cl 1.810 (4) 1.812 (4) c-Cl 1.809 (6) 105.1 (4.9) L HCH 101.4 (3.4) C;-C, 2.464 (3) L HCCl 111.9 (1.6) 110.6 (1.5) 113.1 (1.1) iCCH 0.429 (30) LfCCl 4oc 0.394 (35) 110.6 (0.5) cy 39.4 (1.7) 41C -0.04 (9) -0.10 (5) 0.057 (1) 0.048 (1) qc-C) l(C-C) 0.049 (1) 0.075 (5) 0.064 (8) 1(C.*.c ) l(C-.C) 0.071 (4) 0.062 (3) 0.065 (3) l(C-C1) l(C-Cl) 0.065 (4) 0.078 (4) 0.092 (4) l(C,.*.Cl) 1( C,.-Cl) 0.089 (5) 0.181 (45) 0.159 (28) l(C,-.Cl) 1( c ;..C1) 0.265 (44) 0.070 (4) 0.070 (3) l(C-H) I( C-H) 0.070 (4) 0.107 (7) 0.120 (8) 0.124 (11) l(C*.*H) I( C*.*H) 0.45 (15) 0.12 (15) wax 0.52 (16) VI 2.0 (1.5) 1.4 (0.5) we, 0.48 (16) v, Distances are rg values in angstroms, and angles are r, values in degrees. Vibrational amplitude parameters are also in The angstroms. V , and V , are in kcal/mol. a is the flap angle between the C,C,C,C, plane and the C,C,C, plane. parameter C-H
295 K 1.096 (4) 1.541 (1) 1.810 (4) 2.467 (2) 112.5 (0.7) 110.3 (0.3) 35.9 (1.6) 0.057 (1) 0.077 (3) 0.062 (3) 0.077 (3) 0.273 (35) 0.070 (3) 0.110 (7) 0.64 (12) 0.36 (12)
puckering amplitude is given by q = q o + q1 cos @ where cp is the pseudorotational amplitude.
At first a single conformer model involving only the axial conformer was tried. This model, while it fit the data much better than an equatorial model, did not reproduce the region of the radial distribution curve around 4.0 A. The radial distribution curves (Figures 2 and 3) indicate two pronounced features a t 3.2 and 4.0 A which may be attributed to the nonbonded C3.-C1 distances for the axial and equatorial conformers, respectively. A careful inspection of these two peaks also reveals that as the temperature is increased from 295 to 387 K the peak at 3.2 A decreases in size while the peak at 4.0 A becomes more pronounced. This may be taken as conclusive evidence for the presence of two conformers in chlorccyclopentane, and it also indicates that the lower energy form is indeed the axial form. Next a two conformer model was tried in which the mole fractions of the axial and equatorial conformers were varied. Introduction of the second conformer greatly improved the agreement with the experimental data, particularly in the region of the radial distribution curve around 4.0 A. The axial/equatorial ratios obtained in these refinements were 64/36 (12)% at 295 K and 52/48 (16)% a t 387 K. The complete set of structural parameters obtained for this model are shown in Table IV under the heading model I. The equilibrium constants when translated into free energy differences yield values of AGOB6 = 340 cal/mol and AGOs7 = 60 cal/mol. Pseudorotational Model Analysis. In order to investigate a pseudorotating model for chlorocyclopentane, it became necessary to devise a suitable set of expressions for the Cartesian coordinates of the cyclopentane ring as a function of the puckering amplitude, q, and the pseudorotational phase angle, 4. Equation 1 gives the perpendicular displacements, zj, for such a model; however, if the radial displacements, x j and yj, are not also adjusted as functions of 4, the lengths of the C-C bonds in the ring vary over a wide range during the pseudorotation. What was needed was a model which constrained the ring distances to some fixed average value while the perpendicular displacements varied according to eq 1. If one assumes that the motion of the carbon atoms in the ring is confined to lie in the five symmetry planes of the planar ring, then a pseudorotating model can be generated which satisfies eq 1and also constrains the five C-C distances to a single value. If we define rj as the distance from the center of the planar five-membered ring to the j t h atom in the distorted ring, and if the angle between
the projections of the vectors r; and rj+lonto the reference plane is 2?r/5, then the distance between atoms j and j + 1 is given by the equation
rjj+12= r t
+ rj+12- 2rjr;+l COS (2?r/5) + (2;
- ~ ; + 1 ) ~(3)
If these five simultaneous nonlinear equations are solved for the r; distances, then the Cartesian coordinates of the ring atoms are given by x j = r; sin ( 2 ~ 0-' 1)/5) (4)
y; = r; cos ( 2 ~ 0-' 1)/5) z j = ( 2 / 5 ) ' / 2 q COS (4~0' - 1)/5
+ 4)
The simultaneous equations in (3) are not readily soluable in their original form; however, they can be solved quite easily if they are linearized by setting
r; = ro + Ar;
(7)
By choosing ro to be the radius of an equilateral pentagon with an edge length of rcc, and by setting rjJ?' in the linearized equations to rcc, one obtains a solution for rj of the form
r; =
rcc (2[1 - COS ( 2 ~ / 5 ) ] ) ' / ~
This result, together with eq 4-6, completely specifies the geometry of the five-membered ring as a function of rcc, q, 4. For the values of q typically encountered (0.3 < q < 0.5 A) this approximation constrains the C-C distances to be identical within about 0.005 8,which is adequate for the present treatment. This small variation is expected to have some influence on the fitted values of the vibrational amplitudes, however, and will be discussed in more detail below. The structural parameters which were used to define the pseudorotating model were then chosen as follows: (1) the C-H bond length, (2) the C-C bond length, (3) the C-C1 bond length, (4) the puckering amplitude q, (5)the LHCH val nce angle, and (6) the LHCCl valence angle. In this mo el the LHCH and LHCCl angles were used instead of the LCCH and LCCCl angles because it was found upon
b
592
Hilderbrandt and Shen
The Journal of Physical Chemistry, Vol. 86,No. 5, 1982
closer inspection of the molecular mechanics calculations that these angles changed less as a function of the pseudorotational phase angle. In addition the following amplitude parameters were also included in the analysis: C-H, C-C, C-Cl, C-C,, C2-C1, C,-Cl, and C--H,,,. The C3...C1 amplitude was introduced as the following function of 4: 1C&1
=
1OC3C1
- 0.02 cos 4
(9)
This was done to take into account the rather large variation in this parameter with the phase angle. A total of nine pseudoconformers was included in the analysis between 4 = Oo and 4 = 180O. The two Fourier components of the pseudorotational potential function Vl and V2 were also varied where V1
V(4) = -(1 2
v2
+ cos 4) + $1 + cos 24)
1
(10)
"
v
c
20
I
I
n
I
40
30
A
- - A - - v v I
60
50
1
70
,.-
I
1
BC
I
90
I
IOC
1tc
OIs-',
The weight assigned to each pseudoconformer was taken as
P(4i) =
exp(-V(@i)/ R T ) Cexp(-V($i) / R T )
(11)
The formulation of the Jacobian elements of the molecular intensity curve with respect to the potential function parameters has been described elsewhere.34 At first the results obtained from the least-squares refinement of this model were not entirely satisfactory. In fact, the values initially obtained for V2 were negative at both temperatures. This would imply that the minima in the pseudorotational potential energy function occurred at conformations which were slightly twisted axial forms without symmetry planes. After some reflection it was realized that this is exactly what one would expect if one constrained the pseudorotational trajectory to be circular when in fact it was actually elliptical. There is good reason to believe that this may be the case since the two minima are not of equivalent depth. Alternatively, this may be viewed as a coupling term between the pseudorotation and the puckering. Ellipticity was introduced into the model as an additional adjustable parameter by the equation 4 = 40
+ 41 cos 4
Flgure 4. Leveled molecular intensity function for chlorocyclopentane at 295 K.
(12)
When eq 12 was incorporated into the analysis, and when the parameter q1 was allowed to vary as well, an excellent fit to the experimental data was obtained at both temperatures. In addition, the values obtained for the parameter V2 at both temperatures were more reasonable. The final values for all of the parameters obtained from the least-squares analysis of the pseudorotational model are shown in Table IV under the heading of model 11. The final radial distribution curves for this model are shown in Figures 2 and 3 for the 295 and 387 K data, respectively, and the corresponding molecular intensity curves are shown in Figures 4 and 5. Discussion The structural parameters obtained for cyclopentyl chloride at the two temperatures used in the analysis are in good agreement with each other, and with corresponding parameters reported for similar molecules. The average C-C bond lengths [1.542 (1)8, at 295 K and 1.543 (1)A at 387 K] agree well with the average C-C bond length reported for cyclopentane [1.546 (1) A]. The slight de(34) H. Schei, Q. Shen,R. F. Cunico, and R. L. Hilderbrandt,J.Mol. S t r u t . , 63, 59 (1980).
v
I
,
1C
- -
A
-
I 20
30
_
_
A
1 r10
l
, 50
.
A -
- "
A .
v 1
70
1
BO
I
90
00
1 c
I
13 &O1
Flgure 5.
at 307 K.
Leveled molecular Intensity function for chlorocyclopentane
crease in the average bond length in chlorocyclopentane may be attributed to the influence of the chlorine atom. The avera e C-H bond length [1.096 (4) A at 295 K and 1.090 (4) at 387 K] are also slightly shorter than the reported C-H bond length in cyclopentane [1.113 (1) A], but are typical of methylene C-H distances found in such molecules. The amplitude parameters which were determined from the least-squares analysis show some rather unusual trends most of which can be explained in terms of the approximate models used in the analysis. For example, the rather dramatic decrease in the C-C and C-C,, amplitudes with increasing temperature can be accounted for by a failure of the linearized constraint eq 4-8 to maintain constant C-C bond lengths throughout the pseudorotation. Since the puckering amplitude and ellipticity determined by least-squares analysis were quite a bit larger at 387 than at 295 K, the C-C distances produced by the model were found to vary over a wider range at 387 K thus artificially decreasing the effective fitted value of the C-C and C..C, amplitudes. It is also expected that many of the amplitude parameters depend quite strongly on both the radial and pseudorotational coordinates. Since it was not practical to include all of these variations in the analysis, the amplitude parameters shown in Table IV should all be considered as effective values.
x
J. Phys. Chem. 1982, 86, 593-598
The average puckering amplitude is found to increase quite a bit with temperature as might be expected. At 295 K the amplitude varies between 0.35 and 0.43 A. This range of values lies below the amplitude reported by Ad[q = 0.43 (2) A]. ams, Geise, and Bartell for ~yclopentane'~ The smaller puckering amplitude for cyclopentyl chloride indicates that the ring is somewhat more flattened on the average than cyclopentane. The sign of the ellipticity parameter, ql, indicates that the axial C, conformer is less puckered than the equatorial form. At 387 K the puckering amplitude varies between 0.33 and 0.53 A indicating again a rather large variation in the puckering angle in going from the axial to the equatorial form. The results obtained for the pseudorotational potential function parameters must be considered very critically since they have rather large uncertainties. First, it is clear that the data definitely indicate a contribution from an equatorial conformer. The fact that a peak appears at 4.0 A in the radial distribution curve and the fact that the area of this peak increases with increasing temperature leave little doubt that the equatorial form is present. Both the two conformer model and the pseudorotational model give consistent free energy differences for these two forms, N 340 cal/mol, and N 60 cal/mol. The temperature variation of the energy difference and the pseudorotational barrier height may be due to classical treatment of the probability distribution function given by eq 11. Theoretical calculations currently under way in our laboratory indicate that quantum effects may be very important in determining large amplitude potential functions from electron diffraction data, and that the effective values observed depend critically on the number of quantum states with energy less than RT. For this reason, the high temperature results may be somewhat more reliable in estimating the potential function parameters than the low temperature results. In any event, the energy differences obtained are actually in excellent agreement with the results obtained by Durig and co-
593
workers from the spectroscopic data.24.25 The present results, while they are consistent with the results of the infrared and Raman experiments, still do not explain the results of the microwave experiments of Loyd, Mathur, and Harmony.26 The answer may lie in the magnitude of the V2potential function parameter. The uncertainty in this parameter obtained from the present analysis is unfortunately too large to make any definitive conclusions; however, it is possible that the potential barrier at the C2 conformation is somewhat smaller than indicated by the diffraction experiments. If this were the case then it may also be possible that the minimum in the potential function at the equatorial position is too shallow to contain any bound vibrational states. This is a possible explanation for the fact that an equatorial conformation is observed in the diffraction experiment but not in the microwave experiment. Model calculations using molecular mechanics and a newly written quantum mechanical program to calculate energy levels of a pseudorotating molecule are currently under way to test this hypothesis. In order to further the work on this very interesting case of molecules we have also recently undertaken additional studies of the bromo-, methyl-, and cyano-substituted compounds. Cyanocyclopentane should be a particularly interesting test case since Choe and Harmony27have observed both conformers of this compound in approximately equimolar concentrations.
Acknowledgment, The authors gratefully acknowledge the financial assistance of the National Science Foundation Grant No. CHE-7908614. We are also grateful to the computer center of The North Dakota State University for providing computer time for the calculations involved in the data analysis. Supplementary Material Available: Tables of experimental intensity data, and correlation and error matricies (8 pages). Ordering information is given on any current masthead page.
Quadratic Force Fields for Phosphorus Pentafluoride and Thionyl Tetrafluoride Llse Hedberg oepertment of Chemistry, Oregon State Universw, Confallis, Oregon 9733 1 (Received: August 14, 198 1; In Final Form: October 2, 1981)
The quadratic symmetry force fields for PF5 (D%)and SOF4(C,) have been reanalyzed with the aid of criteria drawn from the points-on-a-sphere model of Bartell and Plato. The results differ importantly from those previously proposed for the e' block of PF5 and the al block of SOFl in respect to those elements involving bending modes. For SOF4the results strongly suggest an exchange in the assignment of two fundamentals different from that proposed by earlier investigators. They account for the Berry-type inversion generally acknowledged to occur in these molecules and lead to calculated rms amplitudes of vibration in better agreement with experiments than has been heretofore obtained. The force fields for PF5 and SOF, are shown to be internally consistent and consistent with each other as well as with force fields of the related molecules SiF4and SFG. It is found that there is a rough correlation between the values of symmetry bending constants and the bond angles representing the principal component of the deformation; the constants decrease in value as the angles increase. I. Introduction In the structure determination of SOF4 (following arti&) where both electron diffraction intensities and rotational constants were used as experimental data it was necessary to w e correction factors derived from a quadratic 0022-3654/82/2086-0593$01.25/0
force field in order to establish parameters which were applicable to both types of data. A force field of SOF4 based on observation of all fundamental frequencies and several 32S-34Sisotopic shifts has been reported by Christe et al.' A question as to the suitability of this force field 0 1982 American Chemical Society
