Molecular structure and conformation of peroxydisulfuryl difluoride, S2O6F2, as determined by gas-phase electron diffraction and ab initio molecular orbital calculations

Journal of Molecular Structure 567±568 (2001) 1±10

www.elsevier.nl/locate/molstruc

Molecular structure and conformation of peroxydisulfuryl di¯uoride, S2O6F2, as determined by gas-phase electron diffraction and ab initio molecular orbital calculations q Kolbjùrn Hagen a,b, Kenneth Hedberg a,*, Gary Gard c, Felix Aubke d b

a Department of Chemistry, Oregon State University, Corvallis, OR 97331-4003, USA Department of Chemistry, Norwegian University of Science and Technology, Rosenborg, N-7491 Trondheim, Norway c Department of Chemistry, Portland State University, Portland, OR 97207-751 USA d Department of Chemistry, University of British Columbia, Vancouver, BC, Canada V6T 121

Received 17 July 2000; accepted 19 September 2000

Abstract The structure and conformational composition of peroxydisulfuryl di¯uoride, S2O6F2, have been investigated by gas-phase electron diffraction. Some of the results from ab initio molecular orbital calculations (MP2/6-311 1 G p) were used as constraints in the analysis. There is both experimental and theoretical evidence that only conformers with a gauche X±O± O±X torsion angle are present in the gaseous sample. Of these, only two conformers of symmetry C2 (G 1G 1and G 2G 2) and one of symmetry C1 (G 1G 2), where G ^ designates positive/negative rotation around the O±S bonds at either end of the molecule) were found to be plausible components of the gaseous mixture. In experiments at 298 K, about equally good ®ts were found with two models, model A consisting of a ratio of G 2G 2/G 1G 1 equal to 57/43 …2s ˆ 27†; and model B consisting of a ratio of G 2G 2/G 1G 2 equal to 38/62 …2s ˆ 14†: The composition of model A corresponds to DG 0 ˆ G0 …G1 G1 † 2 G0 …G2 G2 † ˆ 0:17 …s ˆ 0:24† kcal/mol, and that of model B to DG 0 ˆ G0 …G1 G2 † 2 G8…G2 G2 † ˆ 20:29 …s ˆ 0:12†: A system composed of only C2 symmetry conformers, such as model A, is favored by IR and Raman data, but our electron-diffraction results do not allow a choice. However, the bond lengths and bond angles for all conformers are similar so that, except for the torsion angles, the parameter values for the G 2G 2 form are also reasonably close to those in the other forms. These Ê )) and angles (/a (8)) values with 2s uncertainties are r(SyO) ˆ 1.406(2) A Ê , r(S±F) ˆ 1.539(3) A Ê , r(O± distances (rg (A Ê , r(O±O) ˆ 1.453(14) A Ê , k/(O±SyO)l ˆ 1/2[(O±SyO4) 1 /(O±SyO5)] ˆ 107.2(12)8, D/(O±SyO) ˆ / S) ˆ 1.620(4) A (O±SyO4) 2 /(O±SyO5) ˆ 8.18 (assumed), /(O±S±F) ˆ 98.2(18)8, /(O±O±S) ˆ 108.6(10)8, /(OySyO) ˆ 126.7(15)8, and /(S±O±O±S) ˆ 122.7(56)8. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Peroxydisulfuryl di¯uoride; Molecular structure; ab initio calculations

1. Introduction

q Dedicated to Professor Marit Trñtteberg on the occasion of her 70th birthday. * Corresponding author. Tel.: 11-541-737-2081; fax: 11-541737-2062.

Peroxydisulfuryl di¯uoride, FO2SOOSO2F, (Fig. 1, hereafter PODSF) has been known for more than 40 years [1]. It is a very strong oxidizing agent often used in synthetic chemistry [2]. Information about the molecular structure is sparse, but an IR and Raman

0022-2860/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(01)00529-4

2

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

Fig. 1. Diagrams of important conformers of peroxydisulfuryl ¯uoride.

spectroscopic investigation has been carried out [3] from which it was concluded that the compound was a true peroxide, that it had a nonplanar S±O±O±S structure, and that the two SO2F groups are oriented in such a way that the molecules have C2 symmetry. The structural problem presented by PODSF is a dif®cult one due to possible coexistence of several conformers. Together these conformers give rise to multiple sets of interatomic distances many of which differ only slightly and cannot be independently measured. For example, if one assumes C2 symmetry for the molecules and nonplanar (gauche) S±O±O±S groups in accordance with the spectroscopic ®nding [3], and further assumes three potential minima exist for rotation about each O±S bond, then six different conformers are possible. However, these occur as

enantiomeric pairs, which reduces the number having distinct sets of interatomic distances to three. They may be designated as G 2G 2, G 1G 1, and AA, where the two symbols refer to anti or gauche O±O±S±F torsion angles and a negative sign indicates clockwise rotation of the forward group. If, still with a gauche conformation of the S±O±O±S group, one admits the possible existence of molecules with C1 symmetry, the conformers G 1G 2, AG 1, and AG 2, each representing an enantiomeric pair, must also be considered. There are several questions of structural interest concerning these conformers. One is the composition of the system, which is related to the conformational energy differences. Another is the torsion angle around the O±O bond. Peroxides and peroxide-like molecules have been observed with quite different X±O±O±X torsion angles Ð e.g. from 818 when X ˆ Cl [4] to 1668 when X ˆ t-Bu [5]. A third is the length of the O±O bond, which also can be quite different in such molecules: it is observed to be very short Ê ) in F2O2 [6], intermediate (1.426 A Ê ) in (1.216 A Ê ) in (Me3Si)2O2 [5]. Cl2O2 [4], and long (1.481 A Equally interesting are the questions of the torsion angles about the O±S bonds linking the SO2F groups to the peroxy group and, particularly, the structure of ±SO2F groups themselves. The valence angles around the sulfur atom are expected to have quite different values, and VSEPR theory [7] has been used to make predictions about them in similar molecules. Will the angles in PODSF also ®t this theory? 2. Experimental PODSF was prepared and puri®ed by procedures described in a recent report [8]. Electron-diffraction data were collected using the OSU apparatus (nominal accelerating voltage of 60 kV) with a nozzle-tip temperature of 298 K and a bulk sample temperature of 260 K. The nominal nozzle-to-plate distances were 75 cm (long camera, LC) and 30 cm (middle camera, MC). Exposure times were 1.5±2.5 min, beam currents were 0.42±0.50 mA, and the electron Ê calibrated in separate wavelength was 0.04893 A experiments against CO2 as the standard. The scattered intensities were recorded on 8 £ 10 in. Kodak Electron Image plates and developed for 10 min in

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

3

Fig. 3. Radial distribution curves. The experimental curve is calculated from the average of the six intensity curves shown in Fig. 2 Ê 21. The convergence with theoretical data for the region s # 1.75 A Ê 2. Vertical bars indicate interatomic factor B was equal to 0.002 A distances in the molecules of model A, the lengths of the bars are proportional to the weights of the terms. The difference curve is experimental minus theoretical for model A.

Fig. 2. Intensity curves in the form sIm(s). Each experimental curve is the average of three photometric traces. The theoretical curve is calculated from the ®nal model shown in Tables 4 and 5. Difference curves are experimental minus theoretical.

D19 diluted 1 £ 1. Three plates from each of the two camera distances were used in the data analysis. Each plate were scanned three times for optical densities, making a total of 18 data sets. The ranges of the data Ê 21) # 15.50 and 8.00 # s were 2.00 # s (A 21 Ê (A ) # 39.00 for the LC and MC distance experiÊ 21. A ments and the data interval was Ds ˆ 0.25 A calculated background [9] was subtracted from each data set to yield experimental intensity data in the form sIm(s), and the three traces from each photographic plate were averaged. These intensity curves are shown in Fig. 2. An experimental radial distribution (RD) curve (Fig. 3) was calculated in the usual way from the modi®ed molecular intensity curve I 0 …s† ˆ sI m …s†ZS ZO …AS AO †21 exp…20:002s2 †; A ˆ s2 F and F

is the absolute value of the complex electron scattering amplitude. Theoretical intensity data were used for Ê 21 in the experimental intensity curve before s # 1.75 A the experimental RD curve was calculated. The scattering amplitudes and phases (used in subsequent calculations) were taken from tables [10].

3. Theoretical calculations The gas-phase electron-diffraction (GED) method is incapable of measuring accurately the individual interatomic distances in complex systems such as PODSF, and it is now usual to employ ab initio calculations for indications of some of these distanceand angle relationships. The guiding principle is that the differences between parameter values that are experimentally inaccessible are predicted with good reliability: the de®ciencies of theory concerning prediction of absolute values tend to cancel out in these differences. Ab initio calculations have also been shown to produce good starting values of force

4

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

Table 1 Symmetry coordinates for peroxydisulfuryl di¯uoride (For atom numbering, see Fig. 1) Coordinate

Approximate description

S1 ˆ 1=2D…r24 1 r25 1 r79 1 r710 † S2 ˆ 1=2D…r p 24 2 r25 1 r79 2 r710 † S3 ˆ 1=p2 D…r23 1 r78 † S4 ˆ 1= 2D…r12 1 r67 † S5 ˆ Dr16p S6 ˆ 1=2 3D…a425 1 a325 1 a324 1 a123 1 a124 1 a125 2 a9710 2 a8710 2 a879 2 a678 2 a679 2 a p6710  † S7 ˆ 1= 6D…2a425 2 a325 2 a324 1 2a9710 2 a8710 2 a879 † S8 ˆ 1=2D…a325 2 a324 1 a8710 2 a879 † p S9 ˆ 1= 6D…2a123 2 a124 2 a125 1 2a678 2 a679 2 a6710 † S10 ˆ 1=2D…a125 2 a9710 1 a679 2 a6710 † p S11 ˆ 1= 2D…a216 1 a167 † S12 ˆ 1=6D…t6123 1 t6124 1 t6125 1 t1678 1 t1679 1 t16710 † S13 ˆ Dt2167 S14 ˆ 1=2D…r24 1 r25 2 r79 2 r710 † S15 ˆ 1=2D…r p 24 2 r25 2 r79 1 r710 † S16 ˆ 1=p2D…r23 2 r78 † S17 ˆ 1= p 2D…r  12 2 r67 † S18 ˆ 1=2 3D…a425 1 a325 1 a324 2 a123 2 a124 2 a125 2 a9710 2 a8710 2 a879 1 a678 1 a679 1 ap6710  † S19 ˆ 1= 6D…2a425 2 a325 2 a324 2 2a9710 1 a8710 1 a879 † S20 ˆ 1=2D…a325 2 a324 2 a8710 1 a879 † p S21 ˆ 1= 6D…2a123 2 a124 2 a125 2 2a678 1 a679 1 a6710 † S22 ˆ 1=2D…a125 2 a9710 2 a679 1 a6710 † p S23 . ˆ 1= 2a…a216 2 a167 † S24 ˆ 1=6a…t6123 1 t6124 1 t6125 2 t1678 2 t1679 2 t16710 †

SyO str SyO str S±F str S±O str O±O str F±SyO/OySyO bend

F±SyO/OySyO bend F±SyO bend O±SyO/OySvyO bend O±SyO bend S±O±O bend S±O tor O±O tor SyO str SyO str S±F str S±O str F±SyO/OySyO bend

F±SyO/OySyO bend F±SyO bend O±SyO/OySyO bend O±SyO bend S±O±O bend S±O tor

constants needed for estimation of amplitudes of vibration and for certain well-known quantities such as perpendicular amplitude corrections, used in the analysis of GED data. Ab initio optimizations [11] were carried out for the six rotational conformers of PODSF described above, ®rst at the HF level with the 6-311G p basis, and later with this and the 6-3111G p bases at the MP2 and

B3LYP levels. The HF/6-311G p calculations were judged suf®ciently reliable for those of our needs dependent on a vibrational force ®eld; the others found use in comparisons of predicted conformational composition and parameter values. All calculations predicted the G 2G 2 form (C2 symmetry) to have the lowest energy. The theoretical cartesian force ®eld obtained from the HF/6-311G p optimization of this form was symmetrized in the normal coordinate program ASYM40 [12] and the resulting symmetry force ®eld adjusted by re®nement of scale factors to ®t the observed vibrational frequencies [3]. The results were used to calculate the vibrational amplitudes and the perpendicular amplitude corrections mentioned above. The symmetry coordinates are shown in Table 1 and the theoretical force ®eld and the re®ned scale constants for the G 2G 2 conformer are given in Table 2. Table 3 shows the theoretical (relative) conformer energies and the corresponding system compositions from the different levels of theory and basis sets. 4. Structure re®nement With assumption of C2 symmetry, the geometrical structure of each of the conformers of PODSF can be described by 10 parameters. The picture for C1 symmetry is much more complicated, but since conformers of this symmetry are predicted to be present in smaller amounts, a satisfactory model can be de®ned with the same parameters, connecting the structure of one ±SO2F group to the other via differences between corresponding theoretical values. We chose four distance parameters, r(SyO), r(S±F), r(S±O), and r(O±O); four angle parameters, k/(O±SyO)l ˆ 1/2] /(O±SyO4) 1 /(O±SyO5)], D/(O±SyO) ˆ /(O± SyO4) 2 /(O±SyO5), /(O±O±S), and /(O±S±F); and two torsion angles, /(S±O±O±S), and /(O±O± S±F). Trial values for all geometrical and vibrational parameters were obtained from the theoretical calculations and/or from results for related molecules. Re®nements of the molecular structure were made by the method of least squares [13], adjusting a theoretical sIm(s) curve to the six experimental data sets with use of a unit weight matrix. Since the conformers in our models of PODSF differ only in the orientation of the ligands in the FO2S- groups, and since these

F14 F15 F16 F17 F18 F19 F20 F21 F22 F23 F24

0.833(8) b 0.833(8) b 0.833(8) c 0.833(8) b 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.83 d

d

f

c

b

a

14.001 20.009 0.377 0.113 20.009 0.138 0.149 20.002 20.108 20.066 0.026 0.004 0.013

F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13

A species 0.833(8) b 0.833(8) b 0.833(8) c 0.833(8) b 0.833(8) b 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.813(17) c 0.83 d 0.83 d B species

Ref. [3]. Re®ned as a group. Re®ned as a group. G 1G 2 conformer. Not re®ned.

F14 13.821 20.055 0.332 0.43 0.286 0.201 20.007 20.141 0.001 0.038 20.011

F1

Scale factors

F16 6.695 0.372 0.224 20.442 20.010 0.485 0.001 20.050 0.007

13.603 0.055 20.006 0.007 0.028 20.386 20.010 0.396 20.119 20.015

6.733 0.267 0.020 0.152 20.440 20.029 0.451 0.034 20.013 0.008 20.008

F3

F15

13.644 20.021 20.032 0.030 0.049 20.041 20.396 0.071 0.343 20.138 0.018 0.032

F2

5.029 20.773 20.068 0.008 0.121 0.006 0.483 0.040

F17

5.545 0.394 20.508 0.005 0.025 0.106 0.097 0.522 20.007 20.127

F4

2.226 20.207 0.008 0.034 20.023 20.058 20.014

F18

6.480 0.037 0.069 0.083 20.144 20.278 0.830 20.016 0.004

F5

1.580 0.035 20.410 20.052 20.045 0.023

F19

2.417 20.186 0.018 0.063 20.050 20.082 20.016 0.025

F6

1.530 20.015 20.249 0.007 20.017

F20

1.588 0.021 20.438 0.003 20.013 0.023 20.026

F7

1.725 0.070 20.078 20.018

F21

1.530 20.011 20.260 0.037 20.019 20.017

F8

1.405 20.079 0.004

F22

1.781 0.016 20.149 0.003 0.042

F9

1.362 0.057

F23

1.546 20.137 20.027 20.022

F10

0.047

F24

1.610 0.025 20.112

F11

F13

0.083 0.048 0.164

F12

1467 1239 847 794 588 532 517 437 378 211

1485 1248 1080 878 822 598 532 481 385 302 191

1466 1221 863 774 582 526 516 421 370 210 68

1473 1245 1088 886 833 605 523 472 395 297 187 62 50

Observed a Calculated

wavenumbers

Table 2 Scale factors, theoretical force constants (HF/6-311G p), and wavenumbers/cm 21 for the G 2G 2 conformer of peroxydisulfuryl di¯uoride (units are in aJ/? 2 for stretches, aJ/rad 2 for bends; coordinates are those of Table 1)

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10 5

6

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

Table 3 Theoretical conformer energies and system compositions of peroxydisulfuryl di¯uoride (Energies in kcal/mol) Conformer HF/6-311 1 G p

G 2G 2 G 1G 1 AA G 1G 2 AG 2 AG 1 a b c

B3LYP/6-311 1 G p

MP2/6-311 1 G p

HF/6-31 1 G p

MP2/6-31 1 G p

B3LYP6-31 1 G p

Ea

x b,c

Ea

x b,c

Ea

x b,c

Ea

x b,c

Ea

x b,c

Ea

x b,c

0 1.37 6.27 0.75 3.27 3.62

0.73 0.07 ± 0.2 ± ±

0 1.06 5.93 0.68 3.07 3.48

0.68 0.11 ± 0.21 ± ±

0 1.04 5.88 0.75 3.12 3.53

0.69 0.12 ± 0.19 ± ±

0 1.27 5.71 0.62 3.02 3.2

0.68 0.08 ± 0.24 ± ±

0 1.07 5.11 0.62 2.74 3.05

0.66 0.11 ± 0.23 0 ±

0 0.97 5.39 0.61 2.85 3.1

0.64 0.13 20.23 0.23 ± ±

Energies in kcal/mol. Mole fraction. Dashes indicate amounts ,0.01. Values include thermal corrections to Gibbs free energy. In kcal/mol these were G 2G 2 ˆ 23.39, G 1G 1 ˆ 23.62, and G 1G 2 ˆ 23.89.

ligands (F and O) have similar scattering powers, it was no surprise to ®nd that a fairly good ®t to experiment could be obtained with any of the conformers tested singly. The largest R-factor, 0.112, (and thus the poorest agreement) was obtained for the AA

conformer of C2 symmetry which has the two S±F bonds anti to the ±O±O± bond. The best agreement …R ˆ 0:084† by this standard was obtained for the G 2G 2 conformer where the two S±F bonds are gauche to the ±O±O± bond and point away from

Table 4 Ê ); //deg) for peroxydisulfuryl di¯uoride Parameter values (r/A Parameter

model A a,bra //a

model B c,bra //a

HF/6-311 1 G(d)

B3LYP/6-311 1 G(d)

MP2/6-311 1 G(d)

r(SyO) r(S±F) r(S±O) r(O±O) /O±S±F k/O±SyOl D(/O±SyO) /O±O±S /(S±O±O±S) /(S±O±O±S) /(O±O±S±F) /(O±O±S±F) % G 2G 2 Rg

1.389(2) 1.517(3) 1.608(4) 1.445(14) 98.2(18) 107.2(12) [8.1] 108.6(10) 122.7(56) d [135.5] e 271.7(50) d [70.5] e 57(27) 0.082

1.389(2) 1.519(3) 1.608(3) 1.444(13) 99.3(11) 105.6(9) [8.1] 108.7(9) [114.0] d 133.8(44) f [268.9] d [67.5] f 38(14) 0.084

1.387 1.528 1.612 1.376 97.4 107.2 6.3 111.3 121 142.6 269.9 69.0

1.428 1.603 1.677 1.448 97.2 107 8.5 110.2 114.8 132.7 271.8 74

1.423 1.591 1.664 1.451 97.2 106.8 8.1 108.8 114.3 135.5 271.0 70.5

111.2(12) 103.1(12) 126.7(15) 106.3(5) 107.6(3)

109.7(9) 101.5(9) 128.7(10) 106.2(3) 107.7(2)

Dependent angles /O1 ±S2 ±O4 /O1 ±S2 ±O5 /O4 ±S2 ±O5 /F3 ±S2 ±O4 /F3 ±S2 ±O5 a b c d e g

110.4 104.0 125.9 107.2 108.2

Mixture of conformers G 2G 2 and G 1G 1 (both C2 symmetry). With exceptions noted values are for G 2G 2 conformer. Mixture of conformers G 2G 2 and G 1G 2 (C2 and C1 symmetry). G 2G 2 conformer. G 1G 1 conformer. R ˆ [S iwiDi2/S iwi(siIi(observed) 2] 1/2, where Di ˆ siIi(observed) 2siIi(calculated).

111.2 102.8 126.8 106.9 107.0

110.8 102.7 127.2 106.8 108.0

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

7

Table 5 Ê ) and vibrational amplitudes (l/A Ê ) for model A (C2 system) (Values in parentheses are 2s and include estimates of Interatomic distances (r/A uncertainties in voltage/camera distances and correlation in the experimental data) G 2G 2 conformer

G 1G 1 conformer

Distance type

rg

la

SyO S±O S±F O±O O1´´´O4 O1´´´O5 O1´´´F3 F3´´´O4 F3´´´O5 O4´´´O5 S2´´´O6 F3´´´6 O4´´´O6 O5´´´O6 S2´´´S7 F3´´´S7 O4´´´S7 O5´´´S7 F3 ±F8 O4´´´F8 O5´´´F8 O4´´´O9 O5´´´O9 O5´´´O10

1.406(2) 1.620(4) 1.539(3) 1.453(14) 2.496(19) 2.373(21) 2.387(31) 2.359(10) 2.376(7) 2.511(17) 2.490(9) 2.857(49) 2.743(32) 3.632(17) 3.647(44) 4.367(45) 3.611(73) 4.619(46) 4.977(62) 4.728(60) 5.074(56) 3.434(132) 4.344(106) 5.759(52)

0.040 0.051 0.046 0.051 0.069 0.071 0.074 0.066 0.066 0.058 0.070

a b

0.085 0.135

3 7 7 5

…3†

b

3 7 7 7 7 7 7 7 7 7 7 5



…4†b

…14†b

lcalculatedd

r

la

0.034 0.045 0.041 0.045 0.064 0.066 0.069 0.061 0.062 0.054 0.065 0.170 0.123 0.065 0.114 0.161 0.218 0.140 0.171 0.190 0.239 0.328 0.281 0.125

1.407(2) 1.616(3) 1.547(3) 1.466(14) 2.368(19) 2.494(19) 2.392(31) 2.377(7) 2.359(10) 2.511(17) 2.482(9) 2.840(36) 3.631(18) 2.734(35) 3.738(15) 3.654(39) 4.703(26) 4.242(33) 2.992(82) 4.532(27) 4.364(32) 5.835(35) 4.871(55) 4.984(54)

0.040 0.051 0.046 0.051 0.069 0.071 0.074 0.066 0.067 0.059 0.070

0.143

lcalculatedd 3 7 7 5

b

…3†

3 7 7 7 7 7 7 7 7 7 7 5

…4†b

(14) b

0.034 0.045 0.041 0.045 0.065 0.064 0.068 0.062 0.063 0.053 0.067 0.154 0.067 0.141 0.122 0.266 0.156 0.177 0.390 0.328 0.305 0.153 0.253 0.152

Where no value is given, the amplitude was held at the theoretical value. Re®ned as groups.

each other, but the G 1G 1 conformer was nearly as good …R ˆ 0:086†: Not surprisingly, the G 1G 2 conformer (C1 symmetry) also gave a good ®t …R ˆ 0:085†: It was clear from these results that the identities of the conformers present in the system could not be determined. However, based on the assumption drawn from the ab initio results that the lowest-energy conformer was the G 2G 2, there was a possibility that some experimental information about the composition of the system (G 2G 2 versus a second, unidenti®able species) could be obtained. Accordingly, we also re®ned models consisting of a mixture of (a) G 2G 2 and G 1G 1, and (b) G 2G 2 and G 1G 2 in which the structural differences between the conformers were in each case tied to G 2G 2 by the ab initio (MP2/63111G p) values. The choice of a `best model' for PODSF must necessarily be somewhat arbitrary because several

models give ®ts of essentially equal quality. Since there is good evidence that the system consists of more than one conformer, we choose the model representing the G 2G 2/G 1G 1 mixture partly because the R factor obtained from its re®nement was slightly lower than for any other combination and partly because the components of the model each have the C2 symmetry consistent with the spectroscopic indications [3]. We were able to re®ne a composition parameter, three amplitude parameters, and all geometrical parameters except D/O±SyO; this parameter was held at the ab initio value. The results for models A and B are given in Table 4 in terms of the G 2G 2 conformer; the corresponding parameter values for the accompanying G 1G 1 and G 1G 2 conformers may be deduced from the parameter descriptions and the data of Table 5. As Table 4 shows, it was found that the parameter values for the system are essentially independent of the

8

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

model make-up. The results of Table 4 thus carry no uncertainty related to the model and may be accepted with con®dence. 5. Discussions Our experimental results for the composition of the PODSF system are consistent with the ab initio calculations in identifying the G 2G 2 conformer as the most stable. However, as is seen in Table 4, the measured amounts of this conformer differ substantially depending on whether the second conformer is assumed to be G 1G 1 (model A, 57(27)%) or model B, G 1G 2 (38(14)%). These amounts are not measured with high precision, but the former is in reasonable agreement with theoretical prediction (Table 3), which in our series of calculations ranges from 69 to 73% at the Hartree±Fock level and from 64 to 69% at MP2 and B3LYP levels. Although the identity of the next most abundant conformer clearly is experimentally indeterminate, it is surely either the G 1G 1 form of C2 symmetry or the G 2G 1 one of C1 symmetry: conformers with an anti F±S±O±O torsion angle are of much higher energy than either of these and deserve no consideration. The geometrical parameter values for some peroxides similar to PODSF (general formula X±O±O±X) are listed in Table 6. The O±O bond in F2O2 (1.216(2) Ê ,[6]) is much shorter than in any of the other A molecules and is almost like a double bond. This value is con®rmed by our theoretical calculations Ð

Ê ) or speci®cally those from MP2/6-311G(d) (1.167 A Ê ). The O±O bonds in the B3LYP/6-311G(d) (1.237 A remaining molecules are similar, but there is signi®cant variation. Shorter bonds are found when X is very electronegative, e.g. Cl, COF, CF3, and of course, F, and longer bonds when it is less electronegative, e.g. H, CH3, SiMe3, and t-Bu. The G 2G 2 conformer of our PODSF has an O±O bond length close to the average of those in Table 6 if the F2O2 value is excluded. There is less variation in the values of /(O±O±X), with the exception of that in H2O2, but signi®cant differences in the values of this parameter do exist. The values seem to re¯ect steric interaction, becoming larger as the size of X increases, such as is seen in the values for the series CH3, CF3, SO2F, and SF5. Both the groups SiMe3 and t-Bu are also bulky, but in each of these cases the torsion angle /(X±O± O±X) is very large which reduces the steric repulsion. The most striking differences among the molecules is found in the values of the X±O±O±X torsion angle which range from less than 908 to more than 1608. Again, the size of X seems to play a role, but so also may its electronegativity. The angle tends toward smaller values when X is very electronegative X ˆ F, Cl and COF), and larger values when X is less electronegative and/or bulky X ˆ CH3 and particularly t-Bu and SiMe3). However, neither greater electronegativity nor smaller size of X can be the whole explanation for smaller torsion angles because the X±O±O±X angle in Cl2O2 is smaller than in F2O2 (81.0 vs. 88.18). Everything considered, the structure of F2O2 is the hardest to understand in terms of the

Table 6 Parameter values in some symmetric peroxides (Distances (r) are in Angstroms, angles (/) are in degrees. The uncertainties are as quoted in the original papers and may have different de®nitions) Parameter

r(O±O)

/O±O±X

f (X±O±O±X)

Ref.

H±O±O±H F±O±O±F Cl±O±O±Cl FOC±O±O±COF H3C±O±O±CH3 F3C±O±O±CF3 FO2S±O±O±SO2F F5S±O±O±SF5 Me3Si±O±O±SiMe3 t-Bu±O±O± t-Bu

1.464(3) 1.216(2) 1.426(2) 1.419(9) 1.457(12) 1.419(20) 1.455(13) 1.43(2) 1.481(8) 1.480 c

99.4(12) 109.2(2) 110.1(1) 109.4(9) 105.2(5) 107.2(12) 109.7(11) 110.3(11) 106.6(14) 103.9(12)

120.4(7) 88.1(4) 81.0(1) 83.5(14) 119(10)/135(5) a 123(4) 119(5) 129(2) 144(6) 166(2)

[15] [6] [4] [16] [17] [18] This work [19] [5] [5]

a

Torsion angles obtained using a dynamic/static model.

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

9

Table 7 Parameter values in molecules containing a O±SO2F group (Distances (r) are in Angstroms, angles (/) are in degrees. Uncertainties are quoted as in the original papers and may have different de®nitions) Molecule

r(SyO)

r(S±F)

r(O±S)

k/O±SyOl b

/O±S±F

/OySyO

k/F±SyOl b

Ref.

FO2SOOSO2F FO2SOSO2F (FO2SO)2SO2 FO2SOF FO2SOCl FO2SOCH3

1.405(2) 1.398(2) 1.402(2) 1.409(6) 1.401(3) 1.410(2)

1.537(4) 1.525(5) 1.525(12) 1.545(6) 1.537(8) 1.545(6)

1.618(3) 1.611(5) 1.613(6) 1.606(8) 1.589(10) 1.558(7)

105.9(13) 106.1(9) 106.5(8) 108.8(10) 108.3(8) 109.5(6)

98.7(29) 102.4(18) 101.3(15) 94.0(22) 100.1(26) 96.8(6)

127.5(14) 126.8(12) 128.8(14) 123.6(10) 124.8(10) 124.4(7)

107.7(9) 106.6(6) 105.5(12) 108.0(10) 107.1(10) 106.8(5)

This work [20] [20] [21] [21] [22]

a

Average values.

simple ideas outlined above. Since F2O2 is the only molecule in which the substituent X is more electronegative than oxygen, one is inclined to attribute its structural peculiarities to some aspect of this fact. Thus, the short O±O bond may be due to contributions from the valence-bond structures F 2 OyO 1 2 F $ F± O 1 ˆ O F 2, which suggest a bond length similar to that in O2 viewed as arising from one single and two threeelectron bonds (O±O) [14]. These structures also suggest a long O±F bond, which is exactly what is observed experimentally 2rg …O 2 F† ˆ 1:586 …2† [6]. The F±O±O±F torsion angle is also consistent with this picture: the p (or pp) orbitals for the two three-electron bonds are perpendicular to each other and the two valence-bond structures may each be derived from one of these. Our theoretical calculations (Table 4) do not reproduce the experimental bond lengths of PODSF very well. Although both the MP2 and B3LYP results for r(O±O) are good, those for r(S±F) and r(S±O) are too Ê . On the other hand, the HF results long by 0.06±0.08 A for r(S±F) and r(S±O) are good, but that for r(O±O) is Ê . The angle predictions from too short by about 0.07 A all calculations are satisfactory. PODSF is a complicated molecule for such calculations, and out of interest we also carried out similar calculations for H2O2 and F2O2. For H2O2 the HF, B3LYP, and MP2 calculations with the basis 6-3111G p respectively Ê for yielded the values 1.385, 1.453, and 1.448 A r(O±O); 103.0, 100.7, and 100.48 for /(O±O±H); and 117.4, 123.2, and 124.68 for the torsion angle. The results from Hartree±Fock theory are in poorest agreement with experiment (Table 6), but there is little to choose between DFT and MoÈller±Plesset. For F2O2 a similar series of calculations gave 1.301, 1.215, and

Ê for r(O±O); 106.4, 109.8, and 114.88 for / 1.130 A (O±O±F); and 84.5, 88.5, and 90.28 for the torsion angle. In this case the DFT results are in very good agreement with experiment, but both the Hartree± Fock and the MoÈller±Plesset ones are poor, especially Ê for in respect to the experimental value of 1.586 A r(O±F) cited above Ð our HF, B3LYP, and MP2 Ê. values are ,respectively, 1.354, 1.552, and 1.856 A These results support the conventional wisdom that accurate bond lengths involving ¯uorine are dif®cult to predict theoretically and that caution must be used in the interpretation of such results. Parameter values for some molecules containing one or more 2OSO2F groups are given in Table 7. Most bond distances of a given type have similar values, as do the valence angles. By far the largest bond angle in these molecules is between double bonds (/OySyO), with those between a single bond and a double bond (/(O±SyO) and /(F± SyO)) some 15±208 smaller, and that between the two single bonds (/(O±S±F)) the smallest. These relative angle sizes are generally consistent with predictions from VSEPR theory [7]. Acknowledgements This work was supported by the National Science Foundation under grants CHE95-23581 and CHE9987359, and by the Research Council of Norway (NFR) through a travel grant to K. Hagen during a stay at Oregon State University. We are grateful for a grant of computing time from NFR's Program for Supercomputing. Both K. H authors wish to express their appreciation and pleasure to our friend Marit

10

K. Hagen et al. / Journal of Molecular Structure 567±568 (2001) 1±10

Trñtteberg for many years of fruitful scienti®c association. References [1] F.B. Dudley, G.H. Cady, J. Am. Chem. Soc. 79 (1957) 513. [2] R.A. DeMarco, J.M. Shreeve, Adv. Inorg. Chem. Radiochem. 16 (1974) 115. [3] A.M. Qureshi, L.E. Levchuk, F. Aubke, Can. J. Chem. 49 (1971) 2544. [4] M. Birk, R.R. Friedl, E.A. Cohen, H.M. Pickett, S.P. Sander, J. Chem. Phys. 91 (1989) 6588. [5] D. KaÈss, H. Oberhammer, D. Brandes, A. Blaschette, J. Mol. Struct. 40 (1977) 65. [6] L. Hedberg, K. Hedberg, P.G. Eller, R.R. Ryan, Inorg. Chem. 27 (1988) 232. [7] R.J. Gillespie, Molecular Geometry, Van Nostrand Reinhold, London, 1972. [8] D. Zhang, C. Wang, F. Mistry, B. Powell, F. Aubke, J. Fluorine Chem. 76 (1996) 83. [9] L. Hedberg, Abstracts, Fifth Austin Symposium on Gas Phase Molecular Structure, Austin, TX, 1974, p. 37. [10] A.W. Ross, M. Fink, R. Hilderbrandt, International Tables of Crystallography, vol. 4, Kluwer Academic Publishers, Dordrecht, 1992, p. 245. [11] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A.

[12]

[13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, gaussian 94, Revision C.2 and D.4, Gaussian, Inc., Pittsburgh PA, 1995. L. Hedberg, I.M. Mills, J. Mol. Spectrosc 160 (1993) 117 (This article describes ASYM20. The later ASYM40 version is described in: L. Hedberg, Abstracts, 15th Austin Symposium on Molecular Structure, Austin, TX, March 1994. A manuscript has been submitted for publication). K. Hedberg, M. Iwasaki, Acta Crystallogr. 17 (1964) 529. L. Pauling, Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, NY, 1960. G.A. Khachkuruzov, I.N. Przhevalskii, Opt. Spectrosc. 36 (1974) 299. H.G. Mack, C.O. Della VeÂdova, H. Oberhammer, Angew. Chem., Int. Ed. Engl. 30 (1991) 1145. B. Haas, H. Oberhammer, J. Am. Chem. Soc. 106 (1984) 6146. C.J. Marsden, L.S. Bartell, F.P. Diodati, J. Mol. Struct. 39 (1977) 253. P. Zylka, H. Oberhammer, K. Seppelt, J. Mol. Struct. 243 (1991) 411. J.L. Hencher, S.H. Bauer, Can. J. Chem. 51 (1973) 2047. F. Aubke, B. Casper, H.S.P. MuÈller, H. Oberhammer, H. Willner, J. Mol. Struct. 346 (1995) 111. I. Hargittai, R. Seip, K.P. Nair, C.O. Britt, J.E. Boggs, B.N. Cyvin, J. Mol. Struct. 39 (1977) 1.