- Email: [email protected]
The molecular structure of gaseous 1,4-dioxane: An electron-diffraction reinvestigation aided by theoretical calculations
Journal of Molecular Structure xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
The molecular structure of gaseous 1,4-dioxane: An electron-diffraction reinvestigation aided by theoretical calculations Mitchell Fargher, Lise Hedberg, Kenneth Hedberg ⇑ Department of Chemistry, Oregon State University, Corvallis, OR 97331, USA
h i g h l i g h t s Our structure results for dioxane are both more complete and more accurate than before. Our results are consistent with the theoretical prediction of only a chair form for the molecule. The distances, bond-, torsion-, and flap angles are similar to those in other ether-like molecules.
a r t i c l e
i n f o
Article history: Received 17 February 2014 Received in revised form 16 April 2014 Accepted 16 April 2014 Available online xxxx Keywords: Molecular shape Bond distances and bond angles Electron diffraction Molecular orbital calculations
a b s t r a c t The structure of the molecule 1,4-dioxane (DIOX) has some features in common with other ring systems previously studied in this laboratory. In contrast to 1,4-cyclohexanedione, however, which consists both of a twisted boat form of D2 symmetry and a chair form of C2h symmetry, DIOX was reported, in two much earlier studies, to exist only as the chair form. The results of our work are in agreement with the earlier conclusions that gaseous DIOX exists either entirely, or essentially entirely (less than a few percent) in the chair form. Our work is much more extensive than the previous studies, and, aided by high-level theoretical molecular orbital- and normal-coordinate calculations, yielded the following bond distances (rg/Å) and bond angles (\a/deg). hC–Hi = 1.104 (4), C–O = 1.420 (2), C–C = 1.514 (4), hC–C–Hi = 105.4 (55), H–C–H = 108.0 (26), C–C–O = 111.1 (3), C–O–C = 110.9 (10). The ‘‘flap’’ angle — the angle by which the COC plane is tilted up from the plane of the four carbon atoms — is equal to 50.6 (7)°. The structure is discussed and compared with the previous work and with predictions from theory. Ó 2014 Elsevier B.V. All rights reserved.
Introduction The molecule 1,4-dioxane (DIOX) may be regarded as similar to that of 1,4-cyclohexanedione (CHDO) in that the carbonyl groups of the latter are replaced by oxygen atoms to generate the former. Since the ring bonds are in each case formal single bonds, it seems possible that in the gas phase the molecules would have similar structures. CHDO has recently been shown to exist as a mixture of the twisted boat and chair forms [1] in which the chair of C2h symmetry is rigid and the twisted boat of D2 symmetry is flexible. The nature of this flexibility is pseudorotation (internal rotations about bonds without angle strain). An important conclusion from the CHDO work was that the twisted boat form is the more stable, but that the vapor also contains about 23% chair.
⇑ Corresponding author. Address: Department of Chemistry, GilbH 153, Oregon State University, Corvallis, OR 97331, USA. Tel.: +1 541 737 6734. E-mail address: [email protected] (K. Hedberg).
There is an X-ray-diffraction investigation [2] of crystalline DIOX at 106 K in which the chair form (Fig. 1) was found. Also, two early investigations of this molecule by gas-phase electron diffraction [3,4] (GED) each detected only the chair form. Nevertheless, it seemed possible that in the gas phase the twisted boat form could be present in amounts too small to have been identified with the GED methods used by these early investigators many decades ago. For example, modern methods make use both of molecular orbital- and normal-coordinate calculations as an aid in the structure analysis, methods that lead to estimates of interatomic distances and amplitudes of vibration that cannot be experimentally measured. The theoretical approach was likely not available to the early investigators and the vibrational analysis appears not to have been done in either study. We decided to reinvestigate the vapor-phase structure of DIOX as a part of some current research on organic ring systems. The main purpose was to expand the structural information available from the previous studies, neither of which included measurements of some of the parameters involving hydrogen atoms. The
http://dx.doi.org/10.1016/j.molstruc.2014.04.053 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
2
M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
Experimental
7
Long Camera
3
1 2
5
Middle Camera
4
6 8
Fig. 1.
Theoretical
investigation would also provide a check on the values of the heavy-atom parameters and was expected to improve the precision of the parameter measurements. Theoretical calculations
Difference
Molecular-orbital predictions of the structure and energy of the chair form of DIOX were carried out with the program Gaussian 03 [5] at several levels of theory and basis sets. The matter of the possible presence of a twisted-boat form quickly turned out to be a non-question: all calculations predicted this form to be of such high energy relative to the chair that its amount could be taken as negligible. The optimized energies from the B3LYP calculation can be seen in Table 1. Since results from B3LYP theory had been used in the CHDO analysis, this theory was deemed appropriate for the current project on DIOX. The calculation also yielded Cartesian force constants which were used in the program ASYM40 [6,7] to calculate a number of quantities useful as constraints in the experimental structure analysis: in particular, vibrational amplitudes and conversion terms that relate the various distance types (ra, rg, and ra).
0
10
20
30
40
S/A-1 Fig. 2.
Experimental section The commercial sample of DIOX (Alfa Æsar, 99 + percent) was used as received. The diffraction experiments were made with the Oregon State University apparatus at a nozzle-tip temperature of 21 °C. Three diffraction photographs from the long camera distance (LC, 747 mm) and three at the middle camera distance (MC, 299 mm) were selected for analysis. Data concerning the experiments are the following. Film: Kodak electron image; development: 10 min in Kodak D-19 diluted 1:1; nominal accelerating voltage: 60 kV; electron-beam currents: 0.57–0.73 lA; sector
experimental
C-O C-H
C..C O..H C…H C…H C.H;O..H C…H C-C C..O C..C;O..O
Table 1 Theoretical (B3LYP/cc-pVTZ) thermochemical dataa for forms of 1,4-dioxane.
Chair Twisted boat Boat a b c
0
Symmetry
\(OCCO)/deg
E
C2h D2 C2v
56.6 60.7 0
0 6.3 8.3
In kcal/mol at 298 K. Estimated mole fraction. Transition state.
0
difference b
G
m.f.
0 6.0 tsc
1.0 <104
1
2
3
r/Å
4
Fig. 3.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
5
6
M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
function: r3; ambient chamber pressure during sample run-in: 5.5 106–1 105 Torr; exposure times: ca. 1.5 min; calibration standard for electron wave-length: CO2 (ra(CO) = 1.1608 Å, ra(OO) = 2.3113 Å). Each film was traced twice with use of a modified Joyce–Lobel microdensitometer. The ranges of the digitized data were 2.00 6 s/Å1 P 16.25 (LC) and 9.00 6 s/Å1 P 39.25 (MC); the data interval was Ds = 0.25 Å1. Curves of the molecular scattered intensity in the variable coefficient form used in this laboratory (sIm(s)) are shown in Fig. 2 and the corresponding radial distribution curve is seen in Fig. 3. Calculations concerning the data reduction and generation of intensity and radial distribution curves have been described [8,9]. The scattered intensity data in the form used for our least squares refinement procedure are available from the corresponding author.
3
less than 1 percent of the latter present in the vapor, and thus its possible presence was ignored. For the chair form with its C2h symmetry, the structure of the ring is determined by two bond distances, a bond angle, and a flap angle. We chose a convenient set of equivalent parameters for our model of the ring as follows. hr(C–C,O)i = [2r(C–C) + 4r(C–O)]/6, Dr(C–C,O) = r(C–C) r(C–O), \(C–O–C), and flap, with flap equal to the angle by which the COC plane lies out of the plane of the four carbon atoms. The hydrogen-atom parameters were hr(C–H)i = [r(C–H8) + r(C–H7)]/2, Dr(C–H) = r(C–H8) r(C–H7), h\(CCH)i = [\(CCH8) + \(CCH7)]/2, D\(CCH) = \(CCH8) \(CCH7), as well as a pair involving the methylene groups best described as a scissor and a rocking angle. The vibrational amplitude parameters were placed in seven groups in which the differences between group members were held at values obtained from our normal coordinate calculations.
Structure analysis Refinements Model The large theoretical energy difference between the chair and twisted boat forms of DIOX seen in Table 1 corresponds to much
The structure refinements were based on the model specified in ra space (in which structures are defined by the average positions of the atoms) and were done by least squares fittings of theoretical
Table 2 Interatomic distances (r/Å), bond angles (\/deg), and rms amplitudes of vibration (l/Å) for 1,4-dioxane.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
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M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
Table 3 Correlation matrix (100) for bond distances and bond angles in 1,4-dioxane.
1 2 3 4 5 6 7 8 9 10 11 12 a
Parameter
100 rLSa
r1
r2
r3
r4
\5
\6
\7
\8
\9
\10
\11
\12
r(C–H8) r(C–O) r(C–C) hC–C,Oi \(HCH) \(OCH7) \(OCH8) \(CCH7) \(CCH8) \(CCO) \(OCO) Flap
0.1 0.1 0.1 0.1 168. 142. 136. 110. 113. 13. 117. 27.
100 3 8 7 29 16 4 16 2 8 2 7
100 25 60 10 7 2 2 5 28 4 32
100 92 24 14 5 9 8 62 5 57
100 23 14 5 8 8 62 3 60
100 90 40 8 34 46 19 64
100 59 43 54 31 31 61
100 70 92 74 10 34
100 62 4 20 22
100 19 4 23
100 48 56
100 46
100
Standard deviation from least squares refinement.
scattering curves to the six experimental ones. The corrections necessary for generation of the ra and rg distances from the ra values were obtained from the normal coordinate calculations described previously. (The numerical values of these corrections for the final model may be deduced from Table 2 that contains our final results.) The refinements presented no convergence problems and, with the exception of the difference between the lengths of the two types of carbon–hydrogen bonds, we were able to determine values for all the structural and vibrational parameters. The interatomic distances and bond angles for the final model are given in Table 2. Missing from Table 2 are specific values and associated uncertainties of five of the structure-defining parameters described above. Although their values may be deduced from those of the parameter components, their (2r) uncertainties are not evident. Results for these parameters are hra(C–C,O)i = 1.448(2) Å, Dra(C–CO) = 0.093(3) Å, hra(C–H)i = 1.086(4) Å, Dr(C–H) = 0.008 Å (taken from theory), h\a(CCH)i = 105.4(28)°, and D\(CCH) = 6.6(28)°. An abbreviated correlation matrix for some of the distances and angles is given in Table 3.
and flap angles are in substantially better agreement with theory than DH’s, which also leads, in most cases, to a corresponding better agreement between our nonbond distances and theory. The X-ray results for the average bond lengths and bond angles are the following. r(C–O) = 1.4300 Å, r(C–C) = 1.5152 Å, r(C–H) = 1.012 Å, \(COC) = 109.90°, and \(CCO) = 110.55°; the listed uncertainties are roughly 0.0006 Å for the distances and 0.0004° for the angles. Detailed comparisons of the X-ray and GED values are not very useful because the former can be perturbed by near-neighbor interactions and because the effects of thermal averaging differ in gas and solid phases. (The latter is clearly seen in the very different carbon–hydrogen distances in the two phases.) Taking these matters into consideration, the GED and X-ray results are in good agreement.
Discussion
References
The values found for the bond distances in the DIOX ring are about as expected; the carbon–oxygen and carbon–carbon values (rg), respectively equal to 1.420(2) Å and 1.514(4) Å, are virtually identical to those in the trans–trans form of diethyl ether (DEE) in which they are equal to 1.419(1) Å and 1.514(2) Å [10]. The DIOX bond angles differ a bit from those in DEE, however: the DIOX/DEE values for \aCOC and \aCCO respectively are 110.9(10)°/113.5(4)° and 111.1(3)°/108.6(1)°. It is likely that the angle differences in these compounds is due to the constraining effect of the ring in DIOX, leading to a distribution of strain among the ring angles that tends to equalize them. The older of the two previous GED studies of DIOX measured only the C–O distance (1.42 ± 0.02 Å) and the bond angles COC (109.5 ± 1.5°) and CCO (109 ± 1°). The more recent work by Davis and Hassel (DH), offers a better comparison with our DIOX parameter values. As is seen in Table 2, DH’s ring-bond distances (ra) are slightly larger than ours, but the values lie within the combined range of uncertainty for C–O and barely outside it for C–C. It could be argued that DH’s values are in better agreement with theoretical prediction since the latter are expected to be smaller than the experimental ones. On the other hand, our measured COC, CCO,
Acknowledgement We thank the National Science Foundation for partial support of this work under grant CHE061298.
[1] M. Frogner, R.D. Johnson, L. Hedberg, K. Hedberg, J. Phys. Chem. A 117 (2013) 11101. [2] T. Koritsánszky, M.K. Strumpel, J. Buschmann, P. Luger, N.K. Hansen, V. PichonPesme, J. Am. Chem. Soc. 113 (1991) 9148. [3] M. Kimura, K. Aoki, Nippon Kagaku Zasshi 72 (1951) 169. [4] M. Davis, O. Hassel, Acta Chem. Scand. 17 (1963) 1181. [5] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T.Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian Inc, Wallingford CT, 2004. [6] L. Hedberg, I.M. Mills, J. Mol. Spectrosc. 203 (2000) 82. [7] L. Hedberg, I.M. Mills, J. Mol. Spectrosc. 160 (1993) 117. [8] G. Gundersen, K. Hedberg, J. Chem. Phys. 5 (1969) 2500. [9] L. Hedberg, Abstracts, Fifth Austin Symposium on Gas Phase Molecular Structure, Austin, TX, March 1974, No. T9. [10] N. Kuze, N. Kuroki, H. Takeuchi, T. Egawa, S. Konaka, J. Mol. Struct. 301 (1993) 81.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
The molecular structure of gaseous 1,4-dioxane: An electron-diffraction reinvestigation aided by theoretical calculations Mitchell Fargher, Lise Hedberg, Kenneth Hedberg ⇑ Department of Chemistry, Oregon State University, Corvallis, OR 97331, USA
h i g h l i g h t s Our structure results for dioxane are both more complete and more accurate than before. Our results are consistent with the theoretical prediction of only a chair form for the molecule. The distances, bond-, torsion-, and flap angles are similar to those in other ether-like molecules.
a r t i c l e
i n f o
Article history: Received 17 February 2014 Received in revised form 16 April 2014 Accepted 16 April 2014 Available online xxxx Keywords: Molecular shape Bond distances and bond angles Electron diffraction Molecular orbital calculations
a b s t r a c t The structure of the molecule 1,4-dioxane (DIOX) has some features in common with other ring systems previously studied in this laboratory. In contrast to 1,4-cyclohexanedione, however, which consists both of a twisted boat form of D2 symmetry and a chair form of C2h symmetry, DIOX was reported, in two much earlier studies, to exist only as the chair form. The results of our work are in agreement with the earlier conclusions that gaseous DIOX exists either entirely, or essentially entirely (less than a few percent) in the chair form. Our work is much more extensive than the previous studies, and, aided by high-level theoretical molecular orbital- and normal-coordinate calculations, yielded the following bond distances (rg/Å) and bond angles (\a/deg). hC–Hi = 1.104 (4), C–O = 1.420 (2), C–C = 1.514 (4), hC–C–Hi = 105.4 (55), H–C–H = 108.0 (26), C–C–O = 111.1 (3), C–O–C = 110.9 (10). The ‘‘flap’’ angle — the angle by which the COC plane is tilted up from the plane of the four carbon atoms — is equal to 50.6 (7)°. The structure is discussed and compared with the previous work and with predictions from theory. Ó 2014 Elsevier B.V. All rights reserved.
Introduction The molecule 1,4-dioxane (DIOX) may be regarded as similar to that of 1,4-cyclohexanedione (CHDO) in that the carbonyl groups of the latter are replaced by oxygen atoms to generate the former. Since the ring bonds are in each case formal single bonds, it seems possible that in the gas phase the molecules would have similar structures. CHDO has recently been shown to exist as a mixture of the twisted boat and chair forms [1] in which the chair of C2h symmetry is rigid and the twisted boat of D2 symmetry is flexible. The nature of this flexibility is pseudorotation (internal rotations about bonds without angle strain). An important conclusion from the CHDO work was that the twisted boat form is the more stable, but that the vapor also contains about 23% chair.
⇑ Corresponding author. Address: Department of Chemistry, GilbH 153, Oregon State University, Corvallis, OR 97331, USA. Tel.: +1 541 737 6734. E-mail address: [email protected] (K. Hedberg).
There is an X-ray-diffraction investigation [2] of crystalline DIOX at 106 K in which the chair form (Fig. 1) was found. Also, two early investigations of this molecule by gas-phase electron diffraction [3,4] (GED) each detected only the chair form. Nevertheless, it seemed possible that in the gas phase the twisted boat form could be present in amounts too small to have been identified with the GED methods used by these early investigators many decades ago. For example, modern methods make use both of molecular orbital- and normal-coordinate calculations as an aid in the structure analysis, methods that lead to estimates of interatomic distances and amplitudes of vibration that cannot be experimentally measured. The theoretical approach was likely not available to the early investigators and the vibrational analysis appears not to have been done in either study. We decided to reinvestigate the vapor-phase structure of DIOX as a part of some current research on organic ring systems. The main purpose was to expand the structural information available from the previous studies, neither of which included measurements of some of the parameters involving hydrogen atoms. The
http://dx.doi.org/10.1016/j.molstruc.2014.04.053 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
2
M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
Experimental
7
Long Camera
3
1 2
5
Middle Camera
4
6 8
Fig. 1.
Theoretical
investigation would also provide a check on the values of the heavy-atom parameters and was expected to improve the precision of the parameter measurements. Theoretical calculations
Difference
Molecular-orbital predictions of the structure and energy of the chair form of DIOX were carried out with the program Gaussian 03 [5] at several levels of theory and basis sets. The matter of the possible presence of a twisted-boat form quickly turned out to be a non-question: all calculations predicted this form to be of such high energy relative to the chair that its amount could be taken as negligible. The optimized energies from the B3LYP calculation can be seen in Table 1. Since results from B3LYP theory had been used in the CHDO analysis, this theory was deemed appropriate for the current project on DIOX. The calculation also yielded Cartesian force constants which were used in the program ASYM40 [6,7] to calculate a number of quantities useful as constraints in the experimental structure analysis: in particular, vibrational amplitudes and conversion terms that relate the various distance types (ra, rg, and ra).
0
10
20
30
40
S/A-1 Fig. 2.
Experimental section The commercial sample of DIOX (Alfa Æsar, 99 + percent) was used as received. The diffraction experiments were made with the Oregon State University apparatus at a nozzle-tip temperature of 21 °C. Three diffraction photographs from the long camera distance (LC, 747 mm) and three at the middle camera distance (MC, 299 mm) were selected for analysis. Data concerning the experiments are the following. Film: Kodak electron image; development: 10 min in Kodak D-19 diluted 1:1; nominal accelerating voltage: 60 kV; electron-beam currents: 0.57–0.73 lA; sector
experimental
C-O C-H
C..C O..H C…H C…H C.H;O..H C…H C-C C..O C..C;O..O
Table 1 Theoretical (B3LYP/cc-pVTZ) thermochemical dataa for forms of 1,4-dioxane.
Chair Twisted boat Boat a b c
0
Symmetry
\(OCCO)/deg
E
C2h D2 C2v
56.6 60.7 0
0 6.3 8.3
In kcal/mol at 298 K. Estimated mole fraction. Transition state.
0
difference b
G
m.f.
0 6.0 tsc
1.0 <104
1
2
3
r/Å
4
Fig. 3.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
5
6
M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
function: r3; ambient chamber pressure during sample run-in: 5.5 106–1 105 Torr; exposure times: ca. 1.5 min; calibration standard for electron wave-length: CO2 (ra(CO) = 1.1608 Å, ra(OO) = 2.3113 Å). Each film was traced twice with use of a modified Joyce–Lobel microdensitometer. The ranges of the digitized data were 2.00 6 s/Å1 P 16.25 (LC) and 9.00 6 s/Å1 P 39.25 (MC); the data interval was Ds = 0.25 Å1. Curves of the molecular scattered intensity in the variable coefficient form used in this laboratory (sIm(s)) are shown in Fig. 2 and the corresponding radial distribution curve is seen in Fig. 3. Calculations concerning the data reduction and generation of intensity and radial distribution curves have been described [8,9]. The scattered intensity data in the form used for our least squares refinement procedure are available from the corresponding author.
3
less than 1 percent of the latter present in the vapor, and thus its possible presence was ignored. For the chair form with its C2h symmetry, the structure of the ring is determined by two bond distances, a bond angle, and a flap angle. We chose a convenient set of equivalent parameters for our model of the ring as follows. hr(C–C,O)i = [2r(C–C) + 4r(C–O)]/6, Dr(C–C,O) = r(C–C) r(C–O), \(C–O–C), and flap, with flap equal to the angle by which the COC plane lies out of the plane of the four carbon atoms. The hydrogen-atom parameters were hr(C–H)i = [r(C–H8) + r(C–H7)]/2, Dr(C–H) = r(C–H8) r(C–H7), h\(CCH)i = [\(CCH8) + \(CCH7)]/2, D\(CCH) = \(CCH8) \(CCH7), as well as a pair involving the methylene groups best described as a scissor and a rocking angle. The vibrational amplitude parameters were placed in seven groups in which the differences between group members were held at values obtained from our normal coordinate calculations.
Structure analysis Refinements Model The large theoretical energy difference between the chair and twisted boat forms of DIOX seen in Table 1 corresponds to much
The structure refinements were based on the model specified in ra space (in which structures are defined by the average positions of the atoms) and were done by least squares fittings of theoretical
Table 2 Interatomic distances (r/Å), bond angles (\/deg), and rms amplitudes of vibration (l/Å) for 1,4-dioxane.
Please cite this article in press as: M. Fargher et al., J. Mol. Struct. (2014), http://dx.doi.org/10.1016/j.molstruc.2014.04.053
4
M. Fargher et al. / Journal of Molecular Structure xxx (2014) xxx–xxx
Table 3 Correlation matrix (100) for bond distances and bond angles in 1,4-dioxane.
1 2 3 4 5 6 7 8 9 10 11 12 a
Parameter
100 rLSa
r1
r2
r3
r4
\5
\6
\7
\8
\9
\10
\11
\12
r(C–H8) r(C–O) r(C–C) hC–C,Oi \(HCH) \(OCH7) \(OCH8) \(CCH7) \(CCH8) \(CCO) \(OCO) Flap
0.1 0.1 0.1 0.1 168. 142. 136. 110. 113. 13. 117. 27.
100 3 8 7 29 16 4 16 2 8 2 7
100 25 60 10 7 2 2 5 28 4 32
100 92 24 14 5 9 8 62 5 57
100 23 14 5 8 8 62 3 60
100 90 40 8 34 46 19 64
100 59 43 54 31 31 61
100 70 92 74 10 34
100 62 4 20 22
100 19 4 23
100 48 56
100 46
100
Standard deviation from least squares refinement.
scattering curves to the six experimental ones. The corrections necessary for generation of the ra and rg distances from the ra values were obtained from the normal coordinate calculations described previously. (The numerical values of these corrections for the final model may be deduced from Table 2 that contains our final results.) The refinements presented no convergence problems and, with the exception of the difference between the lengths of the two types of carbon–hydrogen bonds, we were able to determine values for all the structural and vibrational parameters. The interatomic distances and bond angles for the final model are given in Table 2. Missing from Table 2 are specific values and associated uncertainties of five of the structure-defining parameters described above. Although their values may be deduced from those of the parameter components, their (2r) uncertainties are not evident. Results for these parameters are hra(C–C,O)i = 1.448(2) Å, Dra(C–CO) = 0.093(3) Å, hra(C–H)i = 1.086(4) Å, Dr(C–H) = 0.008 Å (taken from theory), h\a(CCH)i = 105.4(28)°, and D\(CCH) = 6.6(28)°. An abbreviated correlation matrix for some of the distances and angles is given in Table 3.
and flap angles are in substantially better agreement with theory than DH’s, which also leads, in most cases, to a corresponding better agreement between our nonbond distances and theory. The X-ray results for the average bond lengths and bond angles are the following. r(C–O) = 1.4300 Å, r(C–C) = 1.5152 Å, r(C–H) = 1.012 Å, \(COC) = 109.90°, and \(CCO) = 110.55°; the listed uncertainties are roughly 0.0006 Å for the distances and 0.0004° for the angles. Detailed comparisons of the X-ray and GED values are not very useful because the former can be perturbed by near-neighbor interactions and because the effects of thermal averaging differ in gas and solid phases. (The latter is clearly seen in the very different carbon–hydrogen distances in the two phases.) Taking these matters into consideration, the GED and X-ray results are in good agreement.
Discussion
References
The values found for the bond distances in the DIOX ring are about as expected; the carbon–oxygen and carbon–carbon values (rg), respectively equal to 1.420(2) Å and 1.514(4) Å, are virtually identical to those in the trans–trans form of diethyl ether (DEE) in which they are equal to 1.419(1) Å and 1.514(2) Å [10]. The DIOX bond angles differ a bit from those in DEE, however: the DIOX/DEE values for \aCOC and \aCCO respectively are 110.9(10)°/113.5(4)° and 111.1(3)°/108.6(1)°. It is likely that the angle differences in these compounds is due to the constraining effect of the ring in DIOX, leading to a distribution of strain among the ring angles that tends to equalize them. The older of the two previous GED studies of DIOX measured only the C–O distance (1.42 ± 0.02 Å) and the bond angles COC (109.5 ± 1.5°) and CCO (109 ± 1°). The more recent work by Davis and Hassel (DH), offers a better comparison with our DIOX parameter values. As is seen in Table 2, DH’s ring-bond distances (ra) are slightly larger than ours, but the values lie within the combined range of uncertainty for C–O and barely outside it for C–C. It could be argued that DH’s values are in better agreement with theoretical prediction since the latter are expected to be smaller than the experimental ones. On the other hand, our measured COC, CCO,
Acknowledgement We thank the National Science Foundation for partial support of this work under grant CHE061298.
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