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1,4-Cyclohexanedione. Composition, Molecular Structures, and Internal Dynamics of the Vapor: an Electron-Diffraction Investigation Augmented by Molecular Orbital Calculations Matthew Frogner, Robert David Johnson, Lise Hedberg, and Kenneth Hedberg J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 26 Sep 2013 Downloaded from http://pubs.acs.org on September 30, 2013
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The Journal of Physical Chemistry
1,4-Cyclohexanedione. Composition, Molecular Structures, and Internal Dynamics of the Vapor: An Electron-Diffraction Investigation Augmented by Molecular Orbital Calculations
Matthew Frogner, Robert D. Johnson, Lise Hedberg, and Kenneth Hedberg*
Department of Chemistry, Oregon State University, Corvallis, Oregon 97331-4003
*Corresponding author: Kenneth Hedberg tel: (541) 737-6734 FAX: (541) 737-2062 e-mail:
[email protected]
Other information: Number of pages of text: 19 Number of tables: 2 Number of figures: 5 Supplementary information: 2 tables
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Abstract:
Electron-diffraction experiments on the vapor of 1,4-cyclohexanedione have been
carried out at a nominal temperature of 435 K. The results are consistent with the presence of a mixture of a chair form of C2h symmetry and a twisted boat form of D2 symmetry. The former has the familiar dynamic properties of a semi-rigid molecule, but the D2 form undergoes a large amplitude twisting motion (pseudorotation) that degrades the symmetry to C2. The analysis was designed to elucidate parameter values and internal dynamics of each conformer and the composition of the system. The large amplitude motion of the twisted boat form was modeled by placement of 10 pseudoconformers at approximately 5° intervals along a pseudorotational coordinate that began at the D2 position and that reflected the angle between the C=O bond vectors. A Gaussian weighting of the pseudeoconformers centered on the (lowest energy) D2 position was assumed. Differences in the interatomic distances and bond angles of these pseudoconformers were calculated via B3LYP/cc-pVTZ theory and introduced as constraints. The bond-length averages over the twisted boat forms followed by values for the chair in square brackets, are (rg/Å; p"/deg) r(C–H) = 1.115(11) [1.124(11)], r(C=O) = 1.211(3) [1.233(6)], r(C1–C2) = 1.524(5) [1.526(5)], r(C2–C3) = 1.533(11) [1.539(11)]. The corresponding ring-angle values are p(C1C2C3) = 111.1(5) [111.0(4)], and p(C6C1C2) = 116.3(8) [115.7(8)]. In the twisted boat form, pseudorotation leads to a weighted average displacement of the angle between the C=O bond vectors, p)(CO,CO), equal to 21.3° from the 180° value in the D2 form corresponding to an average angle between the CO bond vectors of 158.7(1)°.
The amount of the chair form in the gas at 435 K is 24(10) percent. The listed
uncertainties are estimated 2F. Keywords: pseudorotation, quantum mechanical calculations, vibrational analysis, interatomic distances, molecular conformation
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-3O Introduction The molecule cyclohexane-1,4-dione (CHDO) can exist in two forms that are characterized as a chair or a twisted boat. The chair has C2h symmetry and a rigid frame with a 180° angle between the C=O bond vectors and is not interconvertible with the twisted boat by the process of pseudorotation (internal rotations about bonds without angle strain). The equilibrium form of the twisted boat has D2 symmetry and is calculated to be more stable than the chair; however, it is flexible in a pseudorotational sense—a motion that leads to distorted forms of C2 symmetry. Diagrams of these configurations are shown are shown in Figure 1.
Figure 1. Diagrams of CHDO system components with atom numbering.
Information about the structure of CHDO in condensed phases has been obtained from dipole-moment measurements,1-3 NMR,4,5 IR and Raman spectroscopy,6-8 and x-ray diffraction.9,10 The dipole moment measured in solution is about 1.3 D and is consistent with a structure of C2
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-4symmetry while ruling out both the pure C2h and D2 forms as well as a mixture of them. Similarly, the spectroscopic data, almost all from condensed phases, uniformly indicate the structure to have the C2 symmetry. Finally, both x-ray investigations show that the molecule in the crystal indeed has C2 symmetry and that the angle between the carbonyl groups is equal to 154°–155°. The evidence from these experiments leaves little doubt that CHDO in condensed phases exists entirely as a twisted boat of C2 symmetry. The remaining question is the form of the molecule in the gas phase. A partial answer is found in the results of gas-phase molecular-beam electricdeflection experiments11 which show the molecule to be nonpolar, implying a structure of D2 and/or C2h symmetry. More recently, the question of the nature of the gas phase has been taken up again through IR and Raman experiments and ab initio calculations,12 and electron diffraction (GED).13 The authors of both studies conclude that their data indicate the presence of both D2 and C2h forms with the former having the lower enthalpy. A picture consistent with all the results mentioned in the foregoing is the following. The basic form of the molecule is the one of D2 symmetry that is easily distorted to forms of C2 symmetry via the process of pseudorotation. In the gas phase the basic form persists in the absence of intermolecular interaction, possibly together with some of the chair form, but in condensed media near neighbor contacts lead to detectable distortions of the basic form to the one of lower symmetry. The question of the gas-phase structure of CHDO was addressed by us many years ago with a GED investigation,14 but the results of the work were never published. Several models were tested, including single species of the chair (C2h), D2, and C2 forms, as well as ones consisting of the first two and several of the last designed to emulate the flexibility of the twisted boat forms. Excellent agreement with experiment was obtained with several of these models, but from a current perspective they contain some limiting assumptions that are not necessary in modern GED work. Accordingly, we decided to reinvestigate the structure in terms of a more sophisticated model designed to incorporate the phenomenom of pseudorotation of the twisted-boat ring, and results from
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-5molecular orbital calculations that were not available at the time of the earlier work. In addition to better parameter values, it was hoped that the possible presence of the chair form, which could not be unambiguously established before, could now be settled. O Experimental Section The current work made use of the data obtained in the original investigation.14 The following is a summary. The sample of CHDO (Aldrich, 98 %) was sublimed before use. Fifteen diffraction photographs were made in the Oregon State apparatus at a nozzle-tip temperature of 162 °C. Apparatus parameters were: sector function, r3; plates, 8" x 10" Kodak projector slide medium contrast; development, 10 minutes in Kodak D-19 developer diluted 1:1; exposures, 45 – 180 s; nominal camera distances, 75 cm (LC) and 30 cm (MC); apparatus pressure during run-in, 3-4 x 10-6 Torr; electron beam currents, 0.40 – 0.45 :A; electron wavelengths 0.05662 – 0.05669 Å calibrated in separate experiments against CO2 ( ra(C=O) = 1.1646 Å and ra(O@@O) = 2.3244 Å). Six plates of the best quality were chosen for analysis. These were traced by a microdensitometer, the traces digitized, the structure-unrelated backgrounds extracted, and the results put into a form mathematically consistent with the theoretical scattered intensity functions used in this laboratory. Details of the procedures have been previously cited.15,16 Averages of the experimental intensities thus obtained at the long (LC) and intermediate (MC) camera distances are shown in Figure 2. O Structure Analysis Theoretical calculations. The results of the early GED work on CHDO required that consideration be given to a system model comprising both the chair and twisted boat forms. Although in the present work the chair could be characterized as having a rigid frame, the twisted boat required a scheme that represented changes in the molecular skeleton (bond distances and bond angles) resulting from its flexibility. To investigate this matter, quantum mechanical calculations
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Figure 2. Curves of the scattered electron intensities for CHDO were carried out with the Gaussian 03 package17 at several levels of theory and basis set size for the chair and several of the twisted boat forms corresponding to different pseudorotational displacements of the six-member ring. Table 1 shows the optimized energies from the B3LYP/cc-pVTZ calcula-
Table 1. Theoreticala Thermochemical Data (in kcal/mol) for Some Forms of 1,4-Cyclohexanedione symmetry p(CO,CO)
Erel
G°rel(435K)
twisted boat
D2
180.0
0.0
0.0
twisted boat
C2
161.7
0.09
–
chair
C2h
180.0
0.13
0.41b
pure boat
C2v
110.2
5.3
–
a
B3LYP/cc-pVTZ. bCorresponds to about 38 percent chair.
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tions. (The corresponding optimized distances for the forms of lowest energy, D2 and chair, are found in the table of final results.) The results of these calculations, including quadratic force fields, were chosen as an appropriate basis for generation of quantities helping to define the model to be tested experimentally. These quantities (amplitudes of vibration, perpendicular amplitude- and centrifugal distortion corrections) were obtained from normal coordinate calculations with use of the program ASYM4018,19 and the theoretical force fields. Model. Previously available structural information about gaseous CHDO suggests the existence of both a chair form and a slightly lower D2 twisted boat form that (hypothetically) undergoes pseudorotational displacements to forms of instantaneous C2 symmetry. Support for the hypothesis is found in the vibrational analysis described above that reveals one normal mode of B symmetry with a very low wave number (29 cm-1) the dynamics of which are consistent with the start of pseudorotation. Assuming the existence of pseudorotation for the D2 form of CHDO, the low (harmonic) wave number implies the motion to be of large amplitude and is supported by the data of Table 1 which show that the energy of this form changes only very slowly as a function of the angle between the C=O bonds. Table 1 also shows that the energy of the chair form is scarcely greater than that of the D2 twisted boat, which suggests that substantial amounts of it could be present in the vapor of CHDO. (However, the free energy difference, which determines the vaporphase equilibrium, is calculated to be much greater, implying that very little of this form is present.) Despite the earlier conclusion that little if any chair form was present in the vapor—supported by the calculated value of )G° for the reaction—it seemed unwise to adopt this limiting assumption, partly because the theoretical calculation of the thermal correction E ÷ G is subject to great uncertainty when low frequency vibrations are present, and partly because this form has played an important role in previous investigations of the conformational problem. Accordingly, we felt that ACS Paragon Plus Environment
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-8our model should incorporate the possible presence of some chair. We have found that for molecules like CHDO in which large amplitude motion is important, a suitable model for the dynamics of the motion consists of a collection of pseudoconformers positioned at suitable intervals along the pseudorotational or torsional coordinate, each with a Boltzmann weight proportional to its relative abundance determined by a potential expressed in terms of the changing coordinate. The parameter values for these pseudoconformers may differ importantly, but cannot be measured independently. Our method for taking account of these changes is to define the system in terms of suitable adjustable parameters of one of the pseudoconformers and to include the remaining forms by linking their structures to the chosen form through parameter differences calculated theoretically. Based on experience, we concluded that for CHDO ten pseudoconformers distributed at regular intervals along a suitable torsional coordinate would be sufficient to represent the dynamics of the twisted boat. The choice of a torsional coordinate is not simple. The pseudorotation is most easily visualized in terms of the angle between the C=O bond vectors (or the change in this angle from the 180° in the D2 form), neither of which are convenient vehicles for definition of the necessary theoretical calculations or for the structure of the pseudoconformers programed into our GED analysis. However, an important criterion was that this angle should be essentially a linear function of the coordinate chosen for these purposes in order to simplify the Boltzmann weighting given to the individual pseudoconformers. We found the torsion angle C2-C3-C4=O (equal to C5-C6-C1=O) to be satisfactory. The starting position of this coordinate corresponded to the D2 form of the twisted boat for which p(CO,CO) equaled 180° and ended with the latter essentially equal to 110°. The changes in the values of bond distances and bond angles for the ten pseudoconformers as obtained from theory are seen in Figure 3; the structure of each pseudoconformer was thus defined in terms
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Figure 3. Predicted changes in bond distances and bond angles for pseudoconformers of the twisted boat form of CHDO. The pseudorotational angle is the angle between the two C=O bond vectors where the 180° form has D2 symmetry.
of those corresponding to the D2 twisted boat by adding the parameter differences. Incorporation of the chair form in the model was done in similar fashion, i.e., by defining its parameter values in terms of theoretical differences from those of the D2 form, and defining its relative amount with a composition parameter. Determination of the system structure then follows from determination of the parameter values of the D2 form, a parameter determined by the pseudoconformational distribution, and a composition parameter indicating the relative amounts of the twisted boat and chair form. ACS Paragon Plus Environment
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- 10 There remains the problem of the form of the potential that determines the weighting of the twisted-boat pseudoconformers. It was found that a plot of the theoretical (B3LYP/cc-pVTZ) energy variation against the angle between the two C=O bond vectors has, to reasonable approximation, a parabolic form near the minimum. This suggests that an empirical fit to it could be obtained with a harmonic form of the potential, i.e., V = ½k()2)2, with )2 = )p(CO,CO), i.e., the difference between 180° and the angle between the two C=O vectors. The value of k, or a quantity related to it, then becomes a parameter to be adjusted during the structure refinement. We described the structure of the basic D2 model with a set of parameters in cyclindrical coordinates that made use of the C2 symmetry of the pseudoconformers. Each of these was defined by the differences between its parameters and those of the D2 form. In the following, R means the distance between an atom and the C2 axis, p refers to the angle between the x-axis and the radius vector of an atom, and Z the distance along the C2 axis measured from an origin at the midpoint of the line connecting atoms C1 and C4. The coordinates of the heavy atoms for the D2 form were +R, = (RC1 + RC2 + RC3)/3; +R, – RC2; (RC2 – RC3); +p(C2,C3), = (pC2 + pC3)/2; pC2 – pC3); +Z(C2,C3), = (ZC2 – ZC3)/2; ZC2 - ZC3; RO; pO; and ZO. The hydrogen-atom coordinates for the D2 form were also defined by similar radii, angles, and Z values, but during tests it was found that most of these could not be refined. The exception was the average C–H bond length, +r(C–H),. This parameter was introduced via a scaling factor that was applied to the distances calculated from theory. The last parameter affecting the structure of the system was one that determined the distribution of the pseudoconformers by adjustment of their relative weights defined by the formula wi = [exp(-Vi/RT)]/3exp(-Vi/RT). Here Vi is the energy of a pseudoconformer corresponding to a chosen value of )N according to the harmonic potential described above. Although the magnitude of the potential constant k determines the distribution, it was more convenient to use the rms standard deviation of the angle displacement, F()N) = (RT/k)½, as the adjustable parameter. ACS Paragon Plus Environment
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- 11 Refinements. The structures of twisted boat and chair forms comprising the system were defined in r" space. Several refinements explored the parameters for the hydrogen atoms, but as previously mentioned, values for these could not be reliably established. The cylindrical coordinates for the heavy atoms, however, were well determined. They are +R, = 1.442(5) Å, +R, - RC2 = 0.021(5) Å, pC2 - pC3 = -57.3(6)°, and H(factor) = 1.003(3) for our final model. The corrections necessary for generation of the ra and rg distances from the r" values were obtained from the normal coordinate calculations mentioned above. The rg (thermal average) values are listed in Table 2; with use of the amplitudes of vibration the corresponding ra distances may be deduced. An abbreviated correlation matrix for some of the interatomic distances is given in the Supplementary Information.
O Discussion
In addition to our results, Table 2 lists those for one of the models from the earlier investigation that most closely resembles ours.20 This model consists of a mixture of five species of molecule: twisted boats of symmetry D2 and C2, and a chair of symmetry C2h. It was defined by bond distances, bond angles and a composition parameter, with the assumption that corresponding distances and angles had the same values for all five conformations. This model is obviously considerably simpler than ours. Nevertheless, the fits to the experimental data given by both models are very good, judged by the small values of the quality-of-fit factor for each seen in Table 2 and the difference curves shown in Figures 2 and 4. (Similar curves for models from the first investigation are essentially identical to ours. There are important similarities and differences between the results from our two investigations. One of the major conclusions from the earlier work was that there was no evidence for the presence of a chair form, but that small amounts could not be ruled out. A different con-
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Table 2. Bond Angles (p/deg), rms Amplitudes of Vibration (l/Å), and Thermal Average Interatomic Distances (r/Å), for Twisted-Boat and Chair Conformations of 1,4-Cyclohexanedione earlier worka
this work twt’d boatc rg; p",ave
parameter
D2d,e
l
rg;p"
chair rg;p"
l
theoryb
twt’d boat +
D2
chair
rg; p"
re
re
l
+r(C–H),
1.115 (11)
0.092 (8)
1.122 (12) 1.124 (11)
0.091 (9)
1.114 (5)
0.093 (7)
1.092 1.092
r(C=O)
1.211 (3)
0.053 (3)
1.211 (3)
1.233 (6)
0.051 (3)
1.217 (2)
0.054 (3)
1.208 1.208
r(C1–C2)
1.524 (5)
0.065 X
1.522 (5)
1.526 (5)
0.064 X
1.531 (7)
0.066 X
1.521 1.519
r(C2–C3)
1.533 (11)
0.064 M
1.522 (15)
0.066 M
r(C1@C3)
2.511 (6)
0.094
(3)
Z
1.533 (11) 1.539 (11)
0.064 M
2.526 (6)
0.104
2.521 (6)
(3)
(3)
1.533 1.542
2.537 (9)
0.077
2.550 2.541
2.978 (62)
0.090 Z (9)
3.009 2.928
r(C1@AC4)
2.943 (16)
0.091 (9)
2.970 (16) 2.891 (16)
0.090 Z (12)
r(C2@C6)
2.587 (18)
0.089 O
2.588 (17) 2.577 (17)
0.090 O
2.605 (28)
0.077 O
2.577 2.564
r(C2A@O15)
2.395 (5)
0.072 (4)
2.392 (5)
0.071 (4)
2.400 (3)
0.069 (4)
2.393 2.395
r(C2@AC5)
2.820 (19)
0.108 (11)
2.848 (19) 2.982 (19)
0.106 (10)
2.876(103) 0.094 (16)
2.858 2.992
r(C2@AO16)
3.641 (8)
0.098 (11)
3.609 (8)
0.175 (11)
3.631 (140) 0.130 X
3.644 3.539
r(C1@AAO16)
4.120 (16)
0.122 X
4.170 (16) 4.036 (16)
0.170 X
4.189 (130) 0.130 M
r(O15@AAO16)
5.275 (16)
0.130 M
5.369 (16) 5.198 (16)
0.168 M
p(C1C2H7)
108.9 (5)
(20)
107.6 (4)
2.418 (5)
3.520 (8)
(19)
5.403 (62)
(9)
0.094 (38)
4.217 4.076 5.424 5.251
108.0 (4)
112.1f
108.3 107.5
f
112.2 109.0
p(C3C2H7)
113.2 (7)
111.5 (8)
110.9 (8)
112.1
p(C1C2H8)
107.3 (9)
107.1 (9)
107.9 (9)
112.1f
106.6 108.8
f
109.8 111.6
p(C3C2H8)
112.0 (8)
112.1 (8)
111.3 (8)
112.1
p(C1C2C3)
111.1 (5)
112.0 (4)
111.0 (4)
112.7 (4)
113.2 112.2
p(C6C1C2)
116.3 (8)
116.4 (8)
115.7 (8)
116.8 (11)
115.8 115.1
p(C2C1O15)
122.4 (4)
121.8 (4)
122.2 (4)
121.6 (5)
122.1 122.4
p(C6C1O15)
121.4 (3)
121.8 (4)
122.2 (4)
121.6 (5)
122.1 122.4
158.7 (1)
180.0 –
180.0 –
180.0 –
180.0 180.0
p(CO,CO) F()p(CO,CO))
g
25.0 (66)
+)p(CO,CO), h mol fraction
21.3 0.76 (10)
Ri a
0.14 –
0.24(10)
0.047 (whole system)
0.94 (8) 0.036
Ref 9, model B. The model incorporates a D2 , three C2 , and a chair form. bB3LYP/cc-pVTZ. cAverages of D2 form plus
all pseudoconformers of C2 symmetry. d Amplitudes do not differ significantly from those for the twisted boat. eValues for the D2 form only. f Uncertainty for RDJ’s model not available. gStandard deviation of change from p(CO,CO) = 180°. h
Weighted average displacement from p(CO,CO = 180°. iAgreement factor: R = [3 iwi)i2/3 iwi(siIm,i(obsd))2]½ where )i =
siIm,i(obsd) - siIm,i(calc.). ACS Paragon Plus Environment
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Figure 4. Radial distribution curves. The vertical lines under the top curve indicate the locations of the interatomic distances for both forms; the more important contributions from each form are shown separately below. The dashed lines show the largest differences between forms. The difference curve is experimental minus theoretical.
clusion is obtained from the current work: this form is predicted to be present in the amount of about 24 % at 435 K, and is in much better agreement with the theoretical result seen in Table 1. A second major conclusion from the earlier work was that either only a C2 form of the molecule existed that underwent very large “frame” vibrations, or that the system was a dynamic one comprising a D2 form which underwent large amplitude pseudorotation of the ring that generated a manifold of C2 forms. Apart from the different amount of chair form indicated as a component, the present work is consistent with the dynamic picture of internal molecular motion suggested previously. Other differences as well as some similarities between the two models are found in the corresponding values of the heavy-atom bond distances, geminal distances, and bond angles. The weighted average values with uncertainties (rg/Å; p/deg) of these parameters for the combined twisted boat and chair ACS Paragon Plus Environment
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- 14 forms listed in Table 2, followed by those from the earlier study in brackets, are C=O = 1.217(4) [1.217(2)], C1–C2 = 1.524(5) [1.531(7)], C2–C3 = 1.535(10) [1.522(15)], C1@C3 = 2.513(7) [2.537(9)], C2AC6 = 2.583(17) [2.605(28)], C2AO15 = 2.402(5) [2.400(3)], C1C2C3 = 112.1(5) [112.7(4)], C6C1C2 = 116.6(8) [116.8(11)], and CCO = 122.2(4) [121.6(5)]. The agreement is very good for all parameters except C1@C3 where the difference exceeds the sum of the uncertainties, and in the relative lengths of the C1–C2 and C2–C3 bonds. The latter are respectively of types sp2–sp3 and sp3–sp3. As has been abundantly confirmed by experiments on other molecules, the former are always found to be the shorter. Our results agree with this expectation, but the earlier ones do not. (However, the significance of this comparison is doubtful because of the large uncertainties associated with the values.) Theory also predicts that the C1–C2 bonds should be shorter than the C2–C3 ones by about 0.012 Å (D2 form) and 0.023 Å (chair). These are, or course, the equilibrium bond lengths, re. In the present work the best experimental distance type for comparison with the re value is r". The average r" values (not shown in Table 2) for the sp2–sp3 and sp3–sp3 bonds in the twisted boat form are respectively 1.519 Å and 1.522 Å, and in the chair form 1.519 Å 1.531 Å. The relative magnitudes of these distances agree with theory, but the differences are less. Lastly, the results of Shen and Samdal13 for CHDO need mention. For the static twisted boat/chair they find the following. Composition ratio: 70(9)/30(9), bond lengths (rg/Å): +C–H, = 1.116(5)/1.117(5), C=O = 1.220(2)/1.220(2), C1–C2 = 1.528(8)/1.525(8), and C2–C3 = 1.535(17)/1.545(17), bond angles (p" /deg): C-C-H = 108.3(7)/108.3(7), C1-C2-C3 = 113.3(10)/109.5(5), and C6-C1-C2 = 117.9(20)/115.5(10). Unlike ours, their model does not incorporate allowance for pseudorotation. Also, the constraints introduced by each of us were drawn from different levels of molecular orbital theory. Together, these differences make comparison of structural details from the two studies of uncertain value. However, it is pleasing that we agree very well on the relative amounts of the two forms as well as most of the parameter values when account is taken of their uncertainties. ACS Paragon Plus Environment
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- 15 The similar quality of the agreement between our current and earlier models may seem a bit surprising because of the more sophisticated ideas invoked for the current one, in particular those involving the structure of the C–C(O)–C group. As in the earlier model, the current one contains the assumption of C2 symmetry for all except one of the pseudoconformers (the D2 form); however, the earlier model also imposed the additional restriction of local C2v symmetry for the C–C(O)–C groups. The current model equates differences between bonds to the carbonyl groups in each of the pseudoconformers to those calculated from theory. An explanation for the similar quality of agreement lies in the weighted averages of these bond lengths. The average rg lengths of bonds C1–C2 and C1–C6 in the current model differ by only 0.002 Å, which suggests that the averages of these distances and others dependent upon them would be essentially the same as was found earlier. However, because each distance is slightly different for each pseudoconformer in the current model, the associated amplitudes of vibration should be slightly smaller. It is pleasing that this is indeed the case. The normalized experimental distribution of pseudoconformers at 435 K, assumed to be Gaussian in shape, is seen in Figure 5 as a function of the angle change 180° - p(CO,CO) = )p(CO,CO) = )N. Also shown is the distribution calculated from B3LYp/cc-pVTZ theory. The two distributions are in excellent agreement—evidence that the assumption of a Gaussian form for the experimental distribution was a very good one. The experimental weighted average deviation of this angle, depicted by the solid vertical lines, is 25.1°, insignificantly different from the theoretical value of 24.6° shown by the dashed vertical lines. The experimental standard deviation of the angle is 25.0 (66)°. The formula F()N) = (RT/k)½ based on the gaussian approximation for the distribution of )p(CO,CO) = )N allows an estimate of the “experimental” harmonic force constant for the torsional motion. The value is 0.021 aJ/rad2, in excellent agreement with the theoretical value of 0.015 aJ/rad2 for the normal mode of B3 symmetry which most closely ACS Paragon Plus Environment
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Figure 5. Distribution of pseudoconformers in the twisted boat form of CHDO. The dotted curve is theoretical (B3LYP/cc-pVTZ); the solid curve is the gaussian approximation to it used in the experimental analysis of the system structure. The corresponding dotted and solid vertical lines indicate the weighted averages of the change in the angle between the two C=O bond vectors from 180° in the D2 form.
approximates our ring-twist coordinate.
O Conclusion
The structure and composition of gaseous 1,4-cyclohexanedione has been shown to consist of a twisted boat form of D2 symmetry and a chair form of C2h symmetry in relative proportions of 76 to 24 percent with 2F uncertainty of 10 percent. This result differs from the structure in the crystal which consists of only a twisted boat form of C2 symmetry and is consistent with conclusion from molecular-beam-deflection-, and more recent IR and Raman experiments which indicate that the gaseous molecules have no dipole moment. The twisted boat form of the molecule experiences internal rotation that leads to an average value of 159° for the angle between the C=O bond vectors, in excellent agreement with the 154° - 155° found in the crystal. Values for the bond distances and bond angles for both forms have been determined and are consistent with theory. ACS Paragon Plus Environment
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- 17 Acknowledgment. We are grateful for support of this work by the National Science Foundation under grants CHE78-02458 and CHE-0613298.
Supporting Information Available. Table of the scattered electron intensities and one of a correlation matrix for the more important parameters. This information is available free of charge via the Internet at http://pubs.acs.org.
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- 18 References and Notes
(1) Allinger, N. L.; Blatter, H. M.; Freiberg, L. A.; Karkowski, F. M. Conformational Analysis. LI. The Conformations of Cyclohexanone Rings in Simple Molecules. J. Am. Chem. Soc. 1966, 88, 2999-3011. (2) Aihara, A.; Kitazawa, C. A Remark on the Dipole Moment of Cyclohexane-1.4-dione in Relations to Its Flexible Molecular Conformation. Bull. Chem. Soc. Japan 1971, 44, 99-103. (3) Rogers, M.; Canon, J. Electric Dipole Moments of Some Disubstituted Cyclohexane Derivatives in the Vapor State J. Phys. Chem. 1961, 65, 1417-1419. (4) Lambert, J. R. A direct, Qualitative Determination of Nonchair and Distorted-Chair Conformations of Six-Membered Rings. J. Am. Chem. Soc. 1967, 89, 1836-1840. (5) Chen, C.-Y.; Le Fevre, R. J. W. The Conformation of 1,4-Cycloxexanedione and the Two Isomeric 1,4-Dithiane-1,4-Dioxides. Aust. J. Chem. 1963, 16, 917-920. (6) Bailey, D. S.; Lambert, J. B. Chair-Twist Differentiation by Vibrational Spectroscopy. J. Org. Chem. 1973, 38, 134-137. (7) Bhatt, M. V.; Srinivasan, G.; Neelakantan, P. On the Conformation of Cyclohexane1,4-dione and Its Derivatives—1: Infrared and Raman Spectra of Cyclohexane-1,4-dione and Infrared Spectrum of Its Octadeutero Analogue. Tetrahedron, 1965, 21, 291-297. (8) Allinger, N. L.; Freiberg, L. A. Conformational Analysis. XXV. The Molecular Structure of 1,4-Cyclohexanedione. J. Am. Chem. Soc. 1961, 83, 5028-5029. (9) Mossel, A.; Romers, C. Investigations of the conformation of Non-aromatic Ring compounds. XIII. The Crystal Structure of Cyclohexane-1,4-dione at -140 °C. Acta Cryst. 1964, 17, 1217- 1223. (10) Groth, P.; Hassel, O.; Crystal Structure Determination of Cyclohexane-1.4-dione from Three-dimensional Data Obtained at Room Temperature. Acta Chem. Scand. 1964, 18, 923931. (11) Doud, P.; Dyke, T.; Klemperer, W. On the Conformation of 1,4-Cyclohexanedione. J. Am. Chem. Soc. 1970, 92, 6327.
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- 19 (12) Egawa, T.; del Rosario, A.; Morris, K.; Laane, J. . Vibrational Frequencies and Conformational Stability of 1,4-Cyclohexanedione in the Gas Phase As Studied by Infrared and Raman Spectroscopy and ab Initio Calculations. J. Phys. Chem. A, 1997, 101, 8783-8787. (13) Shen, Q.; Samdal, S. The Molecular Structures and Conformational Compositions of 1,3-Cyclohexanedione and 1,4-Cyclohexanedione As Determined By Gas-phase Electron Diffraction and Theoretical Calculation. J. Mol. Struct. 2011, 1005, 156-160. This overlooked work was brought to our attention by a reviewer, to whom we are grateful. (14) Johnson, R. D. A Reinvestigation of the Molecular Structure of Cyclohexane-1,4dione by Electron Diffraction. M.S. Thesis, Oregon State University, 1980. (15) Gundersen, G.; Hedberg, K. Molecular Structure of Thionyltetrafluoride, SOF4 J. Chem. Phys. 1969, 51, 2500-2507. (16) Hedberg, L. Determination of Molecular Structures by Analysis of ElectronDiffraction Data. Method for Automatic Removal of Background. Abstracts, Fifth Austin Symposium on Gas Phase Molecular Structure, Austin, TX, 1974, No. T9. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A. Jr.; Vreven, T. K.; Kudin, N.; Burant, J. C.; et al. Gaussian 03, Revision E.01, Gaussian, Inc., Wallingford CT, 2004. (18) Hedberg, L.; Mills, I. M. Harmonic Force Fields from SCF Calculations: Program ASYM40. J. Mol. Spectrosc. 2000, 203, 82-95. (19) Hedberg, L.; Mills, I. M. ASYM20: A Program for Force Constant and Normal Coordinate Calculations, with a Critical Review of the Theory Involved. J. Mol. Spectrosc. 1993, 160, 117-142. (20) Three different models that give about equally good fits to experiment and have similar distance and angle values were discovered in the early investigation.
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