Molecular Structure, Equilibrium Conformation, and Ring-Puckering

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Molecular Structure, Equilibrium Conformation, and Ring-Puckering Motion in 1,1,3,3-Tetramethylcyclobutane. An Electron-Diffraction Investigation Augmented by Molecular Orbital and Normal Coordinate Calculations Kenneth Hedberg, Lise Hedberg, and Jason Sandwich J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b05428 • Publication Date (Web): 24 Jul 2017 Downloaded from http://pubs.acs.org on July 27, 2017

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The Journal of Physical Chemistry

Molecular Structure, Equilibrium Conformation, and Ring-Puckering Motion in 1,1,3,3-Tetramethylcyclobutane. An Electron-Diffraction Investigation Augmented by Molecular Orbital and Normal Coordinate Calculations Jason W. Sandwisch, 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: 14 Number of tables: 1 Number of figures: 5

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Abstract. The molecule cyclobutane (CB) has a non-planar carbon skeleton folded around a line connecting diagonally opposite atoms. The puckering angle (the change from planarity) of about 30° is generally attributed to steric repulsion between the four sets of adjacent methylene groups which would be opposed in a planar ring and is relieved by the puckering. According to this criterion, a similar molecule, 1,1,3,3-tetramethylcyclobutene (TMCB), in which adjacent methylene groups do not exist, would be expected to have a planar ring in the equilibrium form. We have investigated the structure of TMCB to test this expectation. Two models were designed for the tests: one having D2h symmetry (planar ring) and one of C2v symmetry nonplanar ring. Each model incorporated the dynamics of large-amplitude bending around a line joining the methylene groups. Our results suggest the D2h model is to be preferred. Dynamic averages (rg/Å; pg/deg) of the more important distances and angles in the D2h model with estimated 2F uncertainties, are as follows. = 1.105 (5), C1–C5 = 1.524 (10), C1–C2 = 1.559 (11), C2–C1–C4 = 87.4 (8), C1–C2–C3 = 92.0 (7), C5–C1–C6 = 109.0 (13), and C2–C1–C5 = 115.8 (8). The large-amplitude bending of the ring leads to a thermal average value of the folding angle equal to 177.1°. The results, including the differences between TMCB and CB are discussed.


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The Journal of -Physical Chemistry 3-

INTRODUCTION Cyclobutane, C4H8, (CB) is the simplest alicyclic molecule that offers the possibility for non-planarity of the carbon skeleton. A number of theoretical1 and experimental2,3,4,5,6,7 studies have shown that non-planarity is indeed the case, with the amount of the bending around a line joining diagonally disposed carbon atoms equal to 29°-30°. A related molecule is 1,1,3,3tetramethylcyclobutane (TMCB), which may have structural properties quite different from CB because of the heavy loading of the carbons across the ring. Among the more interesting of these properties are the equilibrium conformation of the molecule, the near certain existence of largeamplitude bending around a line joining C2 and C4, and the potential surface defined by the ringbending vibration. Figure 1 shows two likely8 equilibrium conformations: one a planar fourmember ring of D2h symmetry and another with a folded ring of C2v symmetry. Recent work from this laboratory has included structural studies of several molecules with

Figure 1. Diagrams of likely equilibrium forms of 1,1,3,3-tetramethylcyclobutane with atom numbering for distance identification. small rings of carbon atoms, such as 1,2-dimethoxycylobutene-3,4-dione,9 but none with saturated four-member rings. A study of TMCB is a natural extension of this line of research into that area, and which was undertaken to address the questions posed above. Except for an unlikely high


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barrier to inversion in the C2v form of the molecule, both forms were likely to be undergoing a large-amplitude bending vibration of the type mentioned above. Such motion leads to correspondingly large changes in some of the interatomic distances and requires a model of the structure that takes appropriate account of these distance changes. EXPERIMENTAL Electron-diffraction experiments were carried out on the vapor of TMCB. The sample, of unknown origin, was determined to be about 95 % pure by 13C and proton NMR. The apparatus parameters consisted of an r3 sector, a nominal accelerating potential of 60 kV, nominal long camera (LC) and middle camera (MC) distances of 70 cm and 30 cm, and a room-temperature sample. The recording medium was Kodak Electron Image film developed for 15 minutes in D19 developer diluted 1:1. The electron wavelength was calibrated against CO2 (ra(CO = 1.1646 Å, ra(OO) = 2.3244 Å). Three films from the LC distance and one from the MC distance were chosen for analysis. Digitized data were obtained from the films by use of a high-resolution scanner rather than a microdensitometer that was formerly the instrument of choice in our laboratory. The scanning parameters were 400 dots per inch (DPI) with an eight-bit gray scale; the results were values for optical absorbance. The data were assembled in the form of radial distributions of intensity with the program ImageJ.10 These distributions were converted to a form that could be handled by our standard data-reduction package. The experimental molecular scattering in the form customarily used for refinement in this laboratory is shown in Figure 2. ANALYSIS OF THE STRUCTURE Quantum-chemical Calculations. To help with the design of model(s) for TMCB, we carried out a large number of ab initio (HF and MP2) and DFT (B3LYP) molecular orbital calculations with use of the Gaussian09W package11 that included basis sets up to cc-pvtZ. With the structure-optimized molecule in the D2h conformation, use of the theoretical force constants from the MP2/cc-pvtZ and MP2/6-311G(d) calculations gave, respectively, one negative wave


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Figure 2. Intensity curves. The theoretical curve is for the D2h model of Table 1. The difference curves are experimental minus theoretical. number of -47 cm-1 and one of -39 cm-1. However, use of the latter basis with a C2v molecule yielded no imaginary wave numbers, (the smallest having the value 54 cm-1) and a C1C2C4C3 angle of 189.4°. Further, use of DFT theory (B3LYP/cc-pvtZ) yielded only positive wave numbers for the molecule with D2h symmetry, the smallest being 11 cm-1. Each of these wave numbers corresponds to the ring-folding mode of the molecule and each mode is in thermal equilibrium at room temperature. Figure 3 shows the ring-folding potentials and the corresponding Boltzmann distributions of molecular conformation as predicted from the computations. The calculated barrier height for the C2v form is 0.05 kcal/mol. Models and Refinements. TMCB presents a difficult problem for the design of models because the thermal averaging of the folding mode tends to blend the plausible conformations shown in Figure 1. The key to an experimental determination of the equilibrium symmetry of the



Figure 3. Theoretical (B3LYP/cc-pvtZ) ring-folding potentials and pseudoconformer distributions. The black curves are for the D2h model and the red for the C2v model. molecule is whether the difference in the distance distribution for planar- or folded ring models of the structure is large enough to be detected. In studies of other systems that presented a similar structural problem (large-amplitude motion), we have used models consisting of a distribution of Boltzmann-weighted “pseudoconformers” arranged along the coordinate that undergoes large changes. For TMCB most of the bond lengths and distances across a bond angle are not much affected by the bending mode, and thus are of no help in an experimental determination of the molecular symmetry at the minimum of the potential energy surface. The distances undergoing the largest range of change under envelope-type folding of the four-member ring are C3@@C5 (0.4 D) and C5@@@C7/C6@@@C8 (1.2 D). The distribution of these distances as a result of the envelope-folding mode is shown in Figure 4. Unfortunately, the difference between these distributions is very small, and thus there is no hope of help from the theoretical side with an experimental determination of the equilibrium symmetry of TMCB. There is some hope from the experimental side alone, however, in the quality of fit to scattering data that can be obtained from structure refinements of the models designed to test the two likely symmetries for the TMCB molecule. We designed two models to address the symmetry question. Each consisted of nine pseudoconformers distributed at )N = 4° intervals along the folding coordinate Tests revealed


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Figure 4. Theoreticl scattering distribution from distances that change the most as a consequence of the envelope folding parameter. The black curve corresponds to a molecule of D2h symmetry and the dotted red curve to one of C2v symmetry. that the function V()N) = V4()N)4 - V2()N)2, where the pseudoconformers were weighted according to exp(-V()N i)/RT)/Giexp(-V()N i/RT) and the potential constants V4 and V2 had appropriate values, gave very good fits to the curves of Figure 2. In addition to the potential constants, the structural parameters for each model were (atom numbers according to Figure 1) +r(C–H),; +r(C–C), = [r(C1–C2) + r(C2–C3) + r(C1–C5) + r(C1–C6)]/4; +r(C1,5–C1,6), = [r(C1–C5) + r(C1–C6)]/2; )r(C1,5–C1,6) = r(C1–C5) - r(C1–C6); p(C2C1C4); p(C5C1C3); p(C5C1C6); p(C1C2C4C3); p(H9C2H10); p(C3C7H15); p(H13C7H14); and p(Hflap), equal to the angle between the C3–C7 bond and the vector between C3 and the midpoint of the line joining H13 and H14. C..H distances separated by more than one angle were ignored. There are also vibrational amplitude parameters (frame amplitudes). We used the program ASYM4012,13 and the theoretical force constants from the optimized structures to calculate starting values for these quantities. As is usual, these were collected into various groups as needed during the course of the refinements. Some groups could be refined, but others had to be held at the theoretical value(s). Our initial work quickly made clear that the potential constants V2 and V4 could not be



successfully refined. Since their values bear on the molecular symmetry question, it became necessary to carry out refinements of the remaining parameters with fixed values of these constants, with the intention of selecting “best model(s)” by comparison of the quality-of-fit factors R. We began with tests of sets of potential constants for each of the two symmetries. From the form of the potential function we have assumed, it is clear that molecules of D2h and C2v symmetry are generated by giving V2 respectively negative and positive values. It is also true that the barrier separating the two minima in the C2v potential reflects the magnitude of V2. It seemed most likely that the potentials of the two forms did not differ much. We refine several models defined by V4 equal to 0.006 and V2 equal to -0.500 (D2h), and +0.500 to +5.000 (C2v), keeping the amplitude groupings and intragroup differences the same. Results for models of each symmetry that gave the best — and matching — fits are given in Table 1. All geometrical and all groups of vibrational parameters were successfully refined for each of these models. The radial distribution of distances for each of the models is shown in Figure 5. RESULTS AND DISCUSSION The main question we have sought to answer in the present work is whether the fourmember ring in molecules of TMCB is planar in the equilibrium structure or slightly twisted as in cyclobutane itself. The results listed in Table 1 (and seen in the details of Figure 5) do not provide the answer when the twisted form differs from the planar one by only the small amount represented by our C2v model: the refined parameter values of the two models are very similar and the qualities of fit shown by the R factors are identical. Nevertheless, there is strong evidence that TMCB has D2h equilibrium symmetry. In a series of refinements characterized by V2 having progressively larger positive values (which leads to an increasing barrier height in the double minimum potential), the quality of fit for the C2v form of the molecule became progressively worse. These observations are consistent with a D2h molecule in which small distortions of the four-member ring do not degrade the fit, but do so as the distortions become significantly larger. The probable existence of a planar four-member ring in TMCB contrasts with the bent ring in CB. The most likely explanation lies in the manner that repulsive steric interaction


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Table 1. Selected Distance/Å and Angle/deg Values for Models of 1,1,3,3-Tetramethylcyclobutane Experimental

Theoretical

C 2v parameters c

r "/p "a

D 2h

r g/p gb

la

r "/p "a

rg/p gb

la

C 2v

D 2h

re

re

+C-H,

1.076

1.104(5)

0.075(6)

1.076

1.105(5)

0.075(6)

1.092

1.092

C1–C5

1.519

1.523(10)

0.054(5)

1.52

1.524(10) 0.055(5)

1.525

1.526

C1–C6

1.521

1.524(10)

0.054(5)

1.52

1.524(10) 0.055(5)

1.527

1.526

C1–C2

1.577

1.559(11)

0.055(5)

1.556

1.559(11) 0.055(5)

1.561

1.561

C2@C4

2.155

2.154(18)

0.065(7)

2.158

2.159(18) 0.064(7)

2.186

2.189

C1@C3

2.241

2.242(24)

0.055(7)

2.243

2.245(23) 0.054(7)

2.225

2.226

C5@C6

2.48

2.481(19)

0.072(7)

2.48

2.483(18) 0.070(8)

2.505

2.506

C2@C5

2.607

2.608(11)

0.075(7)

2.589

2.612(12) 0.074(8)

2.596

2.589

C2@C6

2.572

2.578(11)

0.075(2)

2.589

2.572(11) 0.074(8)

2.584

2.589

C3@@C5

3.439

3.442(19)

0.058(33)

3.36

3.419(19) 0.062(33)

3.394

3.341

C3@@C6

3.268

3.264(22)

0.083(33)

3.36

3.300(22) 0.062(33)

3.284

3.341

C5@@@C7

4.246

4.257(51)

0.063(33)

4.002

4.179(52) 0.066(33)

4.130

3.968

C6@@@C8

3.732

3.723(52)

0.063(33)

4.002

3.820(52) 0.066(33)

3.800

3.968

C5@@@C8

4.69

4.686(15)

0.088(34)

4.708

4.702(15) 0.090(35)

4.687

4.693

p(C2C1C4)

87.6

87.4(8)

87.8

87.4(8)

88.9

89.0

p(C1C2C3)

92.1

91.9(8)

92.2

92.0(7)

90.9

91.0

p(C5C1C6)

109.4

109.1(19)

109.3

109.0(13)

110.3

110.4

p(C2C1C5)

115.9

115.6(8)

116.8

115.8(8)

114.5

114.0

p(C2C1C6)

113.4

113.4(8)

114.6

113.2(7)

113.6

114.0

180

177.1

173.8

180.0

p(C1C2C4C3) 175.2

n

V 4 /V 2 d

0.006/0.500

0.006/-0.500

R e(exp)

0.123

0.123

a

Values at minima of potentials. bWeighted thermal averages. Weights are from refinement results and are similar to those seen in Fig. 3. cSee Fig 1 for atom numbering. dPotential constants. eR = [3 iwi) i2 /3 iwi(siIm,i(obsd))2 ]½ where ) i = siIm,i(obsd) - siIm,i(calc.).


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Figure 5. Radial distribution curves. The experimental curves are for the models of Table 1. The vertical bars show the locations of the designated distances. The horizontal arrows indicate the ranges of movement of the distances shown by the imbedded dots. The difference curves are experimental minus theoretical can be relieved in each case. In CB with a planar ring, the four pairs of C-H bonds on adjacent carbon atoms would be eclipsed, an energetically unfavorable circumstance that can be mitigated by folding the ring which tends to stagger the bonds. In TMCB with D2h molecular symmetry as represented in Figure 1 there are also pairs of eclipsed C-H bonds, but they are further away from each other than in CB and in any case the repulsive forces can be relieved by small rotations of the methyl groups. In short, there is no need to bend the ring in TMCB to relieve steric repulsion. It is worth noting that, although the theoretical structures yield only real wave numbers, we made no attempt to calculate the effect of varying the methyl-group torsions. To ignore them seemed justified because the primary effect of these torsions on our experimental analysis is negligible: only the very long carbon-hydrogen terms are involved and they would surely be rapidly damped out. The thermal-average ring bond lengths (rg) in TMCB, equal to 1.559 (11) Å, are about the same as in CB (1.554(1) Å),14 but the bonds to the methyl groups at 1.524 (10) Å are slightly shorter than the 1.535 Å usually seen in an sp3 environment. This is not surprising: if the bonding power of the linking carbon atoms is the same as it is in unstrained circumstances, the weaker


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The Journal of- Physical Chemistry 11 -

bonding implied by the longer ring bonds suggests stronger bonding to the methyl groups with consequent bond shortening. We also note that the angle involving a pair of methyl groups is larger than the tetrahedral value, in accordance with usual experience when the opposing angle is smaller than tetrahedral. This is consistent with the picture of less s- and more p-character for the ring bonds which tends toward 90° angles, and greater sp2 character for the peripheral bonds, which tends toward 120° angles. Finally, we call attention to the thermal average value of the folding angle C1C2C4C3, which as a consequence of the vibrational averaging of the bending vibration obtains a value (177.1°), slightly different from the 180° implied by the D2h equilibrium symmetry of the molecule.

Acknowledgement. We are grateful to the Dreyfus Foundation for support of this work by a grant to K.H.



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1952, 20, 1703-1707. (8) Verified by molecular obital calculations. (9) Costello, L. L.; Hedberg, L.; Hedberg, K.. Molecular Structure and Conformations of 1,2Dimethoxycyclobutene-3,4-dione. An Electron-Diffraction Investigation Augmented by Quantum Mechanical and Normal Coordinate Calculations. J. Phys. Chem. A 2015, 119, 15631567. (10) Schneider, C.A.; Rasband, W. S.; Eliceiri, K. W. NIH Image to ImageJ; 25 years of image analysis. Nature Methods 2012, 9 671-675. The ImageJ analysis programs ae available at https://imagej.nih.gov/ij/index.html.


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(11) Gaussian09W, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al., Gaussian, Inc., Wallingford Ct 2010. (12) Hedberg, L.; Mills, I. M. Harmonic Force Fields from SCF Calculations: Program ASYM40. J. Mol. Spectrosc. 2000, 203, 82-95. (13) 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.



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Possible equilibrium forms for 1,1,3,3-tetramethylcyclobutane 254x190mm (96 x 96 DPI)


Molecular Structure, Equilibrium Conformation, and Ring-Puckering

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