Gas-Phase Infrared and NMR Investigation of the Conformers of

Article pubs.acs.org/JPCA

Gas-Phase Infrared and NMR Investigation of the Conformers of Diacetone Diperoxide (DADP) Chunlei Guo,† John Persons,† Jeffrey N. Woodford,‡ and Gerard S. Harbison*,† †

Department of Chemistry, University of Nebraska at Lincoln, Lincoln, Nebraska 68588-0304, United States Department of Chemistry, Missouri Western State University, 4525 Downs Drive, St. Joseph, Missouri 64507, United States

‡

S Supporting Information *

ABSTRACT: Gas-phase infrared measurements of diacetone diperoxide (DADP) indicate a chair conformation with less than 5% of the predicted twist conformer. Vibrational frequencies are very similar to those previously measured in the solid state. Solution NMR measurements using 2D exchange spectroscopy (EXSY) also set a very low maximum limit on the equilibrium population of the twist conformer, with a roomtemperature free-energy difference in excess of 14.5 kJ/mol. These experimental results are in accord with high-level quantum calculations incorporating full thermochemistry and solvation effects, which indicate a free-energy difference in the range of 14.7−17.5 kJ/mol in polar solvents.

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DADP,5,7,8 indicating TATP is the kinetic and DADP the thermodynamic product. The conformational variability of the molecules is a matter of some interest. Steric considerations dictate that the lower cyclic peroxides of the series possess gâuche O−O bonds, and these have been invariably observed. The two gâuche O−O bonds in DADP can combine to give either g+g+ and its enantiomeric g−g− combination (these structures lead to D2 molecular symmetry in the so-called “twist” structure) or the achiral g+g−, which has C2h molecular symmetry and a chair conformation. These conformers are shown in Figure 1. In crystalline DADP8,9 and in cocrystals formed with electron-deficient aromatics,10 the molecule has a nearly ideal chair conformation. Computational studies have universally concluded that the chair form is more stable than the twist, with all boat conformers unstable; however, the difference of free energy between chair and twist is in some dispute. Pis Diez and Jubert,11 working at the relatively low B3LYP/6-31*G(C,O)/321G**(H) level of theory, found a difference of 11.6 kJ/mol between the two conformers; although their paper is not completely clear on the point, it appears that this is ΔE and not ΔG. Shlykov et al.12 did similar calculations using both density functional (B3LYP) and MP2 methods, using 6-31G(d,p) and 6-311+G(2df,p) basis sets, and found differences in energies of the same order, with a free-energy difference generally about 2 kJ/mol less than the energy difference (although it appears that this may be a result of a sign error because, contrary to our computations (see below), their thermochemical contributions reduced rather than increased the energy difference). They also concluded that their gas-phase electron diffractograms were more consistent with the chair conformation.

INTRODUCTION Because of their widespread use in terrorist bombs, the explosive cyclic peroxides of acetone have attracted considerable research interest in the past decade. The trimeric cyclic peroxide of acetone, triacetone triperoxide (TATP) was first synthesized by Wolffenstein1 from acetone and 50% hydrogen peroxide after the addition of a drop of phosphoric acid as catalyst; the author inferred the correct cyclic structure from the empirical formula and molecular weight. The author noted the explosive character of the material when his first attempt at elemental analysis resulted in the body of the reaction flask being reduced to “the finest glass powder”. Later research2 indicated that the cyclic triperoxide is formed by condensation of open-chain monomeric and dimeric peroxides under acidcatalyzed conditions. The cyclic dimer (DADP) was prepared a few years later by Baeyer and Villiger3 as a product of the treatment of acetone with Caro’s acid (peroxymonosulfuric acid), but the authors originally attributed it to a monomeric structure. They reported it to be shock-sensitive. Subsequent molecular weight measurement4 demonstrated that they could separately isolate the dimer (mp 132−133 °C) and trimer (mp 90−94 °C). Most modern preparations involve mixing acetone, a moreor-less concentrated hydrogen peroxide solution, and a strongacid catalyst. TATP formation is favored by lower temperatures and relatively low catalyst concentrations; DADP is favored by higher temperatures, longer reaction times, and concentrated inorganic acids.5 A recent study6 has shown that for a fixed amount of acetone and a molar ratio of water to sulfuric acid of 5:1 or lower, indicating dilute acid solution, that the product is almost exclusively DADP, regardless of the amount of hydrogen peroxide initially in the mixture; as the mole ratio increases, the product favors TATP over DADP, even as total peroxide yield remains relatively constant. Upon standing for long periods of time, the TATP initially formed converts to © XXXX American Chemical Society

Received: July 21, 2015 Revised: September 18, 2015

A

DOI: 10.1021/acs.jpca.5b07074 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Scheme 1

been observed. In order either to measure the relative free energies of the twist and chair conformers in vacuum and in solution or to set an upper limit on the stability of the twist conformation, we therefore undertook the present study.

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THEORY Exchange of the axial and equatorial methyls in DADP almost certainly occurs via a twist intermediate.12 We can draw a scheme for the exchange as follows:. Note that there are actually two enantiomeric twist conformers. Assuming that all reactions are fundamental and first order, we can write the differential rate equation in matrix form Ṗ = KP, with the rate coefficient matrix K and the polarization vector P given by

Figure 1. C2h (a) and D2 (b) conformers of DADP.

DADP has been subjected to 1H13 and 13C14 NMR analysis. DADP is found to possess two singlets in proton NMR, assigned to the diastereotopic axial and equatorial methyls in slow exchange.13 These coalesce and show a single peak at higher temperature.15 DADP was originally reported14 to have two 13C signals, at 21.2 and 106.5 ppm; this is inconsistent with the 1H NMR, which suggests that the axial and equatorial methyls should be in slow exchange and there should be three 13 C signals, from the diastereotopic methyls and the ketal carbon. More recent 13C NMR15 shows a downfield line from the ketal peak and two upfield signals from the axial and equatorial methyls. Most of the predicted 30 infrared and 30 Raman transitions (Γvib = 18Ag + 12Bg + 13Au + 17Bu) have been identified for solid DADP16−18 and have been assigned by the usual harmonic approximation/normal-mode analysis. DADP19 has a significant vapor pressure at ambient temperatures, and enthalpies and entropies of vaporization have been measured.20 Calorimetric enthalpies of formation have also been determined for both DADP and the trimeric peroxide TATP.21 While the spectroscopy and conformational isomerism of DADP has therefore been rather thoroughly studied, some gaps remain. The gas-phase spectrum of DADP has not previously been recorded, nor has the twist conformer, which some studies indicate should be present in measurable concentration, ever

peq (t ) =

⎛−2k1 k −1 0 ⎞ k −1 ⎜ ⎟ 0 k1 ⎟ ⎜ k1 −2k −1 K=⎜ ⎟ 0 −2k −1 k1 ⎟ ⎜ k1 ⎜ ⎟ k −1 k −1 −2k1⎠ ⎝ 0

(1)

⎛ peq ⎞ ⎜ ⎟ ⎜ ptw,R ⎟ P=⎜ ⎟ ⎜ ptw,S ⎟ ⎜ p ⎟ ⎝ ax ⎠

(2)

peq, ptw,R, ptw,S, and pax correspond to the respective polarizations of the chair equatorial, twist-R, twist-S, and chair axial methyls, respectively. The differential rate equation may be solved in the usual way by resolution of the identity, using the matrix U, which diagonalizes K: Ṗ ′ = UṖ = (UKU−1)UP = ΛP′. In the present case, Λ, the diagonal eigenvalue matrix, has diagonal elements (0, −k1, −k−1, −2(k1 + k−1)). The matrix differential equation has the following solution. P′(t ) = exp( −Λt )P′(0) or P(t ) = U −1 exp( −Λt )P′(0)

(3)

The individual time-dependent polarizations are given as follows

⎧ k −1(peq (0) + pax (0) + ptw,R (0) + ptw,S (0)) 1⎪ ⎨(peq (0) − pax (0))exp( −2k1t ) + k 1 + k −1 2⎪ ⎩ +

k1(peq (0) + pax (0)) − k −1(ptw,R (0) + ptw,S (0)) exp( −2[k1 + k −1]t ) ⎫ ⎪ ⎬ ⎪ k 1 + k −1 ⎭

B

(4a)


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The Journal of Physical Chemistry A ⎧ k1(peq (0) + pax (0) + ptw,R (0) + ptw,S (0)) 1⎪ ⎨(ptw,R (0) − ptw,S (0)) exp( −2k −1t ) + k 1 + k −1 2⎪ ⎩

ptw,R (t ) =

−


⎧ k1(peq (0) + pax (0) + ptw,R (0) + ptw,S (0)) 1⎪ ⎨−(ptw,R (0) − ptw,S (0)) exp( −2k −1t ) + k 1 + k −1 2⎪ ⎩

ptw,S (t ) =

−

pax (t ) =



k + k1 exp(− 2[k1 + k −1]t ) ⎫ 1⎧ ⎨exp(− 2k1t ) + −1 ⎬ 2⎩ k 1 + k −1 ⎭ (5a)

pax (t ) =

1 k1{1 − exp( −2[k1 + k −1]t )} 2 k 1 + k −1

(5b)

k + k1 exp( −2[k1 + k −1]t ) ⎫ 1⎧ ⎨ − exp(− 2k1t ) + −1 ⎬ 2⎩ k 1 + k −1 ⎭ (5c)

In the present case, k−1 ≫ k1, and therefore, the equations can be further approximated by 1 peq (t ) ≅ {exp( −2k1t ) + 1} 2 pax (t ) ≅

1 {− exp(−2k1t ) + 1} 2

ptw,R (t ) = ptw,S (t ) =

(4d)

constant of 2(k1 + k−1). Because the twist peak has a much shorter lifetime under conditions where the chair peaks are appreciably exchange broadened and the twist peak is at low concentration, it will be broadened beyond visibility, and NMR experiments that show no twist peak under these conditions actually say very little. Rather, the above analysis tells us that to detect the twist peak, we should run EXSY spectra at temperatures where the axial/equatorial exchange is slow because the twist cross peaks will reach their limiting intensities much faster than the cross peaks between the axial and equatorial methyls, and the value of k−1, which is equal to the angular frequency width of peaks at half-height, must not be so large as to broaden the peaks beyond the range of visibility. While lower temperature will also reduce the population of the rarer conformer, the tendency of this to decrease peak visibility will be much less pronounced than the increase in visibility due to narrowing of the resonance.

If we start exclusively with methyl signal encoded with the equatorial frequency, as is the case for the slice through the equatorial proton signal in either dimension in the 2D spectrum, then we can set peq(0) = 1 and ptw,R(0) = ptw,S(0) = pax(0) = 0, and the equations reduce to the following three

ptw,R (t ) = ptw,S (t ) =

(4c)

⎧ k −1(peq (0) + pax (0) + ptw,R (0) + ptw,S (0)) 1⎪ ⎨−(peq (0) − pax (0)) exp( −2k1t ) + ⎪ k 1 + k −1 2⎩ +

peq (t ) =

(4b)

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EXPERIMENTAL SECTION TATP was synthesized as follows: 1.1 g (19 mmol) of acetone was added to 2.3 g (20 mmol) of 30% hydrogen peroxide and cooled to 0 °C in ice bath. A drop of concentrated HCl was added, and the entire mixture was gently mixed and allowed to warm to room temperature and precipitate for about a day. The white precipitate formed was filtered and washed with distilled water. The yield of this preparation was about 200 mg (0.9 mmol) of TATP. Previous reports indicated that diacetone diperoxide (DADP) was also formed, and indeed, a small amount of the latter was detected by NMR. DADP was produced from TATP by dissolving in CH2Cl2 and adding a small amount of p-toluenesulfonic acid.8 Proton 1D NMR spectra were obtained at 300.13 MHz at various temperatures using a Bruker Avance spectrometer.

(6a)

(6b)

1 k1 {1 − exp( −2[k1 + k −1]t )} 2 k −1 (6c)

In other words, peq and pax (the on-axis equatorial peak and its cross peak with the axial proton) converge to equal intensities of 1/2 with a time constant of 2k1, while the twist cross peak reaches a much smaller intensity k1/k−1 (both enantiomers contribute to a single NMR peak) with a much faster time C


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The Journal of Physical Chemistry A

using default solvent parameters for acetonitrile, toluene, and methylene chloride. Vibrational self-consistent field (VSCF) computations were carried out using the quartic force field approximation of Yagi et al.,27 with 16 grid points along each normal mode, at the MP2/6-31G++(d) level. Chemical shieldings were computed using the program Gaussian-09 at the MP2/6-311++G(2d,p) level; structures were computed at the same level of theory. Subtraction of the chemical shieldings from those of a fully staggered Td-symmetric structure of tetramethylsilane (TMS), optimized and computed at the same level of theory, gave the computed chemical shifts.

Room-temperature spectra were also collected at 500.153 MHz. The proton π/2 pulse lengths were 6.1 and 8.1 μs at 300 and 500 MHz, respectively. Spectra were converted to a tetramethylsilane (TMS) scale using the solvent residual proton signal as a reference. Phase-sensitive 2D exchange spectroscopy (EXSY) NMR spectra22 were collected with gradient homospoil;23 the pulse sequence, used without modification from the Bruker pulse program library, is shown in Figure S1 of the Supporting Information. The gradients before and after the π pulse were equal in magnitude and opposite in sign. To search for possible cross peaks, the exchange time, temperature, and solvent were all varied. Because computations (see below) suggested a significant effect of solvent dielectric constant on the relative stabilities of the conformers, we ran NMR in a low-dielectric solvent (toluene-d8) from 230 K to room temperature and a high-dielectric solvent (acetonitrile-d3) from 245 K to room temperature, as well as in the usual CD2Cl2; we also carefully examined the baselines of high-quality EXSY spectra taken over a range of temperatures from 230 K through room temperature because the stereochemically most likely route for the interconversion of the C2h axial and equatorial methyls is via the D2 conformer. In order to minimize artifacts, a relaxation delay of 8 s was typically used between acquisitions; 1024 × 1024 time domain data points were routinely acquired. 2D gradient-enhanced heteronuclear single-quantum coherence (HSQC) NMR spectroscopy,24 implemented with the modifications introduced by Schleucher et al.,25 was used to acquire 1H−13C correlation spectra at 500 MHz with the same proton π/2 pulse length and a 13.10 μs 13C π/2 pulse. 2D heteronuclear multiple-bond coherence (HMBC) NMR spectra were obtained by standard methods. Gas-phase infrared spectra were obtained in 1 bar nitrogen gas in a custom-made 21.6 cm path length cell; DADP powder was simply sprinkled through the gas port into the cell; it was then purged with N2 and allowed to equilibrate. The spectrum was taken using a standard undergraduate laboratory FTIR spectrometer, after nitrogen purging, at 1 cm−1 digital resolution, accumulating 32 transients.

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RESULTS Structure. We assessed the correspondence of our computed C2h structure with the two crystallographic structures as follows; the C2 axis was set to intersect with the crystallographic inversion center, and the molecule rotated about three polar angles to minimize the least-squares deviation of the heavy atoms from the relevant computed structure. The resulting root-mean-square deviation (RMSD) for the 10 heavy atoms was 0.11 pm with B3LYP and 0.23 pm for MP2, for both X-ray structures at all levels of theory; differences between basis sets were much smaller than the difference between computed and X-ray structures (which in themselves were not large). This proves the near-identity of the two crystal structures and indicates a lack of structurally significant interactions within the crystal, which almost retains the perfect C2h symmetry of the molecule in the vacuum structure. One should probably not read too much into the apparent superiority of the DFT structure; the DFT calculations give slightly longer bond lengths than MP2, and the effect of anharmonic zero-point and thermally excited vibrational motions is a slight lengthening of average bond lengths, and therefore, the closer correspondence of the DFT result is likely a cancellation of errors. A full set of computed coordinates at all levels of theory is given in Table S1 of the Supporting Information. Vibrational Spectroscopy. The C2h conformer has Γvib = 18Ag + 12Bg + 13Au + 17Bu; because only ungerade modes are electric dipole allowed, this means 30 of the 60 normal modes will be IR active. There are 15 clear peaks in the gas-phase spectrum in the range of 500−3500 cm−1. These were grouped into a series of spectral regions, separated by stretches of flat baseline and fit to Gaussians, with the line width, frequency, and integrated intensity as fit parameters. The extracted frequencies are given in Table 1. By comparing with computed spectra (see below), there were clearly five well-separated single vibrations with no substantial overlap; their mean line width was determined to be 7.7 ± 0.5 cm−1 (mean ±1 standard deviation). In Figure 2, we compare the experimental gas-phase infrared spectrum (e) with a series of simulations, obtained by computing vibrational spectral frequencies and intensities of the C2h conformer, as described, and convolving these delta function lines with the experimental line width. Spectrum (a) is the spectrum computed at the MP2/6-31++G(d) level; spectrum (b) is computed at the same level but with anharmonic effects added via VSCF. Spectrum (c) is computed at the much higher MP2/aug-cc-pVTZ level. Unfortunately, VSCF calculations at this level were well beyond our computational capacity; therefore, we made the approximation that the effects of introducing anharmonicity and the higher basis set level were additive, while the intensities were

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COMPUTATIONS Structures of the D2 and C2h conformations of DADP were optimized using the program GAMESS26 using the B3LYP density functional or using second-order Møller−Plesset perturbation theory (MP2), in conjunction with four different basis sets; in order of number of Gaussians, these were 6-31+ +G(d), aug-cc-pVDZ, 6-311++G(2d,p), and aug-cc-pVTZ. Before final optimization, special effort was made to confirm that the twist conformer was indeed D2; the methyl groups were rotated by various angles, and the molecule was allowed to reoptimize, but the result was invariably a return to the D2 geometry. Following optimization, a full, two-sided Hessian was computed, at the same level of theory as that used for optimization, for each of the 16 structures, yielding infrared frequencies and intensities under the harmonic approximation, as well as vibrational and rotational enthalpies and entropies. All computed vibrational frequencies were real at all levels of theory. In conjunction with the computed equilibrium energy differences, this allowed calculation of the free-energy differences between the two forms at arbitrary temperature. Solvent effects on the equilibrium constant were computed using the polarizable continuum model (PCM) routine within GAMESS, D


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The Journal of Physical Chemistry A Table 1. Gas-Phase IR Frequencies of DADP, Compared with Values Obtained Previously in the Solid State and Computations at the MP2/aug-cc-pVTZ Level gas phase (this work)

solid (ref15)

529.6 693.0 821.5 838.6 878.0 941.5 1006.3 1151.6 1205.5 1270.9 1380.3 1431.3 1469.8

525 687 816 839 860 931, 945 1007

2954.1 3006.5 3033.4

computed

symmetry

527.7 701.9 834.4 836.0 911.5 948.8, 967.6 1024.0

Bu Bu Au Bu Au Bu, Bu Au

1201 1271 1405 1433 1464

1228.9, 1236.3 1309.5 1408.5, 1412.2

Au, Bu Bu Bu, Bu

1490.6, 1493.8, 1503.1, 1521.1

2954 3001 3031

3088.3, 3092.5 3180.4, 3191.0, 3192.6 3215.0

Bu, Au, Bu, Au Bu, Bu Au, Au, Bu Bu

Figure 3. Fingerprint region of the infrared spectrum. (a) Computed for the C2h conformer, at the MP2/aug-cc-pVTZ level. (b) Computed for the D2 conformer, at the same level. (c) Experiment.

+ 15B1 (with the line connecting the C1 carbons defined as the x axis, corresponding to the B3 representation). Forty-four of the 60 vibrational modes are therefore IR active, leading to a spectrum that is predicted to be more cluttered. Many of the additional lines are weak and are closely related to electric dipole forbidden lines in the C2h spectrum. For example, the 562.8 cm−1 line predicted for the D2 conformer maps fairly closely to the forbidden 505.1 cm−1 vibration in C2h and corresponds to a coupled rotation of the O−C−O groups about the approximate ring normal. It is clear that the match with the computed C2h spectrum is much better and also that there is no evidence of any D2 conformer present. We estimate the D2 peaks computed to fall at 562.8 and 797.7 cm−1 in the D2 spectrum. The latter corresponds very roughly to the much lower frequency 527.7 cm−1 peak for C2h. We estimate these peaks could be detected if D2 were present at a 5% concentration (the nearest experimental peak is at 941 cm−1); this means that (assuming the two conformers equilibrate within 1 h) that the vacuum-phase free energy of the D2 conformer is at least −RT ln(0.05) = 7.4 kJ/mol above that of the C2h conformer. Complete computational frequencies and intensities at all levels of theory are given in Tables S2 and S3 of the Supporting Information. NMR. 1H and 13C chemical shifts of DADP are presented in Table 2, where they are compared with computed shifts at the MP2/6-311++G(2d,p) level. The agreement is quite good. Because there are no experimental data for the D2 conformer, we obtained guidance on where to look for its signal from computations, which suggest that the single methyl proton resonance should lie between the signals for the axial and equatorial protons of the C2h conformer. Figure 4 shows a contour plot representation of the methyl proton region of one of the several 2D EXSY spectra collected in this study; this example was collected in CD2Cl2 at 300 K, with a 1 s delay to allow exchange between axial and equatorial

Figure 2. Experimental gas-phase infrared spectrum of DADP, compared with theory: (a) the MP2/6-31++G(d), harmonic approximation, (b) MP2/6-31++G(d), VSCF, (c) MP2/aug-ccpVTZ, harmonic approximation, and (d) MP2/aug-cc-pVTZ with a first-order VSCF correction, as described in the text. (e) Experiment.

computed as the geometric mean of those used in (b) and (c). The result is the spectrum simulated in (d). The fingerprint region of the IR spectrum is shown in Figure 3 and compared with harmonic normal-mode computations at the MP2/aug-cc-pVTZ level. Half of the C2h vibrations are infrared active; for the D2 conformer, Γvib = 16A + 14B3 + 15B2 E


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The Journal of Physical Chemistry A Table 2. Experimental and Computed 1H and 13C Chemical Shifts of DADP with Respect to the Corresponding Shifts of TMS δ 1H, calc. (ppm) D2 C2h

C1 C2 C1 C2eq C2ax.

δ 1H, exp. (ppm)

1.37

−

1.20 1.79

1.32 1.75

δ 13C, calc. (ppm)

δ 13C, exp. (ppm)

116.8 22.1 113.1 24.4 22.2

− − 109.35 22.36 20.45

different threshold levels, relative to the diagonal axial and equatorial peaks, whose average we treat as having unit intensity. The top spectrum has an intensity threshold of 1/64 and shows just the diagonal peaks from axial and equatorial methyls and exchange cross peaks between them; the relative cross peak intensity (the intensity of the cross peak divided by the intensity of the diagonal peak) Ix/Id is 0.378 ± 0.005. The middle spectrum has an intensity threshold of 1/1024 and in addition to the main peaks shows clear diagonal and cross peaks from the 13C satellites, at a theoretical abundance of 0.55% (experimental intensity ratio = 0.51 ± 0.01%). The ratio Ix/Id for the satellites is 0.367 ± 0.017 (mean ±1 s.d.); the slight decrease in Ix/Id is consistent in magnitude with a 13C kinetic isotope effect but is obviously not statistically significant. The bottom spectrum has an intensity threshold of 1/8192 but is still clearly above the noise floor. The circled cross peaks, between 13C satellites belonging to the same methyl groups, result from a 13C spin−flip due to T1 relaxation during the 1 s EXSY delay. The ratio Ix/Id is 0.055 ± 0.007, corresponding to a 13C T1 of 18 s; for a molecule of this size, such a value seems entirely reasonable. More importantly, the ratio of these weak cross peaks to the main diagonal peaks is 0.00028 and represents a plausible value for the weakest peak intensity clearly observable in the EXSY spectrum. From this, and similar spectra, can be extracted the rate coefficient of conversion of axial proton magnetization to equatorial magnetization, which, if k1 ≪ k−1, can be calculated from eqs 6a and 6b. In the present instance, k1 = 0.40 s−1. The half-width at half-height of the cross and diagonal peaks is measured to be 1.01 ± 0.06 Hz or 6.34 rad s−1 and equals k1 + k*, where k* is 1/T2*. Combined with the value of k1 already extracted, this gives k* = 5.95 s−1. Thus, under these conditions, exchange contributes only about 6% of the line width. The observability of the putative D2 conformer depends on two parameters, the equilibrium constant and the line width. The integrated intensity of a D2 signal in a solution of predominantly C2h DADP, whose axial and equatorial signals have unit integrated intensity, is 2K, where K = k1/k−1; the factor of 2 results because all methyl protons in the D2 conformer are equivalent. In a 2D EXSY experiment where the cross peaks between C2h signals have come to equilibrium, the intensity of the cross peaks between twist and axial/ equatorial peaks at long exchange times is also 2(k1/k−1), if the diagonal peak integrated intensity equals 1. The overall intensity is proportional to the integrated intensity divided by the line width; for the cross peak, the line width (half-width at half-height) is given by k−1 + k*, while for the diagonal peak, it is k1 + k*. Because we can observe peaks with an intensity of 0.00028 relative to the diagonal and the ratio of D2 to C2h peak intensity is given by 2k1(k1 + k*)/[k−1(k−1 + k*)] < 0.00028, this gives a value of k−1 > 131 s−1, or K = [D2]/[C2h] = k1/k−1 < 0.0030. We can therefore rule out a D2 percentage greater than 0.30% and place a minimum value on the free-energy difference, ΔG > 14.5 kJ mol−1. In an identical experiment done in CD2Cl2 at 263 K, Ix/Id was 0.072 ± 0.004, leading to k1 = 0.072 s−1. Under these conditions, k* was 3.6 s−1; with the same detectability limit for a C2h−D2 cross peak, we obtained K < 0.0017 or ΔG > 13.9 kJ mol−1. Measurements at this temperature in acetonitrile and at temperatures down to 230 K in toluene and 245 K in acetonitrile also failed to detect a C2h− D2 cross peak; unfortunately, they also lacked of any cross peak between axial and equatorial protons and therefore made

Figure 4. EXSY spectrum of DADP in toluene-d8 at 300 K, plotted at three contour levels. (a) Minimum contour = 1/64, relative to the (nearly equally intense) diagonal peaks. (b) Minimum contour = 1/ 1024, with the diagonal peaks due to the 13C satellites circled in red and the cross peaks between the satellites circled in blue. (c) Minimum contour = 1/8192, with the cross peaks between satellites associated with the same methyl group circled in blue.

methyl peaks of the C2h conformer and presumably also the methyl resonances of D2. For clarity, it is plotted at three F


Article


Table 3. Computed Energy and Free-Energy Differences, in kJ/mol, between the C2h and D2 Conformers of DADP (D2 − C2h) as a Function of the Level of Theory 6-31++G(d) ΔE ΔGvac ΔGsoln

aug-cc-pVDZ

6-311++G(2d,p)

aug-cc-pVTZ

B3LYP

MP2

B3LYP

MP2

B3LYP

MP2

B3LYP

MP2

10.99 11.93 13.61

12.44 14.14 15.96

10.03 12.16 13.84

11.52 14.04 15.78

11.56 12.72 14.41

13.65 15.49 17.27

11.87 13.11 14.68

14.03 15.91 17.52

measurement of k1 impossible. Thus, we can definitively state ΔG > 13.9 kJ/mol in CD2Cl2 at 263 K and >14.5 kJ/mol in toluene at 300 K, although based on lower-temperature spectra and our conservative assumptions about observability, it is likely that ΔG is considerably higher than our limiting value. Computational Thermochemistry. The computed thermochemistries for these two molecules are tabulated in Table 3 using the harmonic approximation without VSCF corrections. While some early studies suggested that the free-energy difference between the stable C2h chair conformer of DADP and the pair of enantiomeric metastable D2 twist conformers might be small enough to allow observation of the twist conformer, Table 3 paints a much more pessimistic picture. While at the low B3LYP/6-31++G(d) level ΔE is a quite tractable 10.5 kJ/mol, as the size of the basis set increases, the stability of the minor conformer decreases. Moreover, addition of vibrational and rotational contributions increases ΔG substantially; the origin for this lies mainly in a difference in vibrational entropies, which are unusually different for two conformers of a single molecule, with that of the twist conformer only 83% of the chair conformer. The reason for this is largely that while at 298 K the relatively flexible chair conformer has five very soft vibrational modes, at energies below RT, the twist conformer has only three. This is a reflection of the higher compactness and rigidity of the twist conformer, which shifts the low-energy ring deformations and the methyl group torsions to higher energies. This contribution increases the difference in vacuum free energy between C2h and D2 to 13.1 (B3LYP) and 15.9 kJ/mol (MP2). Finally, inclusion of solvation contributions via a polarizable continuum model also destabilizes the more poorly solvated twist conformer, adding a 1.5−1.7 kJ/mol additional term to ΔG. The overall result is to increase the computed ΔG difference to 14.7 (B3LYP) and 17.5 kJ/mol (MP2).

largest disagreement between computed IR frequency and gasphase experiment (and, indeed, between the gas phase and solid phase), in the lower-energy region of the spectrum, is for the asymmetric O−O combination stretch (gas 878.0 cm−1; solid 860 cm−1; computed 911.5 cm−1). This might represent a failure of the theory to properly model the O−O bond potential, although it might conceivably also be partially a result of significant populations of excited states of the low-energy torsional modes about the O−O bond. As usual, harmonic normal-mode analysis reproduces well the overall pattern of vibrational frequencies but introduces systematic errors, particularly for the C−H stretch vibrations. That these errors are reduced substantially by VSCF confirms that they are likely due to anharmonic contributions neglected in normal-mode analysis. It is unfortunate that VSCF is possible only at a low basis set level; however, our crude treatment of the effect as additive does seem to lead to a substantial improvement in high-level normal-mode calculations and may be a good alternative to the empirical use of scaling factors. Computed spectra are certainly enough to confirm the C2h conformation (if this were necessary) and rule out a substantial fraction of the D2 conformer in the gas phase. The results also show that DADP obtained by simple room-temperature sublimation of the solid gives a distinct and easily observable gas-phase spectrum, which may be useful for detection of the presence of such materials under real-world conditions. The EXSY NMR results set a new lower limit on the equilibrium concentration of D2 in solution, and, in particular, it emphasizes that the concentration of D2 cannot be properly estimated under conditions where the interconversion of the chair forms contributes to broadening of the NMR spectra. Rather, attempts to find D2 must be conducted under conditions where the chair inversion itself is unobservably slow. The true value of EXSY is that it allows isolation, among the substantial number of very weak signals that appear on the spectral baseline of this relatively unstable material, of only those NMR signals that are in chemical exchange with identified C2h resonances. Our new experimental limits on the D2 free energy are substantially higher than those previously obtained and are tantalizingly only a few kJ/mol lower than predictions of high-level theory incorporating solvent effects. It remains possible, therefore, that higher-field EXSY (to improve sensitivity), at still lower temperatures, with longer delays, and with the k1 rate coefficient determined via an Arrhenius equation rather than measured directly, may yield a D2 signal sharp and intense enough to be observed via EXSY.

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DISCUSSION The gas-phase infrared spectrum of DADP is in overall good agreement with previously published solid-state vibrational spectra. This indicates that intermolecular interactions in the solid state are rather weak. The two vibrations with substantial frequency differences between gas and solid are at 878 cm−1 (solid 860 cm−1), which corresponds to an asymmetric stretch of the O−O bonds, and at 1380 cm−1 (solid 1405 cm−1), which apparently is due to two different, nearly degenerate methyl umbrella mode combinations. It is significant that the O−O bond length represents the largest structural difference between theory and experiment; theory at the aug-cc-pVTZ level gives rO−O = 144.5 (B3LYP) or 146.1 pm (MP2); the two crystal structures give rO−O = 147.1 (8) and 147.5 pm (9). It is worthwhile here to note that a fit to gas-phase electron diffraction data gave rO−O = 146.3 pm (12), in better agreement with theory, which tends to suggest that the gas/solid difference in vibrational frequencies reflects a small but real underlying structural difference. This is also confirmed by the IR data; the

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CONCLUSION This combined experimental and computational study of the relative stability of the conformers of DADP shows a gratifying concordance between the conclusions of computations and experiments. The combination of the two give a predicted lower bound of ΔG = 14 kJ/mol for the stability of the chair conformer over the twist conformer, although the true value is G


Article


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likely several kJ/mol higher. It was disappointing that our extraordinary efforts to observe the minor twist conformer of DADP proved unfruitful, but given that computation again predicts that the twist conformer should lie just beyond the limits of observability, one can hardly complain. Our results also show that the gas-phase and solid-state vibrational frequencies are quite close, indicating weak intermolecular interactions in the solid state.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07074. EXSY pulse sequence, computed coordinates, and computational frequencies (PDF) Additional experimental data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Telephone (402)472-9346. Notes

The authors declare no competing financial interest.

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REFERENCES

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Gas-Phase Infrared and NMR Investigation of the Conformers of

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