Combined Electron-Diffraction, Spectroscopic, and Theoretical

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Combined Electron-Diffraction, Spectroscopic, and Theoretical Determination of the Structure of N-Deutero Trans-Methyldiazene, CHN=ND. Conformational Effects of the N=N Double Bond 3

Joseph W. Nibler, John A. Neisess, and Kenneth Hedberg J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08103 • Publication Date (Web): 01 Oct 2018 Downloaded from http://pubs.acs.org on October 8, 2018

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The Journal of Physical Chemistry

Combined Electron-Diffraction, Spectroscopic, and Theoretical Determination of the Structure of N-Deutero trans-Methyldiazene, CH3N=ND. Conformational Effects of the N=N Double Bond. Joseph W. Nibler*, John A. Neisess, and Kenneth Hedberg Department of Chemistry, Oregon State University, Corvallis, OR, 97332-4003

Number of text pages: 26 Number of Tables: 5 Number of Figures: 6

* Corresponding author. E-mail address: [email protected] FAX: +1 541 737 2062

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ABSTRACT: Gas phase electron-diffraction (GED) data obtained at nozzle-tip temperature of 273 K have been combined with spectroscopic vibrational-rotational constants to determine the structure trans-methyldiazene, an important prototype for the N=N double bond. The N-deutero form CH3N=ND was used in the study since it is appreciably more stable than CH3N=NH. Both the theoretical and experimental results are consistent with a planar Cs trans-CNND framework. The experimental results (rα0 /rg273) are 1.465(2)/1.467(2) Å for the CN bond, 1.248(1)/1.251(1) Å for the N=N double bond, and 1.037(17)/1.048(17) Å for the ND bond.

The NND angle is

105.9(20)/105.6(20)º and the CNN angle is 112.4(5)/112.2(5)º, where the uncertainties in parentheses are twice the standard deviation from a simultaneous least squares fit of the GED and microwave data. For the methyl group, both theory and experiment HOMOs indicate that two CH bonds are symmetrically arranged out of the molecular plane while the third CH′ lies in the plane in an eclipsed Staggered

(not staggered) cis-H′CNN arrangement. Theoretical calculations (B3LYP/cc-PVnZ and CCSD(T)/cc-PVnZ) suggest a slight

Eclipsed

distortion of the methyl group, with a tilt of the methyl top axis about 5º away from the N=N bond. The experimental data are consistent with this picture but are equally consistent with an undistorted methyl group. Inclusion of distortions predicted by theory in a complete basis set limit (CBS) lead to a preferred analysis with average values of 1.086(5)/1.106(5) Å for the CH bond length and an average HCH angle of 108.3(8)/107.8(8)º. Features of the structure of methyldiazene and related compounds are discussed. It is found that the short N=N bond length in the diazenes produces much greater steric repulsion than in analogous ethylenic compounds and this effect leads to some interesting conformational and distortion differences for attached CH3 groups.


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█INTRODUCTION As nitrogen analogs to ethylenic compounds, the diazenes are of considerable interest to chemists, both experimentally and theoretically.1-27 The simplest of these are shown in Figure 1, with a trans arrangement displayed since in all cases this structure is theoretically lower in energy

Figure 1. Structures of the simplest diazenes with their point group symmetries. For both CH3N=NH and CH3N=NCH3 a CH bond from the CH3 groups is eclipsed with the NN bond. The eclipsed (E) and (EE) orientations are lower in energy than staggered (S) or (SS) arrangements produced by 180° methyl rotations.

than the cis form. We note also that, for the trans forms, rotamers with a methyl CH bond eclipsing (E) the N=N bond have lower energy than the ones with staggered (S) CH bonds with respect to the N=N bond. Despite the simplicity of these important prototypes for the N=N double bond, structural parameters have been determined only for trans-HN=NH5-7 and, with some discrepancies, for trans-CH3N=NCH3.20,21 The structure of methyl diazene, the subject of this study, has not been reported previously. Why is the structure of methyl diazene of interest? Beyond providing characteristic values for the N=N distance and HN=N angles, determination of the structure can be expected to give physical insight into the effect of the N=N electron distribution on the orientation and distortions of the methyl group. Additionally, the molecule is small, with only one methyl group, and hence it can serve as a useful benchmark for high-level electronic structure calculations for comparison with the experimental structure. Extended to trans and cis forms of CH3N=NCH3, such calculations turn out to reveal some remarkable differences between the methyl orientations and distortions compared to those of the ethylenic C=C analog. 3 ACS Paragon Plus Environment


How is the structure best determined? With several different hydrogen (deuterium) atoms, which are weak electron scatterers, methyldiazene is a challenge for an accurate structure determination by GED alone. We believe that structure is most accurately obtained from a combined fit of both electron diffraction data and spectroscopic rotational constants, complemented where needed by results from theoretical calculations. Examples of molecules whose structures we have determined in this way include spiropentane28 (C5H8) and radialene29 (C6H6), an unusual isomer of benzene. In the present study, we were particularly interested in seeing to what extent the experimental analysis could reveal the tilt and other possible distortions of the CH3 group. Most of the small diazenes are quite reactive and difficult to study. To provide context, we review briefly prior structural work on both trans and cis forms of the diazenes shown in Figure 1. The parent diazene HN=NH, also termed diimine or diimide, is not isolable at room temperature, but the trans form has been made by microwave discharge of flowing hydrazine,1-2 by photolysis of hydrazoic acid,3 and by thermal decomposition of sodium tosylhydrazide (tosyl(Na)NNH2).4 Trans-HN=NH and its various deuterium and nitrogen-15 isotopomeric forms have been studied extensively by infrared and ultraviolet spectroscopy and, from rotational constants determined by high resolution methods, the structure is well-established.5-7 Its equilibrium re parameters are 1.247(1) Å and 1.029(1) Å for the N=N and N-H bond lengths and 106.3(1)º for the NNH angle.7 The structural and spectroscopic results are generally in good agreement with predictions from theoretical calculations.7-11 A review of much of the work on the diazenes by Craig et al.12 contains a description of their efforts to detect the cis form of diazene. These attempts were not successful, but the cis arrangement is thought to play a transitory role in the stereospecific hydrogen reduction of carbon and nitrogen multiple bonds.13-14 It is also believed to occur as an intermediate complex with the nitrogenase enzyme in the reduction of atmospheric nitrogen to 4 ACS Paragon Plus Environment

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ammonia.15-16 Replacement of the diazene hydrogens by methyl groups confers greater stability on the molecule, and detailed analyses of the vibrational spectra of both trans- and cis-dimethyldiazene (azomethane) and deuterium isotopomers have been reported.17-18 The trans form is quite stable, but, above 273 K, the cis form undergoes facile tautomerization to a hydrazone structure, CH2=N=NHCH3.18 No high resolution vibrational-rotational studies have been done on this tautomer or on either trans- or cis-azomethane, but pure rotational microwave (MW) spectra of a flowing stream of cis-dimethyldiazene have been obtained.19 A large dipole moment of 3.27 ± 0.1 D was determined in this work from Stark-shift measurements, and, from rotational constants and an assumed N=N bond length of 1.254 Å, an outward tilt of 6.7 ± 3º was deduced for the methyl groups. In the case of trans-dimethyldiazene, gas phase electron-diffraction (GED) studies have been reported by two groups.20,21 In their analyses both groups assumed the C2h structure shown in figure 1 and a three-fold symmetry axis for the methyl groups. In the model of reference 20, the methyl axis was assumed to be aligned with the CN bond whereas in reference 21 the methyl group was allowed to tilt. Interestingly, an inward tilt of 4.1º was deduced, in a direction opposite to that found in the cis compound. However, the uncertainty (6.1º) was larger than the tilt value, so a firm conclusion about the interaction of the methyl groups with the nitrogen π-bond cannot be drawn. Moreover, the agreement between the two GED studies was judged “not altogether satisfactory”21 because of the difference in the CN bond lengths deduced: 1.474(2) Å21 vs 1.482(2) Å20. The stability of methyldiazene is intermediate between that of diazene and dimethyldiazene, and both trans and cis forms have been synthesized.

However, neither

compound is stable at room temperature: the cis form rapidly tautomerizes to the hydrazone and 5 ACS Paragon Plus Environment


the trans form readily decomposes to give N2 and CH4.22 Nonetheless, vibrational spectra of various deuterium isotopomers of both trans and cis forms have been reported.17,23-24 No high resolution vibration-rotation spectra have been recorded for either isomer, but some microwave rotational transitions have been measured for trans-CH3N=ND, which is more stable than its H counterpart.25 The MW study yielded a dipole moment of 0.67(10) D26 and accurate values for the rotational constants25 B0 and C0, respectively equal to 10254.50(20) MHz and 9239.13(20) MHz. The analysis also gave 58590(800) MHz as an estimate of A0, but Steinmetz25 indicates that a more accurate value is 59400(300) MHz, obtained from the partially-resolved Q-branch structure of a band seen in the infrared region.22 Shortly after publication of the synthesis method for methyldiazene,22 we prepared the more stable CH3N=ND isotopomer for a GED study. The experiment was complicated by sample decomposition and by an apparatus problem, but the results were included as a chapter in the PhD thesis of one of us (Neisess).27 Reasonable values were obtained for the N=N and C-N distances, but the ND bond length and NND angle were not judged to be reliable and the work was not published. However, since that time a number of improvements in the analysis of GED data30-34 and in the use of information from electronic structure calculations have occurred that have made possible the present reanalysis of this experiment. In particular, the experimental improvement involves the use of a flat-bed scanner instead of a rotating-plate densitometer in the radial averaging of the scattered intensity from the photographic plates used in the diffraction experiments. This gain is significant because some of the data plates showed shadowing in one sector, an effect attributed to aperture scattering caused by momentary beam wander during the experiments. This shadowing could not be eliminated in the rotating-plate averaging, but, as discussed in recent publications,28,35 current software can be used with the digital scan array to 6 ACS Paragon Plus Environment

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eliminate the shadowed regions in obtaining the radial average. Another advance in the analysis procedure involves the explicit inclusion of rotational constants in the least squares fitting, something not possible at the time of the earlier analysis.

This treatment requires small

vibration-rotation corrections of the ground state rotational constants A0, B0, C0 to values Az, Bz, Cz that correspond to an rz structure that is equivalent to an rα0 structure obtainable from GED data. Such corrections can now be reliably determined from the harmonic potential functions given by electronic structure calculations and, as discussed by Robiette,36 these calculations also provide an estimate of the “shrinkage effect” and other corrections necessary to deduce the rα0 structure from the GED data. Finally, we note that the dramatic improvements in computer power make possible ab initio and density functional calculations of anharmonic potentials at high levels with large basis sets, and we have utilized some of these results in the present work.

█ELECTRONIC STRUCTURE CALCULATIONS All electronic structure calculations made use of the Gaussian 09 and 16 packages of programs37 using density functional (B3LYP) or ab initio CCSD(T) methods and standard basis sets of type cc-pVnZ, where n = 2, 3, and 4 correspond respectively to the letters D, T and Q. Table 1 summarizes the predicted equilibrium structures from some of these calculations, which in all cases are consistent with a planar CN=ND arrangement with one of the methyl hydrogen atoms (H′) also in this plane and cis to the N=N bond, as displayed in Figure 1. For both B3LYP and CCSD(T) methods, the bond lengths decrease slightly as the basis set size increases.

For

best agreement with experiment, extrapolation procedures based on CCSD(T) results have been recommended by several groups.38-40 Because of its simplicity, we have chosen an n-3 extrapolation procedure described by Puzzarini.40 We list in the table the complete basis set



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(CBS) re structure resulting from the extrapolation. Table 1. CH3 N=ND structures from electronic structure calculations CCSD(T) CBS limit

r α0-r e B3LYP cc-pVTZ

pred. r α0 CCSD(T) CBS limit

1.0274 106.24 1.2432 1.4604 112.21

0.0058 0.13 0.0026 0.0095 0.12

1.033 106.4 1.246 1.470 112.3

r e structure (Å, Degrees) B3LYP B3LYP CCSD(T) CCSD(T) cc-pVTZ cc-pVQZ cc-pVTZ cc-pVQZ CNND parameters ND 1.0310 1.0298 1.0300 1.0285 NND 106.74 107.00 105.68 106.01 N=N 1.2353 1.2337 1.2505 1.2463 NC 1.4606 1.4594 1.4675 1.4634 NNC 112.99 113.23 111.59 111.95 a

Average methyl (CH'H2) parameters 1.0914 1.0904 〈CH〉 109.61 109.63 〈HCH〉 109.27 109.25 〈NCH〉 Methyl distortions CH'-CH 0.0002 0.0004 HCH'-HCH 3.60 3.72 NCH'-NCH 4.37 4.43 b 5.24 5.34 CH'H2 tilt

1.0912 109.81 109.09

1.0903 109.85 109.04

1.0897 109.88 109.01

0.0014 -0.18 0.18

1.091 109.7 109.2

0.0004 3.31 3.79 4.68

0.0007 3.26 3.75 4.60

0.0009 3.22 3.71 4.55

0.0045 -0.23 0.38 -0.13

0.005 3.0 4.1

a

4.4

b

All calculations predict C s symmetry with the methyl H' atom in the CNND plane. Tilt is the difference between the CN bond and the vector resultant of the three CH bonds and is positive when the CH' bond rotates away from the NN bond.

To compare these re results with the rα0 structure from GED data, small rα0–re adjustments are needed that require anharmonic corrections. These adjustments can be calculated using the “Anharm” option of the B3LYP method, but this option is not available for the CCSD(T) method. Accordingly, we list in the table the differences rα0–re calculated using the B3LYP method with a cc-pVTZ basis, and we add these to the CBS re results to obtain the predicted rα0 structure shown in the last column of the table. Of particular interest to us were the predicted methyl group distortions that were similar for all of the calculations. The re difference for the H′ and H protons is quite small, less than 0.001 Å, but is significantly larger (0.005 Å) when the correction to the rα0 basis is made. Two other independent distortions of the CH3 group are possible. All calculations predict an H′CH HCH angle difference of about 3º as well as a tilt of the methyl top axis of about 4 to 5º relative


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to the CN bond, where a positive tilt value corresponds to a tilt away from the NN bond. These distortions imply a (dependent) NCH′ - NCH angle difference of about 4º. All predictions seem quite reasonable since the H′ and H atoms clearly have different electronic environments, and we were curious whether a combined GED/MW analysis could reveal such distortions. █EXPERIMENTAL ASPECTS Synthesis. The method of preparation of N-deutero methyldiazene for this study was essentially that reported by Ackermann et al.22

A closed reaction system was used, which

consisted of a three-necked flask equipped with a magnetic stirrer, a dropping funnel, a sample collection trap, and a trapped water aspirator that facilitated separation of the gaseous sample from the reaction vessel. A D2O solution of 1.130 g of hydroxylamine-O-sulfonic acid (H2NOSO3H) was added to a basic D2O solution comprising 1.200 g of NaOH and 0.835 g of Nmethyl hydroxylamine-hydrochloride (CH3NHOH•HCl). The total volume of the solutions was 100 ml, which produced final concentrations of all the reactants of about 0.1 M. The evolved gas flowed through a U-tube packed with glass wool and cooled to -45 °C to remove the water vapor, and then was collected in a sample trap cooled to liquid nitrogen temperature (-196 °C). Trace impurities of ammonia were removed by pumping while the sample trap was warmed to 89 °C, and the isolated sample was stored as a yellow solid at -196 °C. Gas phase infrared spectra of the sample showed the same features reported by Ackermann et al.22 The yield of CH3N=ND was not measured, and, due to slow decomposition to CH3D and N2, a total of seven different samples were synthesized in order to complete the GED experiments. Electron-diffraction experiments.

The GED photographs were obtained using the

OSU apparatus with an r3 sector and Kodak “process” plates. The sample bulb was cooled to 63 °C in order to provide a sample vapor pressure that gave nozzle flow rates that produced



reasonable plate exposures in 1 to 3 minutes. The nozzle was cooled to about 0 °C to reduce the possibility of decomposition while the sample was in the nozzle tube. In order to further reduce the possible presence of decomposition products during the exposure of photographic plates, the sample bulb was opened to the diffraction apparatus before each exposure; thus the more volatile N2 and CH3D decomposition products were distilled away from the less volatile methyldiazene by the pumping system of the diffraction apparatus. Confirmation of this was obtained by analyses of the scattering data with explicit inclusion of the known structures of N2 and CH3D; these tests showed no evidence of either impurity (̶ >̶ 3733 209 -80 149

cis EE >̶ ̶< 3958 435 -92 -29

1.231 1.474 1.485 122.5 121.4

1.231 1.475

1.090 1.090 108.8 108.9 110.0 110.0

1.090

-0.002 -0.006 2.9 0.1 10.3 -5.0 8.7 -3.0

-0.002

124.2

108.6 110.1

2.6 11.5 9.1

-1

E=eclipsed, S=staggered indicates a methyl orientation relative to the N=N bond. All energies are expressed in cm -1 c d (349.8 cm = 1 kcal/mol = 4.184 kJ/mol). H' denotes a methyl H atom that lies in the heavy atom plane. Tilt is the difference between the CH2H' resultant vector and the CN bond and is positive when the vector rotates away from the N=N bond.

calculations using the B3LYP method with a cc-pVTZ basis set, a choice which we regard as a reasonable standard since it generally gives good agreement with experimental structures for acceptable computation times. Since the focus is on changes from one structure to another, theoretical defects can be expected to cancel somewhat, so that the results should give meaningful insight into some of the subtle methyl distortions in these diazenes as one goes from eclipsed (E) to staggered (S) orientations. It is noteworthy that, as seen in Table 5, the gross


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structure of the methyl group is unaffected by torsions in CH3N=NH and CH3N=NCH3; the 〈CH〉 value is essentially constant at 1.091 Å, and both 〈HCH〉 and 〈NCH〉 averages are very close to the tetrahedral sp3 value of 109.5° for all geometries. (a) Torsion about N=N bond.

Figure 4 shows the change in relative energy as twisting occurs

about either the N=N or C—N bonds. In the former case (a), the potential rises rapidly as the 25000

HN=NH

(a)

CH3N=NH CH3N=NCH3

20000

Figure 4. Torsional potentials in the diazenes.

15000

Relative energy (cm-1)

(a) Relative torsional energy for torsion about the N=N bond. The curves are quadratic fits.

10000

cis

5000

trans 0 0

30

60

90

120

150

180

Torsional angle about N=N bond

2500

CH3N=NH

(b)

cis (S)

2000 cis (E) Relative energy (cm-1)

1500

(b) Relative torsional energy of CH3N=NH for torsion about C—N bond. The curves are fits to a three-fold cosine function.

1000 trans (S) trans (E)

500

0 0

30

60

90

120

150

Torsional angle about C—N bond


180


dihedral angle about the N=N bond deviates from 0° for the cis forms of the diazenes or from 180° for the ground state trans forms. The curves are very similar for HN=NH, CH3N=NH and CH3N=NCH3; the most notable difference is seen at the cis limit of 0°, where the CH3N=NCH3 energy is higher than that of the other two diazenes.

This difference is presumably a

consequence of increased steric repulsion of the two bulky methyl groups in cis-azomethane. The energy change as twist occurs from either cis or trans geometry is well-described as quadratic over most of the range and produces a cusp at about 24000 cm-1 for all three diazenes. As part of a femtosecond study of the photochemistry of azomethane,53 more detailed calculations for this region have been done that predict a transition state with a dihedral twist of about 93°.53,54 (b) Methyl torsion in CH3NNH.

In both cis- and trans-CH3N=NH forms the eclipsed

arrangement (E) of the methyl group is lower in energy than the staggered form (S), as indicated in Figure 4(b). Here the DFT potentials are accurately described by a simple three-fold cosine function, and the S orientation corresponds to a well-defined transition state with negative values of -227 and -239 cm-1, respectively, for the torsional frequency in trans and cis structures. The barrier for the cis form is 771 cm-1, slightly higher than a value of 655 cm-1 for the ground state trans structure. The v = 0 and 1 torsional levels are shown in Figure 4(b) as dashed lines and lie well below the maximum, so that free rotation of the CH3 group does not occur in either cis- or trans-CH3N=NH. However one would expect a large amplitude of motion for the methyl torsion, and this feature is borne out by the relatively large values of non-bonded H···N amplitudes in Table 3. The methyl torsional frequency itself has not been measured but is estimated to be about 170 cm-1 from combination bands seen for trans-CH3N=NH.24 This value is in reasonable accord with harmonic/anharmonic values of 199/189 cm-1 that we calculate


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using the B3LYP method with a cc-pVTZ basis set. From the CH3N=NH calculations, the energy of the optimized cis structure is 1308 cm-1 greater than that for the optimized trans configuration. If, in the cis arrangement, the parameters are fixed at the trans values, the energy is calculated to be higher than that of the trans form by 2168 cm-1; the difference 860 cm-1 is a measure of the strain relief obtained by changing the bond angles and lengths. Of these, the greatest relief comes from opening the NNC angle by 6.0° (66%) and the NNH angle by 4.8° (26%). Extension of the NH bond by 0.018 Å accounts for 5%, and other minor changes account for the remaining 3% of strain relief. We note that the strain relief obtained from these skeletal distortions is much larger than that obtained by distortions of the methyl group itself. For trans-CH3NND, the optimized energy when the CH3 group is constrained to be symmetric and aligned with the CN axis is only 110 cm-1 higher than that for a relaxed structure. Two thirds of the strain relief comes from a 5.2° tilt of the methyl top and one third from the H’CH – HCH angle change of 3.6° (the latter is equivalent to torsional strain relief); the CH bond distance remains constant at 1.091 Å. (c) Methyl torsion in CH3NNCH3. Torsional motion in azomethane is more complicated since the calculations indicate two favored orientations for each of the CH3 groups, yielding configurations we have labeled as EE, ES=SE, and SS in Table 5. For the trans form, the EE configuration is 1229 cm-1 lower in energy than the SS transition state structure, but, for the cis structure, the order is reversed: the staggered SS arrangement is 435 cm-1 lower than the EE form. A similar ordering has been reported from other calculations,48,49 and the SS form is also that favored over the EE form in a microwave study of cis-azomethane.19 Finally we note that we obtain the same order from higher level CCSD(T)/cc-PVTZ calculations but with about twice the value for EEE -ESS (832 cm-1).



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The lower energy for the SS form of cis-azomethane is noteworthy since analogous calculations for 2-butene yield relative energy values (in cm-1) of 0 (EE), 687 (ES), and 1400 (SS) for the trans form and a similar order 445 (EE), 800 (ES), and 1065 (SS) for the cis structure. The reversal of the order in the cis forms can be attributed to greater steric repulsion in azomethane, mainly due to the shorter skeletal bond lengths: N=N (1.23 Å), CN (1.47 Å) versus C=C (1.33 Å), CC (1.50 Å). For the optimized structures, the smallest H··· H separations between CH3 groups are calculated to be EE (1.86Å), ES (2.24 Å), SS (2.25 Å) for cisazomethane and EE (2.12 Å), ES (2.56 Å), SS(2.65 Å) for cis-2-butene.

Since the van der

Waals distance between hydrogen atoms is 2.4 Å,50 it seems clear that steric repulsion caused by the short distance in the EE form of cis-azomethane is largely responsible for the favored SS geometry. Figure 5 shows the energy variation as the two methyl groups rotate for both cis (a) and trans (b) structures of CH3N=NCH3. In addition to having lower barriers to rotation, the surface of the cis form is seen to be much flatter than that for the trans structure. This flattening is partially caused by compensating changes in the CNN angle as the methyl groups rotate; this angle is 124.2° in the EE orientation versus 120.2° for the SS arrangement of cis-azomethane. In the trans case the angle change is only 0.6 degrees as rotation occurs. In the figure, the path across the potential surfaces for synchronous rotation of the two CH3 groups is shown as a dashed line while that for counter rotation (“grinding of the gears”) is dotted. The stars show the position for a 30 degree change from the minimum energy arrangement. It is seen that the energy rises more quickly for asynchronous rotation of the CH3 groups in the cis geometry. The minimum energy path from one SS point to another involves simple rotation of one methyl


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(a)

Figure 5. Methyl torsional potential surfaces for (a) cis-azomethane (b) trans-azomethane The dashed line shows the path corresponding to synchronous methyl rotation, the dotted line that for asynchronous (“gear grinding”) rotation. The stars show the position after 30 degrees of rotation. (For cis-azomethane and cis-2butene, .avi video files are available that show the effect of rotation of one methyl group on the other methyl group and on the skeletal atoms.)

(b)



group, the other group rotating a lesser amount but in the same direction. The gears “slip” when the first methyl has rotated about 25º and the second about 8º; the latter group then returns to 0º at the ES position corresponding to the top of the barrier to rotation. The calculated barrier is 601 cm-1 for trans-azomethane, slightly smaller than the value 655 cm-1 obtained for trans-methyldiazene but significantly larger than that for cis-CH3NNCH3, 209 cm-1. Corresponding values calculated for propene and 2-butene are 690, 687, and 355 cm-1, respectively. In their classic discussion of steric effects in organic compounds,51 Dauben and Pitzer argue that the fact that the barrier is smaller, rather than larger, in cis-2-butene means that the effect of steric repulsion is to increase the energy of the bottom, but not the top, of the well. In the case of cis-azomethane, the increased steric crowding is apparently sufficient to raise the EE level above the SS level. One might wonder about the situation for the intermediate case of cis-N-methylethanimine CH3HC=NCH3. Here analogous calculations predict a minimum H···H separation of 2.00 Å for the EE state, a value which appears to be still large enough for reduction of the steric repulsion to give an EE level 185 cm-1 lower than the level of the SS form. The barrier to rotation around the CC bond is quite small (99 cm-1) compared to that around the CN single bond (177 cm-1), and the corresponding torsional frequencies are 90 and 103 cm-1, so that rapid tunneling from one minimum to the next is likely.

On the bonding in trans-CH3N=NH. Two structural aspects of CH3N=NH merit comment. The first is the small N=NH angle of 106(2)º which, as discussed earlier, can be attributed to strong repulsion of the nitrogen lone-pair electrons. The second is the favoring of the eclipsed versus staggered arrangement of the methyl group. Why should this be the case and, indeed, why do all of the calculations for both cis and trans forms of CH3N=NH and CH3N=NCH3 show that the energy is increased if one twists the CH3 units slightly to give skewed structures?


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The molecular orbitals give some insight here. Figure 6 shows the levels occupied by the 18 valence electrons, together with the orbital pictures for both E and S orientations of the

Figure 6. Energy and occupied orbitals for E and S forms of trans-methyldiazene. The three levels involving the 1s electrons of nitrogen and carbon are much lower and are not shown. The orbital symmetry is shown to the right.

methyl group. For six of the nine levels the E-S energy difference is negative, indicating that the E form is favored. The E versus S orbital images look quite similar in most cases but, for example, in level 12 (HOMO level) the overlap of the methyl hydrogens with the nitrogen orbitals is noticeably greater for the E geometry. Only two of the orbitals are of A″ symmetry; these are bonding combinations of the carbon and nitrogen out-of-plane pz orbitals with the two



out-of-plane H atoms (1sA-1sB combination). One of these (8) favors the S arrangement, the other (11) the E geometry.

Overall, the A′ in-plane orbital combinations are the main

determining factor in lowering the energy of the eclipsed orientation of the methyl group. In each case, rotation of the CH3 group will reduce the overlap with adjacent orbitals, making a skewed arrangement unfavorable. This is especially apparent for the orbitals of level 7, which lock the methyl hydrogens to the nitrogens for both E and S cases.

█SUMMARY GED data have been combined with rotational constants from microwave measurements in a determination of the rα0 structure of CH3N=ND. This structure, and results for HN=NH and CH3N=NCH3, suggest a value of 1.249(3) Å as the “canonical” length of the N=N double bond. Interaction of the N=N bond with the methyl group favors an eclipsed orientation with one CH bond cis to the N=N bond. The close agreement of the heavy atom structure with that predicted by theory lends confidence in more subtle effects predicted for the methyl group parameters. The calculations indicate that the methyl group is slightly distorted, with a tilt of about 4º away from the N=N bond, and with a methyl rotation barrier of 655 cm-1. Similar calculations yield torsional potential surfaces for cis and trans CH3N=NCH3 and comparisons with surfaces calculated for CH3CH=CHCH3 show that the increased steric repulsion caused by the short N=N distance is responsible for the different conformations seen in the cis forms of these compounds.

SUPPORTING INFORMATION This section contains in Table S1 the experimental conditions for the four plates analyzed. The radial averages and background corrections are provided for each. The correlation matrix for the parameters of the preferred model is given in Table S2.


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ACKNOWLEDGMENTS JWN and KH are grateful for NSF support at the time the original experiments were done.

We also wish to thank Professors T. Darrah Thomas and John Loeser for helpful

discussions.

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Table 1. CH3N=ND structures from electronic structure calculations re structure (Å, Degrees) B3LYP B3LYP CCSD(T) CCSD(T) CCSD(T) cc-pVTZ cc-pVQZ cc-pVTZ cc-pVQZ CBS limit CNND parameters ND 1.0310 1.0298 1.0300 1.0285 1.0274 NND 106.74 107.00 105.68 106.01 106.24 N=N 1.2353 1.2337 1.2505 1.2463 1.2432 NC 1.4606 1.4594 1.4675 1.4634 1.4604 NNC 112.99 113.23 111.59 111.95 112.21 a Average methyl (CH'H2) parameters 1.0914 1.0904 1.0912 1.0903 1.0897 〈CH〉 109.61 109.63 109.81 109.85 109.88 〈HCH〉 109.27 109.25 109.09 109.04 109.01 〈NCH〉 Methyl distortions CH'-CH 0.0002 0.0004 0.0004 0.0007 0.0009 HCH'-HCH 3.60 3.72 3.31 3.26 3.22 NCH'-NCH 4.37 4.43 3.79 3.75 3.71 b CH'H2 tilt 5.24 5.34 4.68 4.60 4.55 a

Page 34 of 40

rα0-re B3LYP cc-pVTZ

pred. rα0 CCSD(T) CBS limit

0.0058 0.13 0.0026 0.0095 0.12

1.033 106.4 1.246 1.470 112.3

0.0014 -0.18 0.18

1.091 109.7 109.2

0.0045 -0.23 0.38 -0.13

0.005 3.0 4.1 4.4

All calculations predict Cs symmetry with the methyl H' atom in the CNND plane. b Tilt is the difference between the CN bond and the vector resultant of the three CH bonds and is positive when the CH' bond rotates away from the NN bond.


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Table 2. Fits of GED data and rotational constants for various rα0 models of CH3N=ND Variablesa Theoreticalb symmetric CH3 symmetric distorted CH3 CH3 preferred (Å, deg) tilted model CNND parameters CBS limit GED only GED/MW GED/MW GED/MW ND 1.033 1.044(81) 1.065(16) 1.061(7) 1.037(17) NND 106.4 111.7(84) 103.4(26) 104.5(13) 105.9(20) N=N 1.246 1.248(1) 1.248(3) 1.247(2) 1.248(1) NC 1.470 1.464(2) 1.466(3) 1.466(2) 1.465(2) NNC 112.3 112.8(4) 112.3(4) 112.3(2) 112.4(5) Average methyl (CH'H2) parameters 1.091 1.078(36) 1.077(5) 1.075(3) 1.086(4) 〈CH〉 109.7 106.5(18) 108.5(8) 108.7(4) 109.3(5) 〈HCH〉 c 109.2 112.3(17) 110.4(7) 110.2(4) 109.6(5) 〈NCH〉 Methyl distortions CH'-CH 0.005 0 0 0 0.005 H'CH-HCH 3.0 0 0 0 3.0 4.1 0 0 5.2(13) 4.1 NCH'-NCHc CH'H2 tilt ED quality of fit parameterd

4.4

0

0

3.5(9)

4.4

R

0.078

0.088

0.080

0.081

Rotational constants (MHz) Cz 9233.0(10)

diff.e

diff.

diff.

diff.

diff.

7.7

114

-0.5

-0.1

0.1

Bz 10247.3(10)

9.9

172

0.4

0.2

0.1

Az 59500(400)

281

-1636

-0.6

1.4

1.2

a

Parameters and distortions are as defined in Table 1. Fitted values are shown in boldface, dependent values in italics. Uncertainties in parentheses are 2σ values, parameters without uncertainties were constrained at the listed value. b Theoretical values are from Table 1. c Dependent variables, not fitted.

d

R = [Σiwi∆i2/Σiwi(siIm,i(obsd))2]½ where ∆i = siIm,i(obsd) - siIm,i(calc.). 35 ACS Paragon Plus Environment

e

Cz - Cz(calc), etc.

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 36 of 40

Table 3. Comparison of CH3NND atom distances and amplitudes with theoretical predictions Distances (Å) Amplitudes (Å) a b Theory Expt. Corr. Theoryb Expt. ND CH CH' NN NC H...H H...H' N…D N...H N...H' N...C N...H' N...H C…D a

b

rα0 1.033 1.089 1.095 1.246 1.470 1.759 1.797 1.829 2.080 2.135 2.259 2.356 2.975 3.149

rα0 1.026(17) 1.097(3) 1.102(3) 1.244(2) 1.461(1) 1.748(3) 1.782(3) 1.842(14) 2.106(6) 2.160(6) 2.247(2) 2.385(7) 2.994(6) 3.144(10)

0.011 0.022 0.018 0.003 0.002 0.028 0.028 0.006 0.013 0.007 0.002 0.011 0.023 0.003

rg273 1.037 1.119 1.120 1.247 1.463 1.776 1.810 1.848 2.119 2.167 2.249 2.395 3.017 3.147

ra273 1.035 1.114 1.115 1.245 1.461 1.767 1.801 1.840 2.113 2.162 2.247 2.393 3.008 3.144

l273 0.063 0.077 0.077 0.038 0.051 0.124 0.124 0.080 0.106 0.103 0.058 0.138 0.145 0.082

l273 0.043(4)

}

0.074(15) 0.047(2) 0.059(1) 0.124 0.124 0.116(22) 0.099(11) 0.131(11) 0.061(2) 0.064(15) 0.168(23) 0.098(24)

CBS limit values as in Table 1. Calculated from B3LYP/cc-pVTZ quadratic potential using ASYM40 program.


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Table 4. Experimental rα0 structural parameters for some nitrogen-containing compounds Variables HN=NH CH3N=NHa CH3N=NCH3 N≡N H2N—NH2 NH3 (Å, deg) trans trans trans N≡N 1.101479(3) N=N 1.252(1) 1.248(1) 1.246(3) N—N 1.447(2) =NC 1.465(2) 1.483(2) NNC 112.4(5) 112.3(3) b =NH 1.041(1) 1.052(17) 1.015(2) 1.023(3) NNH 106.3(8) 106.0(20)b 106(2) Ref. 7 this work 21 35 48 49 a

Preferred model. b Includes corrections of NH-ND = 0.0015 Å, NNH-NND = 0.10° (from Gaussian calculations).



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Table 5. Comparison of theoretical (B3LYP/cc-pVTZ) structural parameters for various diazene conformers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

HN=NH trans cis Methyl orientation Relative energy (cm-1)b

0

1752

Methyl Torsions (cm-1) re structure (Å, Degrees) NH NNH N=N NC

199

1.033 1.039 106.7 112.9 1.237 1.234

NNC Average methyl (CH'H2) parametersa 〈CH〉

〈HCH〉 〈NCH〉

trans Ea >̶ 0

1.031 106.7 1.235 E 1.461 S E 113.0 S E 1.091 S E 109.6 S E 109.3 S

CH3N=NH trans cis S E ̶< >̶ 655 1308 0 -227 215

cis S ̶< 2079 771 -239

1.031 106.8 1.234

1.049 112.0 1.229

1.049 111.6 1.228 1.462

1.473

trans EE >̶ ̶< 0

trans ES >̶ >̶ 601

160 222

-205 191

1.232 1.462

1.231 1.461 1.473 113.3 112.7

1.479 119.0

112.3

113.3 117.7

1.093 1.090

1.091 1.090

109.4 109.4

109.5 109.4

109.5 109.5

109.4 109.6

Methyl distortionsc CH'-CH

1.091 1.090 109.5 109.3 109.4 109.6

CH3N=NCH3 trans cis SS SS ̶̶ ̶̶ 1229 3524 0 -250 85 -168 182

1.230

1.233

1.473

1.479

112.7

120.2

1.090 109.3 109.6

1.091 108.9 110.1

cis ES >̶ >̶ 3733 209 -80 149

cis EE >̶ ̶< 3958 435 -92 -29

1.231 1.474 1.485 122.5 121.4

1.231 1.475

1.090 1.090 108.8 108.9 110.0 110.0

1.090

124.2

108.6 110.1

E 0.000 0.008 0.000 -0.002 -0.002 S -0.004 -0.006 -0.004 -0.004 -0.007 -0.006 HCH'-HCH E 3.6 2.9 3.5 2.9 2.6 S 1.5 0.4 1.3 1.3 1.1 0.1 NCH'-NCH E 4.4 4.0 4.2 4.1 10.3 11.5 S -1.0 -0.2 -1.5 -1.4 -3.7 -5.0 CH2H' tiltd E 5.2 4.1 5.1 5.0 8.7 9.1 S 0.5 0.4 0.0 -0.3 -2.1 -3.0 a E=eclipsed, S=staggered indicates a methyl orientation relative to the N=N bond. b All energies are expressed in cm-1 (349.8 cm-1 = 1 kcal/mol = 4.184 kJ/mol). c H' denotes a methyl H atom that lies in the heavy atom plane. d Tilt is the difference between the CH2H' resultant vector and the CN bond and is positive when the vector rotates away from the N=N bond. 38 ACS Paragon Plus Environment

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TOC figure



Highest occupied molecular orbitals of CH3N=ND showing orbital overlap that favors the eclipsed orientation of the CH3 group. 62x44mm (96 x 96 DPI)

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Combined Electron-Diffraction, Spectroscopic, and Theoretical

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