Analysis of the Rotational Structure in the High-Resolution Infrared

Article pubs.acs.org/JPCA

Analysis of the Rotational Structure in the High-Resolution Infrared Spectrum of trans-Hexatriene-1-13C1: A Semiexperimental Equilibrium Structure for the C6 Backbone of trans-Hexatriene Norman C. Craig,*,† Hengfeng Tian,† and Thomas A. Blake‡ †

Department of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074, United States Pacific Northwest National Laboratory, Richland, Washington 99352, United States

‡

S Supporting Information *

ABSTRACT: trans-Hexatriene-1-13C1 (tHTE-1-13C1) has been synthesized, and its high-resolution (0.0015 cm−1) infrared spectrum has been recorded. The rotational structure in the C-type bands for ν26 at 1011 cm−1 and ν30 at 894 cm−1 has been analyzed. To the 1458 ground state combination differences from these bands, ground state rotational constants were fitted to a Watson-type Hamiltonian to give A0 = 0.8728202(9), B0 = 0.0435868(4), and C0 = 0.0415314(2) cm−1. Upper state rotational constants for the ν30 band were also fitted. Predictions of the ground state rotational constants for tHTE-1-13C1 from a B3LYP/cc-pVTZ model with scale factors based on the normal species were in excellent agreement with observations. Similar good agreement was found between predicted and observed ground state rotational constants for the three 13C1 isotopologues of cis-hexatriene, as determined from microwave spectroscopy. Equilibrium rotational constants for tHTE and its three 13C1 isotopologues, of which two were predicted, were used to find a semiexperimental equilibrium structure for the C6 backbone of tHTE. This structure shows increased structural effects of π-electron delocalization in comparison with butadiene and some differences from the cis isomer of HTE. Structures predicted with the MP2/cc-pVTZ model are also compared.

■

INTRODUCTION Polyenes are of great importance in biological systems. They are essential components of many pigments, they are involved in transferring energy in the photosynthetic apparatus of plants, and they are central in vision. They are also involved in organic electron conductors. It is understood that the extent of πelectron delocalization increases with the length of the chain in polyenes. Evidence for this effect is the red shift in electronic transitions with increased length of polyenes.1 The structural implications of increased π-electron delocalization are lengthening of the “CC” bonds and shortening of the sp2−sp2 “CC” bonds. Such evidence has only recently become available. The effect was shown experimentally for butadiene in comparison with localized bonds.2 The reference localized bond lengths came from the high-level ab initio calculation of the bond lengths in 90°-twisted butadiene.3 In this conformation, the two sets of p-orbitals are orthogonal and thus do not overlap to permit π-electron delocalization. The “CC” bond in butadiene is 0.005 Å longer than the localized CC bond, and the “CC” bond in butadiene is 0.028 Å shorter than the localized sp2−sp2 bond. A preliminary structure for the C6 backbone of cis-hexatriene (cHTE) © 2012 American Chemical Society

obtained from microwave spectroscopy indicates further adjustments in CC bond lengths in this next member of the polyene series.4 Quantum chemical (QC) calculations reinforce this observation. Figure 1 compares the bond lengths for s-

Figure 1. Comparison of CC bond lengths in Å predicted with the B3LYP/cc-pVTZ model for s-trans-butadiene, trans-hexatriene, and trans,trans-octatetraene.

trans-butadiene, trans-hexatriene (tHTE), and trans,transoctatetraene, as computed with the B3LYP/cc-pVTZ model. Although the changes are not systematic, the trend is as Received: December 7, 2011 Revised: February 27, 2012 Published: February 28, 2012 3148

dx.doi.org/10.1021/jp211791r | J. Phys. Chem. A 2012, 116, 3148−3155

The Journal of Physical Chemistry A

Article

ppm for the CH2OH group is a useful marker for this substance. The cis isomer has a doublet (6.5 Hz) at 4.34 ppm for the CH2OH group and bands similar to the trans isomer elsewhere. 90−95% of the product is the trans isomer. Attempts to use 1.5 M diisobutylaluminum hydride in diethyl ether (Aldrich) at −78 °C to reduce the ester selectively to 2,4pentadienal failed. 1.2 mL (10 mmol with the volume adjusted for residual water and ether) of the pentadienol was dissolved in 15 mL of anhydrous dichloromethane (Aldrich). 40 mL (12 mmol) of 0.3 M Dess−Martin periodinane (DMP) in dichloromethane (Aldrich) was put in an addition funnel and dripped into the well-stirred pentadienol solution over 1.5 h at room temperature. The reaction mixture was bright yellow with suspended solids. More DMP solution was added if an NMR spectrum showed any unreacted alcohol. In the workup, the reaction flask was rinsed with three 40 mL portions of anhydrous ether. The ether dispersion was treated with two 80 mL portions of 2 M sodium hydroxide to dissolve reaction byproducts in the water layer. The ether layer was washed with two 50 mL portions of water, filtered, if necessary, of any remaining solids, and freed of ether and dichloromethane by rotoevaporation at room temperature. Water droplets were removed, and molecular sieves were added. The product was distilled bulb-to-bulb on a vacuum system. Yield 80%; over 90% trans isomer. Excepting fine structure, the proton NMR spectrum of trans2,4-pentadienal consisted of a doublet (15.5 Hz) of doublets (10.8 Hz) at 7.10 ppm (C3H), a doublet (16.8 Hz) of triplets (10.5 Hz) at 6.60 ppm (C4H), a doublet (15.5 Hz) of doublets (8.0 Hz) at 6.18 ppm (C2H), and two doublets (17.0 Hz, 10.0 Hz) at 5.68 ppm (CH2). In addition, the characteristic aldehyde peak, a doublet (8.0 Hz), was at 9.60 ppm for the trans isomer and at 10.23 ppm (J = 7.8 Hz) for the cis isomer.10 The cis isomer has other bands similar to those of the trans isomer. For use in Wittig chemistry, 0.33 g (8 mmol) of sodium hydride dispersion (60 wt % in oil, Aldrich) was freed of oil by rinsing four times with anhydrous pentane (Aldrich). 20 mL of anhydrous dimethylsulfoxide (DMSO, Aldrich) was added to the sodium hydride in the reaction flask. An addition funnel containing 3.28 g of dry (over P2O5 in vacuo) methyl-13C1triphenylphosphonium iodide (99 atom % 13C, Aldrich) dissolved in 20 mL of DMSO was attached. The DMSO/ sodium hydride mixture was heated with stirring up to 70 °C until hydrogen gas evolution ceased and all of the sodium hydride reacted to form dimsyl anions in an almost colorless solution. After cooling the reaction flask to room temperature, the solution of the Wittig reagent was added dropwise with vigorous stirring over approximately 1 h to form a golden brown solution of the ylide. 0.75 mL (8 mmol) of the pentadienal was added dropwise to the well-stirred solution with a syringe piercing a rubber septum. The reaction solution, which was stirred for an hour, turned dark brown. The reaction flask was attached to a vacuum system, and the HTE-1-13C1 product was distilled out bulb-to-bulb at room temperature into a liquid-nitrogen-cooled trap. Some DMSO came over as well as byproduct benzene and residual ether and dichloromethane. At best, the yield of HTE was 20%. Preparative gas chromatography with a thermal conductivity detector and a 7 m dicyanoethylether-on-chromosorb column was used at 65 °C to separate the HTE isomers from most of the other substances and to separate the two isomers.4 To separate dichloromethane from cHTE, a 1 m column packed

expected and the lengths of the innermost bonds are affected the most. The overall goal of this current research is to evaluate the structural changes in tHTE by determining the semiexperimental (SE) structure for this substance from rotational constants and from quantum chemical calculation of vibration− rotation constants (spectroscopic alphas).5 A parallel project aims at a full SE structure for cHTE. Rotational constants are needed for various 13C and 2H isotopic species. Because tHTE is nonpolar, the rotational constants must come from analysis of the rotational structure in high-resolution infrared (IR) spectra. A previous investigation of the high-resolution IR spectrum of tHTE demonstrated the feasibility of analyzing the rotational structure obtained with 0.0015 cm−1 resolution at room temperature for this rather large molecule.6 The current study reports the synthesis of tHTE-1-13C1 and the analysis of the rotational structure in two C-type bands. In addition, new evidence shows that the ground state (GS) rotational constants for the singly substituted 13C1 species can also be obtained after some scaling from quantum chemical calculations at the triple-ζ level with sufficient accuracy for use in determining an SE structure. From these additional 13C1 rotational constants, an SE structure is determined for the C6 backbone of tHTE. The synthesis of tHTE-1-13C1 depended on using the Wittig reagent methyl-13C1-triphenylphosphonium iodide to replace the carbonyl oxygen in 2,3-pentedienal with 13CH2.7 The pentadienal was made by controlled oxidation of 2,3pentadienol with Dess−Martin periodinane.8,9 The pentadienol was the product of reducing methyl-2,4-pentadienoate with lithium aluminum hydride.

■

EXPERIMENTAL SECTION Synthesis. Methyl-2,4-pentadienoate (Aldrich/Fluka) was vacuum distilled to remove the inhibitor and some other involatiles. For all subsequent work, glassware was baked at 110 °C, and reaction setups were prepared in a Glas-col polyethylene glovebag purged with dry nitrogen gas. A slow purge of dry nitrogen gas flowed through reaction vessels. 3.6 mL (30 mmol) of the ester was dissolved in 35 mL of anhydrous diethyl ether (Fisher). This solution was dripped from an addition funnel into 15 mL of 1.0 M lithium aluminum hydride (15 mmol) in anhydrous diethyl ether (Aldrich) with vigorous stirring over an hour, followed by refluxing for an hour at the bp of ether. Workup began with cautious addition of 1.5 mL of water and then 40 mL of 2 M sulfuric acid to release the alcohol and dissolve all the inorganic solids in the water layer. Anhydrous ether was used in the workup to avoid the ethanol impurity in laboratory grade ether because ethanol is difficult to separate from the pentadienal in the second step of the synthesis. The reaction flask was rinsed with three 10 mL portions of ether. The water layer was extracted with three 15 mL portions of ether. Ether was removed from the product by rotoevaporation at room temperature. A droplet of water from the alcohol product was removed with a Pasteur pipet, and drying was done with 3 Å molecular sieves (Aldrich). Yield 85%. The alcohol was stored at −15 °C. Excepting some fine structure, the proton NMR spectrum of 2,4-pentadienol in CDCl3 consists of a complex multiplet at 6.32 ppm (C3H, C4H), a doublet (15.3 Hz) of triplets (5.8 Hz) at 5.86 ppm (C2H), and two doublets (15.8 Hz, 10.0 Hz) near 5.16 ppm (CH2). In addition, a doublet (5.3 Hz) at 4.20 3149



Article

Hamiltonians for asymmetric rotors. Although tHTE-1-13C1 is close to a prolate symmetric top (κ = −0.9950), the asymmetric top reduction and the Ir representation were used. Fitting with the symmetric top reduction and predicted d1 and d2 centrifugal distortion constants made a negligible difference in the equivalent rotational constants.

with tricresylphosphate on Fluoropak 80 (finely ground Teflon, Analabs) was used at 65 °C. The proton NMR spectrum of tHTE-1-13 C 1 differs principally from that of tHTE in the CH2 region at 5.2 ppm, where two additional pairs of doublets appear through proton coupling to the 13C nucleus in one-half of the molecule. The stronger central pair of doublets for CH2 (JHHtrans = 16.7 Hz, 5.25 ppm; JHHcis = 9.8 Hz, 5.12 ppm) are each flanked by two pairs of doublets from 13CH2. One pair has JCHtrans = 155.3 Hz and JHHtrans = 16.8 Hz; the other pair has JCHcis = 160.0 Hz and JHHcis = 10.1 Hz. Each peak was split by 1.6 Hz from JHHgem. A multiplet for the C2H protons is at 6.37 ppm, and a multiplet for the C3H protons is at 6.24 ppm. The NMR spectrum of tHTE-1-13C1 is consistent with the high isotopic purity quoted by the supplier of the Wittig reagent. Instrumentation. Proton NMR spectra were recorded on a Varian 400 MR instrument at 400 MHz for samples dissolved in CDCl3 in standard 5 mm tubes. Survey IR spectra were recorded for gas samples on an Perkin-Elmer 1760 FT spectrometer at 0.5 cm−1 resolution or a Nicolet 6700 FT spectrometer at 0.1 cm−1 resolution. The cell had potassium bromide windows of 25 mm diameter and an internal length of 10 cm. High-resolution IR spectra were recorded on a Bruker IFS 125HR Fourier transform instrument at Pacific Northwest National Laboratory.6 For all spectra, the beam splitter was potassium bromide, the detector was a liquid nitrogen-cooled HgCdTe device, the path length in the White cell was 16 m, and the resolution was 0.0015 cm−1. Table 1 summarizes the other conditions for recording the spectra. Spectrometer calibration lines were from OCS11 and H2O.12

■

RESULTS Vibration Wavenumbers. The molecule of tHTE-1-13C1 is shown schematically in Figure 2 with a and b principal rotation

Figure 2. Schematic structure of trans-hexatriene-1-13C1 showing a and b principal axes. The center of mass is shifted slightly to the right and above the center of the central CC bond.

axes. This molecule of Cs symmetry has 36 vibrational fundamentals. Eleven are out-of-plane modes, which give Ctype bands in the gas phase IR spectrum. Such bands are prime candidates for analysis of rotational structure because they fall at lower wavenumbers where Doppler line broadening is decreased and because these bands give a good determination of the A rotational constant as well as B and C. The gas phase infrared spectrum from 2000 to 400 cm−1 at medium resolution is in Figure S1 in the Supporting Information. Table 2 lists the

Table 1. Experimental Conditions for High-Resolution IR Spectra

a

range (cm−1)

no. scans

press. (Torr)

calibr. gas

600−1000 600−1000 900−1300 1400−1660

4096 4096 4096 4096

0.21 0.41 0.23 0.27

OCSa OCSa OCSa H2Ob

Table 2. Vibration Wavenumbers and Infrared Intensities of Out-of-Plane Modes of tHTE-1-13C1 calculated

b

Reference 11. Reference 12.

ν26 ν27 ν28 ν29 ν30 ν31 ν32 ν33 ν34 ν35 ν36

Calculations. Quantum chemical calculations were done with Gaussian 03 (G03) E.01 software for the MP2/cc-pVTZ model with tight convergence limits or with the C.02 version for the B3LYP/cc-pVTZ model with an ultrafine grid and tight convergence limits.13 For use in the vibration−rotation− anharmonic module, Cartesian coordinates from a geometry optimization were transformed into the principal axis system (PAS) for the specific isotopic species and then reinput into the optimization process.14 The result was the calculation of vibration−rotation−anharmonic constants in the PAS. For the B3LYP/cc-pVTZ model, the Fermi resonance corrections were found for intervals up to 100 cm−1 between harmonic wavenumbers of fundamentals and combination modes. Default conditions for applying Fermi resonance were used for the MP2/cc-pVTZ model. A Loomis−Wood pattern-recognition program was used to display the spectra and to facilitate finding subband series.15 In addition, this program allows handling large data sets within the computer environment. A number of locally written Fortran programs aided other aspects of data processing. A variant of Arthur Maki’s ASYMBD7 program was used to fit transitions to

observed

wavenumbera (cm−1)

Ib (km mol−1)

wavenumber (cm−1)

Ic

1033 1003 948 909 901 875 702 606 253 212 96

73 0.0003 3.5 35 37 0.0000 11 0.0001 1.8 0.0001 0.46

1010.7

vs

938 902 893.74

m s s

687

m

a

Anharmonic wavenumbers adjusted for Fermi resonance, as computed with the MP2/cc-pVTZ model. bCalculated at the harmonic level. cQualitative intensities: s, strong; m, medium; w, weak.

wavenumbers for the out-of-plane modes of tHTE-1-13C1 computed at the anharmonic level, intensities predicted at the harmonic level, and wavenumbers with qualitative intensities for the five observed modes. The reported predictions made with the MP2/cc-pVTZ model gave somewhat better agreement for wavenumbers and intensities with the observed spectrum than those made with the B3LYP/cc-pVTZ model. 3150



Article

The band for ν26 at 1011 cm−1 is the most intense in the IR spectrum. Four of the out-of-plane modes, ν27, ν31, ν33, and ν35, correlate closely with IR-inactive modes of the parent species and thus have negligible intensities in the IR spectrum. In the normal species, the counterparts of ν29 and ν30 are almost degenerate, and one is only Raman active.6 For tHTE-1-13C1, ν29 is largely CH2 flapping on the 12C-substituted end of the molecule, whereas ν30 is largely CH2 flapping on the 13C end of the molecule. A similar pair of IR-active bands was found for butadiene-1-13C1.16 The remaining modes, ν34 and ν36, which are predicted to be weak, lie beyond the spectral range of this research. We have analyzed the rotational structure for the bands of ν26 at 1011 cm−1 and ν30 at 894 cm−1. An attempt to analyze the rotational structure for the band of ν29 failed for two reasons. This band has weaker intensity than the interfering band for ν30, and the central Q branch of ν30 obscures a critical region of the structure of the band for ν29. We also investigated the C-type band for ν32 at 686 cm−1 and the A-type band for ν10 at 1621 cm−1. For C-type bands of an asymmetric top, the selection rules for rotational transitions accompanying the vibrational transition are ΔJ = 0, ±1; ΔKa = ±1; and ΔKc = 0, ±2. J and Kc vary along a subband series for fixed Ka″ and either ΔKa = +1 (R branch) or ΔKa = −1 (P branch). For A-type bands, the selection rules are ΔJ = 0, ±1; ΔKa = 0; and ΔKc = ±1. Rotational Analysis of the C-Type Band for ν26 at 1011 cm−1. Figure 3 shows the overall structure of the C-type band

Figures 4 and 5 show two levels of detail of part of the assignment for RRK subband series in the band for ν26 of tHTE1-13C1. In Figure 4, assignments of lines in the RR4, RR5, and RR6 series are displayed. The finer detail in Figure 5 for portions of R R4 and RR5 in the vicinity of RQ6 confirms how dense the spectrum is and how close to the margin of S/N we are working in analyzing these spectra. Without the power of a Loomis−Wood pattern recognition program, it would have been impossible to find these subband series. In the band for ν26, 2131 lines were assigned. These assignments are in Table S1 in the Supporting Information. A total of 865 ground state combination differences (GSCDs) for ΔJ = 2 transitions in the GS were found from RRK/PPK+2 combinations that share the same upper states. These GSCDs are listed in Table S2 in the Supporting Information along with the GSCDs for the ν30 band. The details of the fit of rotational constants of the combined set of 1458 GSCDs to a Watsontype Hamiltonian17 are also in Table S2 in the Supporting Information. Table 3 contains the GS rotational constants obtained in the fit. Because of significant perturbations in the upper state of ν26, it was not feasible to fit upper state lines to a Hamiltonian for an asymmetric top even for a few subband series near the band center. Thus, the wavenumber of 1011.7 cm−1 for the band center, which is the vibrational transition for ν26, is approximate. Rotational Analysis of the C-Type Band for ν30 at 894 cm−1. The overall structure in the vicinity of the C-type band for ν30 is shown for the higher intensity spectrum in Figure 6. The stronger Q branch to lower wavenumber is for ν30, whereas the weaker Q branch to higher wavenumber is for ν29. Satisfactory analysis of rotational structure has only been achieved for ν30. The combs for subband Q branches extend from Ka″ of 5 to 14 in the R branch and 7 to 16 in the P branch. The central Q branch of the band for ν29 interfered with extending subband assignments for the ν30 band lower than a Ka′ value of 6 even though the upper state of ν30 was only lightly perturbed. Subband assignments in the P branch could have been extended inward, but GSCDs formed with corresponding R branch series were unavailable to confirm the assignments. The 593 GSCDs from ν30 were combined with the 865 GSCDs from ν26 for a single fit to GS rotational constants. The concordance of the two sets of GSCDs is strong evidence for correct assignments of the two bands. The GSCDs from ν30 are in Table S2 in the Supporting Information along with the GSCDs for ν26 and the details of fitting the ground state rotational constants. Table 3 reports the GS rotational constants derived from the combined data set. This data set was strong enough to fit the three larger, diagonal quartic centrifugal distortion constants but not the smaller, offdiagonal centrifugal distortion constants.17 Fitting δJ and δK depends on extending assignments into the band center where asymmetry splitting plays a large role. For δJ and δK, the values computed with the B3LYP/cc-pVTZ model were used in the fit. The inertial defect, Δ, of −0.1730 amu Å2 for the ground state is acceptably small for this planar molecule. Upper state rotational constants were fitted to the lines assigned for ν30 with the ground state rotational constants held fixed. Lines (899) for subband series with Ka′ from 7 to 12 were used. Above Ka′ of 12, a weak perturbation occurs in the upper state. The accepted lines and the results of fitting them are in Table S3 in the Supporting Information. Lines for series with Ka′ > 12 are an addendum to this table. In sum, 1245 lines were assigned for the ν30 band and used to find the GSCDs. As in the

Figure 3. Overall structure of C-type band for ν26 of trans-hexatriene at 1011 cm−1. Combs give Q branches of subbands.

for ν26 at 1011 cm−1 from the lower intensity scan, which was used for the analysis of the rotational structure. Combs for the Q branches of the subbands extend from Ka″ of 3 to 16 in the R branch and 3 to 18 in the P branch. The band center is near the high wavenumber edge of the broad central Q branch, which includes several hot bands. The structure of this band is very similar to that of the C-type band for ν14(au) for the normal species at 1011 cm−1.6 Of course, the normal modes for this transition of the two species are essentially the same. The normal mode is the out-of-plane flapping of the interior CH bonds. The irregular spacing of some Q branches in Figure 3 is evidence of significant perturbations for the upper state of ν26 of tHTE-1-13C1, as was found for the corresponding band of the normal species. 3151



Article

Figure 4. Detail of a portion of the R branch of the C-type band at 1011 cm−1, showing assignments for RR4, RR5, and RR6 subband series.

Table 3. Rotational Constants for trans-Hexatriene-1-13C1 −1

A (cm ) B (cm−1) C (cm−1) δJ × 1010 (cm−1) δK × 108 (cm−1) ΔK × 106 (cm−1) ΔJK × 108 (cm−1) ΔJ × 109 (cm−1) κ ν0 (cm−1) std. dev. (cm−1) Δb (amu Å2) no. trans. Ka′ Jmax

Figure 5. Finer detail of the assignments for the C-type band at 1011 cm−1 in the vicinity of RQ6, giving an example of signal/noise in the spectrum.

ground state

ν30(a″) C-type 894 cm−1

0.8728202(9) 0.0435868(4) 0.0415314(2) 0.9747a 0.9277a 2.425(2) −3.38(2) 1.64(2) −0.99505

0.865084(2) 0.043571(1) 0.041532(1) 0.9747a 0.9277a 0.47(1) −2.29(3) 1.665(4) −0.99506 893.7405(1) 0.00025 −0.5207 899 7−12 98

0.00032 −0.1730 1458c 3−17,d 7−15e 98

Calculated with the B3LYP/cc-pVTZ model. bInertial defect, Δ = Ic − Ia − Ib. c865 GSCDs from the 1011 cm−1 band; 593 from the 894 cm−1 band. d1011 cm−1 band (ν28). e894 cm−1 band (ν30). a

fitting of the ground state constants, the off-diagonal quartic centrifugal distortion constants, δJ and δK, were held at the values predicted with the B3LYP/cc-pVTZ model. The upper state rotational constants for ν30 from the fit are in Table 3 along with the ground state rotational constants. The wavenumber for ν30 is 893.74 cm−1. C-Type Band at 686 cm−1 for ν32. A C-type band for the ν32 mode is at 686 cm−1. This band, which arises principally from symmetric out-of-plane flapping of the trans hydrogen atoms on the end carbon atoms, was relatively weak even in the higher pressure scan. In addition, some carbon dioxide got into the single sample available for high-resolution spectroscopy. Lines from CO2 dominated the P branch of the band. Even though credible RRK subband series for Ka″ = 8−16 were found,

it was not possible to find confirming PPK subband series consistent with known GSCDs. Thus, no assignments for this C-type band are reported. A-Type Band at 1621 cm−1 for ν10. The A-type band for tHTE-1-13C1 for the ν10 mode at 1621 cm−1 was also evaluated for analysis of its rotational structure. The overall structure of this band, which arises principally from the antisymmetric stretching of the outer CC bonds, is shown in Figure 7. A high-intensity background dominates the spectrum. In addition, the broad Q branch indicates that the subband centers are dispersed across the overall band center, which makes them hard to find and hard to index with Ka″ in comparison with a band having a sharp central Q branch. Convincing subband series could not be found in the residual structure. At this 3152



Article

Table 4. Comparison of Predicted and Observed Ground State Rotational Constants for 13C1 Species of tHTE and cHTE (in cm−1) observed

theorya

predicted with scalingb

% diff obs. − pred.

tHTEc

Figure 6. Overall structure of the overlapping C-type bands for ν29 and ν30 of trans-hexatriene. Combs give Q branches of subbands for ν30.

A0 B0 C0

0.8742481 0.0446599 0.0425099

A0 B0 C0

0.8728200 0.0435868 0.0415314

A0 B0 C0

0.4887124 0.0528092 0.0476817

A0 B0 C0

0.4872104 0.0514869 0.0465874

A0 B0 C0

0.4863866 0.0524258 0.0473472

A0 B0 C0

0.4807036 0.0527361 0.0475446

0.8876551 0.0445066 0.0423959 tHTE-1-13C1d 0.8862498 0.872864 0.0434352 0.043585 0.0414196 0.041531 cHTEe 0.4975414 0.0522960 0.0473380 cHTE-1-13C1e 0.4960348 0.4872325 0.0509894 0.0514898 0.0462519 0.0465877 cHTE-2-13C1e 0.4951814 0.4863943 0.0519132 0.0524227 0.0470032 0.0473445 cHTE-3-13C1e 0.4894677 0.4807820 0.0522239 0.0527364 0.0472047 0.0475474

−0.0050 0.0046 0.0010

−0.0045 −0.0057 −0.0008 −0.0016 0.0059 0.0057 −0.0163 −0.0006 −0.0061

a

From G03 calculations with the B3LYP/cc-pVTZ model. bScale factors from normal trans species: A0, 0.984896; B0, 1.003444; C0, 1.002689. Scale factors from normal cis species: A0, 0.982255; B0, 1.009814; C0, 1.007261. cReference 6. dThis work. eReference 4.

The favorable result for predicted GS rotational constants for tHTE-1-13C1 led to making a similar comparison between predictions and observations for all three 13C1 species of cHTE. The observed rotational constants came from microwave spectroscopy,4 and the predicted GS rotational constants were obtained from the B3LYP/cc-pVTZ model with scaling. Table 4 also gives these comparisons. With one exception of 0.016%, all of the predictions agree with observations within 0.006%. Predictions of GS rotational constants were also made with the B3LYP/6-311++G** model for the cis isomer but were less favorable, being off by tenths of a percent. rs/re Structure for the C6 Backbone of tHTE. Table 5 gives the 1/2alpha sums for each principal axis of the normal tHTE molecule and each 13C1 species. These sums were calculated with the program VIBROT,18 using unscaled force constants and optimized geometry from the G03 calculation with the B3LYP/cc-pVTZ model. Table 5 also gives the equilibrium rotational constants computed from the GS rotational constants by adding the 1/2alpha sums. Table 5 includes the inertial defects for the equilibrium rotational constants. For an exact equilibrium structure of a planar molecule, the inertial defect is zero. The values in the hundredths range are acceptably small in view of the approximate force field used for the calculation of alphas. From the equilibrium rotational constants and the Kraitchman equations,19 the Cartesian coordinates and the bond parameters of the carbon atoms for the normal species in Table 6 were derived. These coordinates are called “re/rs” coordinates because they are equilibrium (e) coordinates derived from

Figure 7. Overall structure of the A-type band for ν10 of transhexatriene-1-13C1 at 1621 cm−1. Water contributes the sharp, intense features.

wavenumber, Doppler broadening is approximately 0.0022 cm−1, which is 50% greater than the resolution of 0.0015 cm−1. This broadening contributes to stymieing the analysis of the rotational structure of this band in an IR spectrum recorded at room temperature. A shift of 9 cm−1 to lower wavenumber occurs for this mode in going from the normal species6 to the 1-13C1 species. Comparison of Observed and Calculated Ground State Rotational Constants for HTE with Single 13C Substitution. With scaling adjustments, the theoretical ground state rotational constants for tHTE-1-13C1 computed with the B3LYP/cc-pVTZ model agree quite well with the observed values. The scale factors came from the ratio of the observed6 and calculated GS rotational constants for the normal species. The vibration−rotation module of Gaussian reports GS rotational constants determined from the computed equilibrium rotational constants and the sums of computed spectroscopic alphas. Table 4 gives the data used to obtain the scale factors from the normal species and the predictions of rotational constants for tHTE-1-13C1 in comparison with the observed values. The differences between observations and predictions for this species are less than 0.006%. Table 4 also gives the predictions of scaled GS rotational constants for the 2-13C1 and 3-13C1 species. 3153



Article

cHTE, and localized CC and CC (sp2−sp2) bond lengths. The localized values came from high level quantum chemical

Table 5. Equilibrium Rotational Constants for transHexatriene and Its 13C1 Isotopologues 1/2alpha suma (cm−1)

equil. rot. consts. (cm−1) b

Normal a b c Δc

0.0092943 0.0002486 0.0002323

0.8835424 0.0449085 0.0427422 −0.05395 1-13C1d

a b c Δc

0.0092800 0.0002417 0.0002261

0.8821002 0.0438285 0.0417575 −0.03497 2-13C1e

a b c Δc

0.0091214 0.0002453 0.0002292

0.8757880 0.0445023 0.0423562 −0.05500 3-

a b c Δc

13

Figure 8. Comparison of equilibrium structures for the carbon-atom backbones of butadiene, cis-hexatriene, and trans-hexatriene.

C1e

0.0092242 0.0002467 0.0002304

0.8794275 0.0448656 0.0426938 −0.05540

calculations for butadiene twisted 90° around the single bond.3 In this conformation, effects of π-electron delocalization are blocked. Theoretical backbone structures from the MP2/ccpVTZ model for cHTE and tHTE are also given in Figure 8. We consider various comparisons to the localized bond lengths in Figure 8. Butadiene shows an increase in the “CC” bond length and a decrease in the CC bond length compared to localized values in accord with some π-electron delocalization in butadiene.2 Both HTE isomers show structural effects of additional π-electron delocalization, in particular, a significant increase in the length of the central “CC” bond and a further decrease in the “CC” bond length in comparison with butadiene. The smaller decrease in the “CC” bond length in the cis isomer is a likely consequence of repulsion between the H atoms attached to the 2 and 5 carbon atoms. The outcomes for the end “CC” bonds in the HTE isomers differ. For the cHTE, the end “CC” bond is slightly longer than in butadiene. The length of the end “CC” bond for tHTE is intermediate between the localized value and the value for butadiene. Whereas the CCC bond angles in tHTE are essentially the same as in butadiene, the interior CCC bond angle in cHTE is substantially larger than the bond angle in butadiene. The large interior bond angle undoubtedly reflects repulsion between the hydrogen atoms on the 2 and 5 carbon atoms. The exterior bond angles in the cis isomer are smaller than in the trans isomer, another presumed consequence of the HH repulsion. In view of the approximations in the MP2/ccpVTZ model, the differences between the theoretical values for the two isomers are reasonably consistent with those for the SE re/rs structures. The unmistakable conclusion is that an increase in the polyene length from butadiene to hexatriene is accompanied by an increase in the structural effects of πelectron delocalization. We are working toward complete semiexperimental structures for the cis and trans isomers of HTE. The -1,1-d2, cis-1-d1, trans-1-d1, 2-d1, and 3-d1 species have been synthesized, and some of the high-resolution spectra have been recorded and analyzed.

a

Calculated with VIBROT from the G03 output for the B3LYP/ccpVTZ model. bExperimental. Reference 6. cInertial defect: Δ = Ic − Ia − Ib in amu Å2. dExperimental. This work. eUses predicted GS rotational constants from Table 4.

equilibrium rotational constants by the substitution (s) method of the Kraitchman equations. As is well-known, small Table 6. Equilibrium Coordinates for trans-Hexatriene Cartesian Coordinates SEa a (Å) C1 C2 C3

3.055 1.859 0.6015

theoryb b (Å)

a (Å)

b (Å)

−0.180 3.061 0.415 1.859 −0.300 0.604 Internal Coordinates

−0.179 0.419 −0.301

length (Å) C3C4 C3C2 C2C1 a

angle (deg)

SEa

theoryb

1.345 1.447 1.336

1.350 1.446 1.342

C3C3C2 C3C2C1

SEa

theoryb

123.8 123.9

123.7 123.7

SE stands for semiexperimental. bMP2/cc-pVTZ model.

coordinates found with Kraitchman equations from small differences between moments of inertia of normal and isotopic species can be uncertain. Thus, the b coordinate for C1 is the least certain. Table 6 also gives the theoretical Cartesian coordinates and bond parameters found with the MP2/ccpVTZ model. The good agreement between the b coordinate from theory with that from experiment reduces doubt about this small coordinate. The bond length and bond angle comparisons between theory and the re/rs structure are acceptably close. The uncertainties in the SE structure are estimated to be 0.002 Å for bond lengths and 0.2° for bond angles. Figure 8 displays the SE bond lengths and bond angles for the C6 backbone of tHTE in comparison with butadiene, 3154



■

Article

(15) Winnewisser, B. P.; Reinstädtler, J.; Yamada, K. M. T. J. Mol. Spectrosc. 1988, 136, 12−16. (16) Craig, N. C.; Hanson, K. A.; Moore, M. C.; Sams, R. L. J. Mol. Spectrosc. 2005, 742, 21−29. (17) Craig, N. C.; Abiog, O. P.; Hu, B.; Stone, S. C.; Lafferty, W. J.; Xu, L.-H. J. Phys. Chem. 1996, 100, 5310−5317. (18) Groner, P.; Warren, R. D. J. Mol. Struct. 2001, 599, 323−335. (19) Gordy, W.; Cook, R. L. Microwave Molecular Spectra, Techniques of Organic Chemistry, 3rd ed.; Weissberger, E. A., Ed.; John Wiley & Sons: New York, 1984; Vol. XVIII, p 661.

ASSOCIATED CONTENT

S Supporting Information *

A medium-resolution IR spectrum of tHTE-1-13C1; assignments of lines for the C-type band for ν26 at 1011 cm−1; GSCDs from bands for ν26 and ν30 and their fit to ground state rotational constants; and assignment of lines for the C-type band at 894 cm−1 and the fit of upper state rotational constants for this mode. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

We are grateful to Peter Groner for the calculations with VIBROT and to Hannah A. Fuson for developing the synthetic method for making isotopologues of hexatriene. Dreyfus Senior Scientist Mentor grants supported the work at Oberlin College. National Science Foundation Grant 0420717 provided for the purchase and technical support of the Beowulf computer cluster at Oberlin College. The high-resolution spectroscopy was done at the W. R. Wiley Environmental Molecular Science Laboratory, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at the Pacific Northwest Laboratory (PNNL). PNNL is operated for the United States Department of Energy by Battelle under contract DE-AC05-75RLO-1830.

(1) Christensen, R. L.; Faksh, A.; Meyers, J. A.; Samuel, I. D. W.; Wood, P.; Schrock, R. R.; Hultzsch, K C. J. Phys. Chem. A 2004, 108, 8229−8236. (2) Craig, N. C.; Groner, P.; McKean, D. C. J. Phys. Chem. A 2006, 110, 7461−7469. (3) Feller, D.; Craig, N. C.; Matlin, A. R. J. Phys. Chem. A 2008, 112, 2131−2133. (4) Suenram, R. D; Pate, B. H.; Lesarri, A.; Neill, J. L.; Shipman, S.; Holmes, R. A.; Leyden, M. C.; Craig, N. C. J. Phys. Chem. A 2009, 113, 1864−1868. (5) Vázquez, J.; Stanton, J. F. Semiexperimental Equilibrium Structures: Computational Aspects. In Equilibrium Molecular Structures; Demaison, J., Boggs, J. E., Császár, A G., Eds.; CRC Press: Boca Raton, FL, 2011; Chapter 3. (6) Craig, N. C.; Leyden, M. C.; Moore, M. C.; Patchen, A. K; van den Heuvel, T.; Blake, T. A.; Masiello, T.; Sams, R. L. J. Mol. Spectrosc. 2010, 262, 49−60. (7) Gajewski, J. J.; Peterson, K. B.; Kagel, J. R.; Huang, Y. C. J. J. Am. Chem. Soc. 1989, 111, 9078−9081. (8) Dess, D. B.; Martin, J. C. J. Org. Chem. 1983, 48, 4155−4156. (9) Meyer, S. D.; Schreiber, S. L. J. Org. Chem. 1994, 59, 7549−7552. (10) Schneider, M. P.; Goldbach, M. J. Am. Chem. Soc. 1980, 102, 6114−6116. (11) Maki, A. G.; Wells, J. S. Wavenumber Calibration Tables from Heterodyne Frequency Measurements, NIST Special Publication 821, U. S. Department of Commerce, 1991 [updated to 1995 on the internet at http://www.nist.gov/PhysRefData/wavenum/html.E2.html ]. (12) Toth, R. A. J. Opt. Soc. Am. B 1991, 8, 2236−2255. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.: Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revisions C.02 and E.01; Gaussian, Inc.: Wallingford, CT, 2004. (14) McKean, D. C.; Craig, N. C.; Law, M. M. J. Phys. Chem. A 2008, 112, 6760−6771. 3155


Analysis of the Rotational Structure in the High-Resolution Infrared

Recommend Documents