Microwave Spectra of the Deuterium Isotopologues of cis-Hexatriene

Article pubs.acs.org/JPCA

Microwave Spectra of the Deuterium Isotopologues of cis-Hexatriene and a Semiexperimental Equilibrium Structure Norman C. Craig,*,† Yihui Chen,† Hannah A. Fuson,† Hengfeng Tian,† Herman van Besien,† Andrew R. Conrad,‡ Michael J. Tubergen,‡ Heinz Dieter Rudolph,§ and Jean Demaison*,∥ †

Department of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074, United States Department of Chemistry, Kent State University, Kent, Ohio 44242, United States § Department of Chemistry, University of Ulm, D-89069 Ulm, Germany ∥ Laboratoire de Physique des Lasers, Atomes et Molécules, Université de Lille I, 59655 Villeneuve d’Ascq Cedex, France ‡

S Supporting Information *

ABSTRACT: Microwave transitions and ground state rotational constants are reported for five newly synthesized deuterium isotopologues of cis-1,3,5-hexatriene (cHTE). These rotational constants along with those of the parent and the three 13C species are used with vibration−rotation constants calculated from an MP2/cc-pVTZ model to derive an equilibrium structure. That structure is improved by the mixed estimation method. In this method, internal coordinates from good-quality quantum chemical calculations (with appropriate uncertainties) are fit simultaneously with moments of inertia of the full set of isotopologues. The new structure of cHTE is confirmed to be planar and is stabilized by an interaction between the hydrogen atoms H2 and H5, which form a bond and participate in a six-membered ring. cHTE shows larger structural effects of π-electron delocalization than does butadiene with the effects being magnified in the center of the molecule. Thus, strong structural evidence now exists for an increase in π-electron delocalization as the polyene chain lengthens.

1. INTRODUCTION Polyenes are of great importance in biological systems and in organic electronic conductors. Evidence exists for an increase in π-electron delocalization as the chain length increases in polyenes. The well-known red shift in electronic absorption with increased length of polyenes is consistent with this effect.1 Electronic conduction in doped polyacetylenes is another consequence of π-electron delocalization.2 The structural consequences of π-electron delocalization would be an increase in the length of “CC” double bonds and a decrease in length of sp2-sp2 single bonds in the conjugated system. A recent determination of the semiexperimental equilibrium structure of butadiene showed the onset of the effect.3 The “CC” bond increases 0.005 Å in length, and the “C−C” single bond decreases in length by 0.028 Å compared to comparable localized bonds.4,5 Quantum chemical (QC) calculations with density functional theory (DFT) show this outcome to a greater extent for bond lengths in 1,3,5,7,9-decapentaene and in longer polyenes with the effect increasing toward the center of the molecule.6 The current investigation examines the structural effects of π-electron delocalization in cis-hexatriene (cHTE), the next member in the polyene sequence after butadiene. See Figure 1 for the structure of cHTE and the numbering of the atoms. To determine a complete and accurate semiexperimental structure of a substance, rotational constants are needed for a © 2012 American Chemical Society

Figure 1. Structure of cis-hexatriene.

full set of isotopologues. A previous microwave (MW) investigation of cHTE yielded rotational constants for the parent and the three 13C1 isotopologues from measurements on these species in natural abundance.7 Obtaining MW spectra for cHTE is difficult, especially for the 13C species in natural abundance, because the dipole moment of this substance is estimated by QC calculations to be only 0.05 D.7 For the present work isotopic species were synthesized with deuterium replacing hydrogen in each chemically different location. In Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: November 7, 2012 Revised: December 12, 2012 Published: December 13, 2012 9391

dx.doi.org/10.1021/jp311035c | J. Phys. Chem. A 2013, 117, 9391−9400

The Journal of Physical Chemistry A

Article

Figure 2. Schematic structures of the deuterium isotopologues of cis-hexatriene.

trans isomer product was converted into some cis material, which was separated by gas chromatography, as described above. A gas phase IR spectrum of a sample of cHTE-2-d1, contaminated with some tHTE-2-d1 and dichloromethane, is shown in the Supporting Information, Figures S2a and S2b. A new method was used to make cHTE-3-d1. In a typical reaction sequence, which was set up in a nitrogen-purged glovebag in oven-dried glassware and performed under a slow flow of nitrogen gas, 1.47 g (15 mmol) of 1,5-hexadien-3-ol (Aldrich) was dissolved in 12.5 mL of anhydrous dichloromethane (Aldrich) in a 3-neck 100 mL reaction flask. 50 mL of 0.3 M Dess-Martin periodinane in dichloromethane (Aldrich) was placed in an addition funnel and dripped over 1.5 h into the well-stirred reaction mixture at room temperature. The workup began by pouring the products into a separatory funnel and rinsing the reaction flask with 110 mL of anhydrous ether (Fisher) in three portions. The necessary mild-base workup procedure used a solution of 11 g of sodium bicarbonate and 27 g of sodium thiosulfate dissolved in 180 mL of deionized water to convert the solid into water-soluble material.13 Most of the ether/dichloromethane solvent was removed by rotovapping at room temperature. Residual water was removed with 3 Å molecular sieves (Aldrich). The yield was about 60%. A proton NMR spectrum confirmed the formation of 1,5-hexadien-3one.14 The second step was also set up in a glovebag with ovendried glassware and performed under a slow flow of nitrogen. 7.5 mL of 1 M lithium aluminum deuteride in ether (Aldrich) was placed in a 50 mL three-neck flask. The flask was equipped with a reflux condenser for cooling with ice water. The ketone (9 mmol) was put into an addition funnel along with 10 mL of anhydrous ether and was dripped in slowly over 45 min with vigorous stirring at room temperature. The mixture was heated gently in refluxing ether for 1.5 h. Quenching and workup was as described before.11 The yield in this reaction was close to 100%. 1,5-Hexadien-3-ol-3-d1 was confirmed by its proton NMR spectrum. The band for the H3 proton was gone, and the band from neighboring CH2 protons was simplified. 1,5-Hexadien-3-ol-3-d1 was dehydrated by distillation through a column packed with phosphorus pentoxide.7 Although the yield was only about 15%, the product was more than 50% cHTE7 and was suitable for MW spectroscopy. Several preparations of 1,5-hexadien-3-ol-3-d1 were needed to make enough cHTE-3-d1. Gas chromatography, as described above, was used to obtain a sample of cHTE-3-d1 for a reference IR spectrum. The gas phase IR spectrum of cHTE-3d1 is in the Supporting Information, Figures S3a and S3b. 2.2. Spectroscopy. NMR spectra were recorded on a Varian 400MR spectrometer in 5 mm tubes with CDCl3 as the solvent. IR spectra were recorded on a Perkin-Elmer 1760 FT

addition, the 1,1-d2 species was prepared. Figure 2 shows schematically the new species studied. Vibration−rotation interaction constants (spectroscopic alphas) were computed from quadratic and cubic force constants obtained from QC calculations and Peter Groner′s VIBROT program.8 A complete semiexperimental equilibrium structure is proposed for cHTE. In a parallel study, we are working toward a semiexperimental equilibrium structure for the trans isomer of HTE (tHTE). High-resolution infrared (IR) investigations of tHTE,9 the tHTE-1-13C1 species,10 and of a mixture of tHTE1,1-d2 and -cis-1-d1 have been reported.11 For this nonpolar molecule, rotational constants come from the analysis of highresolution infrared spectra, a process that is more arduous than a MW study.

2. EXPERIMENTAL SECTION 2.1. Syntheses. A mixture of cHTE-1,1-d2, -cis-1-d1, and -trans-1-d1 came from the synthesis that was used for the corresponding mixture of the trans isomer.11 The trans-rich material was isomerized with I2-catalysis at 125 °C for one-half hour and then quenched in a darkened room in ice water to preserve the higher temperature equilibrium composition, which gives only 15% of the cis isomer. Higher temperatures cause loss of cHTE by conversion to cyclohexadiene. With residual iodine removed by distillation through a tube containing copper turnings, the mixture was separated by preparative gas chromatography at 65 °C on a 7-m column packed with dicyanoethylether on Chromosorb.7,12 For MW spectroscopy the presence of some trans isomer is acceptable because this nonpolar isomer is MW silent. Repeated isomerizations of recovered tHTE were needed to obtain a useful amount of the cis isomer. During the isomerization some loss of material occurred to give a solid, cellophane-like polymeric material that seemed to incorporate iodine. A gas phase infrared (IR) spectrum of the mixture of cHTE-1,1-d2, -cis-1-d1, and -trans-1-d1 material is in the Supporting Information, Figures S1a and S1b. cHTE-2-d1 was prepared by a method similar to that used for the -1-d species.11 However, methyl-2,4-pentadienoate (Aldrich/Fluka) was reduced with 1.0 M lithium aluminum deuteride in ether (Aldrich) to give 2,4-pentadienol-1,1-d2. The partially deuterated alcohol was confirmed by loss of the CH2 signal in the NMR spectrum.10 The pentadienol was oxidized to the corresponding 2,4-pentadienal-1-d1 with 0.3 M DessMartin periodinane in dichloromethane (Aldrich) and confirmed by the loss of the characteristic aldehyde signal in the proton NMR spectrum.10 A Wittig reaction of the 2,4pentadienal-1-d1 with deprotonated methyl-triphenylphosphonium iodide (Aldrich) gave HTE-2-d1.11 The predominate 9392



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Figure 3. Examples of observed MW lines. See the text for a discussion of the raggedness of these observations.

spectrometer with a resolution of 0.5 cm−1 or on a Nicolet 6700 spectrometer with a resolution of 0.1 cm−1. Samples were in a Wilmad mini-cell of 10 cm path length with 5 cm KBr windows. MW spectra were recorded on the instrument at Kent State University that is based on the original Balle-Flygare design,15 as adapted by Suenram and co-workers into a mini configuration and equipped with modernized electronics and software.16,17 The spectral range is 10−22 GHz. In the initial work with the 13C isotopomers in natural abundance, Suenram used 1 W MW amplifiers in the input circuit for the two spectral ranges.7 The instrument at Kent State has an amplification of only 63 mW in the input circuit. The jetcooled sample beam is coaxial with the direction of the MW pulse. Thus, Doppler doublets are observed for MW lines. The driver gas was 30% He/70% Ne (AGG Specialty Gases of America). A 2 L flask containing a sample of cHTE was pressurized to 2 atm with the driver gas and refreshed by addition of gas when the pressure dropped to about 1.6 atm.

To confirm optimal settings of the instrument, samples of cis/trans mixtures of normal hexatriene were added to the deuterated material. Good observation of known lines of cHTE was a precondition for collecting spectra. The amount of deuterium-substituted samples was approximately 0.5 mmol with a comparable amount of the normal species (55% cis; 45% trans) mixed in. Because of the small dipole moment of cHTE (0.05 D), the low input MW power of the spectrometer, and deuterium quadrupole splitting of the MW lines, as many shots as possible had to be accumulated with limited sample sizes. Figure 3 gives two examples of the compromised spectra that were observed in this study. Q branch transitions were generally stronger and gave better lines.

3. CALCULATIONS Three levels of electronic structure theory have been used in this study: second-order Møller−Plesset perturbation theory (MP2),18 coupled cluster theory including single and double excitations (CCSD)19 augmented with a perturbational estimate of the effects of connected triple excitations, 9393



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Table 1. MW Lines for cis-Hexatriene-1,1-d2, -cis-1-d1, and -trans-1-d1 cHTE-1,1-d2

cHTE-cis-1-d1

cHTE-trans-1-d1

J′

Ka′

Kc′

J″

Ka″

Kc″

freq/MHz

obs-cal

freq/MHz

obs-cal

freq/MHz

obs-cal

1 2 3 4 5 6 7 8 1 2 3

1 1 1 1 1 1 1 1 1 1 1

0 1 2 3 4 5 6 7 1 2 3

1 2 3 4 5 6 7 8 0 1 2

0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 0 1 2

12563.599 12705.859 12921.459 13213.084 13584.263 14039.377 14483.550 15222.612 15233.328 17903.050 20502.730

−0.0045 0.0082 0.0036 −0.0015 −0.0097 −0.0028 0.0032 0.0022 0.0052 −0.0068 0.0028

13110.881 13257.281 13479.138 13779.166 14160.959 14628.937 15188.319

−0.0089 −0.0018 −0.0016 −0.0030 0.0023 0.0036 −0.0025

12696.006 12845.822 13072.988 13380.436 13772.030 14252.563 14827.646

−0.0057 0.0002 0.0008 0.0022 −0.0028 0.0004 0.0003

15878.172 18645.410

0.0230 −0.0118

15448.988 18201.958

0.0093 −0.0047

Table 2. MW Lines for cis-Hexatriene-2-d1 and -3-d1 cHTE-2-d1

cHTE-3-d1

J′

Ka′

Kc′

J″

Ka″

Kc″

freq/MHz

obs-cal

freq/MHz

obs-cal

1 2 3 4 5 6 7 8 9 10 7 1 9 2 3

1 1 1 1 1 1 1 1 1 1 0 1 0 1 1

0 1 2 3 4 5 6 7 8 9 7 1 9 2 3

1 2 3 4 5 6 7 8 9 10 6 0 8 1 2

0 0 0 0 0 0 0 0 0 0 1 0 1 0 0

1 2 3 4 5 6 7 8 9 10 6 0 8 1 2

12453.601 12615.622 12861.555 13194.905 13620.258 14143.286 14770.633 15509.801

−0.0027 0.0043 −0.0015 0.0031 0.0025 0.0009 - 0.0039 0.0008

15288.604

−0.0069

18123.636

0.0034

12100.503 12266.157 12517.752 12859.050 13294.975 13831.632 14476.097 15236.411 16121.168 17139.364 10431.632 14924.393 17352.636 17748.315 20490.872

−0.0002 0.0137 0.0121 0.0153 0.0062 0.0109 −0.0078 0.0019 −0.0037 −0.0079 0.0136 −0.0091 −0.0026 −0.0002 −0.0207

CCSD(T),20 and the Kohn−Sham density functional theory (DFT)21 using Becke′s three-parameter hybrid exchange functional22 and the Lee−Yang−Parr correlation functional,23 together denoted as B3LYP. The MP2/cc-pVTZ and B3LYP/cc-pVTZ QC calculations were done with Gaussian 03 (G03) C.02 software with tight convergence limits, using the basis sets as implemented in G03.24 For the DFT model an ultrafine grid was used. Unless otherwise indicated calculations used frozen core basis sets. The MP2 model gave the quadratic and cubic force constants used with the VIBROT program to compute the alphas needed to find equilibrium rotational constants from ground state rotational constants.8 For computing the centrifugal distortion constants of the different isotopologues for use in fitting the MW lines, the DFT model was applied. A similar set of calculations with the MP2 model would have taken an inordinate amount of computer time with G03. For each isotopologue, the optimized geometry was transformed into the principal axis system and reinput into G03 before using the vibration−rotational module.25 For use in association with fitting a structure by the mixed estimation method, additional calculations were done with the B3LYP/6-311+G(3df,2pd), MP2/cc-pVQZ, MP2/aug-cc-pVQZ, CCSD(T)/cc-pVTZ, MP2/cc-pwCVTZ, MP2/cc-pwCVQZ, and the CCSD(T)/ccpwCVTZ models. The cc-pVnZ basis sets were developed by Dunning,26 the aug-cc-pVQZ basis set was developed by Kendall et al.,27 and the pwCVnZ basis sets were developed by

Peterson and Dunning.28 In these calculations planarity was enforced for all of the out-of-plane torsion angles. The latter three calculations included the core electrons in electron correlation. The latter two calculations were carried out at the Ohio Supercomputer Center (OSC) with Gaussian09 (G09). Additional calculations were done with G09 at the OSC with all of the torsion angles relaxed for the MP2/cc-pVTZ model and the C−CC−C, CC−CC, and H−C−CC torsion angles relaxed with the CCSD(T)/cc-pVTZ model in the frozen core approximation.

4. RESULTS 4.1. MW Spectra. A single sample contained cHTE-1,1-d2, -cis-1-d1, and -trans-1-d1. We estimated the composition to be roughly 3/5 of the 1,1-d2 species and 1/5 each of the cis-1-d1 and trans-1-d1 species.11 The b-type MW transitions observed for these three species are in Table 1 along with the obs-calc values for the fit to a Watson-type Hamiltonian. The asymmetric rotor reduction was used with an Ir representation. Although most of the observed lines were part of a Q-branch progression, at least two R-type transitions, which are needed for a good fit of the A rotational constant, were found for each species. Separate samples of the cHTE-2-d1 and -3-d1 species were used for MW spectroscopy. Table 2 contains the observed MW lines for these two species. More lines were observed for the 39394



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Table 3. Rotational Constants for Deuterium Isotopologues of cis-Hexatriene A/MHz B/MHz C/MHz δJ/kHz δK/kHz ΔK/kHz ΔJK/kHz ΔJ/kHz s. d./MHz κ Δc/amuÅ2 no. lines

cHTE-1,1-d2

cHTE-cis-1-d1

cHTE-trans-1-d1

cHTE-2-d1

cHTE-3-d1

13,898.545(3) 1,475.898(1) 1,334.859(1) 0.02376a 0.5390b 89.831a −4.3277a 0.13715a 0.0061 −0.9775 −0.1824 11

14,494.602(5) 1,528.795(4) 1,383.628(3) 0.02454a 0.5767b 91.060a −4.3972a 0.14540a 0.0116 −0.9779 −0.1839 9

14,072.588(2) 1,524.966(2) 1,376.482(1) 0.02757a 0.6000b 102.077a −4.9951a 0.15272a 0.0051 −0.9766 −0.1633 9

13,871.177(2) 1,577.942(1) 1,417.502(1) 0.02921a 0.6312b 77.878a −4.4428a 0.16448a 0.0041 −0.9742 −0.1833 10

13,512.527(4) 1,575.8974(5) 1,411.9484(6) 0.02905a 0.6052b 82.267a −4.3222a 0.15616a 0.0114 −0.9729 −0.1634 15

Gaussian 03 with B3LYP/cc-pVTZ(ultra fine grid) prediction after scaling. bGaussian 03 with B3LYP/cc-pVTZ(ultrafine grid) prediction. cInertial defect, Δ = Ic − Ia − Ib.

a

that the molecule to be planar (see next section), was taken into account, the equilibrium inertial defect, Δe = −0.013 uÅ2 for cHTE, was quite small in absolute value but still different from zero. However, for a molecule with conjugated double bonds such as hexatriene, the electronic correction might not be negligible.32,33 As no experimental values for the g-constants are known, they were computed, using G03 at the B3LYP/6311+G(3df,2pd) level of theory. In cases where comparison can be made between computed and experimental g constants, they show good agreement.34 The computed values for cHTE are gaa = −0.1624; gbb = −0.0246; and gcc = 0.0037. They give for the electronic contribution to the inertial defect −0.008 uÅ2 [eq (28) of ref 32] reducing the equilibrium inertial defect to Δe = −0.005 uÅ2. Table 4 shows that the derived equilibrium rotational constants for the isotopologues of cHTE have inertial defects, after electronic correction, that are more than thirty times smaller than those for the ground state rotational constants and are almost identical for all isotopologues. This small value for the equilibrium inertial defect confirms that the molecule is likely to be planar. 4.3. Equilibrium Rotational Constants. Equilibrium rotational constants Beβ are related to ground state rotational constants B0β by

d1 species than for the others because better predictions reduced sample loss during the search for the first line. Table 3 gives the rotational constants for all five deuteriumcontaining isotopic species. The data sets were not large and varied enough to permit fitting the quartic centrifugal distortion constants. Values of these constants were computed with the B3LYP/cc-pVTZ model, scaled by factors derived from fitting centrifugal distortion constants (except δK) for the normal species, and used in the fitting to observed lines. At most, scale factors differed from one by 7%. The small values of the inertial defect imply planarity of cHTE in the ground state. 4.2. Planarity. cHTE, a molecule with conjugated double bonds, is expected to be planar. However, cHTE may be sterically strained because the nonbonded distances H2−H5 and C2−C5 are smaller than the sum of the van der Waals radii. See below, the section on Semiexperimental Structure. The strain might affect, among others, the torsional angle τ(C2C3C4C5). An early gas-phase electron diffraction (GED) study29 found that the molecule is essentially planar, but a torsional angle of about 10° around the central C3C4 bond was suggested. On the other hand, a recent MW investigation7 concluded that the molecule is planar. The large negative value of the ground state inertial defect Δ0 = −0.166 uÅ2 for cHTE is explained by the presence of low-frequency out-of-plane vibrations.30 However, as the Δ0 of cis-d1 and 2-d1 species are slightly larger in absolute value, a small nonplanarity cannot be excluded. To explore planarity, we did an optimization at the MP2/cc-pVQZ (frozen core) level of theory with all of the torsion angles unconstrained. The molecule was essentially planar (all torsion angles less than 0.001°) and had the same bond lengths and in-plane bond angles as when constrained to planarity. However, it is known that these levels of theory are not always reliable to predict the planarity of a molecule.31 For this reason, the CCSD(T)/ccpVTZ level of theory (frozen core) was also used with relaxation of some torsional angles. When only the torsion angle C−CC−C was relaxed, its optimized value was essentially zero (0.005°). When, in addition, the CC−C C and H−C−CC torsion angles were relaxed, the final values of the torsion angles were approximately 0.1°. Thus, the optimized values of the torsion angles confirmed the planarity. As a further investigation of planarity, we calculated the equilibrium inertial defect. For exact equilibrium rotational constants for a planar molecule the inertial defect should be zero. After the rovibrational correction, calculated assuming

Beβ ≈ B0β +

1 2

∑ αkβ k

(1)

to first order, where β represents the a, b, and c directions of the principal axes and k scans the normal modes of vibration. The alpha/2 sums were computed by Peter Groner with his VIBROT program from quadratic and cubic force constants obtained with the MP2/cc-pVTZ model,8 assuming that the molecule was planar. The quadratic force constants were not scaled because recent work showed that the average scale factor needed for harmonic frequencies was 0.99.35 Table 4 applies the alpha/2 sums to the ground state rotational constants to obtain equilibrium rotational constants. At most, the adjustments to the ground state rotational constants are 1.2%. For these relatively small adjustments the triple-ζ level of theory suffices. The electronic corrections are included in the equilibrium rotational constants in Table 4. 4.4. Equilibrium Structure of cHTE. The structure was first determined using the semiexperimental rotational constants with Kraitchman′s equations and by a global fit, as reported in subsection 4.4.1 In this result, the value for the bond length C2H2 was suspect. For this reason, in subsection 9395



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Table 4. Conversion of Ground State Rotational Constants to Equilibrium Rotational Constants corrections normal A B C Δa -1-13C1 A B C Δa -2-13C1 A B C Δa -3-13C1 A B C Δa -1,1-d2 A B C Δa -trans-1-d1 A B C Δa -cis-1-d1 A B C Δa -2-d1 A B C Δa -3-d1 A B C Δa

B0/MHz

rovibrationalb

electronic

Be(se)/MHz

residualc

14651.229 1583.181 1429.462 −0.166

183.291 7.640 7.340

1.312 0.021 −0.003

14835.832 1590.843 1436.799 −0.0052

−0.037 −0.012 0.012

14606.201 1543.538 1396.654 −0.166

183.307 7.406 7.134

1.304 0.020 −0.003

14790.8124 1550.96426 1403.78484 −0.0050

−0.029 −0.007 0.013

14581.503 1571.686 1419.433 −0.168

181.358 7.554 7.249

1.300 0.021 −0.003

14764.161 1579.261 1426.680 −0.0055

−0.012 −0.008 0.016

14411.130 1580.989 1425.350 −0.164

179.004 7.576 7.289

1.269 0.021 −0.003

14591.403 1588.586 1432.636 −0.0051

0.037 −0.010 0.013

13898.545 1475.897 1334.859 −0.182

166.278 7.015 6.663

1.180 0.019 −0.003

14066.003 1482.931 1341.520 −0.0052

−0.014 −0.003 0.016

14072.587 1524.966 1376.482 −0.163

175.586 7.198 6.966

1.210 0.020 −0.003

14249.384 1532.184 1383.446 −0.0045

−0.030 −0.014 0.006

14494.602 1528.795 1383.628 −0.184

175.478 7.356 6.963

1.283 0.020 −0.003

14671.363 1536.171 1390.589 −0.0049

−0.033 −0.015 0.006

13871.177 1577.942 1417.503 −0.183

174.964 7.289 7.015

1.176 0.021 −0.003

14047.317 1585.252 1424.515 −0.0047

−1.930 0.102 0.082

13512.527 1575.897 1411.948 −0.163

153.657 7.891 7.407

1.114 0.021 −0.003

13667.298 1583.810 1419.352 −0.0048

0.512 −0.030 0.001

Inertial defect, Δ = Ic − Ia − Ib. bAlpha/2 sum in MHz from the MP2/cc-pVTZ model. cResiduals (obs − calc) of the fit with 13 predicate values (last column of Table 6). a

4.4.1. Semiexperimental Equilibrium Structure for cHTE. Kraitchman′s single substitution equations36 were applied to computing the Cartesian coordinates for the atoms in cHTE from the equilibrium rotational constants in Table 4. Coordinates for the carbon atoms came from 13C substitution, and coordinates for the hydrogen atoms came from 2H substitution. Table 5 gives the Cartesian coordinates for each of the symmetrically equivalent atoms. Most of the c coordinates obtained from Kraitchman′s equations were imaginary. All of the values for the c coordinate were set to zero for calculating internal coordinates of this planar molecule.

4.4.2, we report the calculated structure at the CCSD(T) level of theory, which confirmed that the semiexperimental value of r(C2H2) was inaccurate. Subsection 4.4.3 gives the mixed estimation structure derived from the CCSD(T) results and the semiexperimental rotational constants. Finally, in subsection 4.4.4, we report the analysis of the origin of this discrepancy. The largest difference by far is for the coordinate a(H2). For the later discussion we assess the fact that in Table 5 the semiexperimental value a(H2) = 1.0583 Å essentially depends on the rotational constant Be(se) (-2-d1), that is, on B0(-2-d1) plus its rovibrational and electronic corrections. 9396



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Table 5. Cartesian Coordinates for Symmetrically Equivalent Atoms in cis-Hexatriene as Derived from Kraitchman′s Equationsa and an Optimizedd Fit a/Å

b/Å

atom

Kraitchmana

fitd

Kraitchmana

fitd

c/Åb

rc,d

C1 C2 C3 H1 cis H1 trans H2 H3

2.8706 1.5328 0.6742 3.3707 3.4897 1.0583 1.1854

2.87067(17) 1.53314(28) 0.67440(46) 3.37057(19) 3.48959(18) 1.0690(16) 1.1837(11)

−0.3283 −0.4100 0.7595 0.6323 −1.2131 −1.3900 1.7163

−0.32813(20) −0.41025(18) 0.75957(11) 0.63213(21) −1.21295(12) −1.38815(94) 1.71660(66)

0.0119i 0.0119 0.0092i 0.0142i 0.0195i 0.0175i 0.0158i

0.7596(1) 2.8894(2) 1.5871(3) 1.0158(3) 3.4293(2) 3.6944(2) 1.7520(14)

a

Kraitchman′s equations; used equilibrium rotational constants with the corrections for the electronic contribution. bi, imaginary; values for c coordinates were set to zero for computing internal coordinates. cDistance from the center of mass. dFrom the fit with 13 predicates, see last column of Table 6.

Table 6. Internal Coordinates for cis-Hexatriene (in Å and deg) internal coord. r(C1C2) r(C2C3) r(C3C4) r(C1H1 cis) r(C1H1 trans) r(C2H2) r(C3H3) α(C1C2C3) α(C2C3C4) α(C2C1H1 cis) α(C2C1H1 trans) α(C1C2H2) α(C4C3H3)

MP2a ccpVTZ

B3LYP ccpVTZ

rseb semiexpt. Kraitchman

rec semiexpt. global fit

ab initiod

ree global fit +4 predicates

ree global fit +13 predicates

1.3427 1.4488 1.3530 1.0821 1.0798 1.0823 1.0845 122.754 126.171 120.857 121.432

1.3365 1.4477 1.3486 1.0832 1.0808 1.0837 1.0851 123.668 127.096 121.426 121.651

1.340 1.451 1.348 1.083 1.080 1.089 1.085 122.8 126.3 121.0 121.5

1.33993(28) 1.45041(38) 1.34997(87) 1.08255(35) 1.07982(28) 1.08788(37) 1.08417(28) 122.755(38) 126.273(19) 121.017(34) 121.456(37)

1.3401 1.4526 1.3490 1.0823 1.0799 1.0823 1.0840 122.789 126.251 121.020 121.501

1.3402(6) 1.4508(7) 1.3493(18) 1.0825(4) 1.0799(3) 1.0823(10) 1.0842(6) 122.76(5) 126.28(4) 121.02(3) 121.46(3)

1.3400(4) 1.4512(4) 1.3488(9) 1.0826(3) 1.0798(2) 1.0825(8) 1.0841(5) 122.77(3) 126.28(2) 121.02(2) 121.46(2)

118.720 117.904

118.484 117.528

119.3 118.1

119.320(37) 118.035(27)

118.889 118.038

118.75(14) 117.96(10)

118.91(9) 118.02(7)

Structure used for the force field calculation. bFrom Kraitchman′s method applied for single substitution. cGlobal fit of all the equilibrium rotational constants. dCCSD(T)/cc-pwCVTZ(AE) + MP2/cc-pwCVQZ(AE) - MP2/cc-pwCVTZ(AE). eAb initio equilibrium values (column 5: ab initio) used as predicate observations for internal coordinates of atoms as designated, see text. a

parent species was zero. The subsequent fit was much better, the standard deviations of the parameters being much smaller, the reduced standard deviation of the fit being s = 0.4 and the systematic deviations of the residuals being negligible. However, the parameters of this new fit are almost identical to those of the previous fit, an indication that small systematic errors do not have much effect on the values of the parameters.38 The results of this last fit are given in Table 6, (column 4: global fit). Although they seem to be highly satisfactory and in good agreement with the results of Kraitchman′s equations, there are two problems: (i) the fit is not well conditioned indicating that the errors may be much larger than the estimations given by the standard deviations, and (ii) the value of re(C2H2) = 1.088 Å is much larger than the MP2/cc-pVTZ value, 1.082 Å, even though this level of theory quite generally gives reliable values for CH bond lengths.39 4.4.2. Ab Initio Structures. To assess the discrepancy for the C2H2 bond length and improve the determination of other bond parameters, ab initio calculations were performed with a planar constraint for the molecule. The structure was optimized with the CCSD(T) method with the correlation-consistent polarized weighted core-covalence triple-ζ (cc-pwCVTZ) basis set,28 all electrons being correlated (AE). At this level, the convergence of the structural parameters to the complete basis set limit is not completely achieved. To estimate the rather

Internal coordinates were computed from the Cartesian coordinates given in Table 5. These internal coordinates are listed in Table 6, (column 3: Kraitchman), along with those predicted from the ab initio structures. The structure was also determined from a least-squares fit (LSQ) of the semiexperimental moments of inertia. First, a nonweighted LSQ was tried. The standard deviations of the fitted parameters were found to be rather large, and the residuals of the fit showed large systematic deviations. This outcome is mainly from the Ae rotational constants being less accurate than the other rotational constants. When the ground state rotational constants are accurate, which is probably true here, the uncertainty of the semiexperimental rotational constants is generally roughly proportional to the rovibrational correction.37 Indeed, a weighted fit with an uncertainty corresponding to 300 kHz for Ae, and 10 kHz for Be and Ce gives good results with a reduced standard deviation, s = 1.27, close to one. However, this fit is not yet completely satisfactory because the residuals are still affected by systematic deviations, the median of residuals being −99(11) kHz for Ae, 9(3) kHz for Be and 11(4) kHz for Ce. It is known that the rovibrational correction is affected mainly by a systematic error, which is a few percent of the rovibrational correction.37 We tried to correct for this error by multiplying all the rovibrational corrections by a constant factor f of 1.035 chosen so that the equilibrium inertial defect of the 9397



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small effects of further basis set improvement (cc-pwCVTZ → cc-pwCVQZ), the MP2 method was employed. We also checked that the diffuse functions have a negligible effect on the structure using the MP2/aug-cc-pVQZ level of theory. See the Supporting Information, Table S1. The final ab initio equilibrium structure is given in Table 6 (column 5, ab initio). The details of the different ab initio computations are given in the Supporting Information, Table S1. The final computed structure confirms that the MP2/ccpVTZ(frozen core) value for the C2H2 bond length is accurate, although the CC bonds are off by 0.003−0.004 Å. The B3LYP/ cc-pVTZ structure is also given in Table 6 for comparison. For the bond lengths, this structure is not better than the MP2/ccpVTZ structure, and for the bond angles it is definitely worse, the ∠(C1C2C3) and ∠(C2C3C4) angles being about 0.8° too large and the ∠(CCH) angles in error of about 0.5°. The implication was that the rotational constants of the 2-d1 species were suspicious. We first tried to identify any problem by using the Iteratively Reweighted Least Squares (IRLS) method, whereby data with large residuals are weighted down.40 The advantage of this IRLS method is that it is “robust”, that is, it mitigates the influence of outliers. Nevertheless, all the fits gave compatible results, and the analysis of residuals did not identify any suspect data, including the rotational constants for the 2-d1 species, even though the residuals were abnormally large and very different from one fit to the other. 4.4.3. Mixed Estimation Structure. We down-weighted the constants of the 2-d1 species and used the mixed estimation method where auxiliary information is added directly to the data matrix during the least-squares fit.39,41 This auxiliary information, usually called predicate observations, consisted of carefully chosen values for the C2H2 bond length and the ∠(C3C2H2) bond angle, together with their corresponding uncertainties. We chose the MP2/cc-pVTZ values with an uncertainty of 0.002 Å for the bond length and 0.2° for the bond angle. The fit showed that the Ae and Be rotational constants of the 2-d1 species were inaccurate as expected and that also the Ae rotational constant of the 3-d1 species was inaccurate. This constant was also down-weighted, and we repeated the mixed fit with four predicate observations corresponding to the internal coordinates of the atoms H2 and H3. The resulting fit was good and in satisfactory agreement with the ab initio structure, see Table 6, (column 6: global fit 4 predicates). Another fit with predicate observations for all internal coordinates of the hydrogen atoms gave almost identical results. Finally, to obtain a structure as accurate as possible, in a final fit, the equilibrium ab initio values of the internal coordinates Table 6 (column 5: ab initio) of all atoms were added as predicate observations with an uncertainty of 0.002 Å for the bond lengths and 0.2° for bond angles. The results are reported in the last column of Table 6 (column 7: global fit 13 predicates). This structure for cHTE is good to 0.001 Å. 4.4.4. Problematic Rotational Constants. Remaining to be explained is the origin of the problem with the rotational constants of the 2-d1 isotopologue. The ground state A0 constant of the 2-d1 species is determined from only two lines. However, dropping either of these two lines does not significantly affect the value of the A0 constant. Furthermore, the value of the ground state inertial defect (see Table 4) does not imply any problem. Thus, it may be concluded that the ground state constants are accurate and that the problem comes

from the rovibrational correction, which is traceable to the calculated force field. To go further, we tried a fit without the incriminated rotational constants. The fit was still of acceptable quality and the value of r(C2H2) remained as large. By comparing the semiexperimental (SE) structure and the ab initio (AI) structure, it appears that the only significant difference is the a Cartesian coordinate of atom H2: a(SE) = 1.0582 Å to be compared with a(AI) = 1.0687 Å. From Kraitchman′s equations for a planar molecule a2 =

ΔIb ⎛ ΔIa ⎞ ⎟ ⎜1 + μ ⎝ Ia − Ib ⎠

(2)

it is easy to see that this coordinate is mainly determined by the value of ΔIb = Ib(2-d1) − Ib(parent) with ΔIb(AI) = 1.1428 uÅ2 and ΔIb(SE) = 1.1204 uÅ2. This difference of 0.0224 uÅ2 is relatively quite large, especially compared to the small value of ΔIb and explains the discrepancy for the a-coordinate. See the Supporting Information, Table S2 which shows that the error is the largest for ΔIb(2-d1). This large error is due to the unfortunate incomplete compensation of the small errors of Ib(N), 0.09 uÅ2 and Ib(2-d1), 0.12 uÅ2. Of course, this discussion assumes that the ab initio structure is accurate, which appears most probable but not unquestionable.

5. STRUCTURAL CONSEQUENCES 5.1. π-Electron Delocalization. The main goal of this investigation was to determine the structural consequences of π-electron delocalization as the polyene chain lengthens from four carbon atoms in butadiene to six carbon atoms in hexatriene. Reference values for the length of a localized sp2-sp2 single bond and a localized CC double bond are 1.482 Å and 1.333 Å, respectively.4 As reported in the Introduction, the double bond in butadiene increases in length by 0.005 Å, and the sp2-sp2 bond decreases by 0.028 Å in comparison with the localized values.4 From the values of bond parameters in the last column of Table 6, we see that the central “CC” bond in cHTE lengthens 0.016 Å and the end “CC” bonds lengthen 0.007 Å compared to the localized values. The “sp2-sp2” bond shortens 0.031 Å compared to the localized value. These changes, which require structures good to 0.001 Å to determine, are larger than for butadiene. Thus, the structural effects of π-electron delocalization increase with the length of the polyene chain. In addition, the changes are greatest near the center of molecule. We expect these structural effects of πelectron delocalization to increase with further chain lengthening in polyenes. A significant comparison for the structure of cHTE is with cis-hex-3-ene-1,5-diyne, which also should have structural effects of π-electron delocalization. An equilibrium structure has been determined for this diyne.42 The length of the central “CC” bond in the diyne, re(CC) = 1.347 Å, is very close to the value of 1.349 Å in cHTE. The triple bonds in the diyne are 1.208 Å, 0.005 Å longer than the equilibrium bond length in acetylene.38 Unfortunately, a reference length for a localized sp2-sp single bond is unavailable. Because the adjustments in the lengths of the CC double and triple bonds in the diyne reflect π-electron delocalization, we presume that the sp2-sp bond in the diyne is somewhat shorter than the corresponding localized bond. The CC−C angle in the diyne is 123.9°,42 in good agreement with the corresponding angle of 123.6° in butadiene.3 In the diyne, the H−H interaction is absent, which probably causes opening of this bond angle in cHTE. 9398



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Figure 4. Structure of cis-hexatriene with results of the AIM calculations. An attractor is a critical point where the electron density is maximum, it corresponds to the position of an atom. A bond critical point (BCP) is a saddle point of the electron density and corresponds to a minimum in electron density along the bond path. It is between two neighboring atoms and defines a bond between them. A ring critical point is also a saddle point of the electron density with the maximum in a direction perpendicular to the plane of the ring. This point is to be found in the middle of several bonds forming a ring.44.

5.2. Hydrogen−Hydrogen Interaction. Another striking structural feature in cHTE is the short distance between the hydrogen atoms H2 and H5. At 2.138(3) Å, this distance is shorter than the sum of the van der Waals radii, which is 2.4 Å. This outcome may be the indication of a hydrogen−hydrogen bond. Although such bonds are possible,43 they are not common when two CH bonds are involved. Nevertheless, it is worth investigation. The Atom in Molecules (AIM) theory44 with its implementation in G03 by Cioslowski et al.45 was used for this task because it is particularly fit to characterize hydrogen bonds.46,47 The calculations were performed at the B3LYP/6-311+G(2d,2p) level of theory with the ab initio equilibrium structure (Column 5 of Table 6). Indeed, there is a Bond Critical Point (BCP) between the atoms H2 and H5 with an electron density ρ = 0.010 au, see Figure 4. This indicates the existence of a weak bond between these two atoms. The Laplacian at the BCP is 0.038 au with a large ellipticity ε = 1.39 au. The ellipticity is a measure of the π-character of the bond. All these criteria indicate the presence of a bond, but what is still more interesting is that there is a ring point with an electron density ρ = 0.0099 au corresponding to a sixmembered ring H2C2C3C4C5H5. This effect obviously contributes to the stabilization of the planar cis structure. It is worth noting that a similar interaction was found to stabilize the planar forms of phenanthrene, chrysene, and biphenyl.47 The distance between the carbon atoms C2 and C5 also has to be discussed. At 3.066(1) Å, it is shorter than the sum of the van der Waals radii, 3.4 Å. However, the van der Waals radius of a bonded atom is not a well-defined concept because atoms in molecules are not spherical and are also compressible. It is better to use the intramolecular ligand radius which is defined in the frame of the Ligand Close packing (LCP) model.44b It appears that the distance C2−C5 is not shorter than the sum of the ligand radii, 2.5 Å, which, of course, does not exclude a possible repulsive interaction between the two carbons and may therefore contribute to the opening up of the angle C2C3C4, which is 2.7° larger than in butadiene.3

interaction and electronic effects have given equilibrium rotational constants. Despite this full data set, the semiexperimental equilibrium structure for cHTE is flawed. The equal C2H2 and C5H5 bonds lengths are too long. Ab initio calculations and a mixed estimation procedure have led to an acceptable planar structure. The structural evidence shows increased effects of π-electron delocalization in comparison with butadiene. These effects are largest in the middle of the molecule. Predictions of increased effects of π-electron with increasing length in polyenes now have experimental support. The large value of the C−CC bond angle (2.7° larger than in butadiene) has to be noted. Nonetheless, a weak hydrogen− hydrogen bond forms between the C2 and C5 hydrogen atoms to help stabilize a planar structure.

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ASSOCIATED CONTENT

S Supporting Information *

Table S1 contains the internal coordinates for cHTE, as calculated with three all-electron models and with two MP2 models with enlarged basis sets. Table S2 is an analysis of errors in computing differences in moments of inertia with isotopic substitution. Figures S1 and S2 are the gas phase IR spectrum of the isotopic mixture of cHTE-1,1-d1, -cis-1-d1, and -trans-1d1. Figures S3 and S4 are the gas phase IR spectrum of cHTE-2d1 Figures S5 and S6 are the gas phase IR spectrum of cHTE-3d1.. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.C.C.), Jean.Demaison@ univ.lille1.fr (J.D.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Peter Groner for computing the alphas with his program VIBROT. Emerson E. French, Vincent A. Alessi, and Henrik Ehrhardt contributed to the experimental work. Professor Albert R. Matlin suggested the method for making HTE-3-d1. N.C.C. was supported by a Dreyfus Senior Scientist Mentor grant. This work was supported in part by an allocation of computing time from the Ohio Supercomputer Center.

6. CONCLUSIONS MW spectra have now been observed and ground state state rotational constants have been fitted for all of the isotopologues of cHTE having single substitution of chemically different carbon and hydrogen atoms. Corrections for vibration−rotation 9399



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(35) McKean, D. C.; Law, M. M.; Groner, P.; Conrad, A. R.; Tubergen, M. J.; Feller, D.; Moore, M. C.; Craig, N. C. J. Phys. Chem. A 2010, 114, 9309−9318. (36) Gordy., W.; Cook, R. L. Microwave Molecular Spectra, Techniques of Organic Chemistry, 3rd ed.; Weissberger, A., Ed.; John Wiley & Sons: New York, 1984; Vol. XVIII, p 663. (37) Vogt, N.; Vogt, J.; Demaison, J. J. Mol. Struct. 2011, 988, 119− 127. (38) Liévin, J.; Demaison, J.; Herman, M.; Fayt, A.; Puzzarini, C. J. Chem. Phys. 2011, 134, 064119−064126. (39) Demaison, J.; Craig, N. C.; Cocinero, E. J.; Grabow, J.-U.; Lesarri, A.; Rudolph, H. D. J. Phys. Chem. A 2012, 116, 8684−8692. (40) Demaison, J. In Equilibrium Molecular Structures; Demaison, J., Boggs, J. E., Császár, A. G., Eds.; CRC Press: Boca Raton, FL, 2011; pp 29−52. (41) Belsley, D. A. Conditioning Diagnostics; Wiley: New York, 1991; pp 298−299. (42) McMahon, R. J.; Halter, R. J.; Fimmen, R. L.; Wilson, R. J.; Peebles, S. A.; Kuczkowski, R. L.; Stanton, J. F. J. Am. Chem. Soc. 2000, 122, 939−949. (43) Custelcean, R.; Jackson, J. E. Chem. Rev. 2001, 101, 1963−1980. (44) (a) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, U.K., 1990. (b) Gillespie, R. J. ; Popelier, P. L. A. Chemical Bonding and Molecular Geometry; Oxford University Press: Oxford, U.K., 2001. (45) Cioslowski, J.; Nanayakkara, A.; Challacombe, M. Chem. Phys. Lett. 1993, 203, 137−142. Cioslowski, J.; Surjan, P. R. J. Mol. Struct. (Theochem) 1992, 255, 9−33. Cioslowski, J.; Stefanov, B. B. Mol. Phys. 1995, 84, 707−716. Stefanov, B. B.; Cioslowski, J. J. Comput. Chem. 1995, 16, 1394−1404. Cioslowski, J. Int. J. Quant. Chem. Chem. Symp. 1990, 24, 15−19. Cioslowski, J.; Mixon, S. T. J. Am. Chem. Soc. 1991, 113, 4142−4145. Cioslowski, J. Chem. Phys. Lett. 1992, 194, 73−78. Cioslowski, J.; Nanayakkara, A. Chem. Phys. Lett. 1994, 219, 151−154. (46) Popelier, P. L. A. J. Phys. Chem. A 1998, 102, 1873−1878. (47) Matta, C. F.; Hernández-Trujillo, J.; Tang, T.-H.; Bader, R. F. W. Chem.Eur. J. 2003, 9, 1940−1951.

National Science foundation Grant 0420717 provided for the purchase and technical support of the Beowulf computer cluster at Oberlin College.

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Microwave Spectra of the Deuterium Isotopologues of cis-Hexatriene

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