High-Resolution Infrared and Electron-Diffraction Studies ofTrimethylenecyclopropane ([3]-Radialene)Corey Wright,† Joshua Holmes,† Joseph W. Nibler,*,† Kenneth Hedberg,† James D. White,†

Lise Hedberg,† Alfons Weber,‡ and Thomas A. Blake§

†Department of Chemistry, Oregon State University, Corvallis, Oregon 97332-4003, United States‡Sensor Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States§Pacific Northwest National Laboratory, P.O. Box 999, Mail Stop K3-61, Richland, Washington 99352, United States

*S Supporting Information

ABSTRACT: Combined high-resolution spectroscopic, electron-diffraction, and quantumtheoretical methods are particularly advantageous for small molecules of high symmetry andcan yield accurate structures that reveal subtle effects of electron delocalization on molecularbonds. The smallest of the radialene compounds, trimethylenecyclopropane, [3]-radialene, hasbeen synthesized and examined by these methods. The first high-resolution infrared spectrahave been obtained for this molecule of D3h symmetry, leading to an accurate B0 rotationalconstant value of 0.1378629(8) cm−1, within 0.5% of the value obtained from electronicstructure calculations (density functional theory (DFT) B3LYP/cc-pVTZ). This result isemployed in an analysis of electron-diffraction data to obtain the rz bond lengths (in Å): C−H= 1.072(17), C−C = 1.437(4), and CC = 1.330(4). The results indicate that the effects ofrehybridization and π-electron delocalization affects each result in a shortening of about 0.05 Å for the C−C bond in radialenecompared to ethane. The analysis does not lead to an accurate value of the HCH angle; however, from comparisons of theoreticaland experimental angles for similar compounds, the theoretical prediction of 117.5° is believed to be reliable to within 2°.

■ INTRODUCTIONTrimethylenecyclopropane, better known as [3]-radialene(hereafter radialene), is an isomer of benzene and was firstsynthesized in 1965 by Dorko,1 and later by Waitkus et al.,2

who used a different route. Its structure was investigated3 in1967 by gas-phase electron diffraction (GED) with results thatwere consistent with the expected D3h symmetry for the freemolecule (Figure 1). Several other investigations of radialene,

largely spectroscopic, have also been carried out. Burr et al.4

predicted its infrared-active fundamental vibrational frequencieswith use of the Wilson-GF method and observed many of themin an experiment done with 2 cm−1 resolution. Rhee andMiller5 obtained both Raman and infrared spectra of themolecule, gave a detailed discussion of the various symmetryspecies involved, and assigned transitions for the fundamentalbands predicted by theory (Table 1). (They also pointed outsome noticeable differences between their spectroscopic resultsand those given by Waitkus et al.,2 and suggested that thelatter’s sample may not have been radialene. Waitkus’s group

asserted in a subsequent paper6 that they had indeed producedradialene and suggested that the spectral differences were dueto ether as an impurity in their earlier sample.) In 1966,Heilbronner analyzed7 the electronic spectra of the [n]-radialenes, including the current molecule; unlike in benzene,where the lowest S0(A1g) → S1(B2u) singlet transition isforbidden, in radialene it is allowed, S0(A1′)→ S1(E′). Dorko etal.8 discussed the photophysical properties and ultravioletspectra of the compound and assigned this transition to anintense (εmax = 3750) UV band at 288.5 nm, giving an S1 − S0energy separation that is about 3400 cm−1 less than that inbenzene. Bally and Haselbach9 determined a value of 8.94 eVfor the first ionization potential of radialene, about 2500 cm−1

below that of benzene. (Their synthesis was a slightmodification of that described by Dorko1 and gave a purersample that yielded different energies for some of the higherelectronic states.) They also reported an improved value for theextinction coefficient of the first singlet transition (εmax =9390).9 The differences in the benzene−radialene energyseparations mentioned above can be attributed to the effect ofmore extensive delocalization of the π-electrons in benzenethan in radialene.To our knowledge, no experimental spectroscopic or

structural studies have been reported on radialene for the

Received: February 20, 2013Revised: April 15, 2013Published: April 17, 2013

Figure 1. Structures of some small ring molecules of high symmetry.

Article

pubs.acs.org/JPCA

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past three decades, although several authors have made use ofab initio theory to describe the bonding, aromaticity, electronaffinity,10 and the harmonic vibrational frequencies of themolecule.11,12 Nevertheless, there remain interesting questionsabout the structure of, and bonding in, radialene. Inspectroscopic terms it is a symmetric top, and like severalother small symmetric strained-ring molecules with interestingbonding arrangements studied by our group13−19 (Figure 1),

radialene is expected to give high-resolution vibration−rotationspectra amenable to detailed analysis. Accordingly, we under-took a spectroscopic investigation of radialene using modernhigh-resolution methods. It also seemed worthwhile toreinvestigate the structure of the molecule by GED,incorporating two features not available to the earlierinvestigators: a constraint on the results through use of theexperimental rotational constant, and adopting certain the-oretical predictions from normal coordinate calculations whichcan presently be carried out at a high level of quantum theoryusing large basis sets. The combination of these three types ofdata promised to yield more precise, and possibly moreaccurate, values for the structural parameters as well as offer aclearer picture of the nature of the bonding. The effectivenessof this combination of methods has been discussed in severalreview articles.20−26

■ EXPERIMENTAL SECTION

Synthesis. Radialene is not available commercially, and oursample was obtained using Dorko’s method with some notablemodifications discussed in Appendix A. The compound (VIII)was synthesized in seven steps from ethyl acetoacetate (I) asdepicted in Scheme 1, the overall sequence being similar to thatused by Rhee and Miller.5 The details of the synthesis areprovided in Appendix A. Radialene is quite reactive and at roomtemperature tends to polymerize readily. When stored at liquidN2 temperatures at low pressure, the solid is quite stable, andwe speculate that it would be safe to store it at dry icetemperatures. At room temperature we have found the vapor tobe stable for days if the pressure is less than 100 Pa (≈0.8Torr), but noticeable polymerization occurs over a period of anhour at pressures above 700 Pa (≈5 Torr).

Spectroscopy. High-resolution spectra for radialene wereobtained for the first time with use of a Bruker IFS 125HRFourier transform spectrometer at the Pacific NorthwestNational Laboratory. For studies in the 600 to 1000 cm−1

region relevant to the results reported here, the spectrometerwas evacuated to less than 6 Pa and spectra were recordedusing a Globar light source, a KBr beamsplitter, and an MCTdetector. Survey spectra showed good agreement with the low-resolution results of Rhee and Miller.5 Figure 2 shows a detailedhigh-resolution scan for the most intense infrared feature, the ν9(a2″) parallel band at 874 cm−1. For this measurement, amultipass White-type absorption cell was used with an effectiveabsorption path length of 16 m and a sample pressure of ≈17.7

Table 1. Fundamental Vibrations (cm−1) of Radialene

theory (B3LYP/cc-pVTZ)

Raman int IR int

mode expta anharmonic harmonic Å4/amu km/mol

a′1ν1 3000 2993 3137 411.2ν2 1800 1826 1872 531.5ν3 1422 1436 1481 24.0ν4 779 788 797 54.3

a″1ν5 709 746

a′2ν6 3078 3221ν7 1095 1111ν8 508 513

a″2ν9 885 890 911 125.1ν10 212 208 216 6.8

e′ν11 3095 3077 3221 157.4 7.5ν12 2994 2994 3137 5.2 11.4ν13 1620 1647 1677 81.2 1.3ν14 1398 1407 1446 43.8 10.1ν15 1108 1112 1133 0.3 3.6ν16 779 782 798 1.0 7.6ν17 235b 220 225 11.3 0.0

e″ν18 873b 886 907 8.4ν19 750 769 5.6ν20 340b 328 341 0.2

aWavenumber values are from Rhee et al.5 and are for liquid orcrystalline film samples. bIn ref 5 the assignments of ν17 and ν20 arereversed and the 873 cm−1 e″ fundamental is assigned as ν19. Howeverour calculated frequencies and Raman intensities favor the assignmentsgiven here.

Scheme 1. Reaction Sequence for the Synthesis of Radialene (VIII)

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Pa (0.133 Torr) at 22 °C. 640 scans were progressively takenover a period of 27 h and the spectra were processed with fourtimes zero-filling and boxcar apodization to yield an effectiveresolution of 0.0020 cm−1. Wavenumber calibration of thevarious regions was done from CO2 and N2O gas referencesamples, with wavenumber standards from refs 27a and 27b.The corrections were typically less than 0.0002 cm−1, and theabsolute wavenumber uncertainty of isolated lines is estimatedat ±0.00015 cm−1.Electron Diffraction. The radialene sample (a portion of

that used for the spectroscopy), contained in a glass reservoir,was attached to the nozzle-inlet system of the Oregon Statediffraction apparatus through a metering valve. In order tominimize polymerization, the reservoir was cooled in ice waterto give a vapor pressure of about 800 Pa (≈6 Torr). Theamount of material available was about 0.3 mmol: enough forabout four film exposures. GED experiments are usually madeusing two distances from nozzle-tip to film: the longer distanceyields the lower-angle scattering pattern and the shorterdistance the higher-angle pattern. We elected to record onlythe latter because of the limited amount of sample and itstendency to polymerize. (Data from the higher scattering anglesconsist mostly of scattering from the skeleton of the moleculeand less of the scattering from the hydrogen atoms which ismore rapidly damped due to large-amplitude motion. Thisdecision diminishes the accuracy of the structure measurementof the methylene group in favor of that of the skeleton, which isof greater interest.) Four films (Kodak electron-image 8 in. ×10 in.) were exposed at a nozzle-tip temperature of 25 °C at anominal distance of 30 cm under a (nominal) 60 kVaccelerating potential. Other experimental parameters werebeam currents of 0.77−0.80 μA, an r3-sector, and exposuretimes of 105−240 s. The films were developed (Kodak D-19diluted 1:1, 10 min) and traced on a modified Joyce−Loeblmicrodensitometer. Two of the films were unusable because ofexperimental defects. The remaining two films were tracedseveral times to improve the averaging and reduce the noise,and the molecular scattering distribution (sIm(s)) was obtainedin the way previously described.28,29 The averaged data at

intervals Δs = 0.25 provided information over the scatteringrange 9.0 ≤ s/Å−1 ≤ 37.75 (s = (4π/λ)sin(θ/2), where θ is thescattering angle and λ is the electron wavelength determined inseparate calibration experiments with CO2 (ra(C−O) = 1.646Å, ra(O···O) = 2.3244 Å).

Theoretical Calculations. Electronic structure calculationswere carried out at several levels of theory and various basis setswith use of the program set Gaussian 09.30 We have found theDFT combination B3LYP/cc-pVTZ to be quite satisfactory insimilar investigations for the type of theoretical data neededand hence adopted it for this work. The resultant quadraticpotential constants were used with the normal coordinateprogram ASYM4031 to obtain harmonic corrections used in theelectron-diffraction analysis. In addition, the Anharm/Vibrotoptions of Gaussian were used to obtain cubic and quarticpotential constants for radialene that, with the quadratic terms,gave bond lengths, angles, and the rotational constants Be andCe for the equilibrium structure, as well as the vibration−rotation α corrections necessary to get the ground state B0 andC0 values. Although more time-intensive (for radialene, 32 h ona fast PC with four processors), we have found that suchanharmonic calculations typically yield remarkably accuratevalues for most structural and rovibrational parameters ofsimilar molecules.13−19

■ SPECTROSCOPIC ANALYSISSymmetry and Energy Relations. With its D3h point

group symmetry, the representation of the 3N − 6 normalmodes of vibration of radialene is

Γ = ′ + ″ + ′ + ″ + ′

+ ″

4a (R) a 3a 2a (IR) 7e (IR, R)

3e (R)vib 1 1 2 2

(1)

The infrared and Raman activities for the fundamentaltransitions are shown in parentheses. Table 1 provides acomparison of the fundamental frequencies found in previouswork by Rhee and Miller5 with the theoretical anharmonic andharmonic frequencies; also shown are the predicted Raman andinfrared intensities associated with each fundamental. Accord-ing to symmetry rules, the fundamentals in both a1″ and a2′modes are Raman and infrared inactive. For the radialenemolecule with isotopic composition 12C6H6, the nuclear spinstatistical weights for the rotational levels of the groundvibrational state are 24 for K equal to multiples of 3 and 20otherwise, except for K = 0 where the weight is 16 for J odd and8 for J even.32

Radialene is a planar oblate symmetric top molecule withprincipal moments of inertia IB = IA < IC. The rotationalconstants (in cm−1) are then given as B = A > C which have theform B = h/(8π2cIB). The energy of the ground vibrational stateor of any nondegenerate vibrational state is

= +E G F J K( , )v v v (2)

where Gv is the vibrational term and Fv(J, K) is the rotationalterm, which, for nondegenerate vibrational modes, is

= + + − − +

− + − + +

+ + + +

+

F J K B J J C B K D J J

D J J K D K H J J

H J J K H J J K

H K

( , ) ( 1) ( ) ( 1)

( 1) ( 1)

( 1) ( 1)

v v v v vJ

vJK vK vJ

vJK vJK

vK

2 2 2

2 4 3 3

2 2 2 4

6(3)

Figure 2. The high-resolution ν9 infrared fundamental band ofradialene. The K-structure of the PK(25) cluster in the inset shows theenhanced intensity predicted from the nuclear spin statistics fortransitions with K = a multiple of 3. Features labeled “Hot bands” areanalogous transitions that originate not from the ground state but fromthe v > 0 vibrational levels of ν10 and ν17.

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The quantum numbers J and K have their usual meaning, andthe D and H terms account for the effect of centrifugaldistortion. The contracted subscript v is used to represent bothquantum number and mode number of a vibrational state. Forthe ground state v1 = v2 = v3 = ... = 0. The zero energy is definedas the J = K = 0 level of the ground state, and for any vibrationalmode v, the band origin is ν0 = Gv − G0. For degenerate modes,additional terms involving Coriolis interactions becomeimportant,33 however these were not required in the workpresented here.The ν9 (a2″) Parallel Band at 874 cm−1. The ν9 vibration

of radialene corresponds to an out-of-plane bending mode(depicted in the right inset of Figure 2), and, as predicted bythe B3LYP/cc-pVTZ calculation, it has the highest intensity ofall the infrared-active fundamental bands. The sharp right edgeof the central Q-branch accurately defines the band origin, andthe J assignment of the P- and R-branch features wasstraightforward. For each of these, individual lines are resolvedfor higher values of K, as seen in the left inset. The enhancedintensity of lines with K a multiple of 3 predicted from thenuclear spin statistics and the close match of calculated andobserved spectra confirm the assignments.Although the band profile matches well with that expected

for a parallel fundamental band, there were two complicationsencountered in the analysis. The first of these was the presenceof a number of “hot band” transitions that overlapped andobscured the fundamental band features. The left inset ofFigure 2 shows a case where these are clearly separated fromthe fundamental, but in other regions, particularly for the Q-branch, the overlap was extensive. These hot bands areparticularly strong in radialene because two of the vibrationallevels are low in wavenumber value (ν10 and ν17 at 212 and 235cm−1, respectively) and hence have high thermal populations atroom temperature. The second complication was seen in anumber of irregularities observed in the K structure of many ofthe P and R clusters, particularly at higher J values for K valuesin the range 15 to 20. These are believed to arise from acombination of an allowed Coriolis interaction between nearbylevels of ν9 (a2″) and ν16 (e′) as well as from more localizedvibration−rotation interactions of ν9 with levels of ν18(e″) andν19(e″). A complete analysis of these perturbing effects isunderway and will be reported elsewhere, but here we haveused the combination-difference method33 to deduce groundstate energy differences that are uncontaminated by possibleshifts in the excited state levels. Specifically, we utilized P- andR-branch transitions that have a common upper state and, bydifference, deduced level spacings in the ground state that differby 2 in their J values. A total of 434 such differences wereobtained from the assigned ν9 transitions, extending to Jmax = 50and Kmax = 37.Ground State Rovibrational Parameters. In fitting the

level differences in the ground state, the symmetric-top relationin eq 2 was used and models with and without the sextic Hdistortion constants were explored. As is well-known, in theabsence of perturbations or added information from hot-bandtransitions,34 the K-dependent C0, DK, and HK parameterscannot be determined from the spectra of symmetric tops.However, a useful estimate of these parameters can becomputed from theory at the anharmonic level. It was foundthat inclusion of the H constants made little difference in thefits; the average root-mean-square (rms) deviation of thetransitions was 0.000334 cm−1 if these constants were variedand was only slightly poorer, 0.000343 cm−1, if the H’s were

fixed at zero. Moreover, when fitted, the uncertainties in the Hparameters were comparable to their values, hence we felt itappropriate to set all H values equal to zero. The results areshown in Table 2.

The analysis of the ground state energy difference yields avalue of 0.1378629(8) cm−1 for B0, a result which is in excellentagreement (within 0.5%) of the value obtained from thetheoretical calculations. These calculations make use of thecomputed vibration−rotation α constants to deduce the changefrom the equilibrium Be value that reflects the minimum energystructure; the formula is

α= − ∑B B d /20 e v v v (4)

where the sum is over the 3N − 6 normal modes of vibration,dv is the degeneracy of the normal mode v, and the quantity αincludes an anharmonic as well as a purely harmoniccontribution. The harmonic part can be calculated from thesimple quadratic force constants and in fact is used in adjustingB0 to the so-called Bz value that permits direct comparison withthe adjusted GED results described later. The relation is20−22

α= + ∑B B d(harm) /2z 0 v v v (5)

[see ref 20, p 106, for justification of this relation] and the αsum from the Gaussian calculations is −0.000079 cm−1. Theuncertainty in this correction is unknown, but for similarcompounds we have found13−19 that the theoretical α valuesgenerally agree with experiment to within about 10%.Accordingly, we consider 20% to be a conservative estimate,yielding the value of 0.13778 (2) cm−1 given for Bz in Table 2.Both the equilibrium re and the rz structures have the full D3h

symmetry of the planar molecule, for which the moments ofinertia are defined by the masses MC and MH and by the fourstructural parameters rC−C, rCC, rC−H, and ∠HCH (β),according to the formula

β

β

=

= + +

+ + +

+

− −

− −

−

I I

M r r r r

M r r r

r

12

[ 3 (3/2) ]

3 [( /3 cos( /2))

( sin( /2)) ]

B C

C C C2 1/2

C C C C C C2

H C C1/2

C C C H2

C H2

(6)

Equation 6 provides the link between the spectroscopic Bzvalue and the rz structure from GED.The ground state centrifugal distortion constants DJ and DJK

are also well-determined from the analysis and are within 5% of

Table 2. Rotational Parameters (cm−1) for Radialene

parameter experimenta theoryb

Ce 0.06948C0 0.06917Be 0.13897B0 0.1378629(8) 0.13844Bz 0.13778(2) 0.13836DJ × 107 0.718(1) 0.68DJK × 107 −1.339(4) −1.28DK × 107 0.62

aThe uncertainties in the last digits (twice the standard deviation) aregiven in parentheses. See text for discussion of Bz uncertainty.bB3LYP/cc-pVTZ calculation using Gaussian 09 with Anharm/Vibrotoptions.

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the theoretical values listed in Table 2. The latter values actuallyrefer to the equilibrium structure, for which the planar relation2DJ + 3DJK + 4DK = 0 applies.35 This relation will beapproximately correct for the ground state as well and leads to avalue of DK = 0.64 × 10−7 cm−1, which is also within 5% of thetheoretical value of 0.62 × 10−7 cm−1.

■ ELECTRON-DIFFRACTION ANALYSIS

Model. The determination of a structure by GED is basedon a set of geometrical parameters that specify the size andshape of the molecule and a set of vibrational parameters thatdescribe the associated oscillatory distance changes. The modelused for the GED analysis of radialene was based on anassumed planar molecule of D3h symmetry defined in rα

0 space,details of which are discussed later. The geometrical parameterschosen to describe the structure were the bond lengths r(C1−C2), r(C1C4), and r(C−H) and the bond angle ∠(HCH)(atom numbering is shown in Figure 4). One vibrationalamplitude parameter (l) was chosen for each of the tencarbon−carbon and carbon−hydrogen distances; hydrogen−hydrogen distances were ignored. Amplitudes for distancesC1···H9, C4···H9, C1···H10, and C4···H10 could not bereliably refined independently. Two groups comprising the firstpair and the last pair were formed within which amplitudedifferences predicted by theory were held invariant. Eightindependent amplitude parameters resulted.The determination of the structure of a molecule by GED

augmented by use of rotational constants from spectroscopyrequires some special procedures.21,22 The GED experiment isessentially a measurement of the thermal-average interatomicdistances (rg

T) by way of a distance parameter raT = rg

T − ⟨l2⟩T/ra that appears in the scattering equations. The spectroscopicresult is more limited and consists of the B0 constant that isproportional to the ground state average of the reciprocalmoment of inertia, which depends on the structure defined in r0space. For a structure determination based on both experi-ments, the interatomic distances must be converted to acommon set, most conveniently the distances between theaverage positions of the atoms in the ground vibrational state.

Such a structure has the point-group symmetry of the moleculeand is termed rz (spectroscopy) or rα

0 (GED).From the spectroscopic side, the rz structure leads to a

modified rotational constant Bz as indicated in eq 5. From theGED side, rα

0 for each interatomic distance is calculated as

= − = + ⟨ ⟩ −αr r r lTr

corr corrT T0g a

2

a (7)

where the last term in eq 7 contains corrections derived fromtheory:

δ

= ⟨Δ ⟩ + ⟨Δ ⟩ +

⟨Δ ⟩ − ⟨Δ ⟩ +

x y r a

z z r

corr ( )/2 (3/2)

( )

2 0 2 0e M

2 T 2 0cent (8)

Here Δx, Δy, and Δz are local Cartesian displacementcoordinates for an atom pair with the z axis coincident with aline joining the two atoms and the superscripts T and 0 refer tothe temperatures of interest. The first of these terms accountsfor the so-called shrinkage effect, the second is ananharmonicity correction with aM a Morse anharmonicityconstant (taken to be 2.0 Å−1 in this work), and the third is avery small centrifugal distortion term. Except for aM, all termsin eq 8 must be obtained from a normal coordinate analysis ofthe molecular vibrations using the harmonic force field, which isalmost never completely known from experiment. We used thetheoretical harmonic force field together with the normalcoordinate program ASYM4031 to calculate these correctionterms. Their sum, assembled according to eq 8 as “corr”, isgiven in Table 3. As for αv, the uncertainty in this theoreticalcorrection is assumed to be 20%.

Structure Refinements and Preferred Model. A least-squares refinement of the structure was carried out by fittingtheoretical scattering curves to the observed curve in the usualfashion.36 Model B determined by varying all structuralparameters in fitting the GED data has a calculated value of0.14014(120) cm−1 for the rotational constant Bz that differsfrom the measured one by about 0.00235 cm−1. Both theuncertainty and the difference are much larger than is usuallyobserved, and we regard both as unsatisfactory. A major sourceof the discrepancy is the large HCH angle 126.0(81)° which

Table 3. Values/Å;deg of Structural Parameters and Vibrational Amplitudes for Radialene from Theory and Experiment

GED A (preferred):a,b ∠(HCH) fixedat 117.5° GED B: ∠(HCH) refined GED (ref 3)c theoryd

param rα0 = rz rg l rα

0 = rz rg l rg l rze re l corr

∠(H−C−H) 117.5(20)f 126.0 (81) 121.8 (20) 117.5 117.6

r(C−H) 1.072 (17) 1.092 0.057 (10) 1.073 (12) 1.094 0.057 (10) 1.108 (15) 0.088 (7) 1.081 1.082 0.021

r(CC) 1.330 (4) 1.335 0.044 (8) 1.330 (3) 1.336 0.044 (8) 1.343 (20) 0.069 (11) 1.331 1.329 0.005

r(C−C) 1.437 (4) 1.440 0.048 (9) 1.437 (4) 1.441 0.049 (9) 1.453 (20) 0.065 (11) 1.443 1.438 0.003

r(C1···H7) 2.097 (13) 2.110 0.105 (47) 2.054 (43) 2.069 0.096 (37) 2.144 (−) 0.110 (7) 2.106 2.104 0.097 0.014

r(C1···C5) 2.672 (6) 2.672 0.062 (6) 2.673 (5) 2.677 0.062 (6) 2.695 (−) 0.099 (2) 2.680 2.673 0.059 0.004

r(C4···C5) 3.740 (9) 3.750 0.081 (21) 3.741 (7) 3.744 0.087 (23) 3.758 (−) 0.111 (7) 3.748 3.740 0.089 0.010

r(C1···H9) 3.136 (12) 3.152 0.110 (77) 3.071 (63) 3.081 0.106 (66) 3.186 (−) [0.12] 3.149 3.142 0.139 0.016

r(C4···H9) 3.913 (9) 3.951 0.136 (77) 3.837 (73) 3.846 0.132 (67) 3.947 (−) [0.20] 3.924 3.915 0.186 0.038

r(C1···H10) 3.531 (19) 3.539 0.107 (73) 3.490 (41) 3.500 0.14 (12) 3.590 (−) [0.12] 3.547 3.540 0.101 0.009

r(C4···H10) 4.708 (15) 4.717 0.113 (73) 4.677 (32) 4.685 0.15 (12) 4.760 (−) [0.20] 4.725 4.717 0.107 0.009

Rg 0.188 0.182aUncertainties in the last digits are given in parentheses. These are assumed the same for rα

0 and rg and are 2σ plus estimated contributions from datacorrelation and systematic errors plus 20% of corr values. bBz(obs) = 0.13778(2) cm−1; Bz(obs) − Bz(calc) = −0.00137(116) cm−1 for model A and−0.00235(120) cm−1 for model B. cUncertainties (in parentheses) are given in ref 3 as 2σ. Values of l(rms) in square brackets were assumed.dGaussian 09 DFT calculations (B3LYP/cc-pVTZ). Values of l(rms) and corr are calculated from the harmonic force field using ASYM40. eThe rzvalues are obtained using the Anharm/Vibrot option of Gaussian. fSee text for discussion of uncertainty. gR = [∑iwiΔi

2/∑iwi(siIm,i(obsd))2]1/2 where

Δi = siIm,i(obsd) − siIm,i(calc).

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also has a much larger uncertainty than normal for reasonsdiscussed later. Both the spectroscopic and theoretical resultsfavor a smaller angle, and accordingly a series of fits of the GEDdata were made in which the HCH angle was held fixed atvarious values. The skeletal parameters (C−C, CC, and C−H distances) were invariant to the angle choice, changing byless than a tenth of their standard errors. The corresponding Bzvalues are plotted in Figure 3, along with error bars

corresponding to the standard errors listed for the parameters.Intersection with the spectroscopic value occurs at about 107°,but any angle below 115° would be consistent with theuncertainty range from the GED fits. Also shown on the plot at117.5° is the theoretical result from the quantum calculations,and, in the absence of better experimental data, we have chosento fix the HCH angle at this value in obtaining the preferredmodel A shown in Table 3. This “compromise” angle falls nearthe uncertainty limit of 117.9° for the model B fit, and the Bzuncertainty almost encompasses the spectroscopic value. Thetheoretical HCH angle from B3LYP/cc-pVTZ calculations isconsidered quite reliable; Craig et al.37 find agreement withexperiment to within 0.5° for ethylene and trans-butadiene, andwe have obtained comparable agreement for calculations oncyclopropane, propellane, and bicyclopentane. Thus 2° seems asafe estimate for the HCH angle uncertainty given for ourpreferred model A presented in Table 3 along with the fit basedon model B. Results from the earlier GED study are also shownfor comparison. Figure 4 shows the radial distributions ofdistances for our models; Figure 5 provides a comparison of theexperimental and theoretical scattered intensities.

■ DISCUSSIONAs is seen in Table 3, the parameter values for each of ourmodels are in good agreement with those found earlier3 but,with the exception of the HCH angle, are much more precise.This agreement extends to the apparent out-of-plane angle (theangle that the CC bond deviates from the plane of thecyclopropane ring) which can be nonzero due to the averaging

of nonbonded vibrational amplitudes; our value for this angle is7.6(83)° compared to 7.7(40)° from the earlier work. In bothcases the uncertainty is large due to the low frequency skeletalbending modes of the molecule and the planarity of theequilibrium geometry is not in question. In the case of thedirect bond vibrational amplitudes, the corresponding compar-ison is somewhat less satisfying. Contrary to expectation, theearlier study has the amplitude for the nominal double bondlarger than that for the single bond (although the largeuncertainties on each suggest this may not be significant), and ithas both the C1···C5 and C4···C5 amplitudes significantlylarger than our values, which are themselves in good agreementwith theory.The unusually large difference between the observed value of

Bz and that calculated from the model B structure merits furthercomment. A possible reason for the discrepancy is an error inthe size of the molecule measured by GED. Investigation

Figure 3. Bz values from GED structures obtained at fixed HCHangles. The square symbol corresponds to the HCH angle for the bestGED fit. The diamond symbol corresponds to the theoreticalprediction from Gaussian 09. The solid line corresponds to thespectroscopic value.

Figure 4. Radial distribution curves for radialene. The vertical barsshow the interatomic distances for GED models based on (a) model Awith the HCH angle fixed at 117.5° and (b) model B with the HCHangle =126.0° when included in the refinement. The difference curvesare experimental minus theoretical.

Figure 5. Scattered intensity curves. The theoretical curves are for thefinal models and correspond to (a) model A with the HCH angle fixedat 117.5° and (b) model B with the HCH angle = 126.0° whenincluded in the refinement. The difference curves are experimentalminus theoretical.

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showed that the magnitude of such an error would be about0.5%, which is much larger than is conceivable under theconditions of our experiment. It seemed more likely that thediscrepancy was due to an error in the shape of the molecule.To investigate this possibility we note first that structures of thecarbon skeleton for our two models are virtually identical. Thissuggests that the major cause of the discrepancy lies in thestructure of the methylene groups, most importantly in theHCH bond angle. The value of this angle depends on nonbondC···H distances which are of low weight and severely dampedby molecular vibration. This means that much of theexperimental information about the HCH angle lies belowthe minimum scattering angle in our experiment and is thusmissing; accordingly, this angle is expected to be measured withless accuracy than the other structural parameters. Evidencesupporting this idea can be seen in Figure 4. Whereas thelocations of all carbon−carbon distances and the C−H bonddistance are essentially identical for the two models, thecarbon−hydrogen nonbond distances, connected by the slanteddotted lines, are quite different. However the difference curvesare hardly changed so that the large uncertainty in the HCHangle is to be expected.Perhaps the most interesting feature of the radialene

structure is the length of the carbon−carbon bond in thethree-member ring. In cyclopropane this distance (rg =1.514(1) Å38) is 0.02 Å shorter than the canonical tetrahedralsp3−sp3 value (rg = 1.534(1) Å39) of ethane, a decreasesometimes explained as the result of “banana” bonding in theformer. The corresponding value for our preferred model ofradialene is about 0.10 Å shorter than in ethane and is aconsequence of the change in bonding caused by introductionof the trigonal sp2-hybridized methylene groups. The usualaccounting for a shortening in which the carbon-atom bondingchanges from tetrahedral to trigonal has two components: oneis that a pure sp2−sp2 carbon−carbon single bond is shorterthan an sp3−sp3 bond; the other is that the nominal single bondis actually a “partial double bond” resulting from π bondingacross the single bond. Feller et al.40 suggest that the length of apure sp2−sp2 carbon−carbon single bond is 1.482 Å, 0.052 Åshorter than that of ethane. Our observed 0.10 Å shortening ofthe ring bonds in radialene indicates that the shortening effectof the two components mentioned above is about equal.Qualitative evidence for an important contribution by πbonding between the ring atoms is seen in the calculatedelectron distribution for the three π-system bonding orbitalsshown in Figure 6. These orbitals can be formed as A2″, E″linear combinations of the localized π-orbitals of the three CC bonds in radialene. As seen in the figure, the symmetric A2″

combination, especially, extends appreciably over the ring andwould contribute to stronger, and hence shorter, ring bonds.trans-1,3-Butadiene provides another interesting comparison.

Here the central C−C bond (rg = 1.468(4) Å41) is shorter thanthat of ethane by about 0.07 Å, slightly greater than the 0.052 Åcited above as the difference between unstressed sp3 and sp2

C−C bonds. It is thus reasonable to conclude thatdelocalization of the π electrons occurs but is less importantin trans-1,3-butadiene than in radialene. We note also that inthis butadiene the CC double bond (rg = 1.350(4) Å41) islonger by 0.013(3) Å than in ethylene,42 but in radialene it isabout 0.002(6) Å shorter. However, the smaller changes and theuncertainties in these bond lengths make us hesitant to makemuch of this.Finally, the HCH bond angle in these compounds is of

interest: it is 118.2(8)° in butadiene, and 117.4(2)° in ethylene,very close to our preferred value of 117.5(20)° in radialene.Taking into account the uncertainty in the radialene value,these are essentially the same and characteristic of sp2 bondsthat are unaffected by steric interaction. For comparison, theHCH angle in cyclopropane is equal to 114.5(9)° and is largerthan the ideal sp3 value of 109.5°. Since the CCC angle incyclopropane is 60°, the increased HCH angle is consistentwith general experience that an increase/decrease in the anglebetween a pair of bonds at an sp3 center usually leads to adecrease/increase in the angle between the opposite bond pair.

■ CONCLUSIONS

The reactive molecule trimethylenecyclopropane, [3]-radialene,has been prepared by an improved synthetic method andexamined by high-resolution infrared spectroscopic, electron-diffraction, and quantum theoretical methods. This has led toan accurate determination of the B0 ground state rotationalconstant, and this information is used in combination with theelectron-diffraction and theoretical results to determine thestructural parameters of [3]-radialene. It is found thatrehybridization and π-electron delocalization effects each resultin a shortening of about 0.05 Å for the C−C bond in radialenecompared to ethane.

■ APPENDIX A. SYNTHESIS OF [3]-RADIALENE (SEESCHEME 1)

Ethyl isodehydroacetate (II) was synthesized (40% yield) fromethyl acetoacetonate (I) after the procedure given by Nitta andArakawa.43 Using the procedure given by Goss et al.,44 thebromopyrone (III) was obtained from II with a 95% yield.Feist’s Acid (IV) was obtained in a yield of 91% from thereduction of III using the synthesis given by Gilchrist andRees.45

At this point, rather than directly reducing IV to the diol(VI) as done by Rhee and Miller,5 an extra step was added tominimize complications with the purification of IV and to addlarger leaving groups to IV, making it more easily reduced toVI. This was accomplished by dissolving impure, dry IV (15.06g, 0.10 mol) and monohydrate p-toluenesulfonic acid (5.24 g,0.03 mol) in 300 mL of 200-proof ethanol and refluxing at 85°C for 24 h. After quenching with water, extracting with ether,drying with Na2SO4, and removing the solvent under reducedpressure, the diester (V) (15.68 g, 0.08 mol) was obtained witha yield of 75%. The diester had characteristic proton NMRpeaks (CDCl3) at δ = 1.29 (6H, t, J = 7.0 Hz, CH2CH3), 2.89(2H, s, J = 2.4 Hz, aromatic H), 4.18 (4H, q, J = 7.2 Hz,

Figure 6. View of the A2″, E″ linear combinations of the localized π-orbitals of the three CC bonds in radialene (B3LYP/cc-pVTZ).Equivalent lobes of opposite sign lie below the plane of the molecule.

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CH2CH3), and 5.69 (2H, t, J = 2.4 Hz, CH2). Carbon NMR(CDCl3) peaks for the diester were at δ = 14.1, 25.8, 61.4,106.4, 129.1, and 169.3.The LiAlH4 reduction of V to produce diol (VI) was

performed in a manner similar to that described by Bloomquistand Longone46 with a few notable modifications. The reactionsolvent was dry tetrahydrofuran, and quenching of unreactedLiAlH4 was done not with water but rather with stockdichloromethane and 50% wet Na2SO4. Additional dichloro-methane and Na2SO4 were then used to extract and dry VI, andpurification was completed using a Kugelrohr distillationapparatus heated to 140 °C under high vacuum. This studyconfirmed findings briefly reported by Dorko47 in which VIreadily undergoes decomposition in wet air. Hence, VI wasfrozen in dry benzene immediately after purification to preserveits composition. The yield of VI was 49%. The proton NMR(CDCl3) spectrum for VI contained characteristic peaks at δ =1.67 (2H, sextet, J = 1.5, 1.9, and 2.1 Hz, aromatic H), 3.23(2H, q, diastereotopic, J = 2.4, 9.0, −CH2−OH), 3.91 (2H, q,diastereotopic, J = 3.6, 6.1, −CH2−OH), and 5.47 (2H, t, J =2.0 Hz, CH2). Carbon NMR shifts were at δ = 24.6, 64.1,105.5, and 134.0.With a few noted changes, synthesis of the dibromide (VII)

from VI was similar to that done by Rhee and Miller.5 Diol(3.24 g, 28 mmol), dissolved in benzene (20 mL), was addeddropwise to a solution of phosphorus tribromide (2.7 mL, 28mmol), pyridine (10.3 mL, 0.13 mol), and benzene (100 mL)at 6 °C. After stirring for 2−3 h at room temperature, ethylether was added to quench the reaction and extract VII fromthe bromide and phosphorus salts. The extract was washed with1 M sulfuric acid, saturated cupric sulfate, and slightly acidicwater, respectively, and dried with Na2SO4. After removing thesolvent under reduced pressure, VII was distilled in a Kugelrohrapparatus at 80 °C under high vacuum. This gave 0.68 g (2.9mmol) of very pure VII, with a yield of 10%. The dibromidehad proton NMR (CDCl3) shifts of δ = 1.88 (2H, nonet, J =2.0, 1.4, 2.2, and 4 Hz, aromatic H), 3.36 (2H, q, diastereotopic,J = 2.4 and 7.9 Hz, −CHH−Br), 3.47 (2H, q, diastereotopic, J= 3.6, and 6.8 Hz, −CHH−Br), and 5.58 (2H, t, J = 2.1 Hz, CH2). The carbon NMR spectrum (CDCl3) had characteristicpeaks at δ = 27.0, 34.3, 106.0, and 138.3.In the final step, radialene (VIII) was synthesized in an

elimination reaction of VII in the manner described by Ballyand Haselbach.9 Dibromide was heated to 77 °C and carried bya low pressure (400 Pa ≈ 3 Torr) stream of dry nitrogen (flowrate =2.8 L-Torr/min) through a column of mixed KOH andCaO powder heated to 155 °C. After leaving the column, theproduct was passed through two traps, one at −21 °C and thefinal one at liquid nitrogen temperature (77 K). The entirereaction was carried out while pumping (70 Pa ≈ 0.5 Torr) andgave a 57% yield of VIII. The identity of VIII was confirmed byFTIR and proton NMR spectra (CDCl3, 6H, δ = 5.2, s, CH2).

■ ASSOCIATED CONTENT

*S Supporting InformationTable S1 of fitted and calculated ground state combination-difference wavenumber (cm−1) values, along with the resultantparameters. Table S2 of experimental GED scattered intensities.This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Department of Chemistry, Oregon State University, Corvallis,OR 97331-4003. Fax: 541-737-2062. E-mail: Joseph.Nibler@oregonstate.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe gratefully acknowledge partial support for this work from aSenior Scientist Mentor Award by the Camille and HenryDreyfus Foundation (J.W.N.), and the National ScienceFoundation under Grant CHE 0613298 (K.H.). The researchdescribed here was performed, in part, in EMSL, a nationalscientific user facility sponsored by the Department of Energy’sOffice of Biological and Environmental Research and located atPacific Northwest National Laboratory (PNNL). PNNL isoperated for the United States Department of Energy by theBattelle Memorial Institute under Contract DE-AC05-76RLO1830. Certain commercial equipment, instruments, andmaterials are identified in the paper to adequately specify theexperimental procedure. Such identification does not implyrecommendations or endorsements by the National Institute ofStandards and Technology or the Pacific Northwest NationalLaboratory, nor does it imply that the materials or equipmentidentified are necessarily the best available for the purpose.

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