Accurate Determination of the Structure of Cyclohexane by

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Accurate Determination of the Structure of Cyclohexane by Femtosecond Rotational Coherence Spectroscopy and Ab Initio Calculations Georges Br€ugger, Hans-Martin Frey, Patrick Steinegger, Franziska Balmer, and Samuel Leutwyler* Departement f€ur Chemie und Biochemie, Universit€at Bern, Freiestrasse 3, CH-3000 Bern 9, Switzerland ABSTRACT: We combine femtosecond time-resolved rotational coherence spectroscopy with high-level ab initio theory to obtain accurate structural information for the nonpolar molecules cyclohexane (C6H12) and cyclohexane-d12 (C6D12). We measured the rotational B0 and centrifugal distortion constants DJ, DJK of the v = 0 states of C6H12 and C6D12 to high accuracy, for example, B0(C6H12) = 4306.08(5) MHz, as well as Bv for the vibrationally excited states ν32, ν6, ν16 and ν24 of C6H12 and additionally ν15 for C6D12. To successfully reproduce the experimental RCS transient, the overtone and combination levels 2ν32, 3ν32, ν32 þ ν6, and ν32 þ ν16 had to be included in the RCS model calculations. The experimental rotational constants are compared to those obtained at the second-order Møller
Plesset (MP2) level. Combining the experimental and calculated rotational constants with the calculated equilibrium bond lengths and angles allows determination of accurate semiexperimental equilibrium structure parameters, for example, re(C
C) = 1.526 ( 0.001 Å, re(C
Haxial) = 1.098 ( 0.001 Å, and re(C
Hequatorial) = 1.093 ( 0.001 Å. The equilibrium C
C bond length of C6H12 is only 0.004 Å longer than that of ethane. The effect of ring strain due to the unfavorable gauche interactions is mainly manifested as small deviations from the C
C
C, C
C
Haxial, and C
C
Hequatorial angles from the tetrahedral value.

1. INTRODUCTION The determination of accurate molecular structures has been one of the central endeavors of chemistry for many decades.1
5 Cyclohexane (C6H12)—a prototype molecule for understanding isomerization kinetics of conformers—belongs to a group of saturated cyclic hydrocarbons with zero dipole moment. At room temperature, cyclohexane predominantly occurs in the D3d symmetric chair conformer (Figure 1). The boat and twist conformers lie ∼7.5 and ∼6.5 kcal/mol higher in energy, with room temperature Boltzmann populations of ∼0.0001 and ∼0.001%, respectively.6
8 For a unique structure determination, six internal coordinates have to be known; a chemically intuitive choice consists of the C
C, the axial C
Hax, and the equatorial C
Heq bond lengths and the C
C
C, C
C
Hax, and C
C
Heq angles, denoted R, β, and γ; see Figure 1. The earliest speculations on the structure of C6H12 go back to Sachse, who already in 1890 conjectured the correct chair and boat conformations of cyclohexane, based on mathematical arguments.9 Full recognition of Sachse's conjectures came half a century later when Hassel10 and Barton11 published their works on conformational analysis. In the gas phase, different high-resolution spectroscopic methods have been applied to measure molecular structures via the determination of the rotational constants.2,3,12 Because cyclohexane lacks a permanent dipole moment, microwave (MW) spectroscopy cannot be directly employed. However, the asymmetric substitution of H by D atoms gives rise to a small electric dipole moment that allows the detection of MW spectra. Using the highly sensitive Fourier transform MW spectroscopic method, Dommen et al. measured the ground-state rotational r 2011 American Chemical Society

and centrifugal distortion constants of five asymmetrically deuterated isotopomers of cyclohexane and derived a substitution (rs) structure.13 Later, Bialkowska-Jaworska et al. performed a leastsquares structural fit to the five sets of constants and obtained a ground-state (r0) structure of cyclohexane that reproduced the observed constants13 to within 0.1
0.4 MHz.14 Note that this fit assumes that H/D exchange has no influence on the structure. On the basis of the r0 structure, they predicted rotational constants of B0 = 4305.84(15) MHz for C6H12 and B0 = 3287.40(29) MHz for C6D12.14 Very recently, Durig et al. have confirmed these results.15 High-accuracy structural information on the thermally averaged bond lengths and angles (rg structure) has been obtained from electron diffraction (ED) measurements.16
19 On the basis of the assumption of equal C
C, C
H, and C
D bond lengths for cyclohexane-d0 and cyclohexane-d12, Ewbank et al.19 determined the rg structure and obtained thermally averaged internuclear distances of rg(C
C) = 1.535(2) Å, rg(C
H) = 1.116(4) Å, and rg(C
D) = 1.109(3) Å. Two previous studies have investigated the rotational constants of gas-phase cyclohexane via rotational Raman spectroscopy.20,21 Peters et al. measured the frequency-resolved Raman spectra of gas-phase cyclohexane-d0 and cyclohexane-d12 at room Special Issue: A: David W. Pratt Festschrift Received: January 6, 2011 Revised: April 19, 2011 Published: May 10, 2011 9567

dx.doi.org/10.1021/jp2001546 | J. Phys. Chem. A 2011, 115, 9567–9578

The Journal of Physical Chemistry A

ARTICLE

ground and vibrationally excited states. Combining the experimental results with a basis set extrapolation technique37,39
42 allows us to obtain the equilibrium structure of cyclohexane to high accuracy. The present work highlights the technique of femtosecond time-resolved rotational Raman four-wave mixing (fs-RR-FWM) as a tool to determine the rotational constants of not only the ground state but also the vibrationally excited states of molecules. Figure 1. D3d equilibrium geometry and structure parameter definitions of cyclohexane (chair conformer).

2. METHODS

temperature excited by a CW Arþ laser. They analyzed both sets of spectra as if the entire population were concentrated in the v = 0 vibrational ground state.20 However, at room temperature, only 27% (17%) of the cyclohexane-d0 (cyclohexane-d12) population is in the respective v = 0 state, the rest being distributed over 10
15 low-lying vibrationally excited states. The latter have rotational constants Bv that vary substantially with v; see below. Hence, the rotational and centrifugal constants determined by Peters et al. represent Bv and DJ,v averaged over the vibrational distribution, giving ”effective” values Beff and Deff and not B0 and DJ as stated.20 More recently, Riehn et al. employed rotational Raman femtosecond time-resolved degenerate four-wave mixing spectroscopy on room temperature gas-phase cyclohexane.21 Analogous to Peters et al., they also obtained Beff and Deff.21 Below, we show that the difference of Beff and B0 for cyclohexane-d0 and cyclohexane-d12 is about 0.1%, which is far outside the experimental accuracies of the previous Raman investigations.20,21 Several ab initio studies of the ground-state structure, the ringpuckering intrinsic and nonintrinsic reaction coordinate, and barrier heights have been performed.7,8,14,15,21
24 Riehn et al. have optimized the structure of the chair conformer at the MP2 (secondorder Møller
Plesset) level with basis sets up to aug-cc-pVQZ and at the coupled-cluster CCSD(T) level using basis sets up to ccpVXZ and aug-cc-pVDZ.21 Later computational work has addressed aspects of conformational pathways8 and the ring-puckering deformation induced by vibronic (pseudo Jahn
Teller) couplings.24 Time-resolved femtosecond degenerate four-wave mixing (fsDFWM) can be used as a Raman scattering type of rotational coherence spectroscopy (RCS).25
29 It is a background-free Raman rotational technique30
35 that permits the accurate determination of rotational and centrifugal distortion constants of molecular ground states36
38 and of thermally populated lowlying vibrational states.39,40 Following our studies on cyclopropane and cyclobutane,37,38,40 we here investigate cyclohexane-d0 and cyclohexane-d12. We measured the rotational and centrifugal distortion constants of the v = 0 state of cyclohexane-d0 and of cyclohexane-d12 with a relative accuracy of 10
5, allowing comparisons to the extrapolated values from MW spectroscopy.13,14 Furthermore, we determined the Bv values for the vibrationally excited states ν32, ν6, ν16, and ν24 of cyclohexane-d0 and additionally ν15 for cyclohexane-d12. To accurately model the C6H12 measurements, not only the v = 0, 1 vibrational levels but also the overtone and combination levels 2ν32, 3ν32, ν32 þ ν6, and ν32 þ ν16 were included in the calculations. For C6D12, we additionally considered the levels 4ν32, 2ν16, ν32 þ ν24, 2ν32 þ ν6, and 2ν32 þ ν16. In parallel, we employ ab initio calculations at the MP2 (second-order Møller
Plesset) level to calculate the groundstate equilibrium structures of C6H12 and C6D12 as well as their vibrationally averaged structure and rotational constants for the

2.1. Experimental Section. The experimental setup employed for recording fs-DFWM transients has been described earlier.33,37,39 A Ti:sapphire multipass chirped-pulse amplifier system (ODIN DQC, Quantronix) with a pulse repetition rate of f = 340 Hz, pumped by a continuous wave 10 W frequencydoubled Nd:YLF laser (Darwin 527-30-M, Quantronix), is used to amplify the pulse energy of a Kerr lens mode-locked Ti: Sapphire oscillator (Mai Tai, Spectra-Physics). The pulse energy of the resulting laser beam is 360 μJ at a center wavelength of 802 nm. The temporal and bandwidth properties of the fs pulses were characterized as 75 fs fwhm, 0.45 time bandwidth product, and 12.63 nm (or 196 cm
1) bandwidth, using a single-shot second-harmonic generation frequency-resolved optical gating device (Grenouille 8
20, Swamp Optics).43,44 The spatial beam profile is a collimated Gaussian with a beam waist of w0 = 900 μm. The output of the femtosecond laser system is split into three equal parts, yielding two pumps and one probe beam. The probe beam runs over a protected gold-coated hollow retroreflector mounted on a computer-controlled 1000 mm delay stage (constructed in house). Displacements of the probe beam are measured with a He
Ne laser interferometer with an accuracy of (30 nm (SP2000 D; SIOS GmbH, Germany). An exact position determination is essential because it is the main error source in the determination of the rotational constants. The optical delay line is enclosed in a vacuum-tight container and evacuated to