Impact of Molecular Conformation on Barriers to Internal Methyl Rotation

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J. Phys. Chem. A 2010, 114, 12187–12194

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Impact of Molecular Conformation on Barriers to Internal Methyl Rotation: The Rotational Spectrum of m-Methylbenzaldehyde Amanda J. Shirar,† David S. Wilcox,† Kelly M. Hotopp,† Giana L. Storck,† Isabelle Kleiner,‡ and Brian C. Dian*,† Department of Chemistry, Purdue UniVersity, 560 OVal DriVe, West Lafayette, Indiana, 47907-2084, Laboratoire InteruniVersitaire des Syste`mes Atmosphe´riques (LISA), CNRS UMR 7583 et UniVersite´s Paris 7 et Paris Est, 61 aVenue du Ge´ne´ral de Gaulle, 94010 Cre´teil Ce´dex, France ReceiVed: August 13, 2010; ReVised Manuscript ReceiVed: October 8, 2010

The ground state spectrum of m-methylbenzaldehyde (m-MBA) was measured with a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer. The methyl rotor on m-MBA introduces an internal rotation barrier, which leads to splitting of the torsional energy level degeneracy into A and E states. Ab initio calculations predict a low torsional barrier for both the O-cis and O-trans conformers, resulting in a large doublet splitting up to several gigahertz in the frequency spectrum. The rotational constants, distortion terms, and V3 values for both species have been determined from the ground state rotational spectrum using the BELGI-Cs fitting program. There are significant differences in the torsional potential for the O-cis and O-trans m-MBA conformers. Molecular orbitals and resonance structures for each conformer are analyzed to understand the difference in torsional barrier height as well as the irregular shape of the O-trans torsional potential. Introduction The concept of hindered rotation of a methyl group was introduced in 1936 when Kemp and Pitzer1 explained the noticeable difference between calculated and experimental values of entropy for ethane. At the time, statistical mechanics equations assumed methyl groups freely rotated.2,3 Introduction of a torsional barrier into the theory improved predictions of observed experimental thermodynamic parameters, such as enthalpy and entropy.1,4 The methyl groups in ethane do not freely rotate because of steric hindrance between staggered and eclipsed configurations of the hydrogens. The hindered rotation of ethane leads to a 6-fold symmetric barrier with maxima and minima corresponding to the eclipsed and staggered conformations, respectively. The presence of a C3V symmetric top, such as a methyl group, attached to an asymmetric molecular frame results in a 3-fold torsional potential with a minimum at each staggered configuration. Conversely, a 6-fold potential arises in toluene since the methyl group is attached to a symmetric frame that allows for twice as many equilibrium structures. The number of minima in the potential is determined by the symmetry of the frame, whereas the height of the barrier between the potential wells indicates how easily the group rotates.5 Historically, hindered methyl rotation was attributed to steric effects, but existing comprehensive theories include electronic stabilization as a significant factor.6 In the case of ethane, early studies concluded that steric effects due to the repulsion of closed shell, C-H bond orbitals were largely responsible for the torsional barrier.7 However, more recent studies8,9 concluded that even though steric effects dominate, hyperconjugation stabilization of the staggered form is partially responsible for the barrier. Although electronic * Corresponding author. Phone: (765) 494-9006. Fax: (765) 494-0329. E-mail: [email protected]. † Purdue University. ‡ CNRS UMR 7583 et Universite´s Paris 7 et Paris Est.

interactions have a minimal effect on the ethane torsional barrier, larger molecules introduce more complex electronic configurations. A well-studied system for observing electronic effects is the excited electronic state of stilbene derivatives.6 This molecular system has little steric hindrance for methyl group rotation and increased electronic interaction due to significant conjugation between the benzyl groups. The torsional barrier of p-methylstilbene has been compared with derivatives of p-methylstilbene that have a substituent in the opposite para position. Adding an amino group to the structure lowers the barrier height by a factor of 3; 150 cm-1 in p-methylstilbene reduces to 55 cm-1 in p′-amino-p-methylstilbene.10 Barrier height changes in methylstilbene have been observed for a variety of substituents, including a methoxyl group,11 hydroxyl group,12 cyano group,13 and halogens.14 With large spatial separation between the relative substituents, the change in barrier height can be attributed to changes in electronic configuration rather than steric hindrance. Although steric hindrance has little effect when the substituents are 10 atoms apart, as seen in p′-amino-p-methylstilbene,10 it is important to determine if there are significant interactions at shorter distances. Toluene derivates are ideal candidates for this subject and therefore often used to study methyl torsional barriers. Depending on the substituent’s relative position to the methyl rotor, functional groups have a considerable effect on the torsional barrier height. For example, the torsional barriers for ortho-, meta-, and para-fluorotoluene are 227.3, 15.8, and 4.8 cm-1, respectively.15 The torsional potential changes for each isomer because the methyl rotor encounters different local environments. In the low barrier case of toluene, the molecule is both electronically and structurally symmetric near the methyl group.16 The addition of a fluorine substituent in the ortho position breaks the symmetry of the frame. The torsional barrier of o-fluorotoluene is much larger than toluene because the barrier height is dominated by steric hindrance, since the substituent groups are adjacent to one another on the benzene ring.6 The torsional barrier height is reduced in m-fluorotoluene because

10.1021/jp107679n  2010 American Chemical Society Published on Web 10/29/2010

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Figure 1. (a) Structural orientations for the two conformers of m-MBA related to the dihedral ∠1234. Distinction is made between the aldehyde oxygen oriented toward and away from the methyl group, O-cis and O-trans, respectively. (b) The three orientations of the methyl rotor (dihedral ∠abcd) with respect to the benzaldehyde frame: perpendicular, staggered, and eclipsed.

the methyl group and fluorine atom are farther apart, which creates a symmetric local environment near the methyl group, even though the global frame of the molecule is still asymmetric.6 In the last case of the para- substituted fluorotoluene, the barrier is the smallest because the molecule is now electronically and structurally symmetric. The orientation of the methyl group hydrogens is also dictated by the relative location of the other substituent. For fluorotoluene, each isomer has a unique methyl group position that provides insight into how steric hindrance affects the barrier height to internal rotation. For both o- and m-fluorotoluene, the methyl group is oriented with a single hydrogen in the same plane as the benzene ring.15 In o-fluorotoluene, the hydrogen is pointed away from the fluorine, since steric effects overcome any stabilization due to donor-acceptor interactions between the fluorine and the hydrogen.17 Conversely, the optimized form of m-fluorotoluene has the hydrogen oriented toward the fluorine because the distance between the substituents is large enough to negate steric hindrance. For p-fluorotoluene, the symmetry of the molecule allows the methyl group to optimize with a methyl hydrogen perpendicular to the frame, similar to toluene.15 Although many studies have been conducted on the structural isomers of toluene derivatives, there are fewer examples that focus on conformational isomers. Several studies have explored the isomers of cresol (methylphenol) and noted significant differences in torsional potentials between the rotational conformers.18-20 Methylbenzaldehyde (MBA) is also an excellent molecular candidate for torsional studies because the aldehyde group has two distinct orientations with respect to the methyl group, and only one isomer is needed to study conformational effects. In the case of o-MBA, steric effects are likely to dominate since, C-H · · · O/C-H · · · H interactions will significantly hinder free rotation of the methyl moiety. Because p-MBA has a single conformation, these effects are not present.21 Therefore, meta-methylbenzaldehyde (m-MBA) was selected as the molecule of interest. The two main conformers (Figure 1a) are labeled O-cis and O-trans according to the orientation of the aldehyde oxygen with respect to the methyl group. The methyl group also has multiple orientations with respect to the

Shirar et al.

Figure 2. Block diagram of the chirped-pulse Fourier transform microwave spectrometer separated into (a) microwave generation and (b) molecular detection. A 2.75 GHz broadband pulse is generated by an arbitrary waveform generator stabilized by a rubidium clock and 100 MHz quartz oscillator. The signal is sent through a 5 GHz lowpass filter and amplified. Bandwidth is increased to 11 GHz with a quadrupler, and the attenuated signal is increased with a 200 W amplifier. A circulator is located before the amplifier to protect the microwave circuit from transients. The amplified signal is then sent to the vacuum chamber. The free induction decay is detected and sent through a pin diode limiter and a single pole, single throw switch that protects the following components from the polarizing pulse. The molecular signal is then amplified and down-converted by mixing with a filtered 18.9 GHz phase locked dielectric resonant oscillator signal that is stabilized with the phase-locked loop. The down-converted signal is sent through a DC block and low-pass filter to clean up the signal that is collected by the 12 GHz oscilloscope.

benzaldehyde frame that are labeled perpendicular, staggered, and eclipsed in Figure 1b. Rotational spectroscopy is well suited to study conformational isomers since variation in the inertial moments due to molecular shape will create unique rotational spectra. In addition to observing distinct conformer specific transitions, the presence of a methyl rotor can also be detected with rotational spectroscopy. Tunneling through the torsional potential barrier leads to frequency doublets in the observed ground state spectrum. The two states are labeled on the basis of their symmetry transformation properties: A states (σ ) 0) behave as a normal rigid rotor, whereas the doubly degenerate E states (σ ) (1) contain internal angular momentum and represent tunneling methyl rotation in the presence of the potential barrier.4 A molecule with a high torsional barrier, such as an ortho- substituted toluene, has little splitting at low total angular momentum quantum number J. However, a molecule such as m-MBA with a lower barrier (under 100 cm-1) will generate enough A-E splitting to be observed in the range of 8-18 GHz using a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer. Experimental Methods A diagram of the CP-FTMW spectrometer is depicted in Figure 2. To synchronize the timing of the experiment, the digital electronics were linked to a 100 MHz phase-locked loop (Wenzel Associates 501-10137B) driven by a 10 MHz Rbdisciplined crystal oscillator (Stanford Research Systems FS725)

Rotational Spectrum of m-Methylbenzaldehyde that was up-converted to 100 MHz and phase-locked to an ovencontrolled quartz oscillator to provide phase noise of -125 dBc/ Hz at a 100 Hz offset. A 1 µs polarizing microwave pulse was generated by an arbitrary waveform generator (Tektronix AWG 7101) with a sampling rate of 10 GS/s. The pulse traveled through a 5 GHz low-pass filter (Lorch 10LP-5000-S, (164 MHz) and then leveled in a preamplifier (Mini-Circuits ZX606013E-S+ 6000 MHz, +14.2 dB gain). The 1.875-4.625 GHz chirped-pulse was multiplied with a quadrupler (Phase One PS06-0161) to obtain an 11 GHz bandwidth pulse, 7.5-18.5 GHz. A step attenuator (Weinschel AF117A-69-11) controlled the power of the microwave field entering the 200 W traveling wave-tube amplifier (Amplifier Research 200T8G18A). The pulse was then broadcast into a vacuum chamber to interact with the molecules of interest. The chamber was evacuated using two 10 in. diffusion pumps (Varian VHS 10) and a single water-cooled baffle (Varian F8600310). These pumps were backed by a roots blower (BOC Edwards EH500) and roughing pump (Alcatel 2063). The interior walls of the vacuum chamber were covered with metallined microwave absorber (Emerson and Cuming Eccosorb HR25/ML) to reduce excess noise from chamber resonances that result from the high-power polarizing pulse. A base pressure of 1 × 10-6 Torr was typical for this chamber configuration, resulting in an average operating pressure of 1 × 10-5 Torr while introducing sample molecules. The gas sample was pulsed into the chamber through a 1 mm orifice pulsed valve (General Valve series 9) operating at a repetition rate of 10 Hz. A sample container was filled with cotton, injected with 0.5 mL of m-MBA, and helium/neon (30/70) buffer gas was flowed over the sample. The m-MBA sample was purchased from Aldrich (97%) and used with no further purification. This valve was powered by a pulsed valve driver built in-house by the Jonathan Amy Facility for Chemical Instrumentation at Purdue University. The distance between the valve and the microwave field could be varied with adjustable arms attached to the face of the flange. A 20-output timing control box (Masterclock, Thales Laser) was used to control the timing and duration of the pulsed valve as well as the timing of the microwave pulse. To broadcast the microwave signal across the chamber, two microwave horns with gain enhancers were used (Amplifier Research model AT4004, 8-18 GHz). The broadcasting horn was fixed while the receiver was attached to a home-built XYZ-translation stage, allowing optimization for the collection of the emitted molecular radiation. Once aligned with the broadcasting horn antenna, adjustments on the order of millimeters do not produce a significant change in signal. The molecular signal was then transmitted through a PIN diode limiter (Advanced Control Components ACLS 4619FC36-1K) and a reflective single pole single throw switch (Advanced Technical Materials S1517D isolation 80 dB, 2-18 GHz), which were used to protect the amplifier and oscilloscope from the high-power polarizing pulse. A digital pulse generator (Stanford Research Systems model DG535) closed the switch while the polarizing microwave pulse was broadcast and then opened the switch to allow collection of the free inductive decay (FID). The rotational FID was then amplified by a +45 dB gain low noise amplifier (Miteq AMF-6F-06001800-15-10P). This signal was down-converted using a triple-balanced mixer (Miteq TB0440LW1) and a phase-locked dielectric resonator oscillator (PLDRO, Microwave Dynamics PLO-2000-18.90) operating at 18.9 GHz. To ensure phase stability, this PLDRO was driven by the phase-locked loop through the 100 MHz quartz oscillator plate. The output from the PLDRO was filtered

J. Phys. Chem. A, Vol. 114, No. 46, 2010 12189 TABLE 1: Structural Parameters of m-Methylbenzaldehyde from Ab Initio Calculationsa b

∆E (kJ/mol) ∆Ezpe (kJ/mol) µac (Debye) µb (Debye) µc (Debye) V3 (cm-1) A (MHz) B (MHz) C (MHz)

O-cis

O-trans

0.00 0.00 -3.13 -1.93 0.00 35.26 2856.79 1275.66 886.72

0.69 0.58 4.01 -0.49 0.00 7.73 3575.08 1123.12 859.18

a Gaussian03 B3LYP/6-311++G(d,p) (ref 22). b Energies relative to the O-cis conformer (total energy is -384.997 27 au). c Transition dipole moment.

with an 18.9 GHz cavity bandpass filter (Lorch 7CF7-18900/ 100S, (50 MHz at 3 dB) before mixing with the molecular signal. The low-frequency band (0.4-11.4 GHz) was transmitted through a DC block (MCL 15542 BLK-18) and 12 GHz lowpass filter (Lorch 7LA-12000-S, (92.54 MHz). The resulting time domain signal was recorded on a 12 GHz oscilloscope (Tektronix TDS6124C) and digitized at a rate of 40 GS/s. A 20 µs free induction decay (FID) was recorded and the Fourier transform was performed to achieve the full 11 GHz bandwidth (7.5-18.5 GHz) rotational spectrum in the frequency domain. A Kaiser-Bessel digital filter was applied to the FID to suppress the side lobes of the rotational transition peaks and increase the baseline resolution. Peak widths in the frequency domain were 130 kHz at fwhm. All ab initio calculations were performed using the Gaussian22 calculation package and used density functional theory at the B3LYP/6-311++G(d,p) level of theory. Initial optimizations were performed without any restrictions upon the methyl group. However, the lowest energy structures were found by restricting one C-H bond to the aromatic plane. Molecular orbitals were generated from optimized structure calculations. Relaxed potential energy scans of the torsional potentials were calculated by rotating the dihedral angle of the methyl group (Figure 1 ∠abcd) in 4° steps and optimizing the structure at each step. Small step sizes were needed to ensure that the overall shape of the potential was symmetric due to the small barrier heights of each conformer. Results Gaussian Calculations. The results obtained from the ab initio calculations are presented in Table 1. The initial optimized structure of O-cis m-MBA easily converged to the lowest energy structure; however, there was some difficulty optimizing the O-trans conformer. By not restricting the orientation of the methyl group with respect to the plane of the benzene ring, O-trans m-MBA optimized to a perpendicular conformation 0.96 kJ/mol higher in energy than O-cis m-MBA. Once the hydrogen was restricted to the aromatic plane, the molecule optimized to an eclipsed structure 0.69 kJ/mol relative to O-cis (harmonic zero point corrected energy of 0.58 kJ/mol). Vibrational calculations verified that all optimized structures had positive vibrational frequencies and, thus, were identified as minima. This relatively small difference in energy indicates that the molecule shows little conformational preference with regard to the aldehyde orientation. Relaxed potential energy scans generated barrier heights of 35.26 and 7.73 cm-1 for O-cis and O-trans m-MBA, respectively, and are presented in Figure 3. The barrier heights are

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Figure 3. Relative potential energy scans of the internal methyl rotation for O-cis (top) and O-trans (bottom) m-MBA.

similar to those seen in m-cresol: 22.44 cm-1 for cis and 3.2 cm-1 for trans.19 In addition to the various heights of the torsional barrier, the shape of the potential also differs for the two conformers. The O-cis conformer is a traditional 3-fold potential characteristic of a methyl rotor on an asymmetric frame. However, the O-trans potential contains additional features, which were verified by reducing the DFT grid size. These smaller features have characteristics of a 6-fold potential. Similar differences in the shape of the potential have also been observed for m-cresol20 and acetamide.23 Fitting with BELGI-Cs. A comprehensive article was recently published by Kleiner24 summarizing the various methods and programs used to analyze spectra involving a single methyl rotor. Torsion around the rotor axis yields a 3-fold, periodic potential that can be fit with a Fourier series. The first nonzero expansion term describes the barrier height, V3, and the magnitude of this term (more precisely, the magnitude of the reduced barrier parameter, s)25 determines the theoretical treatment used in interpreting rotational spectra for this class of molecules. Many codes are readily available and appropriate for molecules in the high-barrier limit of methyl rotation, which is generally V3 > ∼100 cm-1 for small molecules. As the barrier decreases below this value, the cross-terms between the total and internal angular momentum in the rotational Hamiltonian become significantly large, and higher-order torsion-rotation terms are required to fit a low-barrier rotational spectrum to experimental accuracy. The code BELGI-Cs, described by Hougen et al.26 and publicly available at the PROSPE Web site,27 is particularly well-suited to fit low-barrier spectra of molecules belonging to the Cs point group, since it directly varies many pertinent parameters, such as the torsion-rotation constant, F, and the barrier magnitude, V3, as well as barrier distortion and other higher-order torsion-rotation parameters. Although BELGICs was written to globally fit both A and E symmetry lines belonging to multiple torsional energy levels, it has been successful in fitting low-barrier (down to ∼7 cm-1)28 A-E doublets at low quantum number J in the ground torsional state and thus was used to fit our spectrum. The BELGI-Cs code uses the Rho-axis method (RAM) to reduce the torsion-rotation terms in the Hamiltonian to one term in the first step diagonalization29 that is purely torsional, diagonal in the quantum number K, and thus computationally viable. For a Cs molecule with an a-b plane of symmetry, this

Figure 4. Rotational spectrum of m-MBA (top panel). The bottom four panels represent stick spectra of each of the four species assigned in m-MBA.

is achieved by rotation of the principal axis about the c-axis so that the a-axis is parallel with the F vector of the methyl top (Ir representation, a, b, c f z, x, y).26 A consequence of the transformation away from the principal axis system is that nonzero terms appear in the off-diagonal elements of the inertial tensor and therefore contribute nontraditional rotational constants to the Hamiltonian. Supplemental programs, also available from the PROSPE Web site,27 were used to predict these constants, construct the input file, and interpret the results from BELGICs. To fit the low-barrier spectrum, a new version of BELGICs was used in which the K labeling is specially tailored for the low-barrier Hamiltonian.21 The pure rotational spectrum of m-methylbenzaldehyde from 6.4 to 18.9 GHz is presented in Figure 4. For such low barriers, the magnitude of torsional splitting of rotational levels from both the O-cis and O-trans conformers ranges from a few kilohertz to several gigahertz. The resulting spectrum is therefore dense with some very nonrigid rotor character contributed by the E symmetry lines. A comparable number of a- and b-type lines were observed from the O-cis conformer, which is consistent with the predicted principal axis dipole moments shown in Table 1. In contrast, the lines contributed by O-trans were predominantly a-type, thus reducing the number of assigned lines relative to O-cis by approximately one-half and introducing a greater uncertainty to the A rotational constant. To initially assign quantum numbers to the observed transitions, JB9530 was used with the 20 kHz spectral resolution interpolated to 5 kHz to aid in locating peak centers. The rigid rotor-like A torsional states were assigned using the ab initio predictions. A V3 dialogue box included in version 2.07.08 of the JB95 package allowed the rotor axis angles and barrier height to be fixed at arbitrary values, which assisted in determining the E type lines. These transitions were used in the first series of fits with BELGI-Cs, and newly predicted lines were assigned and included in subsequent fits. This process was repeated to reduce the uncertainty in the fitted terms. Assigned transitions are available as Supporting Information. All the parameters used to fit the data are listed in Table 2, and the nomenclature follows Table 2 of Xu et al.31 Since all

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TABLE 2: BELGI-Cs Parameters in the Rho Axis for the Conformers of m-Methylbenzaldehyde parameter operator

a

Ja2 Jb2 Jc2 {Ja, Jb} (1/2)(1 - cos 3R) PR2 J aP R -J4 -J2Ja2 -Ja4 -2J2(Jb2 - Jc2) -{Ja2, (Jb2 - Jc2)} J2{Ja, Jb} Ja2{Ja, Jb} (1 - cos 3R)J2 (1 - cos 3R)Ja2 (1 - cos 3R){Ja, Jb} P R2 J 2 J aP R J 2

in program

literature

O-cisb

O-transb

OA B C DAB V3 F RHORHO DJ DJK DK ODELN ODELK DABJ DABK FV AK5 ODAB GV ALV

A B C Dab V3 F Fb ∆J ∆JK ∆K σJ σK DabJ DabK V3J(FV) V3K(k5) V3ab(dab) FJ(GV) FJ(LV)

0.083 051 8(7) 0.054 803 91(2) 0.029 641 21(1) -0.022 142 06(2) 35.925(3) 5.430c 0.012 712(1)b 2.6(2) × 10-9 -9.53(4) × 10-8 1.68(1) × 10-7 9.6(8) × 10-10 -1.81(1) × 10-8 -2.97(4) × 10-8 2.94(2) × 10-8 1.075(2) × 10-5 -7.1(1) × 10-5 1.259(5) × 10-4 N/Ad -3.5(2) × 10-8

0.115 00(4) 0.041 135 63(2) 0.028 725 893(5) -0.016 453 8(9) 4.64(3) 5.464c 0.018 641(3)b 2.3(1) × 10-9 3.7(3) × 10-8 -3.5(6) × 10-8 8.9(7) × 10-10 1.6(1) × 10-8 1.1(1) × 10-8 5.5(4) × 10-8 N/Ad 4.5(4) × 10-4 -1.436(9) × 10-4 4.04(6) × 10-7 -4.3(2) × 10-8

a {A, B} ) AB + BA. The product of the parameter and operator from a given row yields the term actually used in the vibration-rotation-torsion Hamiltonian, except for F, F, and A, which occur in the Hamiltonian in the form F(PR - FJa)2 + AJa2. b Number in parentheses is the uncertainty in the last digit to one standard deviation (Values are reported in cm-1 except for F which is unitless). c Parameter is determined by ab initio and fixed for program. d Not included in the fit.

lines originated from the ground torsional state, certain restrictions were placed on the purely torsional parameters. There is a large correlation between V3 and the reduced rotor rotational constant, F (as suggested by the reduced barrier parameter); generally, the two cannot be simultaneously floated in the fit of a single torsional state, especially when torsion-rotation splitting is small.24 In the case of a low barrier such as in m-MBA, we were able to float both parameters, since the magnitude of internal splitting is large enough, but as a result, many of the other parameters were not well determined. We therefore fixed the magnitude of F to its ab initio value calculated according to Pitzer.32 Higher-order terms in the Fourier expansion of the torsional potential determine the curvature of the potential wells, but multiple torsional states are also needed to experimentally determine these constants. Due to efficient vibrational cooling in the supersonic expansion, we were unable to identify a sufficient number of excited torsional transitions, and therefore, these parameters were not floated in the fit. Both conformers required 17 floated parameters (plus the F parameter fixed) to achieve a global rms value of 5.0 kHz in the ground torsional state (νt ) 0). A total of 446 lines in the spectrum were assigned to either O-trans or O-cis m-MBA and included in the respective fits. Approximately 40 additional lines were suspected to belong to the ground torsional state of either conformer based off predictions from the fit; however, they were excluded for two possible reasons: First, we were unable to resolve the K-stacks of high J transitions, especially for the O-trans conformer, and consequently, those lines were not included. Second, several other lines were removed due to asymmetric or overlapping peak shapes, which became distorted by interpolating the resolution to 5 kHz. Unsuccessful attempts were made to assign the remaining 60 unassigned lines (excluding the 40 suspected ground state transitions) to excited torsional states of either conformer. Our upper frequency limit of 18.9 GHz restricted the number of high J transitions in our spectrum. Compounded with the inability to resolve transitions involving high Ka, relatively large standard deviations are present in the fourth-order distortion terms. Data from higher frequencies or excited torsional states are required to reduce the standard

TABLE 3: Experimental and Calculated Parameters for m-Methylbenzaldehyde in the Principal Axis Systema O-cis A (MHz) B (MHz) C (MHz) θ(i, a)d ∆e θRAMf κg Jmaxh assigned A assigned E global σ (kHz)i

O-trans

exptlb

calcdc

exptlb

calcdc

2853.76(2) 1279.053(6) 888.6210(3) 50.7334(3) 3.489(2) 28.7336(3) -0.60264(2) 13 170 126 5.0

2856.79 1275.66 886.72 50.12 3.13

3552.(1) 1128.30(6) 861.1806(2) 33.808(7) 3.33(7) 12.007(6) -0.8014(9) 14 82 68 5.0

3575.08 1123.11 859.17 33.99 3.14

a Approximate comparison of experimental and calculated rotational constants. BELGI-Cs constants describe all torsional states, whereas calculated values are rigid rotor constants (see text). b Number in parentheses is the uncertainty in the last digit to one standard deviation. Rotational constants are given in the principal axis system. c Values determined in Gaussian03 B3LYP/ 6-311++G(d,p) (ref 22). d Angle in degrees of the methyl top in ´ 2 ) I + I - I . f Angle relation to the a-axis. e Inertial defect (µÅ a b c between the principal and Rho-axis systems in degrees: tan(2 θRAM) g ) 2 Dab/(ARAM - BRAM). Asymmetry parameter; κ ) (2B - A C)/(A - C). h The highest J assigned in each conformer. i Root mean square deviations of the fit.

deviation of these terms. More data of this kind may also sort out the physical interpretation of the sign of the distortion constants, revealing whether they reflect differences in the torsional potential or are only effective values absorbing some higher-order term in the Hamiltonian. The V3 barrier is well determined in our present fit, and the relative differences in barrier heights can be attributed to electronic influence in differing conformers. The rotational constants rotated into the principal axis are presented in Table 3. Direct comparison with ab initio rigid rotor predictions is difficult, since the global rotational constants produced from BELGI-Cs contain interactions from all vibrationally excited torsional states. However, only the ground

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torsional state was fit, and the ab initio rigid rotor constants are similar to the global rotational constants obtained with BELGICs. As noted, the relative uncertainty in the A rotational constant of the O-trans conformer is slightly larger due to the absence of b- and c-type lines in the spectrum. The angle of the top relative to the a-axis, θa, was calculated assuming that the methyl axis was in the symmetry plane of the molecule, that is, θc ) 90°. The angle associated with the rotation between the principal axis and Rho-axis, θRAM, and the inertial defect, ∆, were also calculated (Table 3). Discussion The experimental barrier height of O-cis m-MBA was determined to be 35.925(3) cm-1, whereas the barrier for the O-trans conformer is only 4.64(3) cm-1. This is almost a factor of 8 difference between the two conformational isomers, which differ only in the orientation of the aldehyde group. Calculations addressing both the structure and electronic distribution of the two conformers were performed to further understand this molecular system. Four equilibrium structures for m-MBA have been published by Schaefer et al.33 at the following levels of theory: AM1 and Hartree-Fock (STO-3G and 6-31G basis sets). For the O-cis and O-trans conformers, both eclipsed and staggered methyl orientations were optimized. Schaefer et al. calculated the eclipsed structures to be more stable than their respective staggered conformers, and O-cis was 0.572 kJ/mol more stable than O-trans. The ab initio calculations performed in our lab provided unusual results. For O-cis m-MBA, the lowest energy structure is equivalent to the eclipsed form published by Schaefer et al. However, the O-trans conformer initially optimized to the perpendicular methyl orientation, which corresponds to the lowest energy configuration for the methyl group on toluene.16 This conformer is 0.96 kJ/mol higher in energy than O-cis m-MBA according to our calculations. None of the calculations by Schaefer et al. included a perpendicular form, so no direct comparisons were possible. Since the perpendicular conformation was higher in energy than previously published values, the methyl group was constrained to the eclipsed form and recalculated. This eclipsed O-trans conformer was 0.69 kJ/mol higher in energy than the O-cis conformer and was more comparable to the reported energies. Since calculated structures were agreeable with published structures, calculated and experimental barriers were compared. As seen in Figure 3, there is a noticeable difference between the two calculated torsional potentials. The potential for O-cis m-MBA is a simple 3-fold potential with a calculated barrier height of 35.26 cm-1, which agrees well with our experimental V3 of 35.925(3) cm-1. The potential energy surface of O-trans m-MBA looks different from O-cis, but the calculated V3 of 7.73 cm-1 is within reasonable agreement to the experimental value, 4.64(3) cm-1. The torsional potential of methyl rotation in O-cis m-MBA is representative of a traditional 3-fold rotor on an asymmetric frame with a minimum when the methyl group is eclipsed. However, the potential is not a perfect 3-fold potential. On closer observation, there are slight depressions in the potential. Deviations from the Fourier calculated 3-fold potential are magnified in the lower-barrier conformer. The torsional potential of O-trans m-MBA is a combination of a dominant 3-fold potential and a smaller 6-fold potential. The three prominent wells correspond to the O-cis potential and represent an eclipsed methyl rotor. The other six local minima have a perpendicular conformation that is characteristic of 6-fold behavior observed

Shirar et al. in toluene. This local minimum conformation is the structure that was initially optimized in the ab initio calculations. A lower theory relaxed potential energy scan, comparable to the optimization calculations in Schaefer et al. (Hartree-Fock 6-31G), shows no evidence of local minima and could explain why no perpendicular structural calculations were attempted. Both molecules appear to have a combination 3-fold and 6-fold torsional potential, but the effect of the 6-fold character is influenced by the V3 barrier height. A smaller V3 value allows the V6 term to be more dominant. A torsional potential with similar behavior has been observed by Hellweg et al.19 in m-cresol and by Ilyushin et al.23 in acetamide. This supports the physical existence of the unusual potential. Hellweg et al. determined that though m-cresol has a global C3V symmetry, there is a local C6V symmetry near the methyl rotor. This idea was confirmed by experimental data because Hellweg et al. acquired a V6 value (syn V6 ) -11.2 cm-1) with the same order of magnitude as the V3 term (syn V3 ) 22.44 cm-1). Since the two terms were similar in magnitude, the torsional potential exhibited characteristics of C3V and C6V symmetries, therefore leading to a mixed potential curve. The methyl group on m-MBA is likely experiencing the same environment: a local symmetry that is different from the global symmetry. By fitting the calculated potential to a Fourier series, V3 and V6 terms can be estimated for O-trans m-MBA. The V3 term was 6.96 cm-1, which is in the range of both experimental and ab initio values. The estimated V6 term was 2.66 cm-1, which is on the same order of magnitude as the V3 term. This small difference in magnitude likely accounts for the unusual shape of the torsional potential. Although the calculations indicate the shape of the potential for m-MBA is a real feature, higher torsional states are needed to acquire a V6 term to verify this experimentally. The effect of V6 on the shape of the potential is dependent on the V3 barrier height, which is significantly different for each conformer of m-MBA. No excited torsional states were found in our experimental data, so V6 could not be experimentally verified. According to the present experimental barrier heights and calculated potentials, the two conformers of m-MBA have distinct characteristics. The two factors that affect the shape and height of a methyl rotor torsional barrier are steric hindrance and electronic configuration. The lack of aldehyde conformational preference in the equilibrium structures implies that electronic properties are more likely responsible for this difference. It is therefore instructive to calculate and analyze molecular orbitals to understand the electronic contribution to barrier heights. The highest occupied molecular orbital (HOMO) levels of the two conformers of m-MBA were calculated at the global minimum of each conformer and are presented in Figure 5. In the case of O-trans, the orbitals are primarily π character and contain a node between the ring and the methyl group. For O-cis, the orbital is largely σ in character and localized around the aldehyde group. To understand these differences, it was useful to examine the HOMO for the unsubstituted parent molecule and observe how each substituent alters the orbitals. The HOMO of benzene calculated at the B3LYP/6-311++G(d,p) level of theory shows a predominantly π character orbital and is presented in the top panel of Figure 5. In the middle panel of Figure 5, two monosubstituted forms are presented: benzaldehyde and toluene. Attaching a methyl group to benzene does not significantly modify the HOMO; however, adding an aldehyde group to benzene dramatically changes the orbital shape. Using the monosubstituted benzenes as a model for

Rotational Spectrum of m-Methylbenzaldehyde

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Figure 6. Resonance structures for (a) benzaldehyde (b) O-cis m-MBA, and (c) O-trans m-MBA.

Figure 5. The HOMO of unsubstituted benzene (top panel). The middle panel depicts the HOMO of two monosubstituted benzene derivatives, benzaldehyde and toluene. The bottom panel portrays the HOMO and HOMO-1 of O-cis and O-trans m-MBA.

comparison, O-cis m-MBA most resembles benzaldehyde, and O-trans m-MBA is similar to toluene. It is also interesting to note the structures of the HOMO-1 levels, which are presented in Figure 5. The difference in energy between the HOMO and HOMO-1 in each conformer is only 2.6 kJ/mol, and the relative order of the orbitals switches between O-cis and O-trans m-MBA. This difference in the molecular orbitals may have an effect on the methyl rotor barriers. Although the HOMO levels for the conformers of m-MBA have two distinctive forms, not all molecules behave similarly. The two conformers of m-cresol have nearly identical HOMO shapes and still produce conformer-specific barrier heights and shapes.18 Although molecular orbitals may influence the torsional barriers, other electronic factors should also be considered. Comparing the resonance structures for the two conformers gives additional insight into the torsional potentials of this molecular system. Figure 6 illustrates the resonance structures for both O-cis and O-trans conformers of m-MBA as well as benzaldehyde. One resonance structure for the parent molecule, benzaldehyde, includes an electron localized on the oxygen and a positively charged carbon at the para position.34 Both resonance structures of the m-MBA molecules conform to the

resonance structure seen in benzaldehyde, but the orientation of the charged oxygen relative to the eclipsed methyl hydrogen may have an effect on the torsional barrier. For ortho-halogen substituted toluenes, there is an attractive donor-acceptor interaction between the C-H antibond and the in-plane halogen lone pair when the methyl group is in the eclipsed position.17 However, steric hindrance in ortho substituted molecules has a larger impact on the barrier than any attractive forces. For meta substituted toluenes, steric effects are absent, and alternate mechanisms influence the barrier heights, including long-range interactions. In the O-trans conformer, the oxygen is oriented away from the methyl group, so no donor-acceptor influence is available. With an intramolecular distance of 5 Å between the aldehyde oxygen and eclipsed methyl hydrogen in O-cis m-MBA, it is possible that donor-acceptor interactions are stabilizing the resonance structure of this conformer. For example, in the water dimer system, there is a slight stabilization between the atoms up to an intermolecular separation of 6 Å.35 Although the water dimer and ortho-halogen systems are stronger donor-acceptor pairs than the aldehyde oxygen and methyl hydrogen in m-MBA, some parallels can be made. This long-range electronic interaction in conjunction with orbital effects could be strong enough to cause the considerable difference between the V3 values of m-MBA. Further studies of a molecule such as 3-hydroxybenzaldehyde could be used to observe if this interaction occurs at a distance similar to that in m-MBA. Conclusion The rotational constants, distortion terms, and V3 values for all four possible species of m-MBA have been determined to experimental resolution using BELGI-Cs. The calculated barrier heights of both conformers agree well with the experimental values. The torsional potential of O-cis is a dominant 3-fold potential, whereas the O-trans conformer exhibits a mixture of local 6-fold and global 3-fold behaviors. The calculated HOMO levels are distinctly different for each conformer: O-trans is

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predominantly π in character, and the O-cis conformer exhibits mostly σ characteristics. Although the methyl hydrogen and the aldehyde oxygen are separated by nearly 5 Å in O-cis m-MBA, a possible donor-acceptor interaction may exist. This attractive interaction combined with orbital effects could be influencing the torsional potentials observed in the conformers of m-MBA. Acknowledgment. This material was supported by the Dr. Henry and Camille Dreyfus Foundation New Faculty Award and Purdue University. Supporting Information Available: A full list of transitions is presented in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kemp, J.; Pitzer, K. J. Chem. Phys. 1936, 4, 749. (2) Mayer, J.; Brunauer, S.; Mayer, M. J. Am. Chem. Soc. 1933, 55, 37–53. (3) Kassel, L. J. Chem. Phys. 1936, 4, 276–282. (4) Nielson, H. Phys. ReV. 1932, 40, 445–456. (5) Gordy, W.; Cook, R. MicrowaVe Molecular Spectra, 3rd ed.; Wiley Interscience: New York, 1984. (6) Spangler, L. Annu. ReV. Phys. Chem. 1997, 48, 481–510. (7) Sovers, O.; Kern, C.; Pitzer, R.; Karplus, M. J. Chem. Phys. 1968, 49, 2592–2599. (8) Goodman, L.; Gu, H.; Pophristic, V. J. Chem. Phys. 1999, 110, 4268–4275. (9) Mo, Y.; Gao, J. Acc. Chem. Res. 2007, 40, 113–119. (10) Yan, S.; Spangler, L. J. Phys. Chem. 1995, 99, 3047–3052. (11) Siewert, S.; Spangler, L. J. Phys. Chem. 1995, 99, 9316–9324. (12) Metzger, B.; Spangler, L. J. Phys. Chem. A 1997, 101, 5431–5436. (13) Metzger, B. Ph.D. Thesis, Montana State University, 1996. (14) Siewert, S. Ph.D. Thesis, Montana State University, 1994. (15) Zhao, Z.; Parmenter, C.; Moss, D.; Bradley, A.; Knight, A.; Owens, K. J. Chem. Phys. 1992, 96, 6362–6377. (16) Ilyushin, V.; Kisiel, Z.; Pszczoˇłkowski, L.; Ma¨der, H.; Hougen, J. J. Mol. Spectrosc. 2010, 259, 26–38. (17) Lu, K.; Weinhold, F.; Weisshaar, J. J. Chem. Phys. 1995, 102, 6787–6805. (18) Myszkiewicz, G.; Meerts, W.; Ratzer, C.; Schmitt, M. Phys. Chem. Chem. Phys. 2005, 7, 2142–2150.

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