The microwave spectrum of methyl neopentyl ketone

Journal of Molecular Spectroscopy 281 (2012) 4–8

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The microwave spectrum of methyl neopentyl ketone Yueyue Zhao a, Jing Jin a, Wolfgang Stahl a,⇑, Isabelle Kleiner b a

Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, D-52074 Aachen, Germany Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR CNRS 7583, Universités Paris Est Créteil et Paris Diderot, Institut Pierre Simon Laplace, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France b

a r t i c l e

i n f o

Article history: Received 14 July 2012 In revised form 9 September 2012 Available online 22 September 2012 Keywords: Molecular beam FT microwave spectroscopy Internal rotation Methyl neopentyl ketone

a b s t r a c t The Fourier transform microwave spectrum of methyl neopentyl ketone, CH3AC(@O)ACH2AC(CH3)3 has been measured under molecular beam conditions and a conformer with an effective ground state Cs symmetry was assigned. According to quantum chemical calculations carried out at the B3LYP/6-311++G(d,p) and the MP2/6-311++G(d,p) level of theory no symmetry plane is present in the equilibrium structure of the same conformer. This apparent disagreement is discussed. The barrier to internal rotation of the acetyl methyl group was found to be 173.539(36) cm 1 using an effective internal rotation Hamiltonian. Two different methods and programs (the BELGI code and the XIAM code) were used and the results are compared. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Even with modern quantum chemical methods the barrier to internal rotation of methyl groups is sometimes hard to predict, especially in cases where these barriers are low. Whereas in acetates (acetic acid esters) the barriers to internal rotation of methyl groups are almost always around 100 cm 1, the barriers in ketones vary in a much wider range. Here, experimental data are very important, since they are needed to improve theoretical calculations. Only for a few ketones high resolution microwave spectra have been studied in detail up to know. The most important one is acetone [1]. Methyl vinyl ketone was also recently investigated [2] as well as diethyl ketone [3]. We decided to continue our studies on ketones with the methyl neopentyl ketone (4,4-dimethylpentan-2-one, MNPK) molecule [CH3ACOACH2AC(CH3)3]. This molecule gave us the opportunity to study the influence of such a big bulky group as the neopentyl group on the internal rotation parameters. Therefore we measured MNPK using the molecular beam Fourier transform microwave (MB-FTMW) spectrometer in Aachen in the frequency range from 8 to 16 GHz. The motivation for this work is predominantly to get accurate structural information for this rather large ketone, and precise values for the internal rotation parameters of the methyl internal rotation group. Following our method, which has been successfully applied to a number of esters and ketones [3–7], we combine in the present study quantum chemical calculations and an effective Hamiltonian using two different methods and codes to analyze ⇑ Corresponding author. E-mail address: [email protected] (W. Stahl). 0022-2852/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jms.2012.09.002

the data: the XIAM code and the BELGI-Cs code which allow us to treat internal rotation effects in rotational spectra, either using the combined axis method (CAM) [8] or the rho axis method (RAM) [9], respectively. In Section 2 we briefly present the experimental details. Section 3 is concerned with the quantum chemical calculations. The spectral analysis and the results are presented in Sections 4 and 5.

2. Experimental All spectra were recorded using a molecular beam Fourier transform microwave (MB-FTMW) spectrometer in the frequency range from 4 to 26.5 GHz [10–11]. MNPK was obtained from Sigma–Aldrich, Steinheim, Germany with a stated purity of 99%, and used without further purification. A gas mixture containing 1–3% MNPK in helium at a total pressure of 80–120 kPa was used throughout. The measurement accuracy of isolated lines is estimated to be 2 kHz.

3. Quantum chemical calculations In order to get the rotational constants and the angle between the internal rotor axis and the a axis as starting values for assigning the spectra, quantum chemical calculations were carried out at the workstation cluster of the Center for Computing and Communication at the RWTH Aachen University using the program package Gaussian 03 [12]. In all cases a fully optimized structure was obtained. Also the dipole moment components were calculated to get an estimate of the relative line strengths for the a-, b-, and c-type transitions.

Y. Zhao et al. / Journal of Molecular Spectroscopy 281 (2012) 4–8

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Fig. 1. The two lowest energy conformers of MNPK. The symmetry label Cs refers to an ‘‘effective’’ Cs symmetry obtained by torsional averaging.

To find the lowest energy conformer of MNPK, we optimized 12 geometries at the B3LYP/6-311++G⁄⁄ and at the MP2/6-311++G⁄⁄ level of theory (see Tables S-1 and S-2 in Supplementary data). Using the DFT method, an effective Cs conformer has the lowest energy, whereas with the MP2 method, it is a C1 conformer which has the lowest energy (see Fig. 1). The energy difference for the two lowest optimized structures is only around 2 kJ/mol. If the zero point energy is included, the effective Cs conformer has the lowest energy with both, the DFT and the MP2 method. To get some insight into the shape of the torsional potential curve for the methyl rotation, we carried out quantum chemical calculations on the B3LYP/6-311++G⁄⁄ and MP2/6-311++G⁄⁄ levels of theory for the Cs conformer. For this purpose the dihedral angle of the methyl group was incremented in a grid of 10°. All other structural parameters were allowed to relax. The resulting curve which corresponds to the torsional energy of the molecule is presented in the upper trace of Fig. 2. Depending on the method barrier heights of 134 cm 1 (MP2) and 109 cm 1 (DFT) were found. Surprisingly, significant V6 contributions (of 49 cm 1 and 37 cm 1, respectively) were found with both methods. A parameterization of the potential curves as Fourier expansions is given in Table S-3 of Supplementary data. The V6 contribution can be interpreted in terms of a two-dimensional problem involving both a rotation of the methyl group and a rotation of the entire neopentyl group. The energy minimum path in the potential surface is also shown in Fig. 2 (lower trace). It can be recognized that for the value of the dihedral angle D(2,1,7,10) (with the atom numbers defined in Fig. 1) equal to zero, i.e. when the neopentyl group and the carbonyl group share the same mirror plane, then there is a global maximum or a local maximum in the potential energy curve for the acetyl methyl group. So at the equilibrium configuration, the neopentyl group has to be tilt by about 10°. The rotational parameters (A, B, and C) and the torsional parameters (the angles between the methyl internal rotation axis and the principal axes \(i,a), \(i,b), \(i,c), the moment of inertia of the methyl group Ic, and the components of the electric dipole moments la, lb, and lc are presented in Tables 1 and 2 for the two lowest energy conformers Cs and C1, respectively.

Fig. 2. Potential curve for the Cs conformer of MNPK. In the upper trace the potential curve for the torsional angle D(2,1,3,5) of the methyl group is shown (for atom numbers see Fig. 1). Additionally, the torsional energy levels for J = K = 0 (A and E species for vt = 0 and 1) are given as calculated by the BELGI-C1 code using the parameters given in Table 3. The J = K = 0 energy level for the first excited state vt = 1 can be considered only as an extrapolation because no rotational transitions were analyzed in that state so far. The lower trace is the energy minimum path, where the dihedral angle of the entire neopentyl group D(2,1,7,10) is drawn over the torsional angle of the methyl group D(2,1,3,5). Full circles are data points from MP2 calculations, open circles from DFT calculations.

4. Spectral analysis At the beginning of our measurements broadband scans in the frequency range from 8 to 16 GHz were carried out (see Fig. 3). In total 126 lines were found, many of them were quite strong. All of them were remeasured at high resolution and almost all lines

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Y. Zhao et al. / Journal of Molecular Spectroscopy 281 (2012) 4–8

Table 1 Quantum chemical and experimental results for methyl neopentyl ketone (conformer I, (Cs)). DFTg

Unit a

Energy Energy + ZPEb \(2,1,7,10)c \(2,1,3,5) = ceqd A B C \(i,a)e \(i,b)e \(i,c)e Ic

Hartree Hartree deg deg MHz MHz MHz deg deg deg uÅ2 Debye Debye Debye Debye

laf lbf lcf l a b c d e f g h i j

MP2h

350.513613867 350.317775 ±7.7719 ±13.9247 3.2823028 1.2686491 1.1644966 146.969442 57.034438 88.155239 3.179656 0.0738 2.7215 0.0640 2.7232

349.4455467 349.247050 ±9.2546 ±15.1062 3.2967754 1.2871802 1.1800763 146.813377 56.905676 87.799087 3.195621 0.0269 3.0794 0.1049 3.0813

Exp.i

3.30027(16) 1.2802481(91) 1.1766233(39) 149.2764(49) 59.2764(49) 90.0 (fixed) 3.1982(51)

0.0j

Electronic energy. Electronic energy including vibrational zero-point energy. Dihedral angle describing the equilibrium position of the entire neopentyl group (for atom numbers see Fig. 1). Dihedral angle describing equilibrium position of methyl rotor; upper (lower) sign of \(2,1,3,5) belongs to upper (lower) sign of \(2,1,7,10). Angle between (methyl) internal rotor axis (i) and principal axes of inertia (a, b, c, respectively). Dipole moment component with respect to the principal axes of inertia, signs refers to coordinates given as Supplementary material. B3LYP/6-311++G(d,p) level. MP2/6-311++G(d,p) level Experimental data (XIAM fit). Due to the absence of c-type lines.

Table 2 Quantum chemical results for methyl neopentyl ketone (conformer II (C1)). Unit Energya Energy + ZPEb \(2,1,7,10)c \(2,1,3,5) = ceqd A B C \(i,a)e \(i,b)e \(i,c)e Ic

laf lbf lcf l

Hartree Hartree deg deg MHz MHz MHz deg deg deg uÅ2 Debye Debye Debye Debye

DFTg 350.512850092 350.316620 71.4507 5.2863i 3.1020253 1.3440406 1.2103545 127.428979 140.436688 79.018551 3.184930 1.0254 2.6151 0.5579 2.8638

MP2h 349.4460612 349.247012 75.8005 7.9929 3.1018595 1.3809714 1.2372834 124.789955 142.849979 78.587876 3.199332 1.2126 2.9739 0.6615 3.2791

a

Electronic energy. b Electronic energy including vibrational zero-point energy. c Dihedral angle describing the equilibrium position of the entire neopentyl group (for atom numbers see Fig. 1). d Dihedral angle describing equilibrium position of methyl rotor; upper (lower) sign of \(2,1,3,5) belongs to upper (lower) sign of \(2,1,7,10). e Angle between (methyl) internal rotor axis (i) and principal axes of inertia (a, b, c, respectively) f Dipole moment component with respect to the principal axes of inertia, signs refers to coordinates given as Supplementary material. g B3LYP/6-311++G(d,p) level. h MP2/6-311++G(d,p) level. i During optimization process methyl group rotates, therefore \(2,1,3,6) is given.

were broadened, some lines were clearly split by up to some 100 kHz. These splittings are probably due to either the internal rotation of the neopentyl methyl groups (which have higher barrier heights) or due to spin–spin or spin–rotation interactions. None of these effects were taken into account in the present study. In MNPK the rather large splitting of the rotational lines observed in the spectrum is due to one large amplitude motion, the internal rotation of the acetyl methyl group. We assumed the barrier to internal rotation to be almost the same as in trans-methyl ethyl ketone [13] which has been reported to be 181 cm 1. This

Fig. 3. Broadband scan of MNPK (upper trace) and simulated spectrum at a rotational temperature of 2 K (lower trace). Simulated A species lines in black, E species lines in red.

is a rather low barrier and we expected very large A–E splittings from a few MHz to a few GHz, even in the ground torsional vt = 0 state, depending on the respective J and K transition. At first we tried to assign the A species (r = 0) transitions, treating them as an effective rigid rotor spectrum. Therefore we used rotational constants obtained from quantum chemical calculations on various levels of theory (see columns 3 and 4 of Table 1). By trial and error, a number of a-type R-branch transitions could be identified yielding the B and C rotational constants. Then we were able to also assign some b-type Q-branch transitions allowing us to determine the A constant. This enabled us to predict the whole rigid rotor spectrum with sufficient accuracy to find all the remaining A species lines and, subsequently, to fit the (effective) quartic centrifugal distortion constants. It should be noted that despite an intense search no c-type transitions were found, which means that the out-of-plane (c) electric dipole moment component value is close to zero. This allows us to confirm that the conformer observed in our spectrum is the Cs conformer. In the next step we predicted both the A and E species transitions using the XIAM program [8]. The initial value for the torsional

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Y. Zhao et al. / Journal of Molecular Spectroscopy 281 (2012) 4–8 Table 3 Molecular constants of methyl neopentyl ketone obtained with program XIAM and comparison with results of BELGI-Cs and ab initio results. Unit A B C DJ DJK DK dJ dK Dpi2Jb Dpi2Kb Dpi2 b F0 Ic V3

\(i,a) \(i,b) \(i,c) sg N(A/E)h

ri

GHz GHz GHz kHz kHz kHz kHz kHz kHz kHz kHz GHz uÅ2 GHz cm 1 kJ/mol deg deg deg

kHz

XIAM 3.30027(16) 1.2802481(91) 1.1766233(39) 0.0681(11) 1.3971(47) 1.057(23) 0.00387(41) 3.177(26) 42.05(77) 220(22) 16.60(58) 158.02(25) 3.1982(51)c 5219.6(80) 174.11(27)d 2.0828(32)d 149.2764(49) 59.2764(49)e 90.0000f 14.422949 52/74 9.2

Ab initioj

BELGI-Cs a

3.29545(11) 1.281266(18)a 1.1770915(21)a

159.26(11) 3.1734(20)c 5202.6(11)d 173.539 (36) 2.07598(43)d 149.2818(18) 59.2818(18)e 90.0000f 14.378184 52/74 2.8

3.2967754 1.2871802 1.1800763

obs-calc (XIAM)

obs-calc (BELGI)

0.00349 0.00693 0.00345

0.00133 0.00591 0.00298

2.463 2.371

2.468 2.376

3.1956 134.486 146.8134 56.9057 87.7991

Note: All constants refer to the principal axis system, for the centrifugal distortion constants Watson’s A reduction and a Ir representations was used. a Obtained by transformation from the rho axis system to the principal axis system, see text. b For definition see Ref. [15], Eq. (6), with Dpi2J = DJm, Dpi2K = DKm, Dpi2 = dm. c Moment of inertia Ic of the internal rotor, calculated from its rotational constant F0 [20]. d Hindering potential, calculated from value in other units. e Calculated from \(i,b) = \(i,a) 90°. f Fixed due to symmetry. g Reduced barrier s = 4V3/(9F). h Number of fitted A and E species lines, respectively. i Standard deviation of the fit. j Calculation on the MP2/6-311++G(d,p) level using Gaussian 03.

barrier was taken from Ref. [13], i.e. approximately 181 cm 1. The initial value for the moment of inertia of the methyl group was fixed to 3.2 uÅ2. The predicted spectrum was in good agreement with the lines we observed in the scan and assignment was straight forward for the a-type R branch transitions, where the A–E splittings were only on the order of 10–100 MHz. The assignment of b-type Q branch lines, split by a few 100 MHz up to a few GHz, was more difficult. Here the search for lines which form closed cycles in the energy level diagram turned out to be very helpful. Finally 52 A species lines and 74 E species lines could be assigned. A complete list of assigned lines is given in Table S-4 of Supplementary data.

5. Results and discussion The microwave spectrum of MNPK has been analyzed by means of two different programs, XIAM [8,14] and BELGI-Cs [9,14]. XIAM sets up the Hamiltonian in the principal axis system of the entire molecule. The internal rotation operator of each top is setup in its own rho axis system and after diagonalization, the resulting eigenvalues are transformed (rotated) into the principal axis system. Since this method and code has been explained several times and used for our different studies, we do not give more details here. In our case the A and E species could be fitted using XIAM with a standard deviation of 9.2 kHz. To achieve this result, we had to float higher order terms, i.e. Dpi2J = DJm, Dpi2K = DKm, Dpi2 = dm as defined in [15]. A global fit with BELGI-Cs was also carried out. In this program the calculations are performed in the rho axis system (also often referred to as RAM for ‘‘rho axis method’’ in the literature), and all parameters obtained in the fit are referred to the rho axis

system. The method based on the work of Kirtman [16], Lees and Baker [17], and Herbst et al. [18] takes its name from the choice of the axis system, the rho axis system, which is related to the principal axis system by a rotation chosen to eliminate the 2FPcqxJx and 2FPcqyJy coupling terms in the kinetic energy operator where F is the internal rotation constant, Pc is the internal angular momentum, Jx and Jy are the usual x and y components of the global rotation angular momentum and q is a vector that expresses the coupling between the angular momentum of the internal rotation Pc and the global rotation J. Unlike XIAM, BELGI-Cs which was used successfully to describe spectra for internal rotors with very low internal rotation barriers such as acetamide [19], allows for fitting many higher order terms not only in the total angular momentum J, but also in the angular momentum of the internal rotor Pc and in cross-terms between them. BELGI-Cs proceeds through a two-step diagonalization. In the first step the pure torsional Hamiltonian uses a basis set including torsional functions exp[i(3k + r)]|K>, with k being an integer 10 6 k 6 + 10, |K > is the symmetric top eigenfunction, and r = 0 and ±1 for the A and E species, respectively. In the second step the remaining terms of the Hamiltonian (rotational terms, centrifugal distortion terms and interaction terms between the global angular momentum, and the internal angular momentum) is diagonalized. This procedure has been explained in details in the literature [9,18]. Using BELGI-Cs, the same data set of 52 A species and 74 E species transitions was fitted with 15 parameters to experimental accuracy with a standard deviation of 2.8 kHz. The results are presented in Tables 3 and 4 for the XIAM and BELGI codes respectively. The two sets of parameters are compared in Table 3. We note that the ground torsional states lie at 42.31 and 42.58 cm 1 for the A and the E species, respectively, and therefore above the local maximum of the potential energy calculated to be

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Y. Zhao et al. / Journal of Molecular Spectroscopy 281 (2012) 4–8

Table 4 Molecular constants of methyl neopentyl ketone obtained by a global fit using program BELGI-Cs. Operatora

Constantb

Unit

P 2a P 2b P 2c

A

GHz

3.19340(11)

B

GHz

1.383316(13)

C

GHz

{Pa,Pb} P4

DAB DJ DJK

GHz kHz kHz

P 4a

DK

kHz

2P2(P 2b P 2c )

dJ

kHz

0.01769(17)

{P 2a ,(P 2b –P 2c )}

dK

kHz

1.1092 (30)

F V3 Lv k5

GHz cm 1 unitless kHz MHz

FV c2

MHz MHz

2.0881(69) 0.9974(33)

kHz

2.8

P2P 2a

Pc2 (1/2)(1–cos3c) PaPc PaPc P2 (1–cos3c)P 2a (1–cos3c)P2 (1–cos3c)(P 2b –P 2c )

q

re

Valuec

1.1770915(21) –0.441738(26) 0.09758(39) 1.1232(51) 0.644(10)

160.8177143d 173.539(36) 0.018258(11) 1.25(22) 16.28(39)

a

All constants refer to a rho-axis system, therefore the inertia tensor is not diagonal and the constants cannot be directly compared to those of a principal axis system. Pa, Pb, Pc are the components of the overall rotation angular momentum, Pc is the angular momentum of the internal rotor rotating around the internal rotor axis by an angle c. {u,v} is the anti-commutator uv + vu. b 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, q, and A, which occur in the Hamiltonian in the form F(Pc qPa)2 + AP2a . c Values of the parameters from the present fit. Statistical uncertainties are shown as one standard uncertainty in the last digit. d Fixed to a value obtained in a previous fit where V3 was fixed. e Standard deviation of the fit.

Methyl acetate Ethyl acetate Vinyl acetate Methyl neopentyl ketone trans-methyl ethyl ketone Acetone sp-methyl vinyl ketone ap-methyl vinyl ketone Acetaldehyde

V3 (cm CH3COOCH3 CH3COOC2H5 CH3COOCH@CH2 CH3COCH2C(CH3)3 CH3COC2H5 CH3COCH3 CH3COCH@CH2 CH3COCH@CH2 CH3COH

1

)

101.740(30) 99.57(11) 155.1(1) 173.539(36) 181.0(4) 266.279(49) 376.6(2) 433.8(1) 407.947(2)

Acknowledgments We thank the Center for Computing and Communication of the RWTH Aachen University for free computer time and the Land Nordrhein-Westfalen for funds. We thank Sebastian Kühl and Christian Beceño for their contribution within a student research project. The authors would also like to also thank for PHC PROCOPE grants. Appendix A. Supplementary material Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://library.osu.edu/sites/ msa/jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/ 10.1016/j.jms.2012.09.002. References

Table 5 Comparison of the torsional barriers of some carbonyl compounds. Compound

charges are no longer balanced since one oxygen atom is replaced by other groups. This results in higher barriers depending on the respective substituent (see the trans methyl ethyl ketone [13] and acetone [23]). It should be noted, that with both, XIAM and BELGI-Cs, a strong correlation between V3 and Ic is present which is due to the fact that only vt = 0 ground torsional state transitions are included in the analysis. However, both programs converged at almost the same Ic. Finally it should be mentioned that only about 86% of all measured lines could be assigned. The remaining lines were weak and might be due to the C1 conformer, vibrationally excited states or isotopologues of MNPK.

Ref. [4] [20] [24] This work [13] [23] [2] [2] [25]

less than 20 cm 1 by either DFT or ab initio methods (see Section 4). Thus, we can consider that our fitted parameters describe an ‘‘effective’’ Cs geometry. The torsional barrier determined for the methyl rotor is 173.539(36) cm 1 using the BELGI-Cs code and 174.11(27) cm 1 using the XIAM code (see Table 3). The difference is less than 0.5%. The differences between the methyl rotor angles are only about 0.0054° when comparing the two methods. The rotational constants also agree within less than 0.1%. In Table 5, some values of the V3 barrier of several carbonyl compounds are compared. These molecules have similar molecular structures as MNPK. The acetates (esters of acetic acid) have usually a barrier to internal rotation of about 100 cm 1 (see for example the methyl acetate [4] or ethyl acetate [20]). This is partly due to an almost C2v symmetric charge distribution over the COO group, a similar situation to toluene or nitromethane which are known to have very low barriers (V3 = 0, V6 = 4.83783617(94) cm 1 and V3 = 0, V6 = 2.099649(10) cm 1 for toluene [21] and nitromethane [22], respectively). In the case of the ketones the

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