Microwave rotational spectrum and ab initio equilibrium structure of fumaric acid: Anharmonicity bridging the molecular characterizations

Journal of Molecular Spectroscopy 268 (2011) 16–22

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Microwave rotational spectrum and ab initio equilibrium structure of fumaric acid: Anharmonicity bridging the molecular characterizations Natalja Vogt a, K.P. Rajappan Nair b, Jürgen Vogt a, Jens-Uwe Grabow b,⇑ a b

Chemieinformationssysteme, Universität Ulm, Albert Einstein Allee 47, D-89069 Ulm, Germany Institut für Physikalische Chemie & Elektrochemie, Lehrgebiet A, Gottfried-Wilhelm-Leibniz Universität Hannover, Callinstrasse 3A, D-30167 Hannover, Germany

a r t i c l e

i n f o

Article history: Available online 29 March 2011 Dedicated to Philipp R. Bunker and A. Robert W. McKellar. Keywords: Microwave spectroscopy Rotational spectroscopy Supersonic-jet Structure Force field Dipole moment

a b s t r a c t The rotational spectrum of fumaric acid was studied in a pulsed supersonic jet expansion using Fouriertransform microwave (FT-MW) spectroscopy. The ground-state rotational constants, centrifugal distortion constants and the electric dipole moment of the molecule were determined at high accuracy. Agreement of experimental values with those predicted by ab initio methods for the s-cis,s-trans conformer, one of the three plausible conformers in the gas-phase, has unambiguously confirmed the presence of this conformer in the cold jet. The semi-experimental equilibrium rotational constants BðiÞ e derived ðiÞ from the experimental values B0 and the rovibrational corrections from the MP2/cc-pVTZ cubic force field calculation are in excellent agreement with the high-level ab initio values. The ab initio geometries of low-energy conformers s-cis,s-cis, s-cis,s-trans, and s-trans,s-trans were optimized at the CCSD(T) level of theory. It was shown that the structural and spectroscopic parameters (i.e. bond lengths, rotational constants, and vibrational frequencies) from experimental and theoretical methods are compatible when anharmonic effects are taken into account. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Fumaric and maleic acid, being the trans and cis isomers of butenedioic acid, respectively, are the simplest dicarboxylic acids with a C@C double bond. Besides being a prototype dicarboxylic acid, fumaric acid is of practical interest due to its applications in medicine (e.g. as anti-tumoral agent, an inhibitor of transaminase reactions) and in polymer chemistry [1,2]. The accurate determination of its molecular constants is important for a fundamental understanding of its chemical properties. Previously, the molecular structure of fumaric acid was studied twice by gas-phase electron diffraction (GED). In the earlier study at 533 K [3], the structural analysis was carried out, assuming a single conformer with both C@O bonds in antiperiplanar (ap) positions relative to the C@C bond (s-trans arrangements, see conformer III in Fig. 1). However, the recent GED reanalysis [4] has shown that, in the gas-phase at 480 K, fumaric acid constitutes a mixture of three conformers in approximately equal amounts. These conformers exhibit either two s-cis (I), or two s-trans (III), or one s-cis and one s-trans (II) O@CAC@C arrangements (see Fig. 1). The same conformational composition of fumaric acid was revealed in the analysis of infrared (IR) vibrational spectra observed in an Ar matrix and assigned with use of scaled harmonic

⇑ Corresponding author. Fax: +49 511 762 4009. E-mail address: [email protected] (J.-U. Grabow). 0022-2852/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2011.03.027

frequencies from the B3LYP/6-31G(d,p) calculations [5]. Recent MP2/cc-pVTZ calculations [4], predict six stable conformations for fumaric acid. The low-energy conformers have both O@CAOAH fragments in synperiplanar (sp) positions, while the high-energy conformers have one or two O@CAOAH groups in ap positions. The relative energies of the three low-energy conformers I–III were calculated to be 0 kJ mol1, 1.5 kJ mol1 and 2.7 kJ mol1 (MP2/ccpVQZ), respectively [4]. According to this ab initio prediction, the conformers exist in a ratio of I:II:III = 33:48:19 at 480 K, whereas the high-energy conformers are practically absent at this temperature. Since the conformers I and III, both belonging to the point group C2h, have no permanent dipole moments, only the most abundant conformer II (point group Cs) exhibits a rotational spectrum and can thus be detected by microwave (MW) spectroscopy. The aim of the present work is a high-resolution study of the vibrational ground-state rotational spectra of fumaric acid by supersonic jet expansion Fourier-transform (FT) MW spectroscopy while employing high-level ab initio calculations to deduce semiexperimental equilibrium constants.

2. Experimental As no microwave study on fumaric acid has been reported earlier, spectral surveys for the rotational spectrum of this molecule were done using a high resolution Fourier-transform microwave (FT-MW) spectrometer – a pulsed supersonic jet-expansion

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N. Vogt et al. / Journal of Molecular Spectroscopy 268 (2011) 16–22

II (s-trans,s-cis)

I (s-cis,s-cis)

III (s-trans,s-trans)

Fig. 1. Low-energy conformers of fumaric acid.

Table 1 Microwave rotational transitions of fumaric acid (conformer II). J0K Kþ 111 212 303 312 313 313 404 413 414 423 505 505 515 515 524 606 606 615 616 616 624 625 707 707 716 717 717 725 726 734 735 743 744 808 808 817 818 818 826 827 835 836 844 845 909 909 918 919 919 927 928 936 937 945 946 955 100,10 100,10 1019 101,10

J00K Kþ 000 101 202 211 202 212 303 312 303 322 404 414 404 414 423 505 515 514 505 515 523 524 606 616 615 606 616 624 625 633 634 642 643 707 717 716 707 717 725 726 734 735 743 744 808 818 817 808 818 826 827 835 836 844 845 854 909 919 918 909

Table 1 (continued)

mobs (MHz)

mobs  mcalc (MHz)

6544.836 8197.551 5361.988 5579.928 9782.106 5164.186 7135.448 7436.320 11302.306 7162.901 8897.217 4730.358 12764.256 8597.398 8949.889 10644.802 6777.762 11138.572 14176.304 10309.264 10837.399 10734.387 12376.248 8844.747 12982.421 15548.828 12017.325 12678.726 12515.904 12566.499 12561.450 12553.982 12553.929 14090.415 10917.835 14819.887 16893.803 13721.225 14533.806 14293.957 14371.379 14361.309 14351.427 14351.279 15787.209 12983.821 16649.647 18224.103 15420.715 16402.200 16068.069 16180.963 16162.582 16150.522 16150.165 16141.221 17467.700 15030.807 18470.231 19552.557

0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.000 0.001 0.001 0.000 0.001 0.001 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.002 0.003 0.001 0.000 0.001 0.001

J0K Kþ

J 00K Kþ

mobs (MHz)

mobs  mcalc (MHz)

101,10 1028 1029 1037 1038 110,11 110,11 111,10 111,11 111,11 1129 112,10 1138 1139 1147 120,12 120,12 121,11 121,12 121,12 122,10 122,11 130,13 130,13 131,13 140,14

919 927 928 936 937 101,10 100,10 1019 100,10 101,10 1028 1029 1037 1038 1046 110,11 111,11 111,10 110,11 111,11 1129 112,10 120,12 121,12 120,12 131,13

17115.664 18282.281 17837.781 17996.342 17965.017 17049.163 19134.020 20280.027 20890.909 18806.053 20171.339 19602.654 19818.752 19768.265 19754.708 20789.031 19032.142 22077.300 22248.856 20491.967 22065.883 21362.279 22435.887 20976.061 23633.413 22880.052

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.000 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.000 0.001 0.000 0.000

Fabry–Pérot-type resonator spectrometer of the Balle–Flygare design [6,7]. The sample of fumaric acid (Aldrich, 99%) was used without further purification. Fumaric acid is a white solid at room temperature; it melts at 287 °C. To obtain sufficient vapor pressure to record the rotational spectrum, the sample was heated in a reservoir nozzle installed in the backside of one of the reflectors of the Fabry–Pérot-type resonator. Most measurements were carried out at a nozzle temperature between 160 °C and 170 °C and at a carrier gas (neon) pressure near 200 kPa. All frequency measurements were referenced to a global positioning system (GPS) disciplined rubidium frequency standard. The spectrometer, also used for the Stark-effect measurements described below, utilizes a coaxially oriented beam-resonator arrangement (COBRA), i.e. the molecular jet expands coaxially to the axis of the near-confocal Fabry–Pérot type resonator [8]. The principal advantage of the longer transit time of the molecular jet in the COBRA arrangement can be exploited for Stark-effect experiments if, rather than using external electrode plates, the reflectors are utilized as high-voltage electrodes [9]. In this arrangement, the direction of the electric Stark field is perpendicular to the polarized microwave field leading exclusively to the selection rules DMJ = ±1. The initial survey search scans were carried out in the frequency range of 12.3 GHz to 12.5 GHz starting at a nozzle temperature of about 160 °C. For each measurement, 200 free induction decays (FID) were averaged at a pulse repetition rate of 5 Hz and Fourier transformed at stepped frequency intervals of 0.25 MHz. The

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Table 2 ðiÞ ðiÞ Ground state B0 and equilibrium Be ðiÞ rotational constants and rovibrational corrections D = BðiÞ e  B0 (in MHz) for fumaric acid. i

B0

ðiÞ

BðiÞ e  B0

ðiÞ

BðiÞ e

FT-MW

MP2/cc-pVTZ

FT-MWa

GEDb,c

MP2/cc-pVTZ

MP2/cc-pVQZb

MP2/cc-pV5Z

d r BO e

Watson’s A-reduction

Watson’s S-reduction

A B C

Conformer I –  

  

41.07 5.68 4.44

  

5955(30) 957(4) 825(4)

5767.25 956.87 820.71

5791.57 959.61 823.21

5795.40 960.20 823.72

5832.35 957.46 822.45

A B C

Conformer II 5718.4807(19) 964.952101(78) 826.357408(71)

5718.4807(19) 964.951734(45) 826.357770(35)

46.8 5.46 4.31

5765.28 970.41 830.67

5797(26) 968(4) 829(4)

5713.06 968.99 828.47

5735.40 972.08 831.20

5738.70 972.73 831.75

5764.13 970.31 830.50

A B C

Conformer III   

  

51.10 5.32 4.23

  

5662(25) 978(4) 834(4)

5666.73 980.45 835.84

5688.18 983.93 838.83

5691.20 984.60 839.38

5706.18 982.54 838.21

a

Semi-experimental rotational constants; rovibrational corrections from MP2/cc-pVTZ cubic force field. Ref. [4]. Derived from semi-experimental equilibrium geometry; anharmonic vibrational corrections to thermal average bond lengths were calculated from MP2/cc-pVTZ cubic force field. d Derived from r BO e Born–Oppenheimer equilibrium geometry; see text for details. b

c

Table 3 Experimental and ab initio centrifugal distortion constants (in kHz) of fumaric acid (conformer II). Watson’s A-reduction a

DJ DJK DK dJ dK a b

Watson’s S-reduction b

FT-MW

ab initio

0.03135(16) 0.1801(15) 1.34(182) 0.004732(91) 0.182(27)

0.03061 0.1739 1.25 0.004771 0.175

Exp-calc (%) 2.36 3.44 6.72 0.82 3.85

DJ DJK DK d1 d2

FT-MWa

ab initiob

Exp-calc (%)

0.03005(15) 0.1880(18) 1.33(182) 0.004732(91) 0.00653(98)

0.02933 0.1816 1.25 0.004771 0.00639

2.40 3.40 6.02 0.82 2.14

Ground state values. From the MP2/cc-pVTZ harmonic force field.

frequency range was chosen both for optimum sensitivity of the spectrometer and the predictions of the spectral location for intense transitions. The rotational constants calculated from the structure reported by Vogt et al. [4] guided the search (see Table 2). First, the JKa,Kc = 70,7 60,6 transition was observed at 12376.248 MHz and subsequently verified by observing a total of 63 a-type and 23 b-type transitions above and below this frequency. As expected, no c-type spectrum was found. The measured frequencies listed in Table 1 were least-squares fitted by the parameters of a standard asymmetric rotor Hamiltonian using Watson’s A- and S-reductions. The resulting values of the rotational and quartic centrifugal distortion constants are shown in Tables 2 and 3, respectively. The root-mean-square (rms) deviation of the fit was better than 1 kHz. For Stark-effect measurements it is desirable to limit the number of MJ-components such that an assignment and analysis becomes feasible. Thus, low J transitions are preferred, which also coincides with the boundary conditions introduced by the rotational temperature of the species in the supersonic jet expansion. With a temperature as low as 1 K, only rotational levels with very low J-values are occupied. Transitions involving low J-values are especially valuable when using coaxially aligned electrodes for Stark-effect applied in resonators (CAESAR), since the selection rule of DMJ = ±1 gives rise to a higher (approximately twice) the number of MJ-components as compared to the common parallel plate arrangement with DMJ = 0. In order to determine the dipole moment of fumaric acid, Stark-effect measurements in homogeneous electric fields were performed on the JKa,Kc = 11,1 00,0 (M = 1–0), JKa,Kc = 21,2 10,1 (M = 2–1 and M = 1–0), JKa,Kc = 30,3 20,2 (M = 3–

2), and JKa,Kc = 31,2 21,1(M = 3–2 , M = 2–1) transitions, which lie well within the sensitive frequency range of the instrument and were predicted to display a significant Stark-effect upon the application of an electric field. A typical Stark splitting in the rotational transition J = 21,2 10,1 with MJ = 1 0 and MJ = 2 1 is shown in Fig. 2. The applied high voltages were calibrated for the electric field strengths using the Stark effect in the 1 0 rotational transition of the OC36S and 18OCS isotopologs of OCS using a dipole moment of l = 0.71519(3) D [10] as described in Ref. [11]. A global fit of all measurements given in Table 4 using the computer program QStark [12,13] yielded dipole moment components for fumaric acid of la = 2.5695(67)  1030 Cm (0.7703(20) D) and lb = 8.7442(320)  1030 Cm (2.6215(96) D). In order to account for the systematic errors in the relative mirror positions, the uncertainties may be increased to three times the standard deviation to ensure the confidence error limit. The expanded uncertainties of the dipole moment components, shown in the Table 5, in parentheses are Type A with coverage factor k = 3 or three standard deviations [14]. 3. Quantum-chemical calculations The geometries of low-energy conformers I–III were optimized at the coupled cluster CCSD(T) level of theory [15,16] with the correlation-consistent polarized valence triple zeta (cc-pVTZ) basis set [17]. The coupled cluster T1 diagnostic [18] was also calculated in the CCSD(T)/cc-pVTZ approximation. As it has been shown in Refs. [19–21], the small changes in the geometrical parameters due to the improvement of the basis set and the electron correlation

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N. Vogt et al. / Journal of Molecular Spectroscopy 268 (2011) 16–22 Table 4 Stark splitting in the microwave rotational transitions of fumaric acid. J0K Kþ

J 00K Kþ

Electric field (V/cm)

mexp (MHz)

mcal (MHz)

mexp  mcalc (MHz)

11,1 00,0 M J0 = 1 MJ00 = 0

0 16.8125 33.5604 50.3084 67.0563 83.8043

6544.83640 6544.81001 6544.72869 6544.59533 6544.40662 6544.17603

6544.8373 6544.8096 6544.7277 6544.5929 6544.4079 6544.1760

0.00087 0.00038 0.00102 0.00241 0.00129 0.00001

21,2 10,1 M J0 = 2 MJ00 = 1

0.0 16.8125 33.5604 50.3084 67.0563 83.8043

8197.55070 8197.53518 8197.49051 8197.41541 8197.31014 8197.17574

8197.5526 8197.5374 8197.4920 8197.4165 8197.3112 8197.1763

0.00191 0.00220 0.00145 0.00107 0.00102 0.00056

21,2 10,1 M J0 = 1 MJ00 = 0

16.8125 33.5604 50.3084 67.0563

8197.50833 8197.37242 8197.15385 8196.85064

8197.5083 8197.3760 8197.1558 8196.8481

0.00000 0.00354 0.00196 0.00258

30,3 20,2 M J0 = 3 MJ00 = 2

0.0 16.8125 33.5604 50.3084 67.0563 83.8043 100.5522 117.3002 134.0481 150.7961 167.5440

5361.98761 5361.98901 5361.98990 5361.99152 5361.99460 5361.99825 5362.00300 5362.00820 5362.01490 5362.02214 5362.03002

5361.9896 5361.9900 5361.9914 5361.9937 5361.9968 5362.0009 5362.0058 5362.0117 5362.0185 5362.0261 5362.0347

0.00198 0.00103 0.00150 0.00214 0.00222 0.00263 0.00284 0.00350 0.00356 0.00397 0.00464

31,2 21,1 M J0 = 3 MJ00 = 2

0.0 33.5604 50.3084 67.0563 75.4302

5579.92726 5579.89732 5579.86166 5579.81457 5579.78334

5579.9277 5579.8993 5579.8641 5579.8150 5579.7854

0.00046 0.00200 0.00239 0.00042 0.00203

31,2 21,1 M J0 = 2 MJ00 = 1

16.8125 33.5604 50.3084 75.4302

5579.93004 5579.94736 5579.96692 5580.01582

5579.9321 5579.9453 5579.9672 5580.0167

0.00209 0.00208 0.00031 0.00090

Table 5 Experimental dipole moments in comparison with calculated values (in D) of fumaric acid (conformer II). Fig. 2. Stark pattern of the J = 21,2 electric fields E.

10,1 transition in fumaric acid at different

approximation at the CCSD(T) level can be approximated rather well at the second-order Møller–Plesset perturbation theory (MP2) [22] level, at least for the first-row atoms. To estimate the contribution of the inner-shell correlation effects on the molecular geometry, the correlation-consistent polarized weighted core-valence quadruple zeta (cc-pwCVQZ) basis set [23] was used in the MP2 calculations with and without the frozen core approximation. To extrapolate the results to the higher basis sets, cc-pVQZ and ccpV5Z [17], the geometrical differences to the MP2/cc-pVTZ values were also derived. From the calculated value of the T1 diagnostic of 0.016 it may be concluded that the non-dynamical electron correlation is not too high. Therefore, the CCSD(T) structure is expected to be reliable. Finally, the best ab initio structure was calculated using the following approximation

r BO e ¼ CCSDðTÞ=cc-pVTZ þ MP2=cc-pV5Z  MP2=cc-pVTZ þ MP2ðaeÞ=cc-pwCVQZ  MP2=cc-pwCVQZ where ae indicates all electrons correlated while the frozen core approximation is used elsewhere. The results of all ab initio structure calculations are given in Table 6.

la lb l a

MP2/cc-pVTZ

MP2/cc-pVQZ

FT-MWa

0.76 2.51 2.62

0.77 2.58 2.69

0.77032(201) 2.6215(96) 2.733(10)

3r uncertainty in parentheses.

Rotational constants calculated in different approximations are listed in Table 2 in comparison with experimental values. The harmonic and anharmonic force fields were calculated in the MP2/cc-pVTZ approximation. The optimized molecular geometry was calculated first. Then, the associated harmonic force field was evaluated analytically in Cartesian coordinates at the optimized geometry. The cubic and semi-diagonal quartic normal coordinate force constants were determined with the use of a finite displacement procedure involving displacements along reduced normal coordinates and the calculation of analytic second derivatives at these displaced geometries. The rovibrational corrections to the ground-state rotational ðiÞ constants, D(B0  BðiÞ e ), derived from the cubic force field are given in Table 2. The quartic centrifugal distortion constants computed from the harmonic force field are presented in Table 3 in comparison to the ground-state experimental values.

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Table 6 Geometrical parameters of fumaric acid conformers from ab initio calculations in comparison with experimental data (bond lengths re in Å, bond angles \e in degrees).

a b c d

Parameter

CCSD(T)/cc-pVTZ

MP2(ae)/cc-pwCVQZ

MP2/cc-pwCVQZ

MP2/cc-pVTZa

MP2/cc-pVQZa

MP2/cc-pV5Z

reBOb

GEDa

Conformer I C@C CAC CAO C@O CAH OAH CAC@C OACAC O@CAO C@CAH CAOAH

1.3387 1.4878 1.3517 1.2086 1.082 0.968 120.08 111.04 123.46 121.06 105.87

1.3308 1.4748 1.3457 1.2052 1.0785 0.97 120.06 110.9 123.46 120.78 106.16

1.3341 1.4782 1.3483 1.2074 1.0799 0.9676 120.02 110.85 123.48 120.81 106.06

1.3368 1.4802 1.3513 1.2103 1.0803 0.9692 120.08 110.80 123.52 120.72 105.70

1.3346 1.4786 1.3487 1.2078 1.08 0.9675 120.03 110.85 123.48 120.80 106.04

1.3342 1.4781 1.3483 1.2076 1.0799 0.9675 119.98 110.89 123.45 120.86 106.17

1.3328 1.4823 1.346 1.2037 1.0801 0.9654 120.02 111.18 123.37 121.18 106.44

1.330(3) 1.477(3) 1.344(3) 1.204(3) 1.080d 0.968d 120.3(2) 113.9(4) 123.1(1) 120.801d 106.042d

Conformer II C@C CAC CACc CAO C@O CAOc C@Oc CAHc CAH OAH OAHc CAC@C CAC@Cc OACAC O@CAO OACACc O@CAOc C@CAHc C@CAH CAOAH CAOAHc

1.3399 1.4839 1.4888 1.354 1.2088 1.3522 1.2082 1.081 1.0821 0.9673 0.968 123.61 119.74 113.2 123.16 110.97 123.47 122.05 120.68 105.52 105.86

1.3318 1.4706 1.4761 1.3471 1.2062 1.3462 1.2047 1.0772 1.0786 0.966 0.9667 123.55 119.71 113.19 123.13 110.81 123.5 121.78 120.47 105.77 106.16

1.3352 1.474 1.4795 1.3499 1.2084 1.3489 1.2069 1.0787 1.0801 0.9669 0.9676 123.52 119.68 113.14 123.15 110.76 123.51 121.80 120.49 105.66 106.05

1.3378 1.476 1.4815 1.3533 1.2111 1.3518 1.2098 1.0791 1.0805 0.9685 0.9692 123.7 119.71 113.06 123.19 110.72 123.55 121.76 120.31 105.31 105.69

1.3356 1.4743 1.4799 1.3502 1.2088 1.3492 1.2073 1.0787 1.0801 0.9668 0.9675 123.53 119.69 113.14 123.15 110.76 123.51 121.8 120.48 105.65 106.04

1.3352 1.4739 1.4794 1.3497 1.2087 1.3489 1.2071 1.0786 1.0801 0.9669 0.9675 123.46 119.65 113.18 123.11 110.79 123.49 121.84 120.54 105.75 106.16

1.334 1.4784 1.4834 1.3477 1.2042 1.3466 1.2032 1.0791 1.0801 0.9648 0.9655 123.39 119.71 113.36 123.06 111.1 123.39 122.12 120.89 106.08 106.43

1.331(3) 1.473(3) 1.479(3) 1.345(3) 1.205(3) 1.344(3) 1.204(3) 1.079d 1.080d 0.967d 0.968d 123.9(2) 120.0(2) 116.1(4) 122.8(1) 113.8(4) 123.1(1) 121.795d 120.481d 105.648d 106.036d

Conformer III C@C CAC CAO C@O CAH OAH CAC@C OACAC O@CAO C@CAH CAOAH

1.341 1.485 1.3531 1.209 1.081 0.9673 123.31 113.27 123.24 121.69 105.59

1.3329 1.4718 1.3461 1.2064 1.0773 0.966 123.24 113.25 123.21 121.47 105.84

1.3362 1.4752 1.3488 1.2085 1.0788 0.97 123.22 113.21 123.23 121.49 105.72

1.3388 1.4773 1.3523 1.2112 1.0793 0.9685 123.37 113.14 123.27 121.36 105.38

1.3366 1.4756 1.3491 1.2089 1.0788 0.9668 123.23 113.20 123.23 121.48 105.72

1.3363 1.4752 1.3486 1.2088 1.0788 0.9669 123.16 113.24 123.2 121.53 105.82

1.3351 1.4795 1.3467 1.2045 1.079 0.9648 123.12 113.42 123.15 121.84 106.15

1.332(3) 1.475(3) 1.344(3) 1.205(3) 1.079d 0.967d 123.5(2) 116.2(4) 122.8(1) 121.482d 105.715d

Ref. [4]. r BO e = CCSD(T)/cc-pVTZ + MP2/cc-pV5ZMP2/cc-pVTZ + MP2(ae)/cc-pwCVQZMP2/cc-pwCVQZ. In s-cis fragment. Assumed at the MP2/cc-pVQZ value.

Computed harmonic and anharmonic vibrational frequencies are presented in Table 7. Dipole moments of conformer II calculated at the MP2 level using different basis sets are compared with the determined experimental values in Table 5. All the MP2 calculations were performed with the GAUSSIAN03 (Rev.E.01) program package [24]. For the CCSD(T) calculations the MOLPRO (version 2009.1) [25] and GAUSSIAN03 [24] programs were used. 4. Discussion and conclusions As it can be seen from Table 6, the higher the level of ab initio calculations, the closer the computed structural parameters approach the semi-experimental equilibrium geometry determined from the GED data supplemented by the ab initio cubic force field [4]. The bond lengths in the MP2/cc-pVTZ approximation are longer than the GED values by up to 0.008 Å, while the

differences between the MP2/cc-pV5Z (or MP2/cc-pVQZ) and GED values are outside of experimental uncertainties only by about 0.001 Å. The rBO ab initio structure is in the most favorable agreement with the GED equilibrium structure except for the CAC bond lengths predicted better at the MP2 level. Thus, the best ab initio values of rotational constants can be derived from the rBO structure (see Table 2). In the current study, the values of the spectroscopic constants are determined with sufficient precision to allow for an unambiguous conformational identification. Structural details, such as CAC bond distances, cannot be obtained without additional spectral data from isotopic species, such as the mono-substituted 13C and 18 O species. The modest intensity of the spectrum, due to the low gas-phase abundance of fumaric acid even when heated to 170 °C because of its high melting point of 287 °C, has precluded the identification of the isotopologs in natural abundance at this time. The determined ground-state rotational constants of conformer II exhibit accidentally excellent agreement (better than 99.5%) with

21

N. Vogt et al. / Journal of Molecular Spectroscopy 268 (2011) 16–22 Table 7 Vibrational frequencies calculated from harmonic and anharmonic MP2/cc-pVTZ force fields in comparison with experimental values (in cm1). Approximate descriptiona

Harm

Anharm

Exp IR (Ar) [5]

Dharm

Conformer I m OAH as m CAH as m C@O as m CAO as d CCH as d COH c CAH m CAC as c C@O d OCO as s CAO d CC@O as s C@C d CCC as s CAC

3766.6 3250.6 1808.8 1410.1 1251 1139.2 1026.9 932 791.5 627.4 603.7 539.4 147.7 126.3 49.1

3584.4 3123.9 1775.8 1385.9 1212.5 1111.7 1003.3 913.9 779.1 602.9 598.2 535.6 145.3 126.4 45.4

3560 2948 1765 1369 1217 1115 982 914 777 600 571 537

0.058 0.1026 0.0248 0.03 0.0279 0.0217 0.0457 0.0197 0.0187 0.0457 0.0573 0.0045

0.0069 0.0597 0.0061 0.0123 0.0037 0.003 0.0217 0.0001 0.0027 0.0048 0.0476 0.0026

0.038d

0.014e

3576 3560 2948

0.0561 0.058 0.1068

0.0048 0.0068 0.0619

1765 1763 1650 1364 1338 1274 1234 1158 1120 986 938 909 896 777

0.0276 0.0221 0.0281 0.0274 0.0397 0.0222 0.0168 0.0329 0.0288 0.0473 0.0208 0.0098 0.0193 0.0203

0.0095 0.0004 0.005 0.0049 0.0356 0.0022 0.0051 0.0068 0.0011 0.0225 0.0024 0.0127 0.0077 0.004

589 554 546

0.0236 0.0671 0.0349

0.0073 0.0593 0.0031

0.035d

0.013e

0.0561 0.1073 0.0215 0.0558 0.0049 0.0347 0.0482 0.0238 0.0221 0.0466 0.079 0.0047

0.0049 0.0638 0.0008 0.0341 0.0126 0.0008 0.0234 0.003 0.008 0.0141 0.068 0.0054

0.042d

0.020e

Conformer II m OAH m OAH0 m CAH0 m CAH m C@O m C@O0 m C@C m CAO0 m CAO d CCH d CCH0 d COH d COH0 c CAH m CAC0 c CAH0 m CAC c C@O0 s CAO0 d OCO0 s CAO d OCO c C@O d CC@O d CC@O0 d CCC0 s C@C s CAC0 d CCC s CAC Conformer III m OAH as m CAH as m C@O as m CAO as d CCH as d COH as c CAH m CAC as c C@O d OCO as s CAO d CC@O as s C@C d CCC as s CAC

a b c d e

3776.4 3766.4 3262.7 3249.1 1813.7 1802.1 1696.3 1401.4 1391.2 1302.2 1254.8 1196.1 1152.3 1032.6 957.5 917.8 913.3 792.8 684.2 664.9 602.9 591.2 565.1 548.1 387.2 268.1 146.1 136.1 132.2 46.6

3776.5 3264.4 1803 1388.4 1262.2 1171.3 1035.6 923.5 794.2 586.1 601 539.5 143.5 138.4 44.5

3593.3 3584.3 3130.6 3113.3 1781.8 1762.2 1658.3 1370.7 1385.7 1276.8 1227.7 1150.2 1121.2 1008.2 940.2 897.5 902.9 780.1 674 658.4 584.7 586.9 547.7 543.5 385 264.8 145 134.1 131.7 46

3593.6 3136.2 1766.4 1359.8 1240.2 1132.9 1011.1 904.7 783.2 567.9 594.9 534.1 142.5 138.3 46

3576 2948 1765 1315 1256 1132 988 902 777 560 557 537

Denotations: m, stretching; as, asymmetric; d, bending; c, rocking; s, torsion; 0 , s-cis molecular fragment. Dharm = (harm  exp)/exp. Danharm = (anharm  exp)/exp. Mean value of |Dharm|. Mean value of |Danharm|.

b

Danharmc

22

N. Vogt et al. / Journal of Molecular Spectroscopy 268 (2011) 16–22

the equilibrium MP2/cc-pVTZ values (see Table 2). However, for the correct comparison of the theoretical and experimental values, having slightly different physical meaning, the ground-state rotational constants should be corrected for rovibrational effects. The semiexperimental equilibrium rotational constants derived from the ðiÞ ðiÞ B0 values and D(BðiÞ e  B0 ) rovibrational corrections calculated from the MP2/cc-pVTZ cubic force constants (see above) are presented in comparison with ab initio results in Table 2. As it can be seen from this Table, the higher the level of ab initio calculations, the closer the theoretical values become to the semi-experimental equilibrium rotational constants. The agreement between the MP2/cc-pV5Z and semi-experimental equilibrium values is better than 99.5%. The rotational constants derived from the rBO structure are practically identical with the equilibrium FT-MW values taking into account their accuracy estimated in Ref. [26] to be less than 10% of rovibrational corrections. Thus, the rotational constants calculated from the best ab initio geometries (rBO) can be considered as reliable predictions for conformers I and III without dipole moments. It should be noted that the rotational constants derived from the GED equilibrium geometrical parameters [4] are also in excellent agreement with the equilibrium FT-MW values taking into account the relative large uncertainties of the GED method. A comparison of computed harmonic and anharmonic vibrational frequencies with experimental IR spectra in Table 7 also demonstrates how important it is to account for the anharmonic effects. The mean deviations of the harmonic frequencies from the experimental fundamental vibrational wavenumbers are up to 4.2% (see conformer III) whereas the mean differences between the anharmonic computed and experimental values are less than 2% (for all three conformers). The deviations of ground-state centrifugal distortion constants determined in Watson’s A- and S-reductions from the equilibrium ab initio values are only a few percents (from 0.8% to 6.7%, see Table 3) being partly due to the different physical meaning of these constants. The experimental gas-phase dipole moment components la = 0.7703(20) D and lb = 2.6215(96) D display good agreement with the best computational estimate of la = 0.77 D and lb = 2.58 D in the MP2/cc-pVQZ approximation (see Table 5). The polarity of the molecule arises from the relative orientation of the carboxylic functions in conformer II while exhibiting no pronounced deviation from planarity.

Barbara Mez-Starck Foundation, and especially the assistance of J. Demaison in the treatment of anharmonic effects. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

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Acknowledgments We gratefully acknowledge support from the Deutsche Forschungsgemeinschaft (DFG), the Land Niedersachsen, and the Dr.

[26]

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