ARTICLE pubs.acs.org/JPCA
Microwave Spectrum and Conformational Composition of 3-Fluoropropionitrile (FCH2CH2CN) Harald Møllendal,*,† Svein Samdal,† and Jean-Claude Guillemin‡ †
Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, NO-0315 Oslo, Norway ‡ cole Nationale Superieure de Chimie de Rennes, CNRS, UMR 6226, Avenue du General Leclerc, Sciences Chimiques de Rennes, E CS 50837, 35708 Rennes Cedex 7, France
bS Supporting Information ABSTRACT: The microwave spectrum of 3-fluoropropionitrile, FCH2CH2CtN, has been investigated in the whole 17 75 GHz spectral region. Selected portions of the spectrum in the 75 95 GHz have also been recorded. The microwave spectra of the ground state as well as of three vibrationally excited states of each of two conformers have been assigned. The spectra of the vibrationally excited states belong to the lowest torsional and bending vibrations. The F C C C chain of atoms is exactly antiperiplanar in one of these rotamers and synclinal in the second conformer. The F C C C dihedral angle is 65(2)° in the synclinal form. The energy difference between the two forms has been obtained from relative intensity measurements performed on microwave transitions. It was found that the antiperiplanar conformer is more stable than the synclinal form by 1.4(5) kJ/mol. It is argued that the gauche effect is a significant force in this compound. Quantum chemical calculations at the high CCSD(full)/cc-pVTZ, MP2(full)/cc-pVTZ, and B3LYP/cc-pVTZ levels of theory have been performed. Most, but not all, of the theoretical predictions are in good agreement with experiment.
’ INTRODUCTION 1,2-Ethane derivatives, XCH2CH2Y, exist as a mixture of X C C Y antiperiplanar (obsolete: trans) and synclinal (obsolete: gauche) conformers. It was observed a long time ago that XCH2CH2Y compounds with highly electronegative substituents X and Y often prefers synclinal conformations in spite of the significant electrostatic repulsion between the X and Y substituents that exists in these compounds.1 The best example of this so-called gauche effect1 is perhaps 1,2-difluoroethane, FCH2CH2F, where the synclinal form has been found to be preferred by 3.9(17) kJ/mol in one gas electron-diffraction study,2 while 7.5(21) kJ/mol was reported in a second such study.3 Recent density functional theory (DFT) calculations4 at the B3LYP/ 6-311+G(d,p) and M05-2X/6-311+G(d,p) levels of theory yielded 3.4 and 2.8 kJ/mol, respectively, for this energy difference. The present article deals with the conformational properties of 3-fluoropropionitrile (F CH2 CH2 CtN). The F C C C dihedral angle can conveniently be used to characterize the conformational properties of this compound. A model of its antiperiplanar and synclinal forms with atom numbering is shown in Figure 1. These two rotamers will henceforth be denoted ap and sc, respectively. ap has a symmetry plane formed by the heavy atoms, whereas sc exists as two mirror images. 3-Fluoropropionitrile contains the very electronegative fluorine atom (Pauling electronegativity: 3.985) and the electronegative cyano group. This electronegative tendency is also reflected in the C F and the cyano group bond moments, which are 4.7 and 11.7 10 30 C m, respectively.6 The bond moments have r 2011 American Chemical Society
their negative ends on the fluorine end of the C F bond and on the nitrogen end of the CtN bond. The question is will the gauche effect prevail leaving the synclinal conformer the more stable, or will repulsive forces have the upper hand producing a more stable antiperiplanar form? Very recently we investigated the MW spectrum of 2-fluoroethylisocyanide, FCH2CH2NtC,7 which contains another very polar and similar group, namely, the isocyanide group, NtC, which has its negative end on the carbon atom. The synclinal form was found to be the slightly more stable by 0.7(5) kJ/mol in this case, a clear demonstration of the importance of the gauche effect. The question is now will the gauche effect in the cyanide FCH2CH2CtN be more or less important than in the isocyanide FCH2CH2NtC? No experimental conformational studies of gaseous FCH2CH2CN are available, but the compound in the liquid and solid states has been subject to an infrared and Raman study more than half a century ago.8 No attempt was made in this study8 to measure the enthalpy difference of the two conformers in the liquid phase, but a value close to zero was estimated, although the synclinal form appeared to be the more stable conformer. B3LYP/6-311+G (d,p) and M05-2X/6-311+G(d,p) calculations4 both predicted 2.7 kJ/mol for this energy difference of 3-fluoropropionitrile with sc as the high energy form. Received: November 14, 2011 Revised: December 15, 2011 Published: December 15, 2011 1015
dx.doi.org/10.1021/jp210932k | J. Phys. Chem. A 2012, 116, 1015–1022
The Journal of Physical Chemistry A
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Figure 1. Antiperiplanar (ap) and synclinal (sc) conformers of FCH2 CH2CN. Atom numbering is indicated on ap, which was found to be 1.4(5) kJ/mol more stable than sc by relative intensity measurements performed on microwave transitions.
The fact that no experimental information of conformational properties in the gas phase exists for the title compound was another reason to perform the present microwave (MW) investigation of this 1,2-ethane derivative. MW spectroscopy is an ideal method for the study of conformational equilibria due to its superior accuracy and resolution. The fact that relative intensity measurements can be performed on MW transitions to obtain accurate energy differences is another advantage of this method. The spectroscopic work has been augmented by high-level quantum chemical calculations, which were conducted with the purpose of obtaining information for use in assigning the MW spectrum and investigating properties of the potential-energy hypersurface.
’ EXPERIMENTAL SECTION Synthesis of 3-Fluoropropionitrile. The synthesis of 3-fluoropropionitrile has already been performed by dehydration of the corresponding amide.9 This compound was found in the photodifluoramination of cycloalkanes10 and in the nitrosative decomposition of azido nitriles.11 We prepared this species on a half-gram scale in a 92% yield by flash vacuum thermolysis of the 2-fluoroethylisocyanide7 at 650 °C as previously reported for allylisocyanide.12 The product was collected in pure form in a U-trap equipped with stopcocks and immersed in a 90 °C bath. NMR data of 3-fluoropropionitrile: 1H NMR (CDCl3, 400 MHz) δ 2.78 (dt, 2H, 3JHH = 6.9 Hz, 3JHF = 21.8 Hz, CH2CN); 4.63 (dt, 2H, 3JHH = 6.9 Hz, 2JHF = 46.0 Hz, CH2F). 13C NMR (CDCl3, 100 MHz) δ 19.7 (1JCH = 135.7 Hz, 2JCF = 24.0 Hz (d), CH2CN); 78.0 (t, 1JCH = 155.4 Hz (t), 1JCF = 175.8 Hz (d), CH2F); 116.7 (3JCF = 7.3 Hz (d), CN). 19F NMR (CDCl3) δ 216.9. Microwave Experiment. The MW spectrum of 3-fluoropropionitrile was studied using the Stark-modulation MW spectrometer of the University of Oslo. Details of the construction and operation of this device have been given elsewhere.13 15 This spectrometer has a resolution of about 0.5 MHz and measures the frequency of isolated transitions with an estimated accuracy of ∼0.10 MHz. The whole 17 75 GHz frequency interval was recorded. Selected regions of the 75 95 GHz were also investigated. Radio-frequency microwave double-resonance experiments (RFMWDR), similar to those performed by Wodarczyk and Wilson,16 were conducted to unambiguously assign particular transitions, using the equipment described elsewhere.13 The vapor pressure of the compound was roughly 60 Pa at room temperature. The spectra were measured at room temperature at a pressure of roughly 10 Pa. Quantum Chemical Methods. The present quantum chemical calculations were performed employing the Gaussian09 suite
Figure 2. B3LYP/cc-pVTZ (circles; red) and MP2/cc-pVTZ (squares; blue) electronic potential functions for rotation about the C1 C2 bond of FCH2CH2CN. The F3 C2 C1 C6 dihedral angle is given on the abscissa, and the electronic energies relative to the energy of ap is given on the ordinate. Each curve has its global minimum at 180° for the F3 C2 C1 C6 dihedral angle corresponding to ap. The sc rotamer is calculated by the B3LYP method to have a dihedral F3 C2 C1 C6 angle of 66.3° and an electronic energy that is 2.76 kJ/mol higher than the energy of ap. The corresponding MP2 values are 64.6° and 2.33 kJ/mol. The transition states are located at 0 and 119.2° in both methods of calculation. The B3LYP energies of the first and second transition state are 13.07 and 22.45 kJ/mol, respectively, relative to the electronic energy of ap. The corresponding MP2 values are 15.32 and 23.58 kJ/mol.
of programs17 running on the Titan cluster in Oslo. Becke’s three-parameter hybrid functional18 employing the Lee Yang Parr correlation functional (B3LYP)19 were employed in the DFT calculations. Møller Plesset second order perturbation calculations (MP2)20 as well as coupled-cluster calculations with singlet and doublet excitations (CCSD)21,22 were also undertaken. Both frozen-core and all-electron calculations [MP2(full)) and CCSD(full)] were performed with the last two methods. The CCSD(full) calculations are very costly and were speeded up by making use of a B3LYP force field that was calculated prior to the CCSD(full) calculations. Peterson and Dunning’s23 correlation-consistent cc-pVTZ basis set, which is of triple-ζ quality was used in the calculations.
’ RESULTS AND DISCUSSION Quantum Chemical Calculations. An electronic energy potential function for rotation about the C1 C2 bond was calculated at the B3LYP/cc-pVTZ and MP2/cc-pVTZ levels of theory employing the scan option of Gaussian09. The energies were computed in steps of 10° of the F3 C2 C1 C6 dihedral angle. All the remaining structural parameters were optimized for each dihedral angle. Separate calculations of the energies and optimized structures of the conformers ap and sc and of the transition state near 120° were also performed. The potential functions based on the results of these calculations are drawn in Figure 2. The global minimum of each of the two calculations occurs at the antiperiplanar (180°) conformation, corresponding to the ap conformer. The sc rotamer has a F3 C2 C1 C6 dihedral angle of 66.3° and an electronic energy, which is 2.76 kJ/mol 1016
dx.doi.org/10.1021/jp210932k |J. Phys. Chem. A 2012, 116, 1015–1022
The Journal of Physical Chemistry A
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Table 1. CCSD(full)/cc-pVTZ and MP2(full)/cc-pVTZ Structuresa of FCH2CH2CN method conformer
CCSD(full) ap
sc
Table 2. CCSD(full)/cc-pVTZ and MP2(full)/cc-pVTZ Spectroscopic Constants of FCH2CH2CN
MP2(full)
method
ap
sc
conformer
CCSD(full) a
ap
Bond Length (pm)
MP2(full)
sc
ap
b
sc
Rotational Constants (MHz)
C1 C2
151.7
151.3
151.1
151.2
A (MHz)
27815.6
11721.2
27580.0
11580.8
C2 F3 C2 H4
137.3 108.5
137.2 108.5
137.7 108.4
137.6 108.4
B (MHz) C (MHz)
2305.5 2186.8
3223.9 2738.2
2307.9 2187.5
3248.6 2748.5
C2 H5
108.5
108.5
108.4
108.4
C1 C6
145.8
146.0
145.1
145.3
C6 N7
115.2
115.1
116.6
116.6
C1 H8
108.5
108.6
108.5
108.5
C1 H9
108.5
108.7
108.5
Planar Moments (10 Pccc
Dipole Moment (10
Angle (deg) F3 C2 C1
108.2
109.5
108.3
109.4
108.7 108.7
108.4 108.4
108.7 108.7
108.4 108.4
C1 C2 H4
110.9
111.1
110.8
111.0
C1 C2 H5
110.9
109.7
110.8
109.8
H4 C2 H5
109.4
109.6
109.4
109.7
C2 C1 C6
110.9
112.4
110.6
109.7
109.6
109.6
109.4
C2 C1 H9
109.7
109.4
109.6
109.3
H8 C1 H9 C6 C1 H8
108.1 109.2
108.0 108.9
108.1 109.4
107.9 109.1
C6 C1 H9
109.2
108.9
109.4
108.9
H8 C1 H9
108.6
108.6
108.1
107.9
C1 C6 N7
178.7b
179.9
178.3b
179.7
F3 C2 C1 C6
180.0
180.0
64.5
F3 C2 C1 H8
59.3
56.2
59.3
56.7
F3 C1 C2 H9 H4 C2 C1 C6
59.3 60.9
174.4 54.9
59.3 60.8
174.7 55.1
H4 C2 C1 H8
59.8
176.0
59.9
H4 C2 C1 H9
178.5
u m2) 3.14
30
7.67
C m)
μa
7.21
9.40
6.36
μb
0.50
13.23
2.33
13.38
μc
0.0e
0.66
0.0e
0.676
7.22
16.24
7.21
16.40
μtot
9.45
14
N Nuclear Quadrupole Coupling Constants (MHz)
112.1
C2 C1 H8
7.65 d
108.7
F3 C2 H4 F3 C2 H5
3.14
20
χaa χbb
3.683 1.508
χcc
2.175
χab
2.307
χac
0.0d
2.074 0.035 2.109 3.170 0.878
3.261 1.283 1.978
1.817 0.063 1.880
2.074
2.832
0.0d
0.772
Electronic Energy Differencef (kJ/mol) 0.0 a
2.23
2.01g
0.0 b
Total electronic energy of ap: 711319.92 kJ/mol. Total electronic energy of ap: 711265.78 kJ/mol. c Conversion factor: 505379.05 10 20 MHz u m2. d 1 debye = 3.33564 10 30 C m. e By symmetry. f Relative to the energy of ap. g The energy difference corrected for zeropoint vibrational energies: 2.14 kJ/mol.
Dihedral Angle (deg)
H5 C2 C1 C6
a
60.9
H5 C2 C1 H8
178.5
H5 C2 C1 H9
59.8
64.9
65.8 176.2 62.5 55.5
178.4 60.8 178.4 59.9
176.3 65.7 176.7 62.2 55.8
Atom numbering given in Figure 1. b Bent toward C2.
higher than that of ap according to the B3LYP predictions, whereas the MP2 method indicates 64.6° and 2.33 kJ/mol for the dihedral angle and energy difference. The two transition states appear at 0 and 119.2° in both methods of calculations. The energies of the first of these barrier heights (0°) are 22.45 (B3LYP) and 23.58 kJ/mol (MP2), respectively, relative to the energy of ap, whereas the corresponding relative energies are 13.07 (B3LYP) and 15.32 kJ/mol (MP2) for the second (119.2°) maximum. B3LYP calculations are much less costly than MP2 or CCSD calculations and this method was therefore used to calculate several additional molecular parameters such as the harmonic and anharmonic fundamental normal vibrational frequencies, quartic and sextic Watson S-reduction centrifugal distortion constants,24 and the vibration rotation α constants25 for ap and sc.
The vibrational frequencies are found in Tables 1S (ap) and 3S (sc) of the Supporting Information, while the vibration rotation constants are listed in Tables 2S (ap) and 4S (sc). The B3LYP Sreduction24 quartic centrifugal distortion constants are shown in Table 3 (ap), while quartic and sextic constants of sc are listed in Table 4. Calculations of the structures of ap and sc, their dipole moment components, and 14N nuclear quadrupole coupling constants were repeated at the CCSD(full)/cc-pVTZ and MP2(full)/ cc-pVTZ levels of theory using the B3LYP geometries as starting points. The harmonic vibrational frequencies for these two conformers were calculated only at the MP2(full) level of theory because similar CCSD(full) calculations are too costly. The structures of the two conformers are shown in Table 1, whereas the rotational constants, dipole moments, nuclear quadrupole coupling constants, and electronic energy differences are listed in Table 2. The CCSD(full) rotational constants are repeated in Tables 3 and 4 for convenient comparison with the experimental counterparts. The planar moments, Pcc, defined by Pcc = 1/2(Ia + Ib Ic) where Ia, Ib, and Ic, the principal moments of inertia, have been calculated from the rotational constants. These moments, which are sensitive to nonplanarity, are shown in Table 2. The dipole moment components of these two forms were transformed from the standard orientation of Gaussian09 to the principal inertial axis system using Bailey’s program axis.26 The force field obtained in these MP2(full) calculations allowed the calculation of the zero-point harmonic vibration energies. 1017
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The Journal of Physical Chemistry A Table 3. Spectroscopic Constantsa
c
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of the Antiperiplanar Conformer of FCH2CH2CN exptl
vib state
theor ν21 = 2
ν21 = 1
ground
ν13 = 1
equilibrium
A (MHz)
27009(11)
25941(10)
24964(18)
28076(19)
27815.6
B (MHz)
2292.0710(76)
2292.7496(43)
2293.7311(74)
2298.5657(69)
2305.5
2170.9069(76)
2175.6449(49)
2180.5390(86)
2173.8208(85)
2186.8
3.2028(44)
3.8089(38)
4.404(8)
2.692(6)
3.14
0.4600(25)
0.4684(22)
0.4671(33)
0.4541(31)
0.393
C (MHz) Pccd (10
20
u m2)
DJ (kHz) DJKe (kHz)
18.167(8)
17.432(9)
αA (MHz)
16.546(16)
18.537(13)
1068 [1178]f
αB (MHz) αC (MHz)
2.98
1067 [1079]f
0.68 [ 0.94]f 4.74 [ 4.11]f
6.49[ 5.45]f 2.91[ 2.02]f
rmsg
1.653
1.468
1.702
1.453
no. transh
157
158
89
88
a The experimental constants are Watson’s S reduction, Ir representation.24 The theoretical rotational constants are calculated from the CCSD structure, whereas the theoretical centrifugal distortion constants and vibration rotation constants were obtained in the B3LYP calculations. b Uncertainties represent one standard deviation. c See spectra in Tables 5S (ground state), 6S (ν21 = 1), 7S (ν21 = 2), and 8S (ν13 = 1) (Supporting Information). d Defined by Pcc = 1/2(Ia + Ib Ic) where Ia, Ib, and Ic are the principal moments of inertia. Conversion factor: 505379.05 10 20 MHz u m2. e Further quartic centrifugal distortion constants fixed in the least-squares fit at the B3LYP values DK = 307, d1 = 0.0388, and d2 = 0.00301 kHz; see text. f B3LYP values in parentheses; see text. g Root-mean-square deviation of a weighted least-squares fit. h Number of transitions used in the fit.
Table 4. Spectroscopic Constantsa
c
of the Synclinal Conformer of FCH2CH2CN exptl ν21 = 2
ν20 = 1
equilibrium
11729.819(15) 3176.1124(42)
11827.46(11) 3173.531(10)
11629.763(18) 3183.4204(75)
11721.2 3223.9
2705.7206(11)
2702.3524(43)
2698.7627(97)
2709.2852(72)
2738.2
3.90873(88)
3.861(13)
3.758(29)
4.069(29)
3.51
vib state
ground
A (MHz) B (MHz)
11635.6040(46) 3178.2835(12)
C (MHz) DJ (kHz) DJK (kHz) DK (kHz)
theor
29.6286(82) 111.260(11)
ν21 = 1
30.252(37)
30.10(18)
113.85(76)
120(10)
29.77(13) 114.4(19)
d1 (kHz)
1.17322(54)
1.1713(11)
1.2293(43)
1.1944(23)
d2 (kHz)
0.07975(15)
0.08455(56)
0.0848(15)
0.08155(94)
HJ (Hz) HJK (Hz) HKJ (Hz)
0.01222(19) 0.0101d
24.2 98.9 1.03 0.0839 0.00649 0.0101
1.220(14)
0.815
HK (Hz)
5.196(35)
h1 (Hz)
0.00718(23)
0.00342
h2 (Hz)
0.000623d
0.000623
h3 (Hz)
0.000110d
αA (MHz)
3.49
0.000110 94.22 [ 95.36]e
αB (MHz) αC (MHz)
5.50 [ 4.99]e
2.17 [3.24]e 3.37 [3.87]e
5.10[ 1.59]e 3.57[ 1.58]e
rmsf
1.604
1.907
2.151
1.682
no. transg
354
114
34
59
a
The experimental constants are Watson’s S reduction, Ir representation.24 The theoretical rotational constants are calculated from the CCSD structure, whereas the theoretical centrifugal distortion constants and vibration rotation constants were obtained in the B3LYP calculations. b Uncertainties represent one standard deviation. c See spectra in Tables 9S (ground state), 10S (ν21 = 1), 11S (ν21 =2), and 12S (ν20 = 1) of the Supporting Information. d Fixed in the least-squares fit; see text. e B3LYP values in parentheses; see text. f Root-mean-square deviation of a weighted least-squares fit. g Number of transitions used in the fit.
The energy difference between ap and sc corrected for this effect is 2.14 kJ/mol, nearly the same as obtained for the electronic energy difference (2.01 kJ/mol; Table 2). The results of these calculations warrant further comments. Inspection of Table 1 reveals that there are only small differences
in the CCSD(full) and MP2(full) structures of the ap and sc conformers. Interestingly, both methods predicts that the F3 C2 C1 C6 dihedral angle is practically 65° in sc, almost the same as in the corresponding isonitrile, FCH2CH2NC, which has a F C C N dihedral angle of 67° in its synclinal conformer.7 1018
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The Journal of Physical Chemistry A The present increase of the F3 C2 C1 C6 dihedral angle of sc from the canonical 60 to 65° may indicate that repulsive forces are of importance in this rotamer. The increase of the C2 C1 C6 angle by 1.5° in the sc form compared to the ap conformer (Table 1) is pointing in the same direction. Interestingly, the F C C F dihedral angle in the synclinal conformation of the gauche-effect prototype, namely, 1,2-difluoroethane, is 71.0(3)°,27 11° larger than the ideal value. A significant difference between the CCSD(full) and MP2(full) predictions is seen for the C6tN7 bond length, which is calculated to be 1.5 pm longer in the MP2(full) calculations. The equilibrium bond length of the CtN bond in CH3CN is 115.6(2) pm,28 which is somewhat closer to the CCSD(full) values (115.2 and 115.1 pm; Table 1) than to the MP2 values (116.6 pm; Table 1). The calculation of the C F bond length is critical in quantum chemistry. The equilibrium C F bond length is for example 138.3(1) pm in CH3F,29 values in the 137.2 137.7 pm range are found in the present calculations; see Table 1. These theoretical values are close to the experimental counterpart, which is reassuring. There is not much difference in the theoretical rotational constants of the two calculations (Table 2), which is a consequence of the similarity of the CCSD(full) and MP2(full) structures. This is also the case for the dipole moments and 14N nuclear quadrupole coupling constants. The energy difference between the two forms is predicted to be small, 2.23 kJ/mol in the CCSD(full) and 2.01 kJ/mol in the MP2(full) calculations (Table 1). These energy differences are similar to the results obtained in much lower-level DFT calculations,4 where the B3LYP/6-311+G(d,p) and M05-2X/6-311+G(d,p) calculations both predict 2.7 kJ/mol for this energy difference with sc as the high-energy form. Microwave Spectrum and Assignment of the Spectrum of ap. The small theoretical energy difference between sc and ap indicated that both of these forms should be present in the gas in considerable quantities. ap has its major dipole moment component along the a axis, whereas sc has a predominating μb. The perpendicular b-type spectra of prolate asymmetrical tops, such as sc, are rich with absorption lines occurring throughout the investigated spectral region, whereas a-type lines of highly prolate rotors such as ap are primarily found in pile-ups consisting of aRlines separated approximately by the sum of the B + C rotational constants. Survey spectra revealed a rich MW spectrum with absorption lines occurring every few MHz throughout the investigated spectral range, which was taken as an early indication that both ap and sc were present in significant concentrations. The theoretical predictions above indicate that ap would presumably be the preferred form of 3-fluoropropionitrile, and searches were therefore first made for the spectrum of this conformer. ap is predicted to have Ray’s asymmetry parameter30 k ≈ 0.99 and a major μa of 6 7 10 30 C m (Table 2). The a-type R-branch spectrum of this conformer was therefore predicted to be comparatively strong with characteristic pile-ups separated by B + C ≈ 4.4 GHz. The members of these regions should involve transitions of K 1-pairs with K 1 g 3. These high-K 1 transitions would have rapid Stark effect caused by the near-degeneracy of the K 1-pairs. This pile-up feature was readily recognized in the survey spectra taken at a Stark field strength of roughly 110 V/cm, where K 1 > 3 transitions are fully modulated. An example of a portion involving mainly the ground-state lines of one of these pile-ups involving J = 20 r 19 is shown in Figure 3. RFMWDR
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Figure 3. Microwave spectrum of a portion of the J = 20 r 19 pile-up region of ap taken at a Stark field strength of about 110 V/cm. Most of the absorption lines shown here belong to the ground vibrational state. The numbers above the peaks indicate the values of the K 1 pseudoquantum numbers.
experiments were performed next and unambiguous assignments of several of the K 1-pairs were achieved in this manner. The spectrum was fitted to Watson’s S-reduction Hamiltonian,24 which was chosen because ap is nearly a symmetrical rotor. Sørensen’s program Rotfit31 was used to least-squares fit the transitions. An accurate value of the DJK centrifugal distortion constant24 is generally very useful in order to facilitate the assignments of high-K 1 pairs of the pile-ups. Unfortunately, the B3LYP value of this constant shown in Table 3 was too inaccurate to be helpful in the present case, and the assignments were obtained employing a trial and error procedure. The failure to predict DJK accurately may be due to a comparatively inaccurate B3LYP force field. The said assignments were gradually extended to include additional aR-transitions. The fact that the planar moment Pcc should be approximately 3.20 10 20 u m2 for ac (Table 2) was a useful aid in the assignment process of the low-K 1 R-branch lines, which are much more sensitive to the value of the A rotational constant than the high-K 1 aR-lines are. None of the assigned aR-transitions displayed a resolved quadrupole structure caused by the 14N nucleus. Calculations performed by the MB09 program32 of the quadrupole hyperfine structure of these transitions using the quadrupole coupling constants shown in Table 2 revealed that the splittings of strong quadrupole components would be less than resolution (0.5 MHz) of our spectrometer. b-type lines were also searched for but not assigned presumably because they are too weak, which is not surprising given the small μb component (∼0.50 10 30 C m; Table 2). A total of 157 aR-transitions, which are listed in Table 5S in the Supporting Information, were ultimately used to determine the spectroscopic constants shown in Table 3. The inverse squares of the uncertainties listed in Table 5S of the Supporting Information were used as weights in the least-squares fit. It was not possible to get accurate values for all the spectroscopic constants from the selection of aR-branch lines assigned here, and DK, d1, and d2 were preset to the B3LYP values in the least-squares fit. Inclusion of sextic constants was also attempted, but no significant improvement of the fit was achieved in this manner. No such constants were therefore retained in the final fit. 1019
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The Journal of Physical Chemistry A It is seen from Table 3 that the experimental B and C rotational constants are very close (better than 1% agreement) to the CCSD(full) counterparts. There is also a satisfactory agreement for the A rotational constant. There is good agreement between the experimental and B3LYP centrifugal distortion constant DJ, while a larger discrepancy exists for DJK, for reasons mentioned above. Moreover, it is noted (Table 3) that the planar moment Pcc = 3.2028(44) 10 20 u m2. This value is characteristic for a compound having a symmetry plane and two pairs of sp3-hybridized out-of-plane hydrogen atoms, and it is close to the value of 3.14 10 20 u m2 obtained in the theoretical calculations (Table 2). An effective value larger than the approximate equilibrium value of 3.14 10 20 u m2 has to be expected due to out-of-plane vibrations.33 Vibrationally Excited State of ap. The lowest fundamental vibration (ν21) has a harmonic frequency of 104 cm 1 according to the B3LYP results (Table 1S of the Supporting Information). This mode is the torsion about the C1 C2 bond. A total of 158 transitions were assigned for the spectrum of the first excited state of this mode in the same manner as described above for the ground vibrational state spectrum. The spectrum of this excited state is listed in Table 6S in the Supporting Information, while the spectroscopic constants are displayed in Table 3. The vibration rotation α-constants of this vibrational mode were calculated25 from αX = X0 X1, where X0 and X1 are the rotational constants of the ground and of the first vibrationally excited state of a fundamental vibration, respectively, with the results shown in Table 3 (in parentheses). It is seen that the agreement between the experimental and theoretical α values are in quite good agreement. The increase of the value of Pcc from 3.2028(44) of the ground vibrational state to 3.8089(38) 10 20 u m2 for the first excited state of ν21, (Table 3) is typical for an out-of-symmetry plane vibration such as torsion33 about the C1 C2 bond. Relative intensity measurements performed largely as described by Esbitt and Wilson34 yielded 114(20) cm 1, compared to the B3LYP harmonic and anharmonic frequencies of 104 and 109 cm 1, respectively (Table 1S, Supporting Information). Eighty-nine transitions of the second excited state of ν21 were also assigned. This spectrum is shown in Table 7S of the Supporting Information, and the spectroscopic constants are listed in Table 3. It is seen from this table that the changes of the rotational constants of this mode upon excitation is quite regular, which is typical for an essentially harmonic vibration.35,36 Finally, 88 transitions belonging to the spectrum of the first excited state of the lowest bending vibration (ν13) were assigned, as shown in Table 8S of the Supporting Information. The spectroscopic constants of this excited state are listed in Table 3. The value of Pcc is lower for this excited state than for the ground state (Table 3), which is in accord with theory for excited states of bending vibrations.33,35,36 Relative intensity measurement yielded 152(25) cm 1 for the ν13 vibration, close to the B3LYP value of 166 cm 1 (Table 1S, Supporting Information). Assignment of the Spectrum of sc. This rotamer has a comparatively large μb ≈ 13 and a significant μa ≈ 9.4 10 30 C m, respectively, according to the theoretical calculations (Table 2). The theoretical spectroscopic constants shown in Table 3 were first used to predict the frequencies of strong bQ-lines, which were found close to the values predicted for them. This was also the case for the aR-branch transitions, which were initially assigned using the RFMWDR-method. bR-branch lines were assigned next. The assignments were now gradually extended to include
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transitions with higher and higher values of the J quantum number. Searches for c-type lines were made, but none were found presumably because μc is small (Table 2) producing insufficient intensities for these lines. Ultimately, a total of 354 a- and b-type lines with J up to 66 and K 1 up to 23 were assigned. These transitions were used to determine the S-reduction spectroscopic constants listed in Table 4 from the spectrum shown in Table 9S in the Supporting Information. No fully resolved 14N quadrupole hyperfine structures were observed for these transitions in accord with calculations using the quadrupole constants listed in Table 2. The transitions with high J and high K 1 generally have large centrifugal distortion contributions of several GHz (Table 9S, Supporting Information). It was therefore possible to get accurate values not just for the five quartic but even for four (HJ, HKJ, HK, and h1) of the seven sextic centrifugal distortion constants. The three remaining sextic constants (HJK, h2, and h3) were preset at the B3LYP results. The results of this least-squares fit are listed in Table 4. The CCSD(full) and experimental rotational constants agree to within better than about 1.2%; see Table 4. Comparison of the experimental centrifugal distortion constants with the B3LYP counterparts (Table 4) reveals a better than 20% agreement in the case of the quartic constants, while the sextic constants are seen to have an order-of-magnitude agreement. Vibrationally Excited States of sc. The spectra of three vibrationally excited states belonging to the first excited state of the torsion about the C1 C2 bond (ν21) and the first excited state of the lowest bending vibration (ν20) were assigned in the same manner as described for the ground-state spectrum. A total of 114 transitions were assigned for the spectrum of the first excited state of the torsion, 34 transitions were assigned for the second state of this motion, while 59 transitions were assigned for the spectrum of the first excited state of the lowest bending vibration. The corresponding spectra are shown in Tables 10S 12S of the Supporting Information, while the spectroscopic constants are listed in Table 4. Only quartic centrifugal distortion constants were employed in the least-squares fitting procedure of these three excited states. The B3LYP calculations predict harmonic frequencies of 108 and 206 cm 1 for these two fundamentals (Table 3S, Supporting Information). Relative intensity measurements yielded 115(25) cm 1 for the torsion and 188(25) cm 1 for the bending vibration. The experimental vibration rotation constants are listed in Table 4 (in parentheses) and compared to the B3LYP values (Tables 4 and 4S, Supporting Information). There is a satisfactory agreement in the case of the lowest torsional vibration, whereas somewhat larger deviations are seen for the lowest bending vibration. Experimental information from vibrationally excited states has been used in the past to derive potential energy functions similar to those shown in Figure 2.37 However, the present experimental results refer only to the lower parts of the minima region of the potential functions because only the MW spectra of the ground and the two first torsional states have been assigned. The vibrational frequencies of the torsions are also rather inaccurate, typically (25 cm 1. A potential function derived from this information will be quite uncertain and presumably far inferior to the two potential functions shown in Figure 2, which were obtained in the high-level B3LYP and MP2 calculations. Structures. The three experimental rotational constants obtained for each rotamer ap and sc furnish insufficient information for a complete determination of their experimental geometrical 1020
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The Journal of Physical Chemistry A structures. The effective experimental rotation constants are associated with the r0-structure, whereas the CCSD(full) and MP2 (full) rotational constants are derived from approximate equilibrium structures. A direct comparison of the experimental and theoretical sets of constants is therefore not warranted, but the two structures are in general similar. The good agreement between the experimental and theoretical rotational constants is therefore taken as an indication that the theoretical structures of Table 1 are indeed close to the equilibrium structures of ap and sc. There is not much difference between the CCSD(full) and MP2(full) structures, as remarked above. However, the CCSD(full) structures are calculated at a higher level of theory than MP2(full), and the former structure is therefore our favorite. It is assumed that the bond lengths of the CCSD(full) structure hardly deviate by more than 0.5 pm from the equilibrium values. The bond angles are presumed to vary by less than 0.5° from the equilibrium values. Larger values probably apply for dihedral angles, especially for sc. The important F3 C2 C1 C6 dihedral angle is assumed to be 65(2)° in sc. Energy Difference. The energy difference between the ground vibrational states of the sc and ap rotamers were obtained by comparing the intensities of selected rotational lines observing the precautions of Esbitt and Wilson.34 The energy differences were calculated as described by Townes and Schawlow.38 ap was assigned a statistical weight of 1 due to its symmetry plane, while sc was assumed to have a statistical weight of 2 because of the existence of two mirror forms. The CCSD(full) dipole moments were employed. ap was found to be 1.4(5) kJ/mol more stable than sc in the present relative intensity measurements. This energy difference is lower than the CCSD(full) and MP2(full) results above (2.2 and 2.0 kJ/mol, respectively) and the previous DFT calculations4 (2.7 kJ/mol).
’ DISCUSSION The fact that ap is preferred by 1.4(5) kJ/mol over sc must be a compromise of several intramolecular forces, whose sizes are difficult to estimate quantitatively. Repulsive interactions destabilizing sc seems to be prominent in FCH2CH2CN. One of these repulsions is the weak steric repulsion between the F3 and C6 atoms, which are separated by 290 pm in this rotamer according to the CCSD(full) calculations, compared to 305 pm, which is the sum of the Pauling van der Waals radii of fluorine (135 pm)39 and the half-thickness of an aromatic molecule (170 pm).39Another factor that would greatly favor ap over sc is dipole dipole repulsion, which must be important in sc because of the negative end of the very polar C F bond and the nitrile groups come quite close in this rotamer. Yet another force, namely, electrostatic repulsion between the fluorine atom and the π-orbitals of the triple bond, may destabilize sc. The fact that ap is preferred by only 1.4(5) kJ/mol relative to sc in spite of all this repulsion is a clear indication that the gauche effect plays a significant role in 3-fluoropropionitrile, but what are the main causes of this effect? Theoretical arguments have been4 given that hyperconjugation is the major effect stabilizing the sc rotamer. This interaction is suggested4 to occur between the bonding σ-orbital of the C1 H bond and the antibonding σ-orbital of the C2 F3, when these bonds are antiperiplanar to one another. Hyperconjugation may also occur between the σ-orbital of the C1 H and the antibonding σ-orbital of the C1 C6 bond in a similar way. Hyperconjugation should
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therefore outweigh much of the repulsive interactions leaving ap only 1.4(5) kJ/mol more stable than sc. The sc form of the corresponding isocyanide, FCH2CH2NC, was preferred by a marginal 0.7(5) kJ/mol compared to its ap rotamer,7 whereas the opposite stabilities (1.4(5) kJ/mol preference of ap) were observed in the present nitrile case of FCH2CH2CN. The reasons for this difference are not obvious. However, the electrostatic repulsive interactions are presumably less in the isocyanide because the bond moment of the isocyanide group is significantly less than the bond moment of the nitrile group.6 Moreover, the antibonding σ-orbital of the bond between the carbon atom and nitrogen atom of the isocyanide group, C NC, in FCH2CH2NC seems to be more favorable for hyperconjugation than the C CN bond of FCH2CH2CN because of the significant electronegativity difference between the carbon and nitrogen atoms. These variations between the nitrile and isocyanide may perhaps explain at least part of the conformational energy differences seen for FCH2CH2NC and FCH2CH2CN.
’ ASSOCIATED CONTENT
bS
Supporting Information. Results of the theoretical calculations and the microwave spectra. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: +47 2285 5674. Fax: +47 2285 5441. E-mail: harald.mollendal@ kjemi.uio.no.
’ ACKNOWLEDGMENT We thank Anne Horn for her skillful assistance. The Research Council of Norway (Program for Supercomputing) is thanked for a grant of computer time. J.-C.G. thanks the PCMI program (INSU-CNRS) for financial support. ’ REFERENCES (1) Wolfe, S. Acc. Chem. Res. 1972, 5, 102. (2) Fernholt, L.; Kveseth, K. Acta Chem. Scand., Ser. A 1980, A34, 163. (3) Friesen, D.; Hedberg, K. J. Am. Chem. Soc. 1980, 102, 3987. (4) Buissonneaud, D. Y.; van Mourik, T.; O’Hagan, D. Tetrahedron 2010, 66, 2196. (5) Allred, A. L. J. Inorg. Nucl. Chem. 1961, 17, 215. (6) Smyth, C. P. Dielectric Behavior and Structure; McGraw-Hill: New York, 1955. (7) Samdal, S.; Møllendal, H.; Guillemin, J.-C. J. Phys. Chem. A 2011, 115, 9192. (8) El Bermani, M. F.; Jonathan, N. J. Chem. Soc., A 1968, 1711. (9) Pattison, F. L. M.; Cott, W. J.; Howell, W. C.; White, R. W. J. Am. Chem. Soc. 1956, 78, 3484. (10) Bumgardner, C. L.; Lawton, E. L. J. Org. Chem. 1972, 37, 410. (11) Doyle, M. P.; Whitefleet, J. L.; Bosch, R. J. J. Org. Chem. 1979, 44, 2923. (12) Lattelais, M.; Ellinger, Y.; Matrane, A.; Guillemin, J. C. Phys. Chem. Chem. Phys. 2010, 12, 4165. (13) Møllendal, H.; Leonov, A.; de Meijere, A. J. Phys. Chem. A 2005, 109, 6344. (14) Møllendal, H.; Cole, G. C.; Guillemin, J.-C. J. Phys. Chem. A 2006, 110, 921. 1021
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