Infrared and Raman spectra, conformational stability, ab initio calculations and vibrational assignment of 2-fluorobutane

Article abstract of DOI:10.1016/S1386-1425(03)00308-1

The infrared spectra (3500-50 cm^-1) of gas and solid and the Raman spectrum (3500-50 cm^-1) of liquid 2-fluorobutane, CH ₃CHFCH₂CH₃, have been recorded. Variable temperature studies over the range -105

Full text of DOI:10.1016/S1386-1425(03)00308-1

Spectrochimica Acta Part A 60 (2004) 829–841
Infrared and Raman spectra, conformational stability, ab initio
calculations and vibrational assignment of 2-fluorobutane
a,∗
a
b
James R. Durig , Xiaodong Zhu , Gamil A. Guirgis
a
Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA
Department of Chemistry & Biochemistry, College of Charleston, Charleston, SC 29403, USA
b
Received 27 May 2003; accepted 25 June 2003
Abstract
The infrared spectra (3500–50 cm ) of gas and solid and the Raman spectrum (3500–50 cm ) of liquid 2-fluorobutane, CH
have been recorded. Variable temperature studies over the range −105 to −150 C of the infrared spectra (3500–400 cm ) of the sample
dissolved in liquid krypton have also been recorded. By utilizing the relative intensities of six conformer pairs each for both Me-trans/F-trans
and Me-trans/H-trans, the Me-trans conformer is found to be the lowest energy form with an enthalpy difference to the F-trans conformer of
−1
−1
3
2 3
CHFCH CH ,
◦
−1
−
1
−1
−1
1
(
3
02± 10 cm (1.21± 0.12 kJ mol ) whereas the H-trans conformer is the highest energy form with an enthalpy difference of 208± 21 cm
−1
2.49 ± 0.25 kJ mol ) higher than the Me-trans form. At ambient temperature, it is estimated that there is 50 ± 2% of the Me-trans form,
1± 1% of the F-trans form, and 19± 1% of the H-trans conformer present. Equilibrium geometries and total energies of the three conformers
have been determined by ab initio calculations with full electron correlation by the perturbation method to second order using a number of basis
sets. A complete vibrational assignment is proposed for the Me-trans conformer and many of the fundamentals have been identified for the
other two forms based on the force constants, relative infrared and Raman intensities, and depolarization ratios obtained from MP2/6-31G(d)
ab initio calculations. The spectroscopic and theoretical results are compared to the corresponding properties for some similar molecules.
©
2003 Elsevier B.V. All rights reserved.
Keywords: Conformational stabilities; FT-IR and Raman spectra; Ab initio calculations; Krypton solutions; 2-Fluorobutane
1
. Introduction
form whereas the H-trans conformer with the hydrogen
atom trans to the methyl group has the highest energy
for several molecules. The electron diffraction studies for
2-chlorobutane [4] and 2-bromobutane [4] show that the
Me-trans form is the lowest energy form for both molecules.
Similar conformational stability results have been obtained
for 2-methylbutyronitrile, CH3CH2CH2CH(CH3)CN, and
3-methyl-1-pentyne, HC≡CCH(CH3)CH2CH3, and are
The conformational stabilities, structural parame-
ters, and vibrational spectra of the propyl derivatives
CH3CH2CHXY; X = H, CH3; Y = H, F, Cl, Br, I, CN,
C≡CH, except propane) have been studied extensively
1–8]. For the 1-halopropanes [1,2], the experimental re-
(
[
sults indicate that the gauche conformer is the more stable
form irrespective of the halogen substituents. The values of
found to be in agreement with the molecular mechan-
ics MM2 predictions [6]. However, the ab initio calcu-
lations with smaller basis sets may predict the wrong
conformational stability. For example, the MP2/6-31G(d)
and MP2/6-311G(d) calculations for 1-chloropropane and
1-bromopropane predicted the trans conformer as the more
stable form which are not consistent with the experimental
results [2].
−
1
the enthalpy difference are 99, 52, and 72 cm for fluoride
1], chloride [2], and bromide [2], respectively, which are
consistent with the ab initio predictions with the basis set
[
(
MP2/6-311+G(2d, 2p)). For X = CH3, the compounds
are 2-substitued butanes and three stable conformers are
expected to be present in the fluid phases. It has been previ-
ously shown [4–6] that the Me-trans conformer where two
methyl groups are trans to each other, is the lowest energy
We recently investigated the conformational stability of
4
-fluoro-1-pentyne (HC≡CCH2CHFCH3) [9] which exists
∗
in three stable conformers in the fluid states and the F-trans
form was found lowest in energy. The determination of the
second most stable conformer was a major challenge since
Corresponding author. Tel.: +1-816-235-6038;
fax: +1-816-235-2290.
E-mail address: durigj@umkc.edu (J.R. Durig).
1
386-1425/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S1386-1425(03)00308-1

8
30
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
calculations utilizing the full electron correlation method at
the MP2 level predicted the H-trans conformer the next sta-
ble conformer. However, hybrid density functional theory
(DFT) calculations using the B3LYP method predicted the
Me-trans form more stable with several basis sets and the
least stable form to be the H-trans conformer. Therefore, a
temperature dependent infrared study is essential in deter-
mining the conformational stabilities. In particular, since the
stability of the second conformer has been predicted poorly
from theoretical calculations for many three-conformer
molecules, an experimental investigation is necessary to
eliminate the confusion from theoretical calculations.
In the previous study of 2-fluorobutane [5], the vibrational
assignment was not complete, and the experimental enthalpy
differences among the three conformers was not determined
and neither the Raman nor the far infrared spectra were re-
ported. Therefore, temperature dependent infrared spectra of
the sample dissolved in liquid krypton have been recorded
in this study in order to obtain a reliable value of the en-
thalpy differences among the three possible conformers. The
infrared spectra of 2-fluorobutane in the gaseous and solid
phases and the Raman spectrum of the liquid have been
recorded for the purpose of providing a complete vibrational
assignment for the most stable conformer. In order to facili-
tate the vibrational assignment, ab initio calculations utiliz-
ing the perturbation method to the second order (MP2) and
hybrid DFT calculations by the B3LYP method have been
carried out with various basis sets. The results of these vi-
brational spectroscopic and theoretical studies are reported
herein.
Fig. 1. Mid-infrared spectra of 2-fluorobutane in: (A) gas; and (B) poly-
crystalline solid.
purity was checked by comparing the mid-infrared spectrum
of the gas with the previously reported spectrum [5].
The mid-infrared spectra of the gas and solid (Fig. 1)
were obtained using a Perkin–Elmer model 2000 Fourier
transform spectrophotometer equipped with a nichrome wire
source, a Ge/CsI beam splitter, and a DTGS detector. The
spectrum of the gas was obtained with the sample contained
in 10 cm cell fitted with CsI windows. The spectrum of the
solid was obtained by condensing the sample on a CsI sub-
strate held at ∼77 K by boiling liquid nitrogen, housed in a
vacuum cell fitted with CsI windows. The sample was re-
peatedly annealed until no further changes were observed in
the spectrum. The theoretical resolution used to obtain the
2
. Experimental
All chemicals used in the preparations were pur-
chased from Aldrich Chem. Co., Milwaukee, WI. The
-fluorobutane sample was prepared by the previously re-
2
ported method with modification [10]. The 2-butyltosylate
was prepared by adding pyridine dropwise to 2-butanol
and p-toluenesulfonyl chloride mixture in an ice bath. The
reaction was allowed to proceed for 2 h and quenched
by pouring the mixture into ice-cold water. The tosylate
was extracted by ethyl ether and washed sequentially with
cold water, diluted potassium hydroxide, and cold water.
The ethyl ether was removed by vacuum evaporation. The
−1
spectra of both the gas and the solid was 1.0 cm
.
The far infrared spectra of the gas and solid (Fig. 2) were
recorded on the previously described Perkin–Elmer 2000
spectrometer. A grid beam splitter and a cryostat cell fitted
with polyethylene windows was used to record the spectrum
of the solid with the sample being deposited on a silicon sub-
strate at 77 K and multiple annealings were performed in or-
der to obtain a good polycrystalline solid. For the spectrum
of the gas, the sample was contained in a 10 cm cell equipped
with polyethylene windows. The spectra were recorded at a
2
-fluorobutane sample was obtained by using potassium flu-
oride to fluoronate the 2-butyltosylate. The 2-butyltosylate
sample was mixed with 2-methoxyethyl ether and potas-
sium fluoride while the system pressure was reduced to
−
1
spectral resolution of 1.0 cm . Typically, 128 scans were
used for both the sample and reference data to give a satisfac-
tory signal-to-noise ratio. The interferograms were averaged
and then transformed with a boxcar truncation function.
The mid-infrared spectra of the sample dissolved in
liquefied krypton (Fig. 3A) as a function of temperature
were recorded on a Bruker model IFS-66 Fourier transform
spectrometer equipped with a globar source, a Ge/KBr
1
3.3 Pa with continual stirring. The temperature was then
◦
raised to 70 C and the reaction was initiated and lasted
3
h. The sample of 2-fluorobutane was removed from the
system every 5–10 min by using a liquid nitrogen trap.
Further purification of the sample was performed using a
low-temperature, low-pressure fractionating column. The
sample was stored under vacuum at low temperature and the

J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
831
Fig. 2. Far-infrared spectra of 2-fluorobutane in: (A) gas; and (B) poly-
crystalline solid.
beamsplitter, and a DTGS detector. The temperature studies
Fig. 4. Raman spectra of 2-fluorobutane in: (A) liquid; (B) simulated
◦
ranged from −105 to −150 C and were performed in a spe-
infrared spectrum of the three conformer mixture with the ꢀH of 102
cially designed cryostat cell consisting of a 4 cm path length
copper cell with wedged silicon windows sealed to the cell
with indium gaskets. For each temperature investigated, 100
−1
and 208 cm for Me-trans/F-trans and Me-trans/H-trans conformer pairs
◦
at 25 C; (C) calculated spectrum of the pure H-trans conformer; (D)
calculated spectrum of the pure F-trans conformer; and (E) calculated
spectrum of the pure Me-trans conformer.
−
1
interferograms were recorded at a 1.0 cm resolution, av-
eraged, and transformed with a boxcar truncation function.
The Raman spectrum (Fig. 4A) of the liquid was recorded
on a SPEX model 1403 spectrophotometer equipped with
a Spectra-Physics model 164 argon ion laser operating on
the 514.5 nm line. The laser power used was 0.5 W with
−
1
a spectral bandpass of 3 cm . The spectra of the liquid
and solid were recorded with the sample sealed in a Pyrex
glass capillary. The wave numbers for all of the observed
fundamental bands by the different techniques in the various
physical states are listed in Tables 1–3 for Me-trans, F-trans,
and H-trans conformers, respectively.
3. Ab initio calculation
The LCAO-MO-SCF ab initio calculations were per-
formed with the Gaussian-98 program [11] using Gaussian
type basis functions. The energy minima with respect to
the nuclear coordinates were obtained by the simultane-
ous relaxation of all of the geometric parameters using the
gradient method of Pulay [12]. Calculated energies were
determined at the MP2 level with full electron correlation
with various basis sets up to 6-311+G(2d, 2p) as well as
hybrid density functional theory calculations by B3LYP
method and the results are listed in Table 4 (B3LYP re-
sults not listed). The structural parameters for the three
stable conformers of 2-fluorobutane from RHF and MP2
calculations are listed in Table 4.
Fig. 3. Mid-infrared spectra of 2-fluorobutane in: (A) krypton solution at
◦
−
125 C; (B) simulated infrared spectrum of three conformer mixture with
−1
the ꢀH of 102 and 208 cm for Me-trans/F-trans and Me-trans/H-trans
conformer pairs, respectively; (C) calculated spectrum of the pure H-trans
conformer; (D) calculated spectrum of the pure F-trans conformer; and
To determine the degree of mixing of symmetry coor-
dinates and to obtain a more complete description of the
(E) calculated spectrum of the pure Me-trans conformer.

8
32
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
Table 1
Observed and calculated wave numbers (cm 1) for the Me-trans conformer of 2-fluorobutane
−
Vibration
nunber
Descriptiona
Ab
initio
Fixed
IR
Raman
Gas Krypton Solidf Raman PEDg
b
scaledc intensities activitiese
d
∗
ν1
ν2
ν3
ν4
ν5
ν6
ν7
ν8
CH3 antisymmetric 3220
stretch
3021
3015
3010
2998
2961
2922
2920
2912
17.4
17.3
17.7
28.0
15.6
11.4
23.9
28.6
36.1
60.2
52.5
56.9
47.6
117.8
92.3
21.6
2997
63S1, 34S4
CH3 antisymmetric
stretch
CH3 antisymmetric
3214
2993 2982
2984
2988 2983
2979 2982
2972
92S2
3208
92S3
stretch
∗
CH3 antisymmetric 3196
stretch
2975 2971
2940 2943
2918 2925
2918 2912
2893 2886
65S4, 32S1
94S5
CH2 antisymmetric
stretch
CH3 symmetric
3157
2941 2940
2919 2915
2915
3115
97S6
stretch
∗
CH3 antisymmetric 3113
stretch
96S7
CH2 symmetric
stretch
3104
2884 2888
64S8, 31S9
ν9
CH stretch
CH3 antisymmetric 1574
deformation
3100
2908
1494
13.8
7.5
106.0
11.4
2869 2862
1473 1468
2870 2877
1479
66S9, 32S9
75S10, 12S12
∗
ν10
ν11
ν12
ν13
CH3 antisymmetric
1564
1484
1483
1472
9.8
0.4
4.8
4.1
25.9
21.1
1465
1467
54S11, 23S12
65S12, 25S11
78S13, 11S14
deformation
∗
CH3 antisymmetric 1563
deformation
1456
1462 1458
1450 1449
CH3 antisymmetric
deformation
1551
1449 1445
ν14
ν15
ν16
ν17
CH2 deformation
CH bend (out-plane) 1477
1540
1462
1403
1395
1386
0.3
9.9
15.1
8.3
5.7
3.6
0.6
4.8
1441 1436
1390 1384
1384 1380
1373
1438
1389 1387
1383
81S14
18S15, 28S17, 15S19, 14S16
73S16, 19S17
38S17, 17S19, 28S19, 16S15
CH bend (in-plane)
1470
1460
∗
CH3 symmetric
1376 1375
deformation
CH3 symmetric
deformation
CH2 wag
CH2 twist
CH3 rock
ν18
1431
1361
13.2
6.8
1353 1350
1350 1345
66S18
ν19
ν20
ν21
ν22
ν23
ν24
ν25
ν26
ν27
ν28
ν29
ν30
ν31
1378
1339
1243
1200
1185
1094
1042
1015
955
859
800
503
470
1309
1272
1187
1144
1134
1039
989
963
905
816
761
2.0
0.9
6.1
19.5
15.8
14.7
14.4
8.0
23.3
4.2
1.2
2.8
3.3
3.2
8.9
1.8
4.0
6.0
2.4
5.6
0.3
5.3
7.1
2.5
2.0
0.4
1305 1303
1271 1268
1181 1174
1137 1132
1125 1120
1033 1032
987 991
968 967
904 899
823 823
770 765
493 493
457 457
1303 1304
1268 1271
1179 1175
1126 1129
1115 1120
1032 1031
39S19, 37S15
62S20, 17S26
19S21, 15S28, 12S29, 12S34, 11S26
30S22, 13S27, 13S31
224S23, 12S25, 10S29
53S24, 18S23, 13S27
17S25, 15S22, 12S19
11S26, 35S21, 17S25, 11S15
35S27, 31S22, 11S24
18S28, 17S21, 13S23, 13S26, 10S29
42S29, 19S26, 13S28, 12S27
19S30, 25S32, 17S34, 14S23
49S31, 14S32, 13S29
CH3 rock
C3C4 stretch
C1C2 stretch
∗
∗
CH3 rock
CH3 rock
995
968
890
823
764
496
459
983
971
898
824
765
494
458
CF stretch
C2C3 stretch
CH2 twist
C1C2C3 bend
CCF bend
491
459
(out-plane)
ν32
ν33
ν34
ν35
ν36
CCF bend (in-plane)
CH3 torsion
373
253
246
233
118
370
253
245
236
118
3.6
0.2
0.5
1.4
0.5
0.5
0.03
0.02
0.06
0.02
369
–
–
–
–
–
374
260
252
237
142
372
37S32, 27S34, 12S31
76S33, 12S35
25S34, 37S30, 15S33
62S35
C2C3C4 bend
255
243
108
∗
CH3 torsion
Asymmetric torsion
90S36
a
Asterisk indicates the C1 atom.
b
c
Calculated with the MP2/6-31G(d) basis set.
Scaled MP2/6-31G(d) calculations with factors of 0.88 were used for the CH stretches, 0.9 for the heavy atom stretches and CH bends, and 1.0 for
all other modes.
d
Calculated infrared intensities in kilometer per mole with the MP2/6-31G(d) basis set.
Calculated Raman activities in Å amu with the MP2/6-31G(d) basis set.
Observed solid frequencies are from the infrared spectrum.
e
f
4
−1
g
Calculated with the MP2/6-31G(d) basis set; contributions less than 10% are omitted.

J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
833
Table 2
Observed and calculated wave numbers (cm 1) for the F-trans conformer of 2-fluorobutane
−
Vibration
nunber
Descriptiona
Ab
initio
Fixed
IR
Raman
Gas
Krypton Raman PEDf
55S1, 38S4
b
scaledc intensities
d
activitiese
∗
ν1
CH3 antisymmetric stretch
3196
3211
3216
3205
3165
3116
3109
3113
3100
2998
3012
3017
3006
2969
2924
2916
2920
2908
1495
1491
1485
1473
1470
1403
1399
1361
1382
1304
1263
1187
1125
1161
1043
985
28.7
19.8
13.5
29.0
10.8
6.3
43.7
38.0
66.4
33.2
76.2
122.9
106.7
18.4
94.1
4.6
14.9
5.3
19.1
24.4
3.1
2.9
3.3
5.9
5.6
5.6
0.8
4.3
5.4
ν2
CH3 antisymmetric stretch
CH3 antisymmetric stretch
77S2, 17S3
73S3, 21S2
55S4, 30S1, 11S4
90S5
97S6
82S7, 14S7
81S8, 14S7
92S9
38S10, 38S11, 12S14
29S11, 31S14, 20S12
32S12, 35S10, 18S11
78S13
47S14, 35S12, 11S10
15S15, 40S17, 21S16
71S16
27S17, 32S18, 20S15
17S18, 25S15, 23S19
39S19, 36S18
60S20, 16S26
ν3
∗
ν4
CH3 antisymmetric stretch
2989
2952
ν5
CH2 antisymmetric stretch
CH3 symmetric stretch
ν6
∗
ν7
CH3 antisymmetric stretch
8.3
ν8
CH2 symmetric stretch
33.1
24.9
7.0
5.2
7.4
ν9
CH stretch
∗
ν10
ν11
ν12
ν13
ν14
ν15
ν16
ν17
ν18
ν19
ν20
ν21
ν22
ν23
ν24
ν25
ν26
ν27
ν28
CH3 antisymmetric deformation 1574
1478
1469
1463 1465
CH3 antisymmetric deformation
1571
∗
CH3 antisymmetric deformation 1565
CH3 antisymmetric deformation
CH2 deformation
1552
1550
1477
1475
1432
1455
1373
1329
1245
1176
1216
1098
1039
1004
958
4.9
0.2
CH bend (out-plane)
CH bend (in-plane)
20.2
10.9
6.9
12.7
2.3
∗
CH3 symmetric deformation
1344
1370
CH3 symmetric deformation
CH2 wag
CH2 twist
CH3 rock
CH3 rock
1.6
5.6
1264
1176
1112 1106
1151
19S21, 27S29, 21S26, 13S34
29S22, 24S27, 13S31, 12S25
23S23, 20S28, 13S15
58S24, 13S25, 11S27
13S25, 18S23, 18S27
40.9
5.2
10.2
19.5
5.2
1103
898
C3C4 stretch
C1C2 stretch
3.2
6.5
1.4
4.3
∗
∗
CH3 rock
CH3 rock
952
909
819
963
909
829
13S26, 40S21, 12S20, 11S15
28S27, 31S22, 13S25
CF stretch
C2C3 stretch
17.4
2.9
905
826
862
5.8
19S28, 16S23, 14S21, 11S25,
10S26
ν29
ν30
ν31
ν32
ν33
ν34
ν35
ν36
CH2 twist
C1C2C3 bend
CCF bend (out-plane)
CCF bend (in-plane)
CH3 torsion
812
439
497
397
273
259
226
107
771
432
482
394
272
257
226
107
3.5
3.0
5.1
4.2
0.6
1.4
0.2
1.8
0.9
1.5
0.5
0.05
0.1
0.01
0.04
780
436
490
782
439
47S29, 22S26, 13S23
22S30, 32S34, 19S32
51S31
59S32, 22S34
47S33, 27S35
13S34, 42S30, 25S31, 12S33
59S35, 32S33
90S36
433
488
398
287
C2C3C4 bend
∗
CH3 torsion
Asymmetric torsion
0.62
a
Asterisk indicates the C1 atom.
Calculated with the MP2/6-31G(d) basis set.
Scaled MP2/6-31G(d) calculations with factors of 0.88 were used for the CH stretches, 0.9 for the heavy atom stretches and CH bends, and 1.0 for
b
c
all other modes.
d
Calculated infrared intensities in kilometer per mole with the MP2/6-31G(d) basis set.
Calculated Raman activities in Å amu with the MP2/6-31G(d) basis set.
Calculated with the MP2/6-31G(d) basis set; contributions less than 10% are omitted.
e
f
4
−1
molecular motions involved in the fundamental vibrations
of 2-fluorobutane, a normal coordinate analysis has been
carried out. The internal coordinates defined in Table 4 and
shown in Fig. 5 were used to build the symmetry coordi-
nates listed in Table 5. The B-matrix elements were used
to convert the ab initio calculated force field from Carte-
sian coordinates into the force field in internal coordinates
[13]. These force constants were used in a mass-weighted
Cartesian coordinate calculation to reproduce the ab initio
predicted frequencies and to determine the potential energy
distributions (PED), which are given in Tables 1–3 for the
three conformers. The diagonal elements of the force field
in the internal coordinates were then modified with scaling
Fig. 5. Internal coordinates for 2-fluorobutane.

8
34
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
Table 3
Observed and calculated wave numbers (cm 1) for the H-trans conformer of 2-fluorobutane
−
Vibration
nunber
Descriptiona
Ab
initio
Fixed
IR
Raman
Gas
Krypton Raman PEDf
75S1, 16S4
b
scaledc intensities
d
activitiese
∗
ν1
CH3 antisymmetric stretch
3217
3224
3209
3202
3158
3121
3117
3101
3113
3018
3024
3010
3004
2962
2927
2924
2909
2921
1497
1493
1482
1473
1464
1406
1399
1366
1351
1359
1275
978
1148
1170
1125
998
988
900
790
766
589
368
17.1
16.2
16.8
27.5
14.4
4.2
22.2
8.4
50.4
2.9
7.6
9.7
2.0
1.6
21.2
13.4
3.0
16.1
1.8
0.2
1.2
26.9
4.2
11.7
8.6
30.2
20.4
3.1
0.7
2.0
1.6
5.9
1.6
0.1
0.6
0.9
36.3
41.6
52.7
52.6
74.1
237.1
6.8
51.1
57.9
4.6
17.4
7.0
18.9
20.1
3.3
2.6
1.1
4.3
1.7
14.5
4.9
4.0
1.7
1.9
3.5
4.7
6.1
7.6
1.8
0.3
0.1
0.6
0.2
0.1
0.04
0.1
ν2
CH3 antisymmetric stretch
CH3 antisymmetric stretch
78S2, 12S3
85S3,14S2
82S4, 13S1
96S5
59S6, 31S7
69S7, 26S7
59S8, 40S9
51S9, 33S8, 13S16
42S10, 27S12, 20S11
38S11, 43S10
50S12, 28S11, 10S14
64S13, 19S14
67S14, 21S13
21S15, 35S17, 18S16
57S16, 24S17
31S17, 27S15, 21S18
32S18, 17S19, 14S28, 10S15
42S19, 22S16, 16S18
60S20, 16S26
ν3
∗
ν4
CH3 antisymmetric stretch
ν5
CH2 antisymmetric stretch
CH3 symmetric stretch
ν6
∗
ν7
CH3 antisymmetric stretch
ν8
CH2 symmetric stretch
ν9
CH stretch
2897
∗
ν10
ν11
ν12
ν13
ν14
ν15
ν16
ν17
ν18
ν19
ν20
ν21
ν22
ν23
ν24
ν25
ν26
ν27
ν28
ν29
ν30
ν31
ν32
ν33
ν34
ν35
ν36
CH3 antisymmetric deformation 1578
CH3 antisymmetric deformation
1573
∗
CH3 antisymmetric deformation 1562
1463 1456
1392
CH3 antisymmetric deformation
CH2 deformation
1551
1542
1481
1474
1438
1419
1432
1343
1032
1205
1226
1177
1050
1042
948
831
806
607
370
421
257
294
221
CH bend (out-plane)
CH bend (in-plane)
∗
CH3 symmetric deformation
CH3 symmetric deformation
CH2 wag
CH2 twist
CH3 rock
CH3 rock
1348 1344
33S21, 40S24
1157
993
984
898
787
23S22, 17S27, 11S18
19S23, 15S29, 14S21, 13S26
16S24, 21S25, 11S21
35S25, 17S19, 11S22
16S26, 26S27, 23S23, 18S20
31S27, 27S22, 14S24, 10S25
29S28, 22S23, 10S29
45S29, 25S26, 10S28
22S30, 23S31, 16S34, 10S21
39S31, 31S34
C3C4 stretch
C1C2 stretch
∗
∗
CH3 rock
CH3 rock
995
985
894
794
CF stretch
C2C3 stretch
CH2 twist
C1C2C3 bend
CCF bend (out-plane)
CCF bend (in-plane)
CH3 torsion
898
795
591
420
588
418
417
255
292
221
422
73S32
43S33, 28S30
23S34, 23S30, 22S33, 21S35
55S35, 28S33
C2C3C4 bend
∗
CH3 torsion
Asymmetric torsion
108
108
88S36
a
Asterisk indicates the C1 atom.
b
c
Calculated with the MP2/6-31G(d) basis set.
Scaled MP2/6-31G(d) calculations with factors of 0.88 were used for the CH stretches, 0.9 for the heavy atom stretches and CH bends, and 1.0 for
all other modes.
d
Calculated infrared intensities in kilometer per mole with the MP2/6-31G(d) basis set.
Calculated Raman activities in Å amu with the MP2/6-31G(d) basis set.
Calculated with the MP2/6-31G(d) basis set; contributions less than 10% are omitted.
e
f
4
−1
factors of 0.88 for the carbon-hydrogen stretches, 0.9 for the
heavy atom stretches and carbon-hydrogen bends, and 1.0
for the methyl torsion and skeletal bends. The off-diagonal
elements were scaled with the geometric averages of the
scaling factors involved. The calculations were repeated to
obtain the fixed scaled force fields and scaled vibrational
frequencies.
ties and the predicted frequencies for each normal mode
[14–17]. To obtain the polarized Raman cross sections, the
polarizabilities are incorporated into Sj by multiplying it by
(1 − ρj)/(1 + ρj), where ρj is the depolarization ratio of
the jth normal mode. The Raman scattering cross sections
and the predicted scaled frequencies were used together
with a Lorentzian function to obtain the calculated spectra.
Infrared intensities were calculated based on the dipole
moment derivatives with respect to Cartesian coordinates.
The derivatives were taken from the ab initio calculations
and transformed to normal coordinates by
The Raman (Fig. 4) and infrared (Fig. 3) spectra for
2
-fluorobutane were predicted using “fixed scaled” frequen-
cies; Raman scattering activities and infrared intensities
determined from the Gaussian-98 program [11] from the
MP2/6-31G(d) calculations. The Raman scattering cross
sections, ∂σj/∂Ω, which are proportional to the Raman
intensities, can be calculated from the scattering activi-
ꢁ
ꢂ
ꢀ
∂
µu
Qi
∂µu
∂Xj
=
Lij
∂
j

Table 4
Structural parametersa of 2-fluorobutane for the F-trans, Me-trans, and H-trans conformers from ab initio calculations
Parameter
Sybb
RHF/6-31G(d)
MP2/6-31G(d)
MP2/6-311+G(d, p)
MP2/6-311+G(2d, 2p)
Me-trans
F-trans
H-trans
Me-trans
F-trans
H-trans
Me-trans
F-trans
H-trans
Me-trans
F-trans
H-trans
r(C1–C2)
r(C2–C3)
r(C3–C4)
r(C3–F8)
r(C1–H5)
r(C1–H6)
r(C1–H7)
r(C2–H10)
r(C2–H11)
r(C3–H9)
r(C4–H12)
r(C4–H13)
r(C4–H14)
R1
R2
R3
R4
r1
r2
r3
r5
r6
r4
r7
r8
r9
1.528
1.519
1.516
1.383
1.085
1.083
1.087
1.087
1.087
1.085
1.085
1.085
1.084
113.0
114.0
110.8
110.8
111.2
108.3
110.0
108.4
108.3
110.5
110.7
110.2
179.1
180.4
120.1
−119.8
−120.0
124.3
−122.1
122.2
−57.5
120.3
−119.7
8363
1.529
1.521
1.516
1.382
1.085
1.087
1.085
1.086
1.087
1.085
1.085
1.084
1.084
114.0
115.2
110.4
111.4
112.0
107.3
109.9
107.3
108.6
110.5
111.3
109.8
−67.0
184.8
119.4
−119.7
−119.6
125.0
−121.6
123.4
−55.1
120.8
−119.4
7821
1.529
1.523
1.517
1.383
1.085
1.085
1.084
1.087
1.086
1.084
1.083
1.085
1.084
114.7
115.7
110.3
112.0
110.7
108.3
108.9
108.3
107.4
111.1
110.6
109.9
60.9
174.2
119.6
−119.5
−121.1
124.9
−123.6
121.5
−61.6
120.8
−119.5
6575
1.524
1.514
1.511
1.410
1.093
1.091
1.094
1.096
1.096
1.098
1.093
1.093
1.092
112.6
114.2
111.1
110.2
110.9
107.8
110.0
107.9
108.4
109.8
110.7
110.3
177.8
180.9
120.3
−120.1
−119.5
125.0
−121.9
122.6
−57.2
120.1
−119.6
8228
1.525
1.516
1.512
1.409
1.093
1.094
1.093
1.095
1.096
1.098
1.093
1.092
1.092
113.5
114.9
110.6
111.1
111.7
107.3
110.0
107.5
108.1
109.8
111.3
109.8
−65.7
185.0
119.5
−119.8
−119.2
125.3
−122.0
123.0
−55.2
120.6
−119.3
7798
1.524
1.518
1.512
1.410
1.093
1.093
1.092
1.097
1.095
1.097
1.091
1.094
1.092
113.8
115.4
110.6
111.9
110.1
107.8
109.5
108.4
107.4
110.6
110.6
109.9
59.3
172.6
119.9
−119.5
−120.2
124.4
−123.6
121.4
−61.0
120.6
−119.4
6467
1.526
1.515
1.512
1.407
1.093
1.092
1.094
1.096
1.096
1.407
1.093
1.094
1.092
112.9
113.9
110.9
110.6
110.7
108.2
109.9
108.0
107.7
110.0
110.1
110.4
180.4
179.8
120.2
−119.9
−120.1
124.8
−122.5
122.0
−56.9
119.9
−120.1
8179
1.523
1.517
1.513
1.406
1.093
1.095
1.093
1.095
1.096
1.096
1.094
1.093
1.092
112.9
114.6
110.6
110.9
111.7
107.7
109.9
107.7
108.3
110.1
110.6
110.0
−64.5
186.4
119.5
−119.9
−119.9
125.0
−121.6
122.8
−54.2
120.4
−119.9
7794
1.527
1.519
1.513
1.407
1.093
1.093
1.093
1.097
1.095
1.407
1.092
1.094
1.092
114.2
115.1
110.3
111.7
110.6
108.2
109.3
107.8
107.5
110.7
110.0
110.1
56.2
173.1
119.7
−119.5
−120.7
124.0
−123.1
122.1
−62.6
120.3
−120.0
6455
1.522
1.510
1.507
1.410
1.085
1.085
1.087
1.089
1.089
1.089
1.086
1.086
1.086
112.8
113.9
111.2
110.6
110.8
108.1
110.1
108.0
107.9
110.0
110.2
110.6
180.7
180.3
120.3
−120.0
−119.7
125.2
−122.5
122.1
−56.8
119.8
−120.1
8204
1.524
1.511
1.508
1.409
1.085
1.088
1.086
1.087
1.088
1.089
1.086
1.086
1.085
112.7
114.6
110.8
111.0
111.7
107.7
110.0
107.8
108.3
110.0
110.7
110.2
−65.9
185.1
119.6
−120.0
−119.7
125.2
−121.6
122.8
−54.9
120.3
−119.9
7837
1.523
1.514
1.508
1.410
1.085
1.086
1.085
1.089
1.088
1.088
1.084
1.087
1.085
114.1
115.2
110.6
111.7
110.6
108.1
109.5
107.8
107.6
110.6
110.2
110.2
56.5
174.0
119.7
−119.6
−120.4
124.4
−123.1
122.1
−61.7
120.3
−119.9
6481
∠
∠
∠
∠
∠
∠
∠
∠
∠
∠
∠
∠
C1C2C3
C2C3C4
C2C1H5
C2C1H6
C2C1H7
C2C3H8
C2C3H9
C3C2C10
C3C2H11
C3C4H12
C3C4C13
C3C4H14
Φ
Ψ
α1
α2
α3
Γ 1
σ
γ1
γ2
φ1
φ2
φ3
τ3
τ1
τC1C2C3C4
τC3C2C1H5
τH6C1C2H5
τH7C1C2H5
τF8C3C2C4
τH9C3C2C4
τH10C2C3C1
τH11C2C3C1
τH12C4C3C2
τH13C4C3C12
τH14C4C3C12
A
τ2
B
3468
3437
3866
3496
3438
3914
3475
3449
3900
3498
3462
3926
C
2701
2632
3199
2708
2631
3227
2693
2636
3203
2708
2649
3227
|
|
|
|
µa|
µb|
µc|
µt|
0.078
1.786
0.497
1.8555
0.154133
1.593
1.072
0.331
1.9483
0.152766
300
0.480
1.537
0.918
1.8538
0.152534
351
0.051
1.898
0.517
1.9677
0.870485
1.727
1.108
0.356
2.0821
0.869100
304
0.531
1.633
0.963
1.9687
0.869241
273
.137
1.984
1.231
.401
2.3692
1.140486
146
0.742
1.803
1.115
2.2460
1.140203
208
0.137
2.089
0.563
2.1674
1.215706
1.928
1.204
0.374
2.3034
1.214995
156
0.704
1.760
1.073
2.1777
1.214731
214
−2.154
.583
2.2359
1.141151
c
−
(E + 256)
−1
ꢀ
E (cm )
a
Bond distances in angstrom (Å), angles in degrees, rotational constants in megahertz (MHz), and dipole moments in Debye.
Symbols for internal coordinates.
Energy in hartree.
b
c

8
36
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
Table 5
i j
where the Q is the ith normal coordinate, X is the jth Carte-
Symmetry coordinates for vibrations of 2-fluorobutane
sian displacement coordinate, and Lij is the transformation
matrix between the Cartesian displacement coordinates and
normal coordinates. The experimental Raman spectrum of
the liquid and mid-infrared spectrum of the krypton so-
lution for 2-fluorobutane are included with the calculated
spectra in Figs. 3A and 4A, respectively, for comparative
purposes. The calculated spectrum of the mixture of the
three conformers was obtained using the enthalpy differ-
ences obtained from the temperature study of the liquid
krypton solution (Tables 6 and 7). The agreement between
the calculated spectrum of the mixture of conformers and
the experimental Raman spectrum of the liquid is reason-
ably good where the frequencies and their relative inten-
sities of many of the lines are similar to those predicted
by the ab initio calculations. The agreement between the
calculated and experimental infrared spectra is also satis-
factory. Therefore, these calculated spectra are useful for
analytical purposes and contribute significantly to spectral
interpretation and vibrational assignments, particularly to
distinguishing bands due to the individual conformers.
Descriptiona
Symmetry coordinate
∗
CH3 antisymmetric stretch
S1 = r2 − r3
CH3 antisymmetric stretch
CH3 antisymmetric stretch
S2 = r57 − r9
S3 = 2r8 − r7 − r9
S4 = 2r1 − r2 − r3
S5 = r5 − r6
∗
CH3 antisymmetric stretch
CH2 symmetric stretch
CH3 symmetric stretch
S6 = r7 + r8 + r9
S7 = r1+ r2 + r3
S8 = r5 + r6
∗
CH3 symmetric stretch
CH2 symmetric stretch
CH stretch
S9 = r4
∗
CH3 antisymmetric
S10 = 2ζ2 − ζ1− ζ3
deformation
CH3 antisymmetric
deformation
S11 = 2ε3 − ε1 − ε2
S12 = ζ1 − ζ3
∗
CH3 antisymmetric
deformation
CH3 antisymmetric
deformation
S13 = ε1 − ε2
CH2 symmetric deformation
CH bend (out-of-plane)
CH bend (in-plane)
S14 = 4δ − β1 − β2 − γ1 − γ2
S15 = 2∆ − η − σ
S16 = σ − η
∗
CH3 symmetric deformation
S17 = ζ1 + ζ2 +ζ3 − α1 − α2 −α3
S18 = ε1 + ε2 + ε3 − φ1 − φ2 − φ3
S19 =β1 + β2 − γ1 − γ2
S20 = β2 − β1 + γ1 − γ2
S21 = φ3 − φ1
CH3 symmetric deformation
CH2 wag
CH2 twist
CH3 rock
CH2 rock
4. Vibrational assignment
S22 = 2φ2 − φ1 − φ3
S23 = R3
C3C4 stretch
C1C2 stretch
Although the vibrational spectrum of 2-florobutane has
S24 = R1
been reported previously [5], the data were not complete
and the conformational stabilities were not determined. The
vibrational assignments in the present study are based on
the scaled ab initio MP2/6-31G(d) frequencies, infrared in-
tensities, Raman activities, as well as characteristic “group
frequencies” from similar molecules.
∗
∗
CH3 rock
CH3 rock
S25 = 2α1 − α2 −α3
S26 = α2 −α3
CF stretch
C2C3 stretch
CH2 twist
C1C2C3 bend
CCF bend (out-of-plane)
CCF bend (in-plane)
CH3 torsion
S27 = R4
S28 = R2
S29 = β2 − β1 − γ1 + γ2
S30 = Φ
S31 = Γ 1 + Γ 2
Several bands which were observed in the spectra of the
fluid states were absent in the spectrum of the annealed poly-
S32 = Γ 1 − Γ 2
S33 = τ2
−1
crystalline solid. For example, the band at 588 cm in the
krypton solution disappeared in the solid state. This band
is assigned to the fundamental of the H-trans conformer,
since the nearest bands for the other two conformers are over
C2C3C4 bend
S34 = ψ
∗
CH3 torsion
S35 = τ1
Asymmetric torsion
S36 = τ2
a
Asterisk indicates the C1 atom.
−
1
1
00 cm apart, according to the ab initio MP2/6-31G(d)
Table 6
Temperature and intensity ratios from the conformational study of the Me-trans and F-trans conformers in krypton solutiona
◦
T ( C)
1000/T (K)
I493/I489
I457/I780
I457/I1106
I1174/I780
I1174/I1106
I1174/I436
−
−
−
−
−
−
−
−
−
−
105
110
115
120
125
130
135
140
145
150
5.947
6.129
6.323
6.530
6.750
6.986
7.239
7.510
7.803
8.120
–
7.247
7.374
–
7.499
–
7.545
7.833
–
8.355
9.021
1.635
1.721
1.722
1.736
1.766
1.797
1.852
–
3.268
3.348
3.426
3.495
3.559
3.713
3.856
4.069
4.402
4.723
0.737
0.781
0.800
0.809
0.848
0.885
0.912
0.983
1.028
1.099
–
4.943
5.002
–
5.924
6.224
–
6.651
7.028
7.257
6.220
6.778
6.954
–
7.532
7.664
7.825
8.259
–
1.952
2.100
Hb (cm
−1
)
139 ± 14
63 ± 10
69 ± 6
115 ± 7
122 ± 4
105 ± 11
ꢀ
a
The first frequency is from the Me-trans conformer.
Average value of ꢀH is 102 ± 6 cm (1.21 ± 0.07 kJ mol−1) for Me-trans/F-trans conformers with the Me-trans more stable.
b
−1

J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
837
Table 7
Temperature and intensity ratios from the conformational study of the Me-trans and H-trans conformers in krypton solutiona
◦
T ( C)
1000/T (K)
I457/I588
I1303/I588
I1174/I588
I1174/I794
I1174/I418
I457/I418
−
−
−
−
−
−
−
−
−
−
105
110
115
120
125
130
135
140
145
150
5.947
6.129
6.323
6.530
6.750
6.986
7.239
7.510
7.803
8.120
15.677
18.879
–
20.248
–
22.321
23.662
–
29.894
34.336
4.339
–
5.151
5.302
–
5.800
5.951
7.648
–
7.069
8.571
–
9.438
9.674
10.986
11.649
–
7.061
7.306
7.956
8.061
7.956
8.037
9.216
10.124
12.039
13.015
1.144
1.212
1.282
1.431
1.576
1.639
1.782
1.971
2.130
2.232
2.536
2.669
2.757
3.069
3.283
3.330
3.619
–
15.750
–
4.043
4.262
8.086
Hb (cm
−1
)
224 ± 18
207 ± 2
269 ± 23
190 ± 20
223 ± 9
169 ± 9
ꢀ
a
The first frequency is from the Me-trans conformer.
Average value of ꢀH is 208 ± 8 cm (2.49 ± 0.10 kJ mol−1) for Me-trans/H-trans conformers with the Me-trans more stable.
b
−1
and 894 cm 1 for the F-trans, Me-trans, and H-trans con-
−
calculations. Several bands in the region between 380 and
−1
4
30 cm in the infrared spectrum of the gas also disap-
formers, respectively. However, only one Raman band at
98 cm was observed in the spectrum of liquid and it is
assigned to this mode for all three conformers. The C1C2C3
bending fundamental of the H-trans conformer with the in-
frared intensity of 2.0 km mol is assigned to a weak but
well defined band at 588 cm in the spectrum of the krypton
solution. The corresponding fundamentals for the Me-trans
and F-trans conformers are observed at 493 and 436 cm
respectively, in the same spectrum. The CCF out-of-plane
and in-plane bends are assigned to bands at 457, 369 cm
and 488, 398 cm for the Me-trans and F-trans conform-
ers, respectively. However, only the in-plane mode ν was
observed at 420 cm for the highest energy H-trans form.
Two bands with C- and A-type band contours are observed
at 255 and 243 cm , which are assigned to the ν34 and ν35
fundamentals for the Me-trans conformer. Additionally, the
asymmetric torsional mode is assigned to a broad band cen-
−
1
peared in the solid with two of them arise from the funda-
mentals of the H-trans conformer and one from the F-trans
conformer. Therefore, it is clear that only the Me-trans form
exists in the polycrystalline solid. Thus, all bands in the
spectrum of the solid are assigned to the Me-trans con-
former. Since the Me-trans form is predicted as the most
stable conformer by all MP2 calculations in this study, most
of bands observed in the fluid states are assigned to this con-
former which is consistent with the previous investigations
8
−
1
−
1
−1
,
−1
−
1
[5].
ꢀ
ꢀ
The assignment of carbon-hydrogen stretching modes is
3
2
straightforward on the basis of the scaled ab initio pre-
dicted frequencies and well known “group frequencies”.
Eight Q-branches in the spectrum of the gas and seven bands
in the spectrum of solid are assigned to ν1–ν9 fundamen-
tals for the Me-trans conformer. However, the Q-branch at
−1
−1
−
1
2
952 cm has to be assigned to the CH2 antisymmetric
−1
tered at 108 cm in the far infrared spectrum of the gas
(Fig. 2). The assignments for the observed fundamentals of
ꢀ
stretching fundamental for the F-trans form (ν where the
5
single and double primes indicate the F-trans and H-trans
conformers, respectively), since it disappeared in the spec-
trum of the annealed solid. The fundamentals ν10, ν11, and
ν12, which were not assigned previously, are assigned to dou-
2
-fluorobutane are listed in Tables 1–3 for the Me-trans,
F-trans, and H-trans conformers, respectively.
−
1
blets at 1479 (1473), 1467 (1465), and 1462 (1458) cm
5
. Conformational stability
in the spectrum of the solid, where the numbers in the
parentheses are due to factor group splitting in the solid.
The CH2 twisting fundamentals with the predicted frequen-
There are three stable conformers in the fluid states and
many fundamentals have nearly the same frequencies, but
bands due to each single conformer can still be identi-
fied. As mentioned earlier, a series of bands disappeared in
the spectrum of the polycrystalline solid which must arise
from either the F-trans or H-trans conformer. Aided by the
normal coordinate analysis, many of those bands can be
confidently assigned. For example, the predicted frequen-
−
1
cies of 1275, 1272, and 1263 cm are assigned to the in-
−
1
frared bands at 1278, 1271, and 1264 cm for the H-trans,
Me-trans, and F-trans conformers, respectively, with the first
and the third band vanishing in the spectrum of the solid.
ꢀ
ꢀ
The CH3 rocking fundamental for the H-trans form, ν , is
2
2
−
−
1
assigned to a strong Q-branch (C-type band) at 1112 cm
in the infrared spectrum of the gas and a band at 1103 cm
1
ꢀꢀ
ꢀ
cies of ν28 (H-trans) and ν (F-trans) fundamentals are
29
−
1
in the Raman spectrum of liquid which is in agreement with
the previous reported assignment [5]. The C-F stretches were
790 and 771 cm with the infrared intensities of 3.1 and
3.5 km mol , respectively, are assigned to two weak bands
at 794 and 780 cm in the spectra of the krypton solu-
−
1
−
1
−1
predicted at 909, 905, and 900 cm with strong infrared in-
tensities and they are assigned to strong bands at 905, 899,
tion. Therefore, there were several bands for each conformer

8
38
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
intensity for the Me-trans conformer as the temperature
decreases, which is consistent with the ab initio energy pre-
dictions. The natural logarithm of the ratio of the intensities
of each conformer pair were plotted against the reciprocal
of absolute temperature and these data points were fitted to
the equation −ln K = (ꢀH/RT) − (ꢀS/R). The ꢀH values
were determined from van’t Hoff plot of −ln K versus 1/T
where ꢀH/R is the slope of the fitted line and intensity ratios
of conformer bands were substituted for K. It is assumed
that ꢀH is not a function of temperature over the relatively
small temperature range. The determined ꢀH values ranged
−
1
−1
from a high of 139 ± 14 cm to a low of 63 ± 10 cm
−
1
−1
with an average of 102 ± 6 cm (1.21 ± 0.07 kJ mol
)
with the Me-trans conformer more stable than the F-trans
form. Similarly, the average enthalpy difference between
the Me-trans and H-trans forms was determined to be
−
1
−1
208 ± 8 cm
(2.49 ± 0.10 kJ mol ) with the Me-trans
form being more stable. These enthalpy differences should
be close to the value in vapor state [18–22], since the three
conformers have similar molar volumes and their dipole
moments differ by less than 10%. The uncertainties in these
values are the statistical uncertainties which do not take
into account factors such as the presence of overtone or
combination bands in near coincidence with the measured
fundamentals. Therefore, a more realistic value for the un-
certainty should be at least 10% which results in values of
Fig. 6. Mid-infrared spectra of 2-fluorobutane dissolved in liquid krypton
◦
at −125 C. (MeT, FT, and HT indicate the Me-trans, F-trans, and H-trans
conformer, respectively.)
which could be used for the enthalpy difference determina-
tions (Fig. 6).
Six Me-trans/F-trans and six Me-trans/H-trans con-
former pairs were utilized in this study to determine the
enthalpy differences. The spectra were recorded at temper-
−
1
−1
−1
1
(
02± 10 cm (1.21± 0.1.12 kJ mol ) and 208± 21 cm
−
1
2.49 ± 0.25 kJ mol ) for the enthalpy differences for the
◦
atures from −105 to −150 C with the sample dissolved
Me-trans/F-trans and Me-trans/H-trans pairs. By utilizing
the experimentally determined enthalpy differences in the
present study, the estimated abundances for the Me-trans,
F-trans, and H-trans conformers at ambient temperature are
in the liquefied krypton. The partial spectra of the krypton
solution at different temperatures (Fig. 7), with the bands at
−
1
4
93 and 457 cm due to the Me-trans form and the bands
−
1
at 588 and 418 cm for the H-trans conformer and bands
at 490 and 436 due to the F-trans form, show increased
50 ± 2, 31 ± 1, and 19 ± 1%, respectively.
6. Disscusion
−
1
The average values of ꢀH of 102 ± 10 cm between
−1
the Me-trans and F-trans forms and 208 ± 21 cm be-
tween the Me-trans and H-trans forms with the Me-trans
form the most stable conformer shows that the ab initio
MP2/6-311+G(2d, 2p) calculations with the predicted en-
−
1
ergy differences of 156 and 214 cm for Me-trans/F-trans
and Me-trans/H-trans pairs are reasonably good predictions.
However, the MP2/6-31G(d) calculations gave incorrect pre-
dictions on the relative stabilities of the second and third
stable conformers, i.e. F-trans and H-trans forms, with the
−1
H-trans conformer more stable by 31 cm which is con-
trary to the experimental results. Ab initio calculations may
give the incorrect results when smaller basis sets are em-
ployed and the credibility of the conformational stability
predictions decreases if the energy difference between the
conformers is less than 100 cm . For example, the ab initio
calculations for both 1-chloropropane and 1-bromopropane
resulted in the wrong predictions when the smaller basis sets
were utilized [2]. The RHF/6-31G(d) and B3LYP/6-31G(d)
−
1
Fig. 7. Temperature dependent infrared spectrum of 2-fluorobutane in
−1
◦
liquid krypton (400–530 cm ) in the temperature from −105 to −145 C.

J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
839
calculations gave the correct predictions on the conforma-
tional stabilities, but the value of the energy differences are
too high (Table 4, B3LYP results not listed). Therefore, the
second order perturbation level calculations with larger ba-
sis sets are preferred for obtaining reliable predictions on
the conformational behavior of the alkyl halides such as
conformers. The largest difference among the angles is for
◦
∠C1C2C3 with the value for H-trans conformer 1.3 larger
than those for the other two conformers. The ∠C2C3C4 for
◦
◦
the H-trans form is larger by 1.2 and 0.5 than the cor-
responding angles for the Me-trans and F-trans forms, re-
spectively. Additionally, the ∠C2C3F of the F-trans form is
◦
2
-fluorobutane. Nevertheless, experimental enthalpy deter-
less than the other two conformers by 0.5 . Compared with
minations are frequently necessary to verify the theoretical
predictions.
the fluorine and hydrogen atoms, the methyl group is much
larger, and therefore, the values of the ∠C2C3C4 for the
H-trans and F-trans forms are slightly larger than the cor-
responding angle of the Me-trans conformer where the two
methyl groups are in the gauche position. For the H-trans
conformer, both the fluorine and methyl group are in the
gauche positions to the first methyl group which generates
maximum steric hindrance and consequently, the value of
∠C2C3C4 is the largest among the three forms. This steric
factor has practically no effect on the hydrogen atom and the
values of ∠C2C3H9 which are essentially the same among
the three conformers.
In the previous vibrational study of this molecule [5], only
a few bands were assigned to the high energy F-trans and
H-trans forms. Many of the fundamentals in the “fingerprint”
region have been assigned for the F-trans conformer and
several bands are also identified for the H-trans conformer
in the present study. For example, the C2C3 stretch and the
ꢀ
ꢀ
ꢀ
CH2 twisting fundamentals (ν2 and ν ) for the H-trans
8
29
and F-trans conformers, respectively, were not reported pre-
viously in the Raman spectrum of liquid. These two fun-
−
1
damentals, with predicted values of 790 and 771 cm , are
assigned to the Raman lines at 795 and 782 cm 1, respec-
−
All three conformers of 2-fluorobutane have only trivial
C1 symmetry. Therefore, the PEDs involve extensive mixing
ꢀ
ꢀ
ꢀ
tively. The ν3 and ν fundamentals for the H-trans and
0
30
∗
F-trans conformers are assigned to the two weak bands at
of the symmetry coordinates. For example, the CH3 rocking
−
1
5
88 and 433 cm , respectively, in the infrared spectrum of
fundamental (asterisk indicates carbon-1) for the Me-trans
the krypton solution. These assignments facilitated the en-
thalpy determinations, since values derived from multiple
pairs produce more reliable results.
The infrared bands at 494 and 461 cm in the spectrum
of the solid were assigned to the Me-trans and F-trans con-
formers, respectively, in the previous study [5]. This assign-
ment led to the conclusion that the Me-trans and F-trans
conformers coexist in the polycrystalline solid. However, the
assignment presented herein shows that the second band is
the ν31 fundamental for the Me-trans conformer with the
conformer (ν ) only has 11% contribution from the de-
26
scribed atomic motion. The CH3 rocking fundamental (ν21)
is extensively mixed and no contribution has a value greater
than 20% (Table 1). However, fundamentals for the carbon
hydrogen stretches and torsional modes are much purer with
the major contributions more than 60%. The situations for
the F-trans and H-trans conformers are almost the same and
one-half of the 36 fundamentals have major contributions
less than 50%. Therefore, the descriptions given to the nor-
mal modes are more for book-keeping than to give the atom
motions for the fundamentals, especially in the fingerprint
region.
The predicted potential function (Fig. 8) has been plotted
from the data obtained from the MP2/6-311+G(d, p) calcu-
lations with full geometry optimization at the three transi-
tion states as well as the three stable potential minima and
a subsequent fit of the energies to an asymmetric potential
of the type:
−
1
−
1
predicted value of 459 cm . The calculated values for bands
−
1
in this region for the F-trans conformer are 482 cm for
which is too high and 432 cm for ν which is too low.
Eight fundamentals from the F-trans conformer (ν , ν ,
ꢀ
−1
ꢀ
ν
3
1
30
ꢀ
ꢀ
2
0
22
ꢀ
ꢀ
ν –ν ) and six fundamentals from the H-trans conformer
2
7
32
ꢀ
ꢀ
ꢀꢀ
ꢀꢀ
ꢀꢀ
ꢀꢀ
(
ν , ν –ν , ν , and ν ) disappeared from the spectrum
2
0
26 28 30
32
of the solid with annealing. Therefore, it is very clear that
the Me-trans form is the only conformer remaining in the
crystalline solid. Many bands in the spectrum of the crys-
talline solid show factor group splitting such as the ν10−ν14,
ν24−ν27, ν29, ν30, and ν32 fundamentals which are observed
as doublets. Therefore, at least two molecules must exist per
unit cell in the crystal.
3
ꢁ
ꢂ
3 ꢁ
ꢂ
ꢀ
ꢀ
ꢀ
V
i
Vi
V(φ) =
(1 − cos iφ) +
sin iφ,
2
2
i=1
i=1
where φ and i are the torsional angle and foldness of the
barrier, respectively. The potential coefficients, V , V , V
Most structural parameters obtained from the MP2/6-311
1
2
3
ꢀ ꢀ ꢀ
and V , V , and V along with torsional transitional barriers
1 2 3
+
G(d, p) calculations are similar among the three conform-
ers. However, some significant differences arise from the
backbone structure. The C1C2 bond distances between the
F-trans and H-trans forms differ by 0.004 Å with the H-trans
form having the larger value and its C2C3 bond distance is
also larger than the corresponding bond distances for the
Me-trans and F-trans forms by 0.004 and 0.002 Å, respec-
tively. The C3C4 and CF bond distances and all carbon hy-
drogen bond distances are nearly the same among the three
are listed in Table 8. On the basis of our experience with
other molecules, [1,2,9], it is expected that the barriers be-
tween the F-trans and H-trans forms are slightly larger than
the experimental values.
In the previous vibrational study of n-butane, the trans
conformer is more stable with an enthalpy difference of
−
1
245 cm
[3]. For the 1-halo substituted propanes, the
gauche form is the more stable conformer with enthalpy

8
40
J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
Table 8
Potential barriers and coefficients (cm 1) of 2-fluorobutanea
−
Parameter
Potential coefficient
Torsional transition
Potential barrier
V1
V2
V3
394
Me-trans → F-trans
Me-trans → H-trans
F-trans →H-trans
1249
1719
1847
1103
1511
1785
−138
1518
ꢀ
V
1
−303
−224
196
208
146
F-trans → Me-trans
H-trans → Me-trans
H-trans → F-trans
ꢀ
V
2
ꢀ
V
3
ꢀ
E (Me-trans → H-trans)
ꢀE (Me-trans → F-trans)
a
From MP2/6-311+G(d, p) ab initio calculations.
differences of 100, 52, and 72 cm 1 for the fluoride [1],
chloride, and bromide [2], respectively. Based on these ex-
perimental results, the Me-trans form is expected to be more
stable if both the methyl group and halogen atom are on
the same atom. For 2-chlorobutane and 2-bromobutane, the
electron diffraction studies [4] indicated that the Me-trans
form is the lowest energy conformer whereas the H-trans
and Br-trans forms are the highest energy forms for the
chloride and bromide, respectively. However, studies from
temperature dependent infrared spectra in krypton solution
utilizing seven conformer pairs for both the chloride and
bromide showed the H-trans conformer as the highest en-
ergy form for both molecules with the enthalpy differences
−
atoms, have lone pair electrons and the hyperconjugation
between the methyl group and the substituents is believed
to be the major factor which causes the halo–trans form
to be less stable where the distance between the methyl
group and substitute is large. The CN and C≡C groups are
also electron-rich moieties and we expect the same hyper-
conjugation effects exist and consequently, the Me-trans
form with the substitutents gauche to the methyl group
is the most stable form. Compared with the electronic ef-
fects, the steric factor is probably less important for these
kinds of molecules. For instance, the Me-trans form for
2-bromobutane is more stable even though the Br atom has
a much larger size than the methyl group.
−
1
of 223 and 226 cm , respectively, between the Me-trans
and halo–trans forms [23,24]. Similar results were obtained
for butyronitrile [6] and 2-methylbutyronitrile [8] where the
gauche and Me-trans forms are the lowest energy forms, re-
spectively. For 3-methyl-1-pentyne, the Me-trans form was
predicted as the more stable from the MM2 calculations
but the trans conformer for 1-pentyne [7] is experimentally
Acknowledgements
JRD acknowledges the University of Missouri-Kansas
City for a Faculty Research grant for partial financial sup-
port of this research. The authors thank Sergio Moore for
carrying out most of the initial ab initio calculations.
−
1
determined to be more stable by 113 cm from the kryp-
ton solution. Most of the substituents, including halogen
References
[1] G.A. Guirgis, X. Zhu, J.R. Durig, Struct. Chem. 10 (1999) 445.
[2] J.R. Durig, X. Zhu, S. Shen, J. Mol. Struct. 570 (2001) 1.
[3] H.D. Stidham, J.R. Durig, Spectrochim. Acta A 42 (1985) 105.
[4] K. Aarset, K. Hagen, R. Stolevik, J. Mol. Struct. 567 (2001)
157.
[
[
[
5] G.A. Crowder, T. Koger, J. Mol. Struct. 29 (1975) 233.
6] G.A. Crowder, G.O. Carlisle, J. Comp. Chem. 12 (1991) 880.
7] S. Bell, G.A. Guirgis, Y. Lin, J.R. Durig, J. Phys. Chem. A 101
(1997) 5987.
[8] J.R. Durig, B.R. Drew, A. Koomer, S. Bell, Phys. Chem. Chem.
Phys. 3 (2001) 766.
[9] J.R. Durig, X. Zhu, G.A. Guirgis, S. Bell, J. Mol. Struct., submitted
for publication.
[
[
10] W.F. Edgell, L. Parts, J. Am. Chem. Soc. 77 (1955) 4899.
11] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb,
J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Strat-
mann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N.
Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R.
Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochter-
ski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick,
A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V.
Fig. 8. Potential function governing the internal rotation of 2-fluorobutane
as determined by ab initio calculations (MP2/6-311+G(d, p)).

J.R. Durig et al. / Spectrochimica Acta Part A 60 (2004) 829–841
841
Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,
R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham,
C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W.
Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez,
M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian 98 (Revision
A.7), Gaussian Inc., Pittsburgh, PA, 1998.
[17] G.W. Chantry, in: A. Anderson (Ed.), The Raman Effect, vol. 1,
Marcel Dekker, New York, 1971 (Chapter 2).
[18] W.A. Herrebout, B.J. van der Veken, J. Phys. Chem. 100 (1996)
9671.
[19] M.O. Bulanin, Mol. Struct. 19 (1973) 59.
[20] B.J. van der Veken, E.R. DeMunck, J. Chem. Phys. 97 (1992) 3060.
[21] W.A. Herrebout, B.J. van der Veken, A. Wang, J.R. Durig, J. Phys.
Chem. 99 (1995) 578.
[
[
12] P. Pulay, Mol. Phys. 17 (1969) 197.
13] G.A. Guirgis, X. Zhu, Z. Yu, J.R. Durig, J. Phys. Chem. A 104
(
2000) 4383.
[22] M.O. Bulanin, J. Mol. Struct. 347 (1995) 73.
[23] X. Zhu, S. Shen, W.A. Herrebout, B.J. van der Veken, J.R. Durig,
J. Mol. Struct., submitted for publication.
[
14] M.J. Frisch, Y. Yamaguchi, J.F. Gaw, H.F. Schaefer III, J.S. Binkley,
J. Chem. Phys. 84 (1986) 531.
[
[
15] R.D. Amos, Chem. Phys. Lett. 124 (1986) 376.
16] P.L. Polavarapu, J. Phys. Chem. 94 (1990) 8106.
[24] J.R. Durig, S. Shen, W.A. Herrebout, B.J. van der Veken, J. Phys.
Chem. A, submitted for publication.