Conformational equilibrium and potential energy surface of 1-fluorobutane by microwave spectroscopy and Ab initio calculations

Article abstract of DOI:10.1002/1521-3765(20000818)6:16<3018::AID-CHEM3018>3.0.CO;2-L

The rotational spectra of four (GT, TT, TG, and GG) of the five possible conformers of 1-fluorobutane have been assigned by combining free jet and conventional microwave spectroscopy. The geometry optimization was performed at the MP2 (full) level of theory with the 6-31G (d) and 6-311G (d,p) basis sets and by using the B3LYP (3df, 3pd) density functional method. The relative stability of the five rotamers is calculated at the QCISD (T)/6-311G (d,p) level of theory. In spite of the fact that ab initio calculations indicated the unobserved GG' conformer to be more stable than at least one of the observed conformers it was not possible to detect its rotational spectrum. GT and TG are the most and the least stable species, respectively. The rotational spectra of several vibrational satellites of the four conformers have been studied by conventional microwave spectroscopy. The overall conformational equilibrium is governed by the two-dimensional potential energy surface of the skeletal torsions MeC-CC and FC-CC, which have been evaluated by a flexible model analysis, based on the experimental values of the relative conformational and vibrational energy spacings, and on the shifts of second moments of inertia upon conformational change and vibrational excitation. The relative energy of the fifth stable conformer (GG') was determined to be 333 cm^-1 from flexible model calculations, and to be 271 cm^-1 from the most accurate ab initio calculations.

Full text of DOI:10.1002/1521-3765(20000818)6:16<3018::AID-CHEM3018>3.0.CO;2-L

FULL PAPER
Conformational Equilibrium and Potential Energy Surface of 1-Fluorobutane
by Microwave Spectroscopy and Ab Initio Calculations
Laura B. Favero,[a] Assimo Maris,[a] Alessandra Degli Esposti,[a] Paolo G. Favero,[b]
Walther Caminati,*[b] and Gottfried Pawelke[c]
Abstract: The rotational spectra of four
(GT, TT, TG, and GG) of the five
possible conformers of 1-fluorobutane
have been assigned by combining free
jet and conventional microwave spec-
troscopy. The geometry optimization
was performed at the MP2 (full) level
of theory with the 6-31G (d) and 6-311G
(d, p) basis sets and by using the B3LYP
(3df, 3pd) density functional method.
The relative stability of the five rotamers
is calculated at the QCISD (T)/6-311G
(d, p) level of theory. In spite of the fact
that ab initio calculations indicated the
unobserved GG' conformer to be more
stable than at least one of the observed
conformers it was not possible to detect
its rotational spectrum. GT and TG are
the most and the least stable species,
respectively. The rotational spectra of
several vibrational satellites of the four
conformers have been studied by con-
ventional microwave spectroscopy. The
overall conformational equilibrium is
governed by the two-dimensional po-
tential energy surface of the skeletal
torsions MeC ± CC and FC ± CC, which
have been evaluated by a flexible model
analysis, based on the experimental
values of the relative conformational
and vibrational energy spacings, and on
the shifts of second moments of inertia
upon conformational change and vibra-
tional excitation. The relative energy of
the fifth stable conformer (GG') was
determined to be 333 cmÀ1 from flexible
model calculations, and to be 271 cmÀ1
from the most accurate ab initio calcu-
lations.
Keywords: ab initio calculations ´
conformation analysis
´
density
functional calculations ´ molecular
dynamics ´ rotational spectroscopy
rotamers in such a complex mixture has not been reported for
any of these derivatives so far.
Introduction
Conformational equilibria of alkanes have been extensively
studied and it is well known that local gauche and trans
configurations are stable minima and that the torsional
potential energy surfaces depend on steric and electrostatic
forces.[1] Accordingly linear alkanes have a large number of
conformers; the number of which rapidly increases with an
increase in the length of the chain. The are already nine
minima in the torsional potential energy surface for mono-
substituted n-butanes, corresponding to five different con-
formers. A precise and certain identification of the five
1-Fluorobutane (FB) represents a simple and interesting
model molecule for this kind of study, since it possesses a
permanent dipole moment, which allows the measurements of
the rotational spectra of the various conformers, and it is small
enough to allow high level ab initio calculations. Figure 1
shows the five plausible conformers of 1-fluorobutane: GT,
TT, TG, GG, and GG', according to the configuration (gauche
or trans) of the fluorine atom and of the methyl group,
respectively. In the GG conformer the F atom and CH3 group
are on opposite sides of the plane formed by the three central
carbon atoms of the molecule, while the reverse is true for the
GG' species.
In spite of the fact that 1-fluorobutane is the simplest
1-halogenated derivative of butane, its rotational spectrum
has never been reported, while the microwave (MW) inves-
tigations of Cl-, Br-, and I-butane are, to different, partial
extents, available in the literature. Most of the experimental
data in the gas phase concern the configuration equilibrium of
chlorobutane. The two most recent gas-phase electron dif-
fraction investigations of this molecule suggest the following
room temperature abundance ratios TT/GT/TG/GG/GG': 25/
50/5/15/5 (Fagerland et al. [2]), and 13/60/12/12/1 (Aarset
[a] Dr. L. B. Favero, Dr. A. Maris, Dr. A. D. Esposti
Istituto di Spettroscopia Molecolare del C.N.R.
Via Gobetti 101, 40129 Bologna (Italy)
[b] Prof. W. Caminati, Prof. P. G. Favero
Á
Dipartimento di Chimica ªG. Ciamicianº dellꢀUniversita
Via Selmi 2, 40126 Bologna (Italy)
Fax : (‡39)51-259456
E-mail: caminati@ciam.unibo.it
[c] Dr. G. Pawelke
Anorganische Chemie, FB 9, Universität-Gesamthochschule
42097 Wuppertal (Germany)
Supporting information for this article is available on the WWW under
http://www.wiley-vch.de/home/chemistry/ or from the author.
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Chem. Eur. J. 2000, 6, No. 16

3018±3025
nation of the conformational
surface, which resulted in good
agreement with the ab initio
calculations. Only low-resolu-
tion MW spectra are available
for the Br and I derivatives.[7]
We set ourselves the chal-
lenging goal to obtain more
precise information for fluoro-
butane, for which it was antici-
pated that it should be possible
to observe all the five possible
conformers, especially when
the suggestions given by the ab
initio calculations were taken
into consideration. The results
of such ab initio calculations are
particularly useful in assigning
the microwave spectra of sub-
stituted alkanes, since they help to discriminate between the
large number of features originating from the different
conformers.
Figure 1. Draft of the five possible conformers of 1-fluorobutane.
et al.[3]), but the smaller values have a large uncertainty. We
reported the rotational spectra, first of three conformers,[4]
then of a fourth conformer[5] by combined free jet and
conventional rotational spectroscopy. The fifth conformer,
GG', which is 600 ± 700 cmÀ1 higher in energy than the most
stable conformer (TT), escaped our investigation. We ob-
tained information on the two-dimensional (2D) potential
energy surface of the two skeletal torsions governing the
conformational equilibrium from additional measurements
(e.g. dipole moments, rotational spectra of several vibrational
satellites, and their vibrational energies).[5] The treatment of
these data with a 2D flexible model[6] allowed the determi-
Results and Discussion
Rotational spectra
The rotational spectrum of fluorobutane recorded with a
conventional spectrometer appears very crowded, due to the
large number of rotamers and of low-energy vibrational
satellites. Thanks to the relatively good agreement between
the ab initio and the experimental rotational constant values
of the GT, TT, and TG conformers (see later), the assignment
of their rotational spectra was rather straightforward already
at room temperature. The radiofrequency ± microwave dou-
ble resonance (RFMWDR) technique[10] was very useful,
however, in assigning the first transitions, several ma-R-type
doublets. Many more rotational transitions were then meas-
ured by conventional Stark modulation and by free jet
absorption millimeter wave spectroscopy (FJ-AMMW). The
GG conformer, whose experimental rotational constants were
indeed quite far away from the preliminary ab initio
calculated values, was assigned only by using the FJ-AMMW
spectrometer.[8] We did not succeed, however, in spite of a
long and careful search with the available techniques, in
assigning the spectrum of the GG' conformer. This fact is very
puzzling because the GG' conformer should be more stable
than the TG one and it should have a high mb value.
The rotational spectra of several vibrational satellites were
also assigned by using RFMWDR. All of them correspond to
excited states of the skeletal torsions. We label tF and tMe the
skeletal torsions of the CH2F and CH2CH3 groups, respec-
tively. Correspondingly, the notation (vF, vMe) will indicate the
various excited states. Five, three, two, and two torsional
satellites have been assigned for the GT, TG, TT, and GG
conformers, respectively. The measured transition frequencies
of all conformers and vibrational satellites are available as
Supporting Information. The spectroscopic constants ob-
tained by treating the experimental frequencies with the
Abstract in Italian: Gli spettri rotazionali di quattro (GT, TT,
TG and GG) dei cinque possibili conformeri dell' 1-Fluoro-
butano sono stati assegnati combinando spettroscopia rotazio-
nale in espansione supersonica e spettroscopia rotazionale
convenzionale. L'ottimizzazione della geometria e' stata otte-
nuta al livello MP2 (full) della teoria con i set di basi 6 ± 31G
(d) e 6 ± 311G (d, p), ed usando il metodo funzionale di densita'
B3LYP (3df, 3pd). La stabilita' relativa dei cinque rotameri e'
stata calcolata al livello QCISD (T)/6 ± 311G (d, p). Malgrado i
calcoli ab initio abbiano indicato che il conformero non
osservato, GG', sia piu' stabile di almeno uno dei conformeri
osservati, non e' stato possibile identificare il suo spettro
rotazionale. GT e TG sono la specie piu' stabile e quella meno
stabile, rispettivamente. Gli spettri rotazionali di parecchi
satelliti vibrazionali dei quattro conformeri sono stati studiati
con la spettroscopia a microonde conventionale. L' equilibrio
conformationale e' governato, nel suo complesso, dalla super-
ficie di energia potenziale bidimensionale delle torsioni
scheletali MeC-CC ed FC-CC, che sono state calcolate con
un model flessibile, basandosi sui valori sperimentali delle
energie relative conformazionali e vibrazionali, e sulle varia-
zioni dei momenti planari di inerzia per effetto delle intercon-
versioni conformazionali e delle eccitazioni vibrazionali. L'
energia relativa del quinto conformero (GG') risulta essere
333 cmÀ1 dai calcoli col modello flessibile, e 271cm À1 dai
calcoli ab initio piu' accurati.
Chem. Eur. J. 2000, 6, No. 16
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W. Caminati et al.
FULL PAPER
Table 1. Rotational constants, centrifugal distortion constants and inertial defect of the GT, GG, TG, and TT conformers of flurobutane in the ground and
vibrational excitated states.
vF ˆ 0, vMe ˆ 0 vF ˆ 0, vMe ˆ 1 vF ˆ 1, vMe ˆ 0 vF ˆ 0, vMe ˆ 2 vF ˆ 2, vMe ˆ 0 vF ˆ 1, vMe ˆ 1
vF ˆ 0, vMe ˆ 0 vF ˆ 0, vMe ˆ 1 vF ˆ 1, vMe ˆ 0
8537.082[d]
A [MHz] GT 12586.647(3)[a] 12466.38(2) 12718.60(3) 12353.67(2) 12840.18(2) 12585.86(3) GG 8537.082(3) 8559(2)
B [MHz]
C [MHz]
DJ [kHz]
DJK [kHz]
DK [kHz]
dJ [kHz]
dK [kHz]
HJK [kHz]
HKJ [kHz]
HK [kHz]
hJ [kHz]
Dc [uŠ2][e]
s [kHz]
2331.9187(5) 2335.584(2) 2325.900(3) 2339.269(4) 2320.503(4) 2329.910(2)
2155.3353(4) 2159.739(2) 2150.084(3) 2164.039(4) 2145.476(5) 2154.878(2)
2875.8126(9)
2678.040(1)
6.399(4)
À 45.16(1)
125.86(5)
1.7503(2)
21.37(1)
À 0.276(7)
À 1.6(3)
0[b]
2884.62(3) 2868.7(1)
2679.85(3) 2669.7(1)
0.8277(4)
À 7.619(7)
67.05(3)
0.1365(1)
2.29(2)
±
0.87(1)
0.90(2)
0.82(4)
0.9[c]
À 10.2(4)
67[c]
0.834(6)
5.37(4)
4.71(4)
À 7.57(5)
À 7.8(1)
À 7.84(5)
À 8.22(8)
À 36.9(2)
À 45.16[d]
51(4)
67(9)
59(5)
70.0(8)
386(157)
125.86[d]
0.1427(5)
0.96(8)
±
0.1334(4)
2.9(1)
±
0.1509(2)
0[b]
±
0.1334[c]
0.1421(5)
1.50(7)
±
1.4(1)
21.37[d]
1.75[d]
0.9[c]
21.37[d]
±
±
±
±
±
±
±
±
±
±
±
À 2.2(1)
±
±
±
±
±
±
±
±
±
À 22.9216
54
±
À 21.9679
48
±
À 23.4155
47
±
À 21.5921
75
±
À 22.5359
48
0.0333(1)
À 46.2202
42
±
À 45.4545
77
±
À 22.3963
42
À 46.0641
52
8
Ntrans.
105
42
38
32
12
35
105
29
A [MHz] TG 12555.81(1)
12577(2)
2286.240(4) 2287.877(4)
2114.598(6) 2119.989(5)
0.68(3)
À 4.98(8)
60[d]
0.133[d]
4.7[d]
12455(2)
12355f
2289.91(1)
2124.26(1)
0.71(4)
À 5.92(9)
60[d]
TT 19008.463(6)
1934.331(1)
1837.215(1)
0.195(3)
À 2.34(5)
77.3(41)
0.0168(1)
0[b]
18446(17)
1936.239(4) 1934.997(3)
1842.368(4) 1839.778(3)
18690(10)
B [MHz]
C [MHz]
DJ [kHz]
DJK [kHz]
DK [kHz]
dJ [kHz]
dK [kHz]
Dc [uŠ2]
s [kHz]
Ntrans.
2287.400(2)
2115.262(2)
0.680(4)
À 4.85(3)
60(1)
0.73(3)
À 5.30(7)
60[d]
0.133[d]
4.7[d]
0.181(7)
0.130(8)
8.4(3)
77.3[d]
0.0168[d]
0[b]
À 2.8(2)
77.3[d]
0.0168[d]
0[b]
0.133(2)
4.7(8)
0.133[d]
4.7[d]
À 22.2706
À 22.2415
À 23.0832
À 23.6950
À 12.7762
À 13.5169
À 13.5226
50
57
52
56
50
24
20
68
25
24
20
68
82
48
[a] Standard errors in parentheses are in units of the last digit. [b] Parameter fixed to zero because not statistically significant. [c] Parameter fixed to the
excited state vF ˆ 1 vMe ˆ 0 value. [d] Parameter fixed to the ground state value. [e] Dc ˆ ÀIcc ‡ Iaa ‡ Ibb. [f] Parameter fixed to A2,0 ˆ A1,0 ‡ (A1,0 À A0,0).
quartic Watson Hamiltonian, ªAº reduction, Ir representa-
tion[11] are reported in Table 1, in which some statistical
parameters of the fits are also shown.
determine the dipole moment components of two rotamers.
The cell was calibrated with the 3-2 transition of OCS (m ˆ
0.71521 D[15]). The Stark coefficients and the Dn/E2 slopes of
the various Stark lobes are given as Supporting Information,
while all experimentally estimated dipole moment compo-
nents are given in Table 2.
Relative intensity measurements
Microwave relative intensity measurements have been per-
formed in order to estimate the conformational and vibra-
tional energies. These measurements have been made follow-
ing the method of Esbitt ± Wilson.[12] We needed to take
quantitatively into account the fact that during the measure-
ments the line intensity decreased sensibly. A first-order
kinetic equation satisfactorily reproduces the decay of [FB],
the fluorobutane concentration, according to Equation (1).
The value of k was estimated to be 0.52(9) hÀ1.
GT conformer: It has been possible to measure the Stark
shifts of some lobes of three Q-branch transitions. In addition
four R-type transitions with SGSL have been individuated.
The fitting of these data has allowed a relatively precise
determination of the three dipole moment components, as
shown in Table 2.
TG conformer: Three transitions with a SGSL have been
identified. From these data we could determine ma and mc,
while mb was fixed to zero because mb2 was small and negative.
These assumptions are in agreement with the results of ab
[FB] ˆ [FB]0eÀkt
(1)
Dipole moments
It is not easy to measure dipole moments for a complex
molecular system such as fluorobutane. Nevertheless, based
on some lucky circumstances and approximations, we could
estimate the dipole moments of all four conformers. For
example it has been possible in several cases[13] to find a few
transitions having the M À dependent Stark coefficients
(DBg) much smaller than the coefficients (DAg) which do
not depend on M[14] (g(ˆa, b, c) indicates the dipole moment
component). In these cases, due to the overlapping of several
Stark lobes, a single giant Stark lobe (SGSL) appears when an
electric field is applied. This technique has been used here to
Table 2. Experimental and calculated (B3LYP/6 ± 311G (3df, 3pd)) dipole
moment components (D) for the various conformers of fluorobutane.
Experimental values
mb mc mtot
Calculated values
mb mc
ma
ma
mtot
GT 0.97 (1) 1.50 (2) 0.3 (1) 1.81 (3)
TT 1.7(2) 0.93(2) 0.0[a] 1.98[b]
GG 1.01(7) 1.10(6) 1.02(5) 1.81[b]
TG 1.9(1) 0[c]
0.51(3) 1.98(6)
GG' ±
À 0.78
1.38 0.49 1.66
1.89
0.96 1.04 1.65
À 0.04 0.42 1.88
1.69 0.28 1.73
1.508 À 1.15 0.0
0.85
À 1.83
0.20
±
±
±
[a] Fixed to zero by simmetry. [b] Fixed (see text). [c] Fixed to zero. See
text.
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Conformational Analysis of 1-Fluorobutane
3018±3025
2
initio calculations (see later), which supply the value mb
0.00016.
ˆ
and y denote the tF and tMe skeletal torsions, x ˆ 0 and y ˆ 0
correspond to the values of the dihedral angles F-C-C-C and
C-C-C-CH3 ˆ 1808. The C-C-F [a(1)], C-C-C [a(2)], and C-C-
CH3 [a(3)] valence angles, were also considered as model
parameters, as well as their relaxations upon skeletal torsions,
according to Equation (5).
TT conformer: Two transitions with a SGSL have been found.
In order to give an estimate of the ma and mb dipole moment
components (mc is zero by symmetry), we needed, however, to
assume the value of the total dipole moment to be the same as
for the TG conformer, as indicated by the ab initio calcu-
lations (see later).
a(i) ˆ a0(i) ‡ dax(i)(1 À cosx) ‡ day(i)(1 À cosy)
(5)
These structural relaxations were included in the model
calculations to describe the changes of the reduced mass upon
torsional motions. Only the day(2) and day(3), could be
determined, while the remaining four da values were fixed to
zero. In this way it has been possible to obtain ten parameters:
five of them describing the potential energy function, three
equilibrium valence angles, and two structural relaxation
parameters.
GG conformer: The dipole moment components have been
estimated from relative intensity measurements of ma-, mb-,
and mc-type transitions, assuming the overall dipole moment
to have the same value as for the GT conformer as suggested
by ab initio calculations. The estimated values have been
obtained by averaging various measurements from different
rotational lines.
Table 3 reports the experimental vibrational and conforma-
tional energies and their values calculated with the flexible
model. The ab initio results are also given for comparison. The
Conformational equilibria
By combining microwave relative intensity measurements of
several lines and the values of the dipole moment components
of the various conformers it was possible to estimate the
energies of the TT, GG, and TG conformers relative to GT, in
the vibronic ground states, using Equation (2), where wXY is
the conformational degeneracy (wXY ˆ 1 for TT and wXY ˆ 2
for all the other conformers). IXY and DnXY are the peak height
and line width, mg,XY the considered dipole moment compo-
nent, and gXY and nXY the line strength and frequency,
Table 3. Flexible model results and comparison with experimental data
and ab initio calculations in fluorobutane: vibrational energies [cmÀ1].
[a]
(vF,vMe) À (vF,vMe
)
obs.
Flexible model
Ab initio[b]
GT
TT
(0,0)GT À (0,0)GT
(0,1)GT À (0,0)GT
(1,0)GT À (0,0)GT
(1,1)GT À (0,0)GT
(0,2)GT À (0,0)GT
(0,0)TT À (0,0)GT
(0,1)TT À (0,0)TT
(1,0)TT À (0,0)TT
(0,0)GG À (0,0)GT
(0,1)GG À (0,0)GG
(0,0)TG À (0,0)GT
(1,0)TG À (0,0)TG
(0,1)TG À (0,0)TG
0
0
84
80(18)
120(12)
200(20)
167(10)
110(40)
50(40)
95(30)
170(40)
70(30)
123
205
166
110
100
116
173
66
356
97
109
333[c]
respectively. The following values have been obtained: ETT
,
157.4
EGG, and ETG ˆ 110(40), 170(40), and 360(50) cmÀ1, respec-
tively.
GG
TG
154.2
356.9
EXY ˆ KTln[(wXY
XYˆ TT, GG, TG
I I
GTDnGTm2g,XYgXYn2XY)/(wGT XYDnXYm2g,GTgGTn2GT)],
360(50)
105(40)
120(40)
(2)
GG'
271.0
Two-dimensional potential energy surface of the nF and nMe
skeletal torsions
[a] States between which the energy differences are calculated. [b] Ener-
gies of the potential minima with respect to the GT one [QCISD(T)6 ±
311G** method]. [c] Difference between the potential energy minima of
the GG' and GT conformers.
A total of 45 experimental data, that is three conformational
energies (ETT, EGG, and ETG), nine vibrational energies of the
vibrational satellites relative to the local ground states, the
three planar moments of inertia of the GT ground state, and
30 shifts of second moments of inertia with respect to the GT
ground state, have been used to obtain information on the 2D
potential energy surface of the two torsions. Data relative to
the excited states, for which some assumptions on the
rotational constant were made, have not been included.
Planar (or second) moments of inertia, defined and related to
the rotational constants through Equation (3) represent the
mass distribution along the principal inertial axes.
experimental and calculated values of the planar moments of
inertia of the ground state of the most stable conformer (GT),
and their shifts upon conformational and/or torsional excita-
tion are given in Table 4. They are missing for two excited
states for which the assignment was based on some assump-
tion made on their rotational constants. In Table 5 the
determined parameters are shown. Flexible model calcula-
tions have been performed in the ranges À170 < x < 50 and
À170 < y < 508, so as to include the four observed conformers,
corresponding in first approximation to the four positions (8)
(0,0 ) TT), (0, Æ120 ) TG), (Æ120,0 ) GT), (Æ120,
Æ120 ) GG). Only the upper sign is consistent with the
considered range, which has been numerically solved into
41 Â 41 mesh points.[6] The GG' conformer is roughly located
at (Æ120, Æ120).
Maa ˆ Simiai2 ˆ h/(16p2)(À1/A ‡ 1/B ‡ 1/C), etc.,
(3)
Meyer's 2D flexible model,[6] has been applied to the above-
described data to determine the five parameters of the
potential energy function given in Equation (4), in which x
Table 6 lists the values of the energies and of the dihedral
angles at the stationary points. We can see that EGG', the
V(x, y) ˆ 1/2[V1x(1 À cosx) ‡ V3x(1 À cos3x) ‡
V1y(1 À cosx) ‡ V3y(1 À cos3x) ‡ Vxysinxsiny] (4)
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W. Caminati et al.
FULL PAPER
Table 4. Flexible model results and comparison with experimental data.
Second moments of inertia Mgg [u Š2] of the GT conformer and shifts of the
second moments of inertia DMgg ˆ Mgg(v) À Mgg(0) [u Š2].
energy value of the GG' conformer, extrapolated from
experimental data relative to the other four local minima, is
relatively close to the most accurate ab initio values, which are
there reported, as discussed in the following section.
The potential energy surface is plotted in Figure 2. The four
minima, whose energies relative to the most stable conformer
are 0, 107, 172, and 357 cmÀ1, correspond to GT, TT, GG and
TG, respectively. The energy of GG' has been extrapolated to
be 333 cmÀ1.
(vF,vMe)', (vF,vMe
)
g
Obs.
Calcd
a
b
c
a
b
c
205.52
206.51
29.09
10.46
À 0.60
0.05
28.95
11.20
À 0.60
0.13
GT
(0,1)GT,(0,0)GT
(1,0)GT,(0,0)GT
(1,1)GT,(0,0)GT
(0,2)GT,(0,0)GT
(2,0)GT,(0,0)GT
(0,0)TT,(0,0)GT
(0,1)TT,(0,0)TT
(1,0)TT,(0,0)TT
(0,0)GG,(0,0)GT
(0,1)GG,(0,0)GG
(0,0)TG,(0,0)GT
(1,0)TG,(0,0)TG
(0,1)TG,(0,0)TG
0.26
0.23
a
b
c
a
b
c
0.78
0.31
À 0.20
À 0.21
0.12
À 0.14
À 0.16
À 0.31
À 0.08
0.10
À 0.07
0.07
a
b
c
À 1.19
0.25
0.51
À 1.23
0.11
0.45
a
b
c
a
b
c
a
b
c
1.47
0.63
À 0.39
À 0.40
49.36
À 8.76
À 4.81
À 0.92
0.15
À 0.29
À 0.33
49.49
À 8.98
À 3.86
À 0.69
0.01
TT
0.66
0.25
a
b
c
À 0.46
À 0.29
À 0.17
0.21
Figure 2. The 2D potential energy surface of the vF (x) and vMe (y) skeletal
torsions in 1-fluorobutane referred to the most stable GT conformer. GT,
TT, GG, and TG correspond to the local minima identified by the energy
values 0, 107, 172, and 357 cmÀ1, respectively. The contours are drawn every
0.08
0.37
Gg
a
b
c
a
b
c
a
b
c
a
b
c
À 52.90
À 52.76
300 cmÀ1 starting from 40 cmÀ1
.
7.13
7.36
11.91
À 0.16
0.04
12.09
À 0.21
0.13
Ab initio calculations
À 0.37
À 0.39
TG
4.28
4.59
Our investigation of 1-chlorobutane,[5] performed at the
MP2(full)/6-31G (d) level of the theory[16±18] showed that this
method was reliable to estimate the rotational constants of the
four rotamers observed in the microwave spectral region with
a difference of at most 1.5% from their experimental values.
An excellent agreement among the calculated and exper-
imental relative energies was found using the quadratic
configuration interaction approach with single, double, and
a perturbational estimate of the triple excitations[19] with the
6-311G(d, p) basis set,[20] namely the QCISD(T)/6-311G**
method.
In the present case of fluorobutane, the ab initio calcu-
lations,[21] performed at the same level of the theory using the
Gaussian 98 suite of programs,[22] produced rotational con-
stants, which deviate from the corresponding experimental
values by up to 7% for the GG rotamer. Although the ab
initio and experimental rotational constants are related to
structures with a different meaning (re and r0, respectively),
such a discrepancy is larger than that usually observed. The
experimentally determined rotational constants represent a
thorough test on the accuracy of the calculated molecular
geometry. The molecular orbitals were examined by using the
Mulliken population analysis.[23]
0.16
0.41
0.21
À 0.06
À 0.45
À 0.08
0.41
À 0.30
0.00
0.27
a
b
c
0.13
0.21
À 0.05
À 0.19
À 0.02
À 0.17
Table 5. Flexible model parameters.
Potential energy parameter
Structural parameter
V3x [cmÀ1
V1x [cmÀ1
V3y [cmÀ1
V1y [cmÀ1
Vxy [cmÀ1
]
]
]
]
]
990(25)[a]
À 140(10)
790(25)
340(20)
À 212(50)
ao(1) [8]
ao(2) [8]
day (2) [8]
ao(3) [8]
day (3) [8]
111.8(6)
113.6(4)
1.4(3)
110.7(5)
1.5(4)
[a] Errors in parentheses are expressed in units of the last digit.
Table 6. Values of the energies [cmÀ1] and dihedral angles [8] at the minima
of the potential energy function.
Conformer
x [8]
y [8]
V(x,y) [cmÀ1
]
The difficulty encountered in calculating the geometry of
the five rotamers with the same accuracy arises from the
delicate balancing between the electronegativity effects of the
fluorine atom on the carbon chain and the long-range F ± H
interactions. Therefore, an accurate estimate of these effects
GT
TT
GG
TG
GG'
À 120.8
0.0
À 1.4
À 106.5
0.0
65.2
250.9
226.7
0.0
À 116.9
À 117.6
118.3
À 120.2
À 1.2
À 121.4
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Conformational Analysis of 1-Fluorobutane
3018±3025
turns out to be crucial for the calculation of the most stable
geometry of each rotamer. For this reason the flexibility of the
basis set in the valence region was increased and diffuse and
polarization functions were included to account for long-
range intramolecular interactions, which contribute to stabi-
lizing the various rotamers. The geometry optimizations for
the larger basis set were performed using the B3LYP[24]
density functional method, requiring less computational effort
than the MP2(full) method. It is known, in fact, that the
hybrid functional B3LYP is adequate to accurately calculate
the molecular geometries.[25] This is confirmed for fluorobu-
tane by tests on the basis set convergence using the B3LYP
density functional method, which also showed a good agree-
ment with the rotational constants estimated by the MP2(full)
method for calculations using the same basis set.
Table 7 compares the rotational constants calculated for the
TT, TG, GT, GG, and GG' rotamers of fluorobutane (see
Figure 1) using the MP2(full) method with the 6-31G(d) (set
I) and the 6-311G(d, p) (set II) basis sets along with those
obtained with the B3LYP/6-311G (3df, 3pd)[26] density func-
tional method (set III). The difference between the exper-
imental and the calculated value is reported within paren-
theses. The agreement between the calculated and exper-
imental values of the A rotational constants improves, in
going from set I to set II, for all the observed rotamers but the
TTone. Moreover, the rotational constants of the GG rotamer
are still affected by large deviations from their experimental
values. The B3LYP/6-311G (3df, 3pd) density functional
method shows an impressive improvement of the estimated
rotational constants of the GT and GG rotamers, while the
calculated values of the A rotational constants of both the TT
and TG rotamers are worsened. A comparison of the geo-
metrical parameters of the five rotamers calculated by the
different methods indicates that the largest differences are in
the estimates of the C-C-C-C skeleton angles; for instance, the
dihedral angles of the TG, GG, and GG' rotamers can change
by up to 88. The optimized bond length and angles of the five
rotamers of fluorobutane calculated using the B3LYP/6-311G
(3df, 3pd) and the MP2(full)/6-311G (d, p) methods,
MP2(full)/6-31G (d) for the TT rotamer are available as
Supporting Information.
The B3LYP/6-311G (3df, 3pd) geometry sets the distance of
the C2H and C2H' hydrogen atoms from the fluorine atom (see
Figure 1) both at 2.61 Š for TTand at 2.57 and 2.62 Š for TG,
respectively. That of the GT, GG, and GG' rotamers with the
neighboring C2H hydrogen atom is set at 2.63 Š, 2.63 Š, and
2.61 Š, respectively. In addition, the fluorine atom of the GT
rotamer is 2.62 Š from the C3H hydrogen, while that of the
GG rotamer is close to the C3H' hydrogen atom (2.61 Š), and
that of the GG' rotamer is close to the C4H' hydrogen
(2.46 Š).
In Table 8 the energy differences for the five rotamers,
calculated by using the optimized geometry of the different
methods neglecting the zero-point correction, are reported
with reference to the energy of the most stable GT rotamer.
The results indicate that the B3LYP/6-311G(3df, 3pd) method
tends to overestimate the differences, up to 100 cmÀ1 for the
GG rotamer, with respect to the energies calculated with the
accurate QCISD(T)/6-311G** method using the B3LYP/6-
311G (3df, 3pd) geometries for all the rotamers. The relative
energies calculated with the QCISD(T)/6-311G** method
using the MP2(full)/6-311G(d, p)-optimized geometries in-
dicate a lowering of energy differences for all the rotamers but
the TT, with the largest variation for GG, of 30 cmÀ1. The
QCISD(T)/6-311G** difference between the energy of the
GT rotamer, calculated by using its B3LYP/6-311G(3df, 3pd)-
optimized geometry, and that of the TT and TG rotamers,
calculated by using the geometries obtained with the
Table 7. A, B, and C rotational contants (in MHz) of 1-fluorobutane calculated with the I) MP2(full)/6 ± 31G (d) method, II) MP2(full)/6 ± 31G (d, p) method,
III) B3LYP/6 ± 311G (3df, 3pd) method. The differences between the calculated and the experimental value are given in parentheses.
TT
TG
GT
GG
GG'
I)
A
B
C
A
B
C
A
B
C
18994.33(À14.13)
1940.14(5.81)
1840.96(3.75)
19145.48(137.02)
1939.03(À4.70)
1841.60(À4.39)
19169.64(161.18)
1927.96(À6.37)
1831.08(À6.13)
12676.85(121.04)
2294.03(6.63)
2118.15(2.89)
12563.69(7.88)
2319.22(31.82)
2130.47(À15.21)
12763.40(207.59)
2262.92(À24.48)
2097.85(À17.41)
12383.39(À203.26)
2383.82(À51.90)
2186.88(31.54)
12495.00(À91.65)
2366.46(À34.54)
2179.38(24.04)
12586.43(À0.22)
2330.99(-0.93)
7995.47(À541.61)
3124.53(248.72)
2812.06(134.02)
8045.70(À491.38)
3104.08(228.27)
2800.74(122.70)
8631.40(94.32)
7313.13
3641.90
2702.82
7343.05
3620.31
2696.67
7404.98
3506.08
2639.89
II)
III)
2837.21(À38.60)
2152.64(2.69)
2651.75(À26.29)
Table 8. Energy differences for the five rotamers of fluorobutane with respect to the energy of the GT rotamer. Under the column labeled geometry
optimization is specified the method used to calculate the equilibrium geometry. The energy differences are calculated with I) the B3LYP/6 ± 311G(3df,3pd)
method and II) the QCISD(T)/6 ± 311G** method.
Geometry optimization
TT
TG
GT
GG
GG'
I)
B3LYP/6 ± 311G (3df ,3pd)
183.98
181.36
187.94
157.35
490.08
407.97
399.81
0.00
0.00
0.00
254.12
154.18
124.21
358.10
271.05
258.58
II) B3LYP/6 ± 311G(3df, 3pd)
MP2(full)/6 ± 311G**
MP2(full)/6 ± 31G*(TT) B3LYP/6 ± 311G(3df, 3pd)(GT)
MP2(full)/6 ± 311G**(TG) B3LYP/6 ± 311G(3df, 3pd)(GT)
356.87
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3023

W. Caminati et al.
FULL PAPER
MP2(full)/6-31G(d) and MP2(full)/6-311G(d, p) methods,
respectively, are also reported. A comparison of the calcu-
lated and experimental relative energies is presented in
Table 3 and shows the excellent agreement with the relative
energies calculated with the QCISD(T)/6-311G** method,
using the geometrical parameters corresponding to the rota-
tional constants which better compare with the experimental
data of each rotamer. Relying on the previous results we can
expect that the GG' rotamer is 271 cmÀ1 higher in energy than
the GT rotamer.
It is well-known that a high energy conformer can relax to a
more stable one during a supersonic expansion, provided that
the interconversion barrier is not much higher than kT, where
T is the temperature before of the expansion.[27] To check if
such a phenomenon could explain the nonobservability of the
GG' species, a further investigation was performed to
calculate the interconversion barriers of the GG' rotamer to
the more stable GT and GG rotamers. We optimized the
geometry of the transition states with the B3LYP/6-311G (3df,
3pd) method, and calculated the energy differences using the
QCISD(T)/6-311G** method. Torsional barriers of 696 cmÀ1
and 1541 cmÀ1 were obtained, respectively; they are much too
high to account for a conformational relaxation.
for and that more polarization functions had to be included in
the basis set of the GT, GG, and GG' rotamers. Moreover,
using the B3LYP/6-311G (3df, 3pd) method, it was revealed
that accurate results are obtained from a delicate balancing of
the description of the electronegativity effects and of the
nonbonded F ± H interactions of the fluorine atom.
The assignment of the rotational spectrum of the GG'
conformer would have given completeness to this investiga-
tion. Unfortunately, we were unable to record it. A combi-
nation of factors such as a higher conformational energy with
respect to the ab initio value and a predominant b-type
spectrum could explain this failure. Only a few of its weaker
transitions are suitable to be observed with the RFMWDR
technique in the frequency range available to our conven-
tional spectrometer. Some of these could fall, as predicted by
the calculated rotational constants, in a frequency range
crowded with much more intense signals belonging to other
conformers. As to the jet conditions, only a few calculated
doublet transitions looked promising for the assignment of the
GG' spectrum, but we could not identify them.
The relative energies of the observed conformers obtained
in this work show that the order of stability of the various
conformers changes considerably with respect to chlorobu-
tane; the order of increasing energy is TT, GT, GG, TG, GG'
for chlorobutane, and GT, TT, GG, GG', TG for fluorobutane.
In Table 2 the dipole moments obtained with the B3LYP/6-
311G (3df, 3pd) (set I) and QCISD(T)/6-311G** (set II)
methods calculated at the optimum geometries of each
rotamer are compared to the experimentally estimated values.
Experimental Section
Conclusion
Chemicals: 1-Fluorobutane was prepared from 1-bromobutane and
potassium fluoride in sulfolane at 2008C. A stirred solution of 1-bromo-
butane (67 g, 0.49 mol; Aldrich) in dry sulfolane (600 mL) was heated with
dry potassium fluoride (70 g, 1.2 mol) to 180 ± 2008C under nitrogen for 5 h.
The 1-fluorobutane was collected in a trap at À788C and distilled over a
Vigreux column; b.p. 32.58C; yield 26 g (69%).
The rotational spectra of four conformers of fluorobutane
have been assigned combining conventional and free jet
microwave spectroscopy. This represents, to our knowledge, a
shared ªrecordº as regards the number of rotamers assigned
with microwave spectroscopy for a given molecule. Several
torsionally excited states have also been analyzed. From
experimental data, the 2D potential energy surface of the two
skeletal torsions that generate the conformational equilibria
have been determined by using a flexible model approach.
The quality of the fitting, and even the choice of the potential
energy function, would be improved if precise vibrational
spacings became available, either from far infrared or single
vibronic fluorescence levels experiments. These data are,
however, difficult to obtain due to the presence of numerous
species in the complex equilibrium mixture.
By combining the experimental and the theoretical ab initio
approaches we were able to perform a thorough investigation
on the conformational dynamics and energetics of all the five
rotamers of fluorobutane. The different techniques employed,
on the one hand substantiated the results obtained by giving
complementary information, on the other hand they allowed
better assessment of the accuracy of the theoretical methods
used. In fact, initially the ab initio calculations performed at
the MP2(full) level of theory with the 6-31G(d) and 6-311G(d,
p) basis sets supported the assignment of the rotational
spectra of the GT, TT, and TG rotamers. Subsequently, the
comparison with the experimental data revealed that the
nonbonded F ± H interactions were not properly accounted
Microwave spectrometers: The microwave spectra were recorded with a
free jet millimetre wave spectrometer[8] (FJ-AMMW) in the frequency
ranges 60 ± 78 GHz and with a conventional Stark modulated microwave
spectrometer[9] in the frequency ranges 26 ± 40 GHz. In the latter case the
cell was kept cold at about À408C. The jet was obtained by expanding a
mixture of the sample in argon (ca. 2%) at a stagnation pressure of 0.2 atm
at room temperature, to a final pressure of 10À3 Torr. The nozzle diameter
was 0.35 mm.
Acknowledgements
The authors wish to thank A. Millemaggi for technical assistance. The
Ministero dell' Universita' e della Ricerca Scientifica e Tecnologica and the
Consiglio Nazionale delle Ricerche are acknowledged for financial support.
[1] E.-L. Eliel, N.-L. Allinger, S.-J. Angyal, G.-A. Morrison, Conforma-
tional Analysis, Wiley, New York, 1965.
[2] S. Fagerland, T. Rydland, R. Stùlevik, R. Seip, J. Mol. Struct. 1983, 96,
339 ± 346.
[3] K. Aarset, K. Hagen, R. Stùlevik, P.-C. Sñbo, Struct. Chem. 1995, 6,
197 ± 205.
[4] S. Melandri, P.-G. Favero, the late D. Damiani, W. Caminati, L.-B.
Favero, J. Chem. Soc. Faraday Trans. 1994, 90, 2183 ± 2188.
[5] S. Melandri, P.-G. Favero, W. Caminati, L.-B. Favero, A. Degli Esposti,
J. Chem. Soc. Faraday Trans. 1997, 93, 2131 ± 2137.
[6] R. Meyer, J .Mol. Spectrosc. 1979, 76, 266 ± 300.
[7] W.-E. Steinmetz, F. Hickernell, I.-K. Mun, J. Mol. Spectrosc. 1977, 68,
173 ± 182.
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Conformational Analysis of 1-Fluorobutane
3018±3025
[8] a) S. Melandri, W. Caminati, L.-B. Favero, A. Millemaggi, P.-G.
Favero, J. Mol. Struct. 1995, 352/353, 253 ± 258; b) S. Melandri, G.
Maccaferri, A. Maris, A. Millemaggi, W. Caminati, P.-G. Favero,
Chem. Phys. Lett. 1996, 261, 267 ± 271.
[9] See for example: B. Velino, L.-B. Favero, W. Caminati, J. Mol.
Spectrosc. 1996, 179, 168 ± 174.
[10] F.-J. Wodarczyk, E.-B.Jr. Wilson, J. Mol. Spectrosc. 1971, 37, 445 ± 463.
[11] J.-K.-G.-Watson in Vibrational Spectra and Structure Vol. 6 (Ed.: J.-R.-
Durig,), Elsevier, New York/Amsterdam, 1977, pp. 1 ± 89.
[12] A.-S. Esbitt, E.-B. Jr. Wilson, Rev. Sci. Instrum. 1963, 34, 901 ± 907.
[13] See for example: W. Caminati, S. Melandri, L.-B. Favero, J. Mol.
Spectrosc. 1993, 161, 427 ± 434, and references therein.
[14] S. Golden, E.-B. Jr. Wilson, J.Chem.Phys. 1948, 16, 669 ± 685.
[15] I.-M.-L.-J. Reinartz, A. Dymanus, Chem. Phys. Lett. 1974, 24, 346 ±
351.
[21] W.-J. Hehre, L. Radom, P.-V.-R. Schleyer, J.-A.-Pople, Ab initio
Molecular Orbital Theory, Wiley, New York, 1986.
[22] Gaussian 98, Revision A.5, M.-J. Frisch, G.-W. Trucks, H.-B. Schlegel,
G.-E. Scuseria, M.-A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J.-
A.Jr. Montgomery, R. E. Stratmann, 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. Ochterski, 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. 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, Inc., Pittsburgh PA, 1998.
[23] a) R.-S. Mulliken, J. Chem. Phys. 1955, 23, 1833 ± 1840; b) R.-S.
Mulliken, J. Chem. Phys. 1955, 23, 1841 ± 1846; c) R.-S. Mulliken, J.
Chem. Phys. 1962, 36, 3428 ± 3439.
[16] C. Mùller, M.-S. Plesset, Phys. Rev. 1934, 46, 618 ± 622.
[17] a) R. Ditchfield, W.-J. Hehre, J.-A. Pople, J. Chem. Phys. 1971, 54,
724 ± 728; b) W.-J. Hehre, R. Ditchfield, J.-A. Pople, J. Chem. Phys.
1972, 56, 2257 ± 2261; c) P. C. Hariharan, J.-A.-Pople, Theor. Chim.
Acta. 1973, 28, 213 ± 222.
[24] M.-J. Frisch, J.-A. Pople, J.-S. Binkley, J. Chem. Phys. 1984, 80, 3265 ±
3269.
[18] a) M. Head-Gordon, J.-A. Pople, M.-J. Frisch, Chem. Phys. Lett. 1988,
153, 503 ± 506; b) M.-J. Frisch, M. Head-Gordon, J.-A. Pople, Chem.
Phys. Lett. 1990, 166, 275 ± 280; c) M.-J. Frisch, M. Head-Gordon, J.-A.
Pople, Chem. Phys. Lett. 1990, 166, 281 ± 289; d) M. Head-Gordon, T.
Head-Gordon, Chem. Phys. Lett. 1994, 220, 122 ± 128; e) S. Saebo, J.
Almlof, Chem. Phys. Lett. 1989, 154, 83 ± 89.
[19] a) J.-A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys.
1987, 87, 5968 ± 5975; b) K. Raghavachari, G.-W. Trucks, J.-A. Pople,
M. Head-Gordon, Chem. Phys. Lett. 1989, 157, 479 ± 483.
[20] a) A. D. Mc Lean, G.-S. Chandler, J. Chem. Phys. 1980, 72, 5639 ±
5648; b) R. Krishnan, J.-S. Binkley, R. Seeger, J.-A. Pople, J. Chem.
Phys. 1980, 72, 650 ± 654.
[25] a) A.-D. Becke, J. Chem. Phys. 1993, 98, 5648 ± 5652; c) P.-J. Stevens,
F.-J. Devlin, C.-F. Chablowski, M.-J. Frisch, J. Phys. Chem. 1994, 98,
11623 ± 11627.
[26] J.-A.Jr. Montgomery, M.-J. Frisch, J.-W. Ochterski, G.-A. Petersson, J.
Chem. Phys. 1999, 110, 2822 ± 2827.
[27] R. S. Ruoff, T.-D. Klots, T. Emilson, H.-S. Gutowsky, J. Chem. Phys.
1990, 93, 3142 ± 3150.
Received: December 28, 1999 [F2215]
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3025