The vibrational spectra and normal coordinates analysis of bromofluoromethane, CH2BrF

Article abstract of DOI:10.1016/S0022-2860(99)00251-3

The infrared gas-phase spectra of bromofluoromethane (CH₂BrF) have been studied in the region below 6200 cm^-1 under conditions of medium resolution. All the fundamentals and many overtones, combination and hot bands have been assigned leading to an almost complete set of anharmonicity constants. Rotational analyses have been performed on the observed Q-branch features of over 10 bands. Enriched ⁷⁹Br and ⁸¹Br samples were also employed to confirm vibrational assignment and supply further data. Analyses of Fermi resonance are made. The molecular structure was calculated ab initio at the Hartree-Fock (HF), the second-order Moller-Plesset (MP2) and the density functional theory (DFT) level with the 6M311++G(3df, 2pd) basis set. The ab initio force constants obtained from the vibrational analysis at B3LYP/6-311++G(3df, 2pd) level of theory were employed to fit the experimental data and an optimal harmonic force field was obtained for the CH₂BrF molecule. (C) 2000 Elsevier Science B.V.

Full text of DOI:10.1016/S0022-2860(99)00251-3

Journal of Molecular Structure 517–518 (2000) 197–208
www.elsevier.nl/locate/molstruc
The vibrational spectra and normal coordinates analysis of
bromofluoromethane, CH2BrFଝ
a,
a
b
a
*
A. Baldacci , A. Baldan , A. Gambi , P. Stoppa
a
`
Dipartimento di Chimica Fisica, Universita Ca’ Foscari di Venezia, DCF, Dorsoduro 2137, I-30123 Venice, Italy
b
`
Universita di Udine, DSTC, Via Cotonificio 108, I-33100 Udine, Italy
Received 2 February 1999; accepted 4 March 1999
Abstract
The infrared gas-phase spectra of bromofluoromethane (CH2BrF) have been studied in the region below 6200 cmϪ1 under
conditions of medium resolution. All the fundamentals and many overtones, combination and hot bands have been assigned
leading to an almost complete set of anharmonicity constants. Rotational analyses have been performed on the observed Q-
branch features of over 10 bands. Enriched 79Br and 81Br samples were also employed to confirm vibrational assignment and
supply further data. Analyses of Fermi resonance are made. The molecular structure was calculated ab initio at the Hartree–
Fock (HF), the second-order Møller–Plesset (MP2) and the density functional theory (DFT) level with the 6-311ϩϩG(3df,
2pd) basis set. The ab initio force constants obtained from the vibrational analysis at B3LYP/6-311ϩϩG(3df, 2pd) level of
theory were employed to fit the experimental data and an optimal harmonic force field was obtained for the CH2BrF molecule.
᭧ 2000 Elsevier Science B.V. All rights reserved.
Keywords: Vibrational analysis; Bromofluoromethane; Anharmonicity constants; Ab initio calculation; Harmonic force field
1. Introduction
of the Teller–Redlich product rule to pentatomic
methane derivatives.
Among the di-halogen substituted methanes,
bromofluoromethane (CH2BrF) has received very
little spectroscopic attention over the years. To our
knowledge, the unique vibrational measurement in
the regions of the fundamental modes has been
reported in the early work of Delwaulle et al. [1]
using the Raman technique. From those data, the
assignment of the fundamental bands was reported
by Pitzer et al. [2] in a work concerning the application
Subsequently, El-Sabban et al. [3] revised the posi-
tion of n5, which was assumed in Fermi resonance
with 2n6. This change was supported by means of a
normal coordinate treatment on a series of CH2XY
halomethane derivatives.
The present study was undertaken to obtain a
comprehensive set of vibrational data on the
CH2BrF molecule. Although, there is no doubt
that the fundamental vibrational assignment of
the molecule is correct, an up to date revision
of these data, to be pursued with the IR technique,
is of interest for further theoretical and high-reso-
lution experimental works. In this perspective, the
isotopomers CH279BrF and CH281BrF have also
been synthesized to provide further vibrational
ଝ In honour of Dr. Georges Graner for his many contributions to
science.
* Corresponding author. Tel.: ϩ 39-041-2578508; fax: ϩ 39-
041-2578594.
E-mail address: baldacci@unive.it (A. Baldacci).
0022-2860/00/$ - see front matter ᭧ 2000 Elsevier Science B.V. All rights reserved.
PII: S0022-2860(99)00251-3

198
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Fig. 1. The gas-phase IR spectra of CH2BrF at 2 cmϪ1 resolution: (a) path-length 10 cm, pressure ഡ 8 mbar; and (b) path-length 16 cm,
pressure ഡ 160 mbar. Only some representative absorption bands are labelled.
data and to confirm the assignments. In addition,
Fermi resonance perturbations of the bands near
2900 and 5900 cmϪ1 have been observed and
discussed.
As it was still not possible to generate a quadratic
vibrational force field in the conventional manner
from these data, an ab initio force field calculation
was performed to provide a basis for the optimization
process.
yield of the reaction is increased with regard to the
technique of Raymond [5], allowing exclusively a
gas–solid contact between the two reagents. The salt
precursor was prepared by adding a slight excess of
concentrated aqueous solution of AgNO3 to an ice-
water solution of CH2FCO2Na (Fluka 95%), and
then dried under vacuum over anhydrous P4O10. The
Br2 molecule was obtained from NH4Br (Sigma–
Aldrich, 99.99%) by reaction with MnO2/H2SO4
(1:1) at 75ЊC.
In a typical experiment, the CH2FCO2Ag (1 mmol)
and purified anhydrous bromine (1.15 mmol) were
stored into an evacuable specially designed reaction
vessel [6] connected to a vacuum line. The Borodine–
Hunsdiecker decarboxylation of the powdered silver
salt, contained in the flask, instantaneously started
when gaseous bromine, collected as a liquid in a
small tube, was expanded at room temperature from
one arm to the evacuated reaction vessel. The reaction
was completed by warming to 80ЊC for 1 h. At this
point, the crude product was transferred by the
2. Experimental details
2.1. Synthesis of CH2BrF
In the synthesis of CH2BrF on a 1 mmol scale,
gaseous bromine is brought into contact with solid
CH2FCO2Ag, with a molar ratio 1:1, to realize the
Borodine–Hunsdiecker reaction as described by
Haszeldine [4]. As the oxidation of the silver salt is
a secondary reaction in presence of liquid bromine,

A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
199
Table 1
The observed band centers (cmϪ1) of the gas-phase IR spectra of CH2BrF (vs, very strong; s, strong; m, medium; w, weak; vw, very weak)
Band
Envelope
Relative intensity
Wavenumbera
n6
B
A/B
w
vw
(311.0/310.4)b,c
339 ^ 2
n5 Ϫ n6
2n5 Ϫ n5
n5 ϩ 2n6 Ϫ 2n6
n5 ϩ n6 Ϫ n6
n5
644.8/643.9b
648.2/647.2b
649.4/648.4b
650.5/649.7b
756.8/757.4b
935.2
A
B
C
B
vs
w
m
m
n4 Ϫ n6
n9
n5 ϩ n6
n4 ϩ n6 Ϫ n6
n4
960.2/958.6b
1066.3
1068.1
1223.6
A/B
C
vs
m
n6 ϩ n8 Ϫ n6
n8
1226.7
n3 ϩ n6 Ϫ n6
n3
1313.0
1314.1
1465.4
A/B
B
vs
w
n2
n5 ϩ n9
2n5 ϩ n6
n4 ϩ n5
2n9
n3 ϩ n5
n4 ϩ n9
n4 ϩ n5 ϩ n6
2n4
n8 ϩ n9
n5 ϩ n6 ϩ n8
n3 ϩ n9
n4 ϩ n8
n3 ϩ n4
n2 ϩ n9
2n8
n6 ϩ n8 ϩ n9
n3 ϩ n8
2n3
C
B
A
B
B
C
B
A/B
B
C
C
C
A/B
C
A/B
B
C
vw
vw
w
vw
vw
vw
vw
m
vw
vw
w
vw
w
1582 ^ 1
1602 ^ 1
1715.9
1869 ^ 1
1960 ^ 1
2001.5 ^ 0.4
2022 ^ 2
2119.5
2161 ^ 1
2183 ^ 1
2245.5
2284.2
2376.0
w
2391.5
vw
vw
vw
w
2446.2 ^ 0.4
2470 ^ 1
2532.3
A/B
2612.9
n2 ϩ n3 ϩ n6 Ϫ n6
n2 ϩ n3
2n2
2774.8
2776.9
2907.6
A/B
B
B
w
m
s
n1
2992.6(2980.8)d
3047.2
n7
C
m
n6 ϩ n7 Ϫ n6
3n4
3049.8
A/B
A/B
A/B
A/B
C
C
A/B
B
w
3153.2 ^ 0.4
3304.0 ^ 0.4
3554.8 ^ 0.4
3641.1 ^ 0.4
3698 ^ 1
3918.9 ^ 0.4
3976.6 ^ 0.4
4058 ^ 1
4121.7 ^ 0.4
4263 ^ 1
4306 ^ 1
4347.7 ^ 0.4
n1 ϩ n6
2n2 ϩ n5
n1 ϩ n5
n5 ϩ n7
n1 ϩ n9
n7 ϩ n9
n1 ϩ n4
n4 ϩ n7
n7 ϩ n8
n1 ϩ n3
n3 ϩ n7
vw
vw
w
vw
vw
w
w
w
w
w
C
A/B
B
C
w

200
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Table 1 (continued)
Band
Envelope
Relative intensity
Wavenumbera
n2 ϩ n7
n1 ϩ 2n2
n1 ϩ n7
2n1
2n2 ϩ n7
2n7
C
B
C
B
C
B
m
w
w
w
w
w
4490.5
5861 ^ 1
5887.2 ^ 0.4
5934 ^ 1
5946.9 ^ 0.4
6056 ^ 1
a The experimental error is ^ 0.2 cmϪ1 unless otherwise quoted.
b The two values indicate the 79/81Br measurements observed in the isotopic enriched samples.
c Evaluated by difference of selected bands of the enriched 79/81Br samples (see text).
d Unperturbed value when Fermi resonance (k122) is taken into account (see text).
vacuum line to a 50 ml evacuated glass container
(frozen using liquid nitrogen) into which were
previously added mercury and soda lime to scavenge
the remaining bromine and carbon dioxide, respec-
tively. The purity of the sample, separated by distilla-
tion under vacuum, was tested by IR spectroscopy.
The isotopically enriched samples of CH279BrF and
CH281BrF were synthesized analogously by using
ammonium bromide (EG&G Mound Applied Tech-
nologies) with 90% of 79Br and 90% 81Br isotopic
purity, respectively.
750 FTIR spectrometers. Sample pressures ranged
from 5 to 250 mbar in a 16 cm path sample cell
equipped with KBr windows in the region 400–
6200 cmϪ1 and KRS-5 windows in the region 200–
400 cmϪ1 as appropriate. The absorption spectra were
taken at resolutions of 2.0, 0.5 and 0.25 cmϪ1
.
2.3. Computational method
Ab initio molecular orbital calculations were
performed with the program package gaussian 94
[7] on a SGI Origin 2000 computer system. Normal
mode calculations were carried out using a modified
version of the ASYM20 computer program [8]. Addi-
tional fortran programs were written in order to be
able to take advantage of the ab initio quantum
mechanical generated force field and to interface a
graphic workstation to the main computer system.
2.2. Recording of the spectra
The gas-phase infrared spectra were recorded at
room temperature in the range 200–6200 cmϪ1
using the Bruker Vector 22 and the Nicolet Magna
3. Results and discussion
3.1. Spectral data and assignment of fundamentals
A general survey spectra of CH2BrF in the regions
of interest, recorded at 2 cmϪ1 resolution, are shown
in Fig. 1. Few assignments are given below selected
bands in order to facilitate reading of the spectra. It
will be observed that the spectra provide a rich source
of information on overtone and combination levels, as
well as on the fundamentals themselves. The frequen-
cies and the assignments for the observed bands are
given in Table 1.
In Fig. 2, the structure of CH2BrF with principal
inertial axes drawn is depicted. The symmetry plane
Fig. 2. The structure of CH2BrF with principal inertial axes and
valence coordinates.

A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
201
to the symmetric stretch, while the latter weaker one
to the asymmetric stretch.
Of the four CH2 bending modes, two belong to the
A0 symmetry species (scissoring and wagging), while
the others have A00 symmetry (rocking and twisting).
The scissor mode, n2, originates a weak band with b-
type structure, while the wag mode, n3, produces a
strong hybrid band with predominant a-type char-
acter. The weak band n8, associated to the twisting
mode, shows the typical structure of a c-type band; the
higher edge of the R-branch wavenumber region is
partially overlapped by the n3 features. The weak
CH2 rocking, n9, shows a prominent central Q-branch
and unresolved structures in both the P- and R-branch
regions. The absence of a rotational structure suggests
a perturbation implying at least one of the two nearby
vibrational levels n5 ϩ n6 (A0) and 3n6 (A0).
The CF and CBr stretches n4 and n5, respectively,
exhibit the stronger IR absorption intensity; n4
presents a hybrid band contour with prevalent a-type
character, while n5 definitively shows only structures
of a-type bands.
Fig. 3. The n5 band region of CH2BrF (path-length 16 cm,
pressure ഡ 1.3 mbar, resolution ˆ 0.5 cmϪ1). (a) and (b) The
enriched sample spectra of 79Br and 81Br isotopomers, respectively.
(c) The spectrum of CH2BrF in natural composition.
The weak CBrF bending n6, located in the far IR
region, is characterized by an unresolved b-type struc-
ture whose R-branch is overlapped by the P-branch of
the still less intense difference band n5 Ϫ n6.
The 79/81Br isotopic shift is almost negligible
throughout the entire spectrum investigated. Among
the fundamentals, it has only been observed in the n5
band associated to the C–Br stretching mode. Fig. 3
shows the spectral region of this fundamental for the
two isotopomers with enriched 79/81Br and the natural
sample. From the analysis of the CH279BrF and
CH281BrF spectra, the vibrational value of the lowest
fundamental n6 could be evaluated by difference of
selected assigned bands (n5 ϩ n6=n5 ϩ n6 Ϫ n6;
n4=n4 Ϫ n6).
contains the F, C and Br atoms, whereas the two H
atoms lie one above and the other below that plane.
Because of its Cs symmetry, the CH2BrF molecule has
two types of vibrational bands. The A0 symmetry
species give rise to absorption bands of mixed a-
and b-type contours. The A00 vibrations give rise to
c-type band envelopes having well defined central Q-
branches. The nine fundamental modes may be
expressed in terms of vibrations associated to the
methylene group, i.e. asymmetric and symmetric
stretching, scissoring, wagging, twisting and rocking,
plus the modes arising from the heavy atoms: C–F
and C–Br stretchings and CBrF deformation.
3.2. Overtones and combination bands
Table 1 includes the results obtained for the funda-
mental bands. The band contour envelopes, the rela-
tive intensity and, when observed, the 79/81Br isotopic
shifts are also indicated in the table.
In the most favorable experimental conditions, a
considerable amount of overtones and combination
bands could be observed and positively identified.
The proposed assignment, collected in Table 1, has
been performed taking into account harmonic approx-
imation, relative intensity and expected band contour
derived from the symmetry species of the relative
normal vibrations. Although there are anomalies in
The two CH2 stretching modes n1 (A0 symmetry)
and n7 (A00 symmetry), although partially overlapped,
show the typical structure of b- and c-type bands,
respectively. The former stronger band, located in
the lower wavenumber side, was therefore assigned

202
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Table 2
Molecular parameters (cmϪ1) of b-and c-type bands of CH2BrF (the uncertainties given in parentheses are one standard deviation of the last
significant digits)
ꢀ
0
00
a
ꢀ 0
ꢀ 00
Band
n0
ꢀA ϪB †
ꢀaAϪaB† × 102
ꢀD0K ϪD0K0 † × 104
ꢀA ϪB †
s
Number of data
n1
n2
n3
n4
n7
n8
2n2
2992.44(1) 1.2036(5)
1465.11(1) 1.2032(5)
1314.14(1) 1.2024(4)
1068.36(1) 1.1982(4)
3046.92(2) 1.2039(18)
1226.42(1) 1.2005(6)
2907.19(1) 1.1988(6)
0.506(3)
0.439(6)
0.402(4)
0.870(3)
0.565(19)
0.624(7)
0.757(11)
Ϫ0.16(1)
Ϫ0.15(1)
Ϫ0.14(1)
Ϫ0.15(1)
Ϫ0.24(6)
Ϫ0.15(2)
Ϫ0.10(2)
1.2087(5)
1.2076(5)
1.2064(4)
1.2069(4)
0.036 44
0.027 33
0.026 36
0.036 46
1.2095(18) 0.070 27
1.2067(6)
1.2064(6)
0.038 37
0.032 30
Average: 1.2075(8)b
n2 ϩ n7
n2 ϩ n9
4490.32(3) 1.1987(9)c
0.883(32)
0.082 22
0.079 17
0.026 20
0.036 30
2392.14(4) 1.1982(10)c 0.927(52)
n2 ϩ n6Ϫn6
n4 ϩ n6Ϫn6
1464.01(1) 1.2074(5)
1066.48(1) 1.2053(7)
0.398(12)
0.865(7)
1.2114(5)
1.2139(7)
Ϫ0.13(1)
Average: 1.2126(9)
a Standard deviation (cmϪ1).
b
79/81
Ϫ1
ꢀ
B2 Microwave values (Ref [9]) of ꢀA0ϪB0† ˆ 1.20764/1.20801 cm
.
c
ꢀ
Constant obtained using the average value of ꢀA0ϪB0†.
few cases, the assignment appears to be consistent
throughout the entire spectral region investigated.
In a number of cases, 79/81Br isotopic shifts could be
determined accurately, and these data are also
included in Table 1.
n2 ϩ n6 Ϫ n6 whose analysis has been based on rota-
tional structure of Q and Q sub-branches.
P
R
3.4. Rotational analysis
At the highest resolutions employed in recording
the spectra (0.25 and in few cases 0.5 cmϪ1), a number
of bands exhibit noticeable rotational structure which
could be assigned and analyzed. From the rotational
constants obtained by microwave technique [9], the
Under the best available resolution (0.25 cmϪ1), a
number of bands exhibit rotational structure; among
them 2n2 (b-type), n2 ϩ n9 and n2 ϩ n7 (both c-type)
have been analyzed according to the polynomial
procedure later described.
Ϫ1
¯
parameter 2(A Ϫ B) ˆ 2.4 cm indicates that the b-
and c-type bands can include rotational structure
similar to that observed for perpendicular bands of
symmetric tops. Indeed, from the above value it
appears clear that the observed rotational structure
belongs to the P,RQK clusters of b- or c-type bands,
being the separation between consecutive peaks
around 2.4 ^ 0.3 cmϪ1. The remaining expected
features, allowed by the selection rules, such as the
RR and PP transitions, are too weak to be observed and
merge into the noise level of the background.
3.3. Hot bands
The presence of satellite peaks near the band origin
of some fundamentals provides further information on
the vibrational energy levels of the molecule through
the identification of the hot bands defined as
ni ϩ nnj Ϫ nnj. Taking the intensity of the ni band
as 100%, the expected relative intensities of the
most intense hot bands at room temperature are calcu-
lated to be: 22% for ni ϩ n6 Ϫ n6, 5% for ni ϩ 2n6 Ϫ
2n6 and 4% for ni ϩ n5 Ϫ n5.
Based on these relevant factors, additional assign-
ments were performed in six of the nine fundamental
band regions. All, but one, have been found located in
the lower wavenumber side with respect to the main
band. These data are reported in Table 1 except for
Analyses were performed by least-squares fitting
procedure in terms of the expressions either quadratic
or cubic in K, using, in the approximation for
symmetric tops, the following reduced equation [10]:
0
0
0
ꢀ 0
ꢀ 0
ꢀ 0
nR;P ˆ n0 ϩ ꢀA Ϫ B † ^ 2ꢀA Ϫ B †K ϩ ‰ꢀA Ϫ B †
00
2
0
00
3
ꢀ 00
Ϫ ꢀA Ϫ B †ŠK ϯ 4ꢀDK Ϫ DK†K

A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
203
Fig. 4. The FTIR detailed spectrum of the CH2 stretchings band region of CH2BrF at 0.25 cmϪ1 resolution (path-length 16 cm, pressure ഡ
40 mbar). The rotational structure of the stronger n1 b-type band is labelled.
where the upper and lower sign apply for the R- and P-
In Fig. 5, the rotational structure and the assignment
of the Q-head clusters in the P- and R-branch regions
of the n8, are depicted. This band shows an unex-
ꢀ
branch, respectively, and B ˆ ꢀB ϩ C†=2.
The rotational parameters, the number of data used
and standard deviations for the six fundamental bands
subjected to the least-squares fit are summarized in
Table 2; this table includes also the results for the
overtone 2n2, the combination bands n2 ϩ n7 and
n2 ϩ n9 and the hot bands n2 ϩ n6 Ϫ n6 and
n4 ϩ n6 Ϫ n6.
P
pected behavior in the RQ9(J) and Q11(J) sub-
branches. As evidenced in the illustration, they appear
in the form of broad features with at least two peak
maxima. They were excluded from the fitting proce-
dure, and this effect has been attributed to Coriolis
resonance with one of the nearby vibrational levels,
all of them expected to have an energy value higher
than that of n8. The most plausible interacting level
should be n6 ϩ n9 which has been calculated to be
21 cmϪ1 above n8. With this assumption and using
the reduced energy-level diagram in the prolate
symmetric top limit, it can be shown that the K ˆ
10 sub-level of n8 is near degeneration with the K ˆ
9 sublevel of n6 ϩ n9, corresponding to an interaction
through first-order c-axis Coriolis coupling.
Fig. 4 shows the rotational spectral features of the
2n2, n1 and n7 bands in the region around 3000 cmϪ1
.
P
R
Some assignments of the QK and QK lines of the n1
fundamental are indicated in the lower part of the
illustration. The rotational lines undergoing asym-
metry splitting, when observed, were not used in the
fitting procedure. Measurements were usually
performed at the top of the sharp lines. The PQ
R
heads of n7 are severely mingled with the higher Q
series of the stronger n1 band. In order to verify the
consistency of the assigned rotational structure,
checks were provided by using the ground state
combination differences method in the symmetric
top limit. With the same procedure, and assuming
the vibrational origin of 2n2, given in Table 1, the
P,RQ clusters were accordingly identified.
The rotational features of n2, n3 and n4 were readily
identified, in spite of the fact that in the latter two
cases, the a-type component is prevailing over the b-
type.
A deeper scrutiny of the spectra shows that the Q-
head clusters—especially in the P-branch region of
n3, n4 and to a less extent of n8—are degrading to

204
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Fig. 5. The FTIR detailed spectrum of the n8 c-type fundamental of CH2BrF at 0.25 cmϪ1 resolution (path-length 16 cm, pressure ഡ 40 mbar).
The rotational structure shows the anomalous effect observed for K ˆ 9 and 11 in the RQ- and PQ sub-branches, respectively. The line marked by
asterisk belongs to the hot-band n6 ϩ n8 Ϫ n6.
lower wavenumbers, while the opposite happens in
application of the expression [11]:
ꢀ 0
ꢀ 00
the 2n2 band; this indicates that ꢀB Ϫ B † values is
negative in the former case and positive in the latter
one.
X
X X
Gꢀn1; n2; …† ˆ
viꢀni ϩ 1=2† ϩ
xikꢀni ϩ 1=2†
i
i
kՆi
As further weaker peaks were observed in the n2
and n4 spectral regions, they were analyzed in terms
of hot bands having n6 as lower level. For
n2 ϩ n6 Ϫ n6, the vibrational origin has been obtained
from the polynomial fit of the PQ and RQ sub-
branches; the assignment is consistent with the
evaluation of the anharmonicity term x26 determined
from the assignment of the hot band
n2 ϩ n3 ϩ n6 Ϫ n6. In the n4 ϩ n6 Ϫ n6 hot band, the
 ꢀnk ϩ 1=2†
Of the 45 determinable constants, 41 could be calcu-
lated. Among them, 37 constants were obtained using
the first overtones, combination bands with two quanta
and hot bands observed in the fundamental band
regions. The remaining four constants, namely, x12,
x25, x58 and x69, were derived from three quanta combi-
nation bands eventually using previously calculated
anharmonicity constants. The accuracy of the constants
reported in the table is dependent on the experimental
error of measurements and on their number. The values
of Table 3 should be considered effective, since a
number of vibrational levels show evidence of anhar-
monic vibrational resonance. From these, it is worth
mentioning the levels n5 ˆ 1 and n6 ˆ 2; the latter
band is severely overlapped, and for this reason it is
not measurable. The relative high positive value of x67
might be a sign of a perturbed level.
P
R
numbering of the Q and Q lines was provided by
considering the relative position of the a-type compo-
nent Q-branch.
3.5. Anharmonicity constants and vibrational
resonances
The data set of Table 1 has been used for deter-
mining the anharmonicity constants of the molecule.
The values reported in Table 3 derive from the

A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
205
Table 3
Anharmonicity constants xij (cmϪ1) of CH2BrF (when i,j ˆ 5 and 6, the xij come from the available data of CH279BrF; values in parentheses are
when explicit treatment of Fermi resonance is taken into account (k122 ˆ 58.7 cmϪ1))
i\j
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
Ϫ25.6 (Ϫ39.4)
Ϫ19.6 (Ϫ18.4)
Ϫ11.6 (Ϫ5.7)
Ϫ0.7
Ϫ2.6
Ϫ7.6
Ϫ2.7
Ϫ
Ϫ2.0
Ϫ1.6
Ϫ4.6
Ϫ2.7
Ϫ2.8
0.4
Ϫ152.6 (Ϫ116.3)
Ϫ
Ϫ
Ϫ8.9
Ϫ9.1
Ϫ3.8
Ϫ1.8
Ϫ3.7
1.1
Ϫ5.8
Ϫ0.9
Ϫ0.7
Ϫ1.1
Ϫ1.1
Ϫ1.8
Ϫ1.1
Ϫ
Ϫ22.1
Ϫ13.6
6.4
0.3
2.6
Ϫ19.2
Ϫ6.2
Ϫ8.3
Ϫ8.5
Ϫ10.6
Ϫ1.0
Ϫ3.1
Ϫ10.9
Ϫ3.6
Effects of Fermi resonance are evident in the CH2
constant k122 ˆ 58.7 cmϪ1, the unperturbed values of
the anharmonicity constants x11, x12, x17 and x22 are
obtained; these data, between parentheses, are also
reported in Table 3. In addition, the explicit treatment
of the k122 resonance modifies the value of the n1
fundamental to 2980.8 cmϪ1 (see Table 1).
stretching region where the 2n2 overtone appears
more intense than the fundamental n2; furthermore,
a major resonance effect has been noted in the CH2
overtone region between n1 ϩ n7 and 2n2 ϩ n7, whose
assignments were based on the different intensity of
the examined bands.
In order to achieve a more realistic empirical set of
anharmonicity constants connected with the bands
observed in these spectral ranges, we followed the
procedure of Duncan et al. [12] to deperturb the reso-
nating levels. The n1/2n2 dyad and the pentad
2n7=n1 ϩ n7=2n2 ϩ n7=2n1=n1 ϩ 2n2 should be analyz-
able in terms of the parameters n1, n2, n7, x11, x22, x77,
x12, x17, x27 and k122, according to the scheme proposed
in Ref. [12].
3.6. Normal coordinates analysis
In the present investigation, the most general quad-
ratic potential function based on the valence force
(Fig. 2) would include 34 potential constants. As the
set of internal valence coordinates depicted in Fig. 2 is
redundant, the representation of a force field in these
terms is never unique; therefore only the F matrix
expressed in non-redundant symmetry coordinates
gives a unique representation of the force field.
A non-redundant set of symmetry coordinates can
be defined from the valence coordinates of CH2BrF
applying the method of Typke [13], in order to remove
the redundancy condition in the bond angle definition
for the four bonds on the carbon atom. These
symmetry coordinates are listed in Table 4.
From the diagonalization of the energy matrices
connecting the above terms, with a cubic force
Table 4
The optimized ab initio geometries of CH2BrF (distances are given
˚
in A; angles in Њ; energies in Hartree; and dipole moments in Debye)
6-311ϩϩG(3df, 2pd)
This transformation will give rise to a symmetric
force field having 27 terms: 21 symmetry force
constants of species A0 and six of species A00. Never-
theless, with the experimental data available (nine
fundamentals, two isotopic shifts and five quartic
centrifugal distortion constants [14]) a vibrational
force field in the conventional manner cannot be
determined.
HF
MP2
B3LYP
1.0844
h
f
1.0741
1.3322
1.9341
1.0841
1.3593
1.9255
1.3605
1.9587
110.47
106.85
113.37
109.61
b
a
b
g
d
E
m
110.20
110.51
107.41
112.65
107.18
112.61
109.80
109.41
Quantum mechanical calculations yield useful
information on the molecular potential surface and
force constants. Less dominant off-diagonal force
Ϫ2710.88538
Ϫ2711.47461
1.99
Ϫ2713.34760
1.80
1.99

206
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Table 5
Symmetry coordinates of CH2BrF (R1, R3, R4, R5, and R are obtained from the molecular geometry and from the necessary orthonormality
conditions with the redundant symmetry coordinate [13])
1
A0 S1 ˆ
ꢀh1 ϩ h2†
nꢀCH2† symmetrical stretch
p
2
S2 ˆ R4g Ϫ R3a
S3 ˆ R5ꢀb1 ϩ b2† Ϫ R1ꢀd1 ϩ d2†
(CH2) scissor
(CH2) wag
S4 ˆ f
S5 ˆ b
n (CF) stretch
n(CBr) stretch
(FCBr) deformation
S6 ˆ RR3g ϩ RR4a Ϫ R1ꢀb1 ϩ b2† Ϫ R5ꢀd1 ϩ d2†
1
A00 S7 ˆ
ꢀh1 Ϫ h2†
n(CH2) asymmetrical stretch
p
2
1
S8 ˆ ꢀd1 Ϫ d2 Ϫ b1 ϩ b2†
(CH2) twist
2
1
S9 ˆ ꢀd1 Ϫ d2 ϩ b1 Ϫ b2†
(CH2† rock
2
constants are frequently difficult to determine from
the data, and usually are more accurately determined
from theory than from experiment. This complemen-
tary information of theory and experiment suggests
the joint use of both methods, which has been success-
fully implemented in several cases [15].
levels of theory and the larger basis set are summar-
ized in Table 4 together with the total energies and the
dipole moments.
Selection of the reference geometry around which
the derivatives are evaluated has quite a significant
effect on the harmonic force constants, especially
for the stretching modes. We have chosen the
geometry optimized with B3LYP level of theory
which has been proved to be a very cost-effective
method in predicting vibrational frequencies [19].
This choice was also supported from the dipole
moments: indeed the DFT calculated value of 1.80
D, is consistent with the values of 1.43 D for
CH2Br2 and 1.978 D for CH2F2 [20].
3.7. Ab initio calculations
The LCAO-MO-SCF restricted Hartree–Fock
calculations were performed with the gaussian 94
program [7] using gaussian type basis functions. The
energy minima with respect to the nuclear coordinates
were obtained by simultaneous relaxation of all of the
geometric parameters: the redundant set of internal
coordinates defined in Fig. 2. Successively, larger
basis set have been employed in the calculations,
including polarization functions and augmented
atomic orbital functions; the final basis set was 6-
311ϩϩG(3df,2pd).
We then performed the vibrational analyses at the
DFT level of theory, and the cartesian force constants
obtained from this calculation were used in the normal
coordinates procedure.
3.8. Force field calculation
Further quantum mechanical calculations on
CH2BrF have been carried out using the second-
order Møller–Plesset perturbation theory [16], to
include electron correlation and the density functional
theory (DFT) in the form of Becke’s three parameter
functional hybrid method [17] in combination with
Lee, Yang and Parr correlation functional [18]
(B3LYP). The optimized geometries at the three
The procedure outlined in Refs. [8,21], was used to
convert the B3LYP/6-311ϩϩG(3df,2pd) force field
of CH2BrF from cartesian to symmetry coordinates.
These data are presented in the last three columns of
Table 6; the numbering of the force constants is
consistent with the symmetry coordinates of Table 5.
As a joint fit of vibrational data and centrifugal

A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
207
Table 6
Table 7
The harmonic force field of CH2BrF in terms of symmetric force
Observed and calculated harmonic band centers vi (cmϪ1), 79/81Br
isotopic shifts Dvi (cmϪ1) and centrifugal distortion constants (kHz)
used in the vibrational analysis of CH2BrF. In the last column, the
wavenumbers (cmϪ1) obtained from ab initio calculation are
reported (B3LYP/6-311ϩϩG(3df,2pd))
constants (stretching force constants are in aJ AϪ2; stretch-bend and
˚
Ϫ1
˚
bending force constants are in aJ A and aJ, respectively)
F11 5.3069(11)a 5.4490b F12
F22 0.8258(90)
F33 0.7665(5)
F44 5.8116(34)
0.1035
F13 Ϫ0.0613
F34 Ϫ0.5393
F35 0.3557
F36 Ϫ0.0660
0.8646
0.7603
5.7385
F14
F15
0.2998
0.0715
Observed
Calculated
Ab initio
F45
F46
F56
0.5886
0.0670
0.0517
A0
v1
v2
v3
v4
v5
Dv5
v6
Dv6
v7
v8
v9
DJ
3055.12
1492.56
1334.69
1078.06
658.70
Ϫ0.80
313.05
Ϫ0.80
3055.13
1495.44
1335.11
1077.10
654.34
Ϫ0.83
312.69
Ϫ0.87
3095.9
1492.6
1329.0
1068.1
626.0
Ϫ0.8
307.1
Ϫ0.9
F55 2.8478(322) 2.5551
F16 Ϫ0.0811
F23 Ϫ0.0448
F24 Ϫ0.2611
F25 Ϫ0.2751
F66 0.7582(74)
F77 5.1906(11)
F88 0.6494(10)
F99 0.9274(76)
0.7200
5.3730
0.6540
0.8968
F78 Ϫ0.0380
F79 0.0504
F89 Ϫ0.1159
F26
0.2105
a Refined diagonal symmetry force constants. Values in paren-
theses are standard deviations in units of the last significant digit.
The out of diagonal force constants were held fixed to the ab initio
value during the fitting procedure.
A00
3126.62
1243.92
951.65
3126.62
1243.92
951.65
3180.8
1244.9
938.2
b Ab initio diagonal force constants.
1.7687a
Ϫ24.0380
526.1957
0.1686
1.6625
DJK
DK
dJ
Ϫ24.5687
549.5276
0.1663
distortion constants was to be made, and the
centrifugal distortion constants have only small anhar-
monic contributions, it was decided to correct the
band centers for anharmonicity, in order to have an
approximate set of harmonic vibrational fundamentals
for the force field calculation. This was done using the
dK
2.2784
7.4047
a From Ref. [14].
equation
and the ab initio force constants are the overall scale.
The harmonic fundamentals and quartic centrifugal
distortion constants computed with this force field
are collected (second column of Table 7), whereas
in the last column of this table, the values of the
fundamental modes obtained in the vibrational
analysis of the ab initio calculation (B3LYP/6-
311ϩϩG(3df,2pd)) are reported.
The calculated values of the fundamental vibrations
agree fairly well with the experimental data. The A00
species are reproduced exactly, and of the A0
symmetry species only n5 is about 4 cmϪ1 lower
than the observed wavenumber. The ab initio value
of this fundamental is more than 30 cmϪ1 lower; this
is the largest discrepancy between the calculated and
the observed frequencies, and most likely due to the
Fermi resonance with 2n6, as already discussed. The
centrifugal distortion constants are also computed in
agreement with the observed values; only the dK para-
meter is three times larger than the experimental value
which should, however, be considered only as a preli-
minary result [14].
X
ni ˆ vi ϩ 2xii ϩ 1=2 xij;
i±j
where xij ˆ xji, and the data of Tables 1 and 3 for the
fundamentals and the anharmonicity constants,
respectively. When available, the unperturbed data
were employed. The resulting set of harmonic
frequencies are reported in the first column of Table
7; these data are consistent with the Dennison’s rule
[22].
For the n5 and n6 fundamentals, which present
different values in the two isotopomers, we have
used the shifts Dvi ˆ v7i 9 Ϫ vi81 (i ˆ 5, 6), since the
uncertainty in the shifts is smaller than the uncertainty
in v8i 1, which has to encompass unknown anharmonic
effects [23].
Rather than exploring the possible scaling factors,
we decided to refine only the diagonal force constants
keeping all the off-diagonal constants fixed at the ab
initio values. The force field giving the best fit,
obtained from the experimental data under the restric-
tions given above, is listed in the first column of Table
6. The most obvious difference between these values
In summary, we report the results of the full
vibrational analysis of CH2BrF, comprehensive of

208
A. Baldacci et al. / Journal of Molecular Structure 517–518 (2000) 197–208
Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Inc., Pitts-
burgh, PA, 1995.
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[9] P.A. Curnuck, J. Sheridan, Nature 202 (1964) 591.
[10] H.C. Allen Jr., P.C. Cross, Molecular Vib-rotors, Wiley, New
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[11] G. Herzberg, Molecular spectra and molecular structure,
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unequivocal assignments in terms of the band
contours displayed, rotational analysis and the Fermi
resonance perturbation. Accurate ab initio calcula-
tions provided the molecular structure, and a hybrid
force field, representing the most realistic description
available, has been determined. All this information
will be valuable in the analysis of further measure-
ments of the rotational Ϫ vibrational spectra of
CH2BrF undertaken in this laboratory.
[13] V. Typke, J. Mol. Spectrosc. 64 (1977) 70.
[14] A. Baldacci, P. Stoppa, S. Ghersetti, XV Colloquium on High
Resolution Molecular Spectroscopy, Paper Q20, Glasgow,
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