Rovibrational and dynamical properties of the hydrogen bonded complex (CH2)2S-HF: A combined free jet, cell, and neon matrix-Fourier transform infrared study

Article abstract of DOI:10.1063/1.1780167

The infrared study of the rovibrational and dynamical properties of the hydrogen bonded complex (CH₂)₂S-HF dimer was analyzed. It was observed that the combination of controlled temperature effects over a range of 40-250 K and a sophisticated band contour simulation program allowed the separation of homogeneous and inhomogeneous contributions. It was also observed that with the strengthening of the hydrogen bond upon vibrational excitation of HF, the sign of the coupling constants remained consistent. It was found that effective linewidth provides a lower bound for the predissociation lifetime of 10 ps.

Full text of DOI:10.1063/1.1780167

Rovibrational and dynamical properties of the hydrogen bonded complex ( CH 2 ) 2 S-
HF : A combined free jet, cell, and neon matrix-Fourier transform infrared study
P. Asselin, M. Goubet, M. Lewerenz, P. Soulard, and J. P. Perchard
Citation: The Journal of Chemical Physics 121, 5241 (2004); doi: 10.1063/1.1780167
View online: http://dx.doi.org/10.1063/1.1780167
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 11
15 SEPTEMBER 2004
Rovibrational and dynamical properties of the hydrogen bonded complex
„
CH … S-HF: A combined free jet, cell, and neon matrix-Fourier
2
2
transform infrared study
a)
P. Asselin, M. Goubet, M. Lewerenz, P. Soulard, and J. P. Perchard
ˆ
LADIR, UMR 7075, B aˆ timent F74, Boite 49, Universit e´ Pierre et Marie Curie (Paris VI), 75252 Paris,
Cedex 05, France
͑
Received 10 February 2004; accepted 16 June 2004͒
Fourier transform infrared spectra of the ␯ ͑HF stretching͒ band of the (CH ) S-HF complex have
s
2 2
Ϫ1
been recorded at 0.1–0.5 cm resolution in a cooled cell, in a supersonic jet expansion seeded with
argon and in a neon matrix at 4.5 K. The combination of controlled temperature effects over a range
of 40–250 K and a sophisticated band contour simulation program allows the separation of
homogeneous and inhomogeneous contributions and reveals significant anharmonic couplings
between intramolecular and intermolecular vibrational modes similar to our previous work on
(
CH ) S-DF. The sign of the coupling constants is consistent with the expected strengthening of the
2 2
hydrogen bond upon vibrational excitation of HF which also explains the observed small variations
of the geometrical parameters in the excited state. The analysis of sum and difference combination
bands involving ␯s provides accurate values of intermolecular harmonic frequencies and
anharmonicities and a good estimate of the dissociation energy of the complex. Frequencies and
coupling parameters derived from gas phase spectra compare well with results from neon matrix
experiments. The effective linewidth provides a lower bound for the predissociation lifetime of 10
ps. The comparison between effective linewidths and vibrational densities of states for (CH ) S-HF
2
2
and -DF complexes highlights the important role of intramolecular vibrational redistribution in the
vibrational dynamics of medium strength hydrogen bonds. © 2004 American Institute of Physics.
͓
DOI: 10.1063/1.1780167͔
I. INTRODUCTION
(
(
␯intra) and of very low frequency intermolecular modes
␯inter).
Intermolecular interactions involving polar HX bonds
In the framework of a systematic study of medium
(
XϭN,O,...) are at the origin of molecular stacking in con-
strength hydrogen bonding in the gas phase we have shown
in a previous paper ͑referred to as Paper I͒ that the thiirane-
deuterium fluoride one to one complex is a very favorable
case for studying this type of intermolecular interaction. Mo-
lecular beam experiments on the ␯ ͑DF stretching͒ band
have shown that line homogeneous broadenings are small
enough to allow the rotational structure to be partially re-
solved while complementary informations tied to the pres-
ence of hot band sequences involving intermolecular modes
densed phases and of the three-dimensional structure of
many biomolecules.1 This context continues to provide a
major motivation for detailed studies of a large variety of
hydrogen-bonded flexible complexes and the elaboration of
24
–3
s
theoretical models for weak interactions (D р10 kJ/mol). In
e
the last 20 years, the growth of high resolution absorption IR
laser techniques coupled to molecular beams has led to the
direct observation of intermolecular and intramolecular de-
grees of freedom in weakly bonded dimers. These new in-
strumental developments have opened the way to precise
in the ␯ fundamental band region are obtained from conven-
s
tional spectroscopy in a cooled cell. With the support of a
sophisticated simulation program the rovibrational band con-
tours arising from many transitions involving bending and
stretching intermolecular modes have been accurately fitted.
Significant couplings between the DF stretching and the
three lowest intermolecular modes have been quantified
through their crossed anharmonicity coefficients. Finally the
adjustment of the homogeneous width coefficient ␥ in the
band fitting has established a lower bound for the predisso-
ciation lifetime of about 100 ps.
spectroscopic studies of simple systems like (HF) , (HCl) ,
2
2
and small water polymers4
–16
through the construction of
reliable intermolecular potential energy surfaces which take
into account all internal coordinates1
7–19
and for small het-
2
0
erodimers such as HX (XϭF,Cl) interacting with HCN,
2
1
22
OCO, N2 , or N O ͑Ref. 23͒ to understand various state
2
resolved dynamical processes.
The spectroscopic study of more strongly hydrogen
bonded complexes (D ϭ10–40 kJ/mol) involving larger
molecules generally suffers from heavy thermal congestion
due to their multidimensional vibrational dynamics, related
to the presence of a large number of intramolecular modes
e
The present paper is devoted to the infrared study of the
(
CH ) S-HF dimer. Our range of experimental devices has
2 2
been completed by a closed-cycle helium cryostat for matrix
isolation spectroscopy in solid neon. The soft neon matrix
allows direct access to the low frequency intermolecular vi-
a͒Electronic mail: assel@ccr.jussieu.fr
0021-9606/2004/121(11)/5241/12/$22.00
5241
© 2004 American Institute of Physics
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1

5242
J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
Asselin et al.
brations yet unobserved in the gas phase without introducing
excessive matrix shifts. The availability of data for both
was achieved using a Neocera LTC temperature controller.
Spectra were recorded at about 4.5 K. The accuracy of the
peak frequencies is 0.1 cm and that of the relative inte-
Ϫ1
(
CH ) S-DF and -HF dimers should allow to derive some
2
2
geometrical parameters in the vibrationally excited state and
to shed some light on the relative importance of intramolecu-
lar vibrational redistribution ͑IVR͒ versus predissociation.
The paper is organized as follows: after a brief descrip-
tion of our threefold Fourier transform infrared ͑FTIR͒ facil-
ity, experimental results from cell-, jet-, and neon matrix-
FTIR spectra will be presented. The spectral analysis of the
␯s region, guided by the conclusions obtained about
grated intensities is generally not better than 20%.
HF is obtained from Messer Griesheim ͑99%͒ and thi-
irane from Aldrich ͑98% purity͒. For neon matrix experi-
ments, HF and DF samples were prepared by reaction of
AgF with H or D at about 150 °C and distilled twice
2
2
2
around Ϫ50 °C under vacuum before use. Negligible traces
of SiF and CO have been detected which do not, however,
4
2
interfere with the present spectral analysis.
(
CH ) S-DF, is described next. Rovibrational data involving
Ab initio calculations were carried out using the
GAUSSIAN 98 quantum chemical package.26 Electron correla-
tion was included via second-order Møller-Plesset perturba-
2
2
␯s are then used to interpret the observed series of sum and
difference (␯ Ϯk␯inter) combination bands. The final discus-
s
sion addresses the consistency between parameters derived
from the three kinds of experiments and gives a combined
view and analysis of the data derived from HF and DF
bonded to the same organic base. In the following, the nota-
tion theory ͑MP2͒ ͑Ref. 27͒ with the aug-cc-pVTZ basis of
Dunning et al.2
8,29
Geometries of the monomers and of the
thiirane¯HF dimer were fully optimized. Harmonic vibra-
tional frequencies were calculated at the MP2 level using the
same basis functions but within the frozen core approxima-
tion. The basis set superposition error ͑BSSE͒ was estimated
by the Boys-Bernardi counterpoise procedure ͑CP͒. An an-
harmonic vibrational analysis based on a more complete ex-
ploration of the potential surface of (CH ) S-HF will be
tion
͉v v v v␴͘ involving the four vibrational modes ␯s ,
s ␦ ␦
1 2
␯␦1, ␯ , and ␯ will be used to specify vibrational states.
␦
␴
2
The elements xlm of the anharmonicity matrix are defined
according to the standard anharmonic expansion given in
Paper I.
2
2
published elsewhere.30
II. EXPERIMENTAL AND COMPUTATIONAL DETAILS
III. THEORETICAL AND EXPERIMENTAL RESULTS
A. Energetic and structural calculations
Our supersonic jet-FTIR spectrometer device is quite
similar to that described in Paper I, apart from the cooled
The results of the geometry optimization for the
thiirane¯HF complex and isolated subunits as well as the
energetic aspects and the calculated frequencies for the
modes involved in the experimental study are almost identi-
cal with those obtained for the deuterated complex at a more
modest level of theory ͑cf. Table I of Paper I͒ and compare
well with available experimental data from the gas phase. In
the following the intermolecular bond angle between the
S¯F vector and the C2v axis of (CH ) S will be referred to
bandpass filter centred around the HF stretching region
Ϫ1
͑
3490 cm ͒.
Ϫ1
Cell spectra have been recorded at 0.1–0.5 cm resolu-
tion between 230 and 270 K with the 85 cm cooled cell
described previously.24 In this temperature range, additional
spectral structures could be observed. As the relative inten-
sity of the various hot band sequences associated with ␯ is
s
very little sensitive to moderate temperature changes, the
analysis of the fundamental band is mainly based on a single
cell spectrum recorded at 248 K with relatively low pressures
of (CH ) S and HF. The signal-to-noise ratio for weaker sum
2
2
as ␾, and the angle of nonlinearity of the S¯H͑D͒F bond as
␣. The lengthening of the HF bond correlates well with the
2
2
decrease of the HF bond force constant corresponding to a
and difference combination bands has been maximized by
increasing the temperature and the pressure of both com-
pounds and by recording the cell spectrum at lower resolu-
tion. However, these changes in pressure and resolution con-
ditions remain small enough to prevent the appearance of
additional spectral broadening compared to the 248 K spec-
trum.
harmonic frequency shift ⌬␻ ϭ␻dimerϪ␻monomer of Ϫ485.7
s
Ϫ1
CP
cm . The dissociation energy D0 is estimated to be 2001
cm ͑23.9 kJ/mol͒ after subtracting the change of the har-
Ϫ1
monic zero point energy from the electronic binding energy
CP
Ϫ1
De ͑2637 cm , i.e., 31.5 kJ/mol͒. Harmonic frequencies
are gathered in Table I for comparison with neon matrix
results.
Neon matrix experiments were carried out with a device
already described in another publication.25 Briefly, H͑D͒F
and (CH ) S mixtures with Ne were codeposited through
B. Cooled cell data
2
2
Ϫ1
separate inlets at an average rate of 12 mmol h on one side
of a polished, Rh-plated hexagonal copper prism maintained
at 4.5 K by a closed-cycle helium cryogenerator ͑Cryomech
PT405͒. The Ne/͑CH ) S molar ratio was varied between
Cell spectra of two spectral windows in the HF stretch-
ing region of (CH ) S-HF are shown in Figs. 1 and 2. Figure
2
2
1 displays two 248 K cell spectra of the ␯ fundamental and
s
Ϫ1
the high frequency side ͑3490–3610 cm ͒ recorded, respec-
2
2
Ϫ1
2
00 and 500 and the Ne/H͑D͒F ratio between 125 and 20 000
in order to minimize the formation of H͑D͒F oligomers. The
D/H͒ isotopic rates of the samples were larger than 0.9 or
tively, at 0.5 and 0.1 cm resolution. Figure 2͑a͒ displays
the spectral region of difference bands involving ␯ ͑3300–
s
Ϫ1
Ϫ1
͑
3490 cm ͒ recorded at 268 K in a cell at 0.5 cm . This
spectrum is about eight times more intense than the one ob-
tained at 248 K. The absorptions due to C H ͑main product
smaller than 0.1 allowing to observe mainly one isotopomer.
Ϫ1
Spectra were recorded at 0.1 cm resolution in the 20–4000
2
4
Ϫ1
cm spectral range. Thermal annealing between 8 and 14 K
of the decomposition of thiirane͒ and the HF monomer in the
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J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
The complex (CH ) S-HF
5243
2
2
FIG. 1. Cell spectrum of the ␯s band region of
CH ) S-HF recorded at 248 K at resolutions of 0.5
(
2
2
Ϫ1
Ϫ1
cm ͑a͒ and 0.1 cm ͑b͒. Region F corresponds to hot
bands associated with the ␯ HF stretch fundamental.
s
1
1
Cb1 and Cb2 are hot bands associated with (␯ ϩ␯
)
␦
1
s
and (␯ ϩ␯␦2) sum combinations, respectively.
s
3
(
470–3570 cmϪ1 range have been subtracted from the
CH ) S:HF spectrum. The labeling of the various observed
cmϪ1, well structured on its low frequency side and framed
by much weaker well structured features. The main absorp-
tion consists in a series of doublets F(i) with substructure
which is progressively blurred out in the high frequency tail.
The low frequency component of each doublet, labeled P(i),
is much stronger than the high frequency one, labeled Q(i),
2
2
features is defined as follows: capital letters designate differ-
ent groups of transitions, the ␯s fundamental ͑F͒, sum
(
C) (␯ ϩ␯ ), and difference (D) (␯ Ϫ␯inter) combination
s inter s
bands, respectively. An index, s for stretching and b for
bending, identifies the nature of ␯inter . For each group, three
different subscripts noted i, j, and k can be added: i
Ϫ1
with a Q(i)ϪP(i) splitting of Ϸ3.5 cm . The spacing be-
Ϫ1
tween successive doublets is close to 9 cm . The high fre-
Ϫ1
(
ϭ0,...,␯ ) refers to the total bending quantum number v
␦
␦
quency shoulder shifted by about 70 cm from this main
1
ϭv ϩv involving the bending modes ␯␦1 and ␯␦2 in hot
band sequences, j is a lower-case index ͑ϭ1 or 2͒ which
refers to the bending modes v␦1 involved in combination
bands, k ͑ϭ1 or 2͒ is an upper-case index used to define
distinct difference bands ͓for example, Ds (i), Db (i)] of
the type (␯ Ϫk␯ ) or sum bands ͓for example Cb (i)] of
the type (␯ ϩk␯inter). Finally, the labels P and Q correspond
to the branches of a rovibrational transition. The validity of
the assignments will be justified in detail in Sec. IV.
␦
␦
absorption consists in a series of doublets Cb (i) with a
1
2
j
Ϫ1
splitting of about 1.8 cm ͑inset in Fig. 1͒ between their
components Cb (i) and Cb (i) and spacings between suc-
1
1
2
1
Ϫ1
cessive doublets of about 7 cm
.
k
k
k
A first low frequency shoulder Ds (i) ͓Fig. 2͑a͔͒, start-
ing at 3325 cm ͑about 170 cm below the main absorp-
tion͒, is subdivided in two series of doublets Ds (i) and
Ds (i) separated by about 30 cm . The splittings between
j
k
j
Ϫ1
Ϫ1
s
inter
1
s
2
Ϫ1
Ϫ1
their components are about 2.5 cm while the spacing be-
Ϫ1
Ϫ1
The ␯ spectrum at 0.5 cm resolution ͓Fig. 1͑a͔͒ is
tween successive doublets amounts to 12 cm . A second
s
Ϫ1
characterized by a main absorption spread over about 80
low frequency shoulder, shifted downward by about 60 cm
FIG. 2. Spectral region of the (␯s
Ϫk␯j)kϭ1,2 difference combination
bands: observed cell spectrum re-
corded at 268 K at a resolution of 0.5
Ϫ1
cm ͑a͒ simulated spectrum ͑b͒.
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1

5244
J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
Asselin et al.
FIG. 3. Comparison between experiment and fit for jet spectra of the ␯s
band of (CH ) S-HF recorded in two dilution conditions: HF/͑CH ) S/Ar
2
2
2 2
ϭ1/2.7/13 ͑a͒, 1/8.7/23 ͑b͒. Fit OA uses molecular parameters fixed at val-
ues obtained from our best cell spectrum ͑Fig. 1͒. All parameters are free in
fit OB .
FIG. 4. Neon matrix mid-infrared ͑a͒ and far-infrared ͑b͒ spectra of some
transitions involved in the hydrogen bond of (CH ) S-HF indicating the
2
2
presence of two matrix embedding sites A and B. T is probably a mixed
trimer band.
from the main absorption consists in a series of components
l
Ϫ1
Db (i) spaced by about 10 cm and completely masked
j
maxima P(1), P(2), and P(3) as well as the unresolved
P(i), iϾ3 structures, intense at 248 K, practically disappear
at jet temperatures, which identifies them as hot transitions.
The only remaining spectral features visible in the jet spectra
are: first, the submaxima P(0) and Q(0) already visible in
the cell spectrum which correspond to the same cold transi-
tion F(i); second a notable contribution of P(1) in the hot-
test jet spectrum ͑b͒ in overlap with the high frequency side
of F(0). These observations clearly indicate that the overall
␯s band profile of the (CH ) S-HF complex is very similar
beyond iϭ5 by the strong doublets of the F hot band se-
quence.
The cell spectrum of the ␯ band recorded at higher reso-
s
lution ͓Fig. 1͑b͔͒ does not reveal any additional structure but
several submaxima appear more distinctly within each com-
ponent ͓two for P(1), three for P(2)]. However, the width
of each component P(i) does not increase, suggesting that
the effective homogeneous linewidth ␥ is not significantly
different from the value of the lowest experimental resolu-
2
2
Ϫ1
tion used ͑0.5 cm ͒.
to that of its deuterated homologue.
C. Molecular beam data
D. Neon matrix data
Ϫ1
Two jet spectra of the ␯ band recorded at 0.5 cm
The high detectivity of the matrix isolation technique
reveals the presence of minor quantities of several other
complexes besides (CH ) S-HF. These complexes, (HF) ,
s
resolution are shown in Fig. 3. The concentration range of
the ternary mixture HF/͑CH ) S/Ar was adjusted such that
2
2
2
2
n
the 1:1 complex is the main species formed in the jet. Each
spectrum is the Fourier transform of several blocks ͑10 for
the coldest, 20 for the hottest͒ of 100 coadded interferograms
nу2, and (N ) -(HF) due to impurity traces of N , have
2
n
m
2
3
1,32
been identified and analyzed separately.
These previous
matrix studies provide valuable information on perturbations
of intermolecular vibrations induced by the neon matrix and
allow the spectral features of (CH ) S-HF to be unambigu-
Ϫ1
recorded at 0.5 cm resolution. As for the (CH ) S-DF
2
2
2
4
study, the goal is to improve and quantify the signal-to-
noise ratio for the determination of reliable error bounds for
parameters derived from the spectral analyses. A net decrease
of the rovibrational temperatures between jet spectra ͑a͒ and
2
2
ously assigned.
Figure 4 displays the spectrum of (CH ) S-HF after
2
2
deposition and annealing at different temperatures. The ␯s
band ͓Fig. 4͑a͔͒ is characterized by two components at 3456
͑b͒ is obtained by changing the dilution conditions. The sub-
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J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
The complex (CH ) S-HF
5245
2
2
TABLE I. Observed frequencies ͑cmϪ1͒ and assignments of the (CH ) S-HF and (CH ) S-DF complexes
2
2
2 2
trapped in sites A and B in solid Ne at 4.5 K and comparison with harmonic frequencies for (CH ) S-HF.
2
2
(
CH ) S-HF
(CH ) S-DF
2 2
2
2
Site A
Site B
Site A
Site B
Symmetry
coordinates
ab initio calc.
a
Ϫ1
␯obs ͑cmϪ1
␻harm ͑cm
)
)
q␦2
q␦1
q␴
ql2
77.4
83.4
¯
¯
¯
¯
¯
¯
¯
¯
193.6
633.4
646.3
692.1
836.8
924.6
970.3
1059.4
1076.8
1160.8
1476.5
1502.6
3174.4
3271.0
3640.7
Ϫ482.2
¯
183.3
573.9
617.6
649.3
189.0
577.3
628.6
648.5
182.5
421.9
454.0
649.3
187.0
424.1
461.8
648.5
b
c
b
c
ql1
c
c
q15 (B2)
q11 (B1)
q (A )
824.0c
824.6c
824.0c
824.6c
916.5Ϯ2.0c
916.5Ϯ2.0c
8
2
q10 (B1)
q (A )
952.5c
953.6c
952.5c
953.6c
1032.2c
1033.5c
1032.2c
1033.5c
4
1
q14 (B2)
q (A )
1066Ϯ2.0c
1066Ϯ2.0c
1117.7c
1436.4c
1118.0c
1435.6c
1456.7
1117.7c
1436.4c
1457.6
1118.0c
1435.6c
1456.7
3
1
q13 (B2)
q (A )
c
c
c
c
1457.6
2
1
q (A )
3030.7c
3117.5c
3456.0
3033.1c
3115.0c
3442.5
Ϫ511.9
3653.8
Ϫ22.3
3030.7c
3117.5c
2556.7
Ϫ344.1
2750.0
Ϫ10.8
3033.1c
3115.0c
2547.5
Ϫ353.3
2747.5
Ϫ13
1
1
q (B )
9
1
qs
⌬
qsd
Ϫ498.4
3663.5
Ϫ24.2
qsϩq␴
xs␴
¯
a
C2v symmetry labels for the corresponding modes in free thiirane.
Extrapolated values based on the isotopic ratio ͑cf. Secs. III and IV͒.
b
c
Observed frequencies of intramolecular modes of complexed (CH ) S for both complexes.
2
2
d
⌬
q ϭq Ϫq
.
monomer
s
s
and 3442.5 cmϪ1. An irreversible intensity decrease of the
lations. The A bands are used for this comparison because
Ϫ1
3
3
456 cm component correlated to the increase of the one at
442.5 cm upon annealing is typical of a thermally in-
the (␯monomerϪ␯ ) shift is closer to the gas phase value than
s
Ϫ1
for the B bands, indicating a smaller matrix effect for this
site. The ␯l1 band of (CH ) S-HF which could not be ob-
duced conversion from one embedding site labeled A to an-
other one labeled B. In the following, we will take advantage
of this A→B conversion for the identification of bands be-
longing to the same complex. Indeed three other doublets
2
2
served due to the proximity of the intense band of the ␯s
intramolecular S-C stretching mode of (CH ) S is measured
2
2
Ϫ1
for (CH ) S-DF at 454.0 cm . Then, assuming the same
2
2
with A/B behavior are observed in other spectral ranges: at
HF/DF isotopic ratio for both librational modes one gets:
Ϫ1
3
1
663.5(A)–3653.8 cm (B) in the mid-infrared, and
Ϫ1
␯ ͑DF,X͒
l
83.3(A)–189.0(B) and 573.9(A)–577.3 cm (B) in the
1
␯l1͑HF,X͒ϭ
␯ ͑HF,X͒ with XϭA,B.
l
2
far-infrared ͓Fig. 4͑b͔͒. Based on the ab initio calculations
see Table I͒ and on the identification of the v band, the first
␯ ͑DF,X͒
l
2
͑
␦
Finally, an additional weak signal labeled as T in Fig. 4
and the second ones are, respectively, assigned to the com-
and exhibiting a reverse A→B conversion compared to the
bination mode (␯ ϩ␯ ) and to the hydrogen bond stretching
s
␴
Ϫ1
(
␯ ϩ␯ ) band is observed at 3622.4 ͑A͒ and at 3628.0 cm
s ␴
mode ␯ , which permits the direct determination of x
.
␴
s␴
͑
B͒. The assumption of a Fermi resonance between (␯s
The third doublet is assigned to the in-plane libration mode
␯l2. Note that the two lowest frequency modes, ␯␦1 ͑in plane
ϩ␯ ) and (␯ ϩ2␯ ) has been examined. As a test, the
␴
s
␦2
IT /I
area ratio was measured. Its value strongly in-
␯sϩ␯␴
bend͒ and ␯␦2 ͑out of plane bend͒, as well as the out-of-plane
libration mode ␯l1 have not been observed. The comparison
between spectra of (CH ) S recorded in the presence and in
creases with the HF/Ne ratio, which clearly indicates that T
cannot be assigned to the dimer but rather to a complex of
larger size, probably the (CH ) S-͑HF) trimer in the bifid
2
2
2
2
2
the absence of HF or DF for various (CH ) S/H͑D͒F molar
2
2
configuration.
ratios allows the identification of 11 of the 15 intramolecular
modes of complexed (CH ) S. They are compared in Table I
2
2
IV. BAND ASSIGNMENTS DERIVED FROM JET- AND
CELL-FTIR SPECTRA
to the calculated harmonic frequencies of (CH ) S-HF. The
matrix shifts are systematically 5%–10% smaller than the
2
2
theoretical ones for the three intermolecular modes ␯ , ␯l1
␴
The evident similarities observed between the overall ␯s
and ␯l2 and only 3%–6% smaller for the intramolecular
band shapes of (CH ) S-HF and (CH ) S-DF lead us to
2
2
2 2
modes. This is not surprising considering the large anharmo-
nicity of the intermolecular modes and the harmonic calcu-
propose the same coupling scenario as in Paper I. We take
advantage of the large temperature effects ͑40–250 K range͒
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5246
J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
Asselin et al.
1
in passing from jet- to cell-FTIR spectra for the identification
of the hot or cold character of the transitions.
involving the low frequency intermolecular modes. Ds (i),
Ϫ1
Ϫ1
shifted 172 cm relative to ␯ ͑ab initio ␻ ϭ193.6 cm
)
s
␴
2
The observation of two intense bands labeled P(0) and
and Ds (i) are, respectively, assigned to the difference band
sequences 0v v 1 1v v 0 and 0v v 2
involving the hydrogen bond stretch. The
Ϫ1
Q(0) at 3494.5 and 3497.3 cm in the jet spectra allows the
͉
͘
→
͉
͘
͉
͘
2
␦
␦
␦
␦
␦
␦
1
1
2
1
2
clear assignment of this doublet to the P and Q branches of
→
͉
1
v v
1
͘
␦
2
␦
1
the ␯ fundamental transition. The redshift relative to the
s
width of the cluster of bending states in both (␯ Ϫ␯ ) and
␯ Ϫ2␯ ) difference bands does not increase much with v
s ␴ ␦
which suggests that the spacing between ␦ and ␦ differs
very little within these sequences. In this case the progressive
overlap of rovibrational structures of Ds (i) and Ds (i) be-
yond iϭ1 can be only interpreted as a width effect caused by
the cluster of bending states. The narrowing of the spectral
features of Db (i) when v increases, strongly suggests that
this component is constituted by two progressions labeled
s ␴
Ϫ1
monomer band of 464.3 cm ͑MP2 harmonic value: 482.2
cm ͒ corresponds to a 11.7% frequency decrease, typical of
(
Ϫ1
1
2
medium strength hydrogen bonding.
Above the P(0)–Q(0) doublet the cell spectrum devel-
ops a series of P(i) and Q(i) doublets assignable to one or
several hot sequences whose rotational contour P(0)Q(0) is
the first member. The strong asymmetry within these rota-
tional contours at cell temperatures is due to the positive
difference BЈϪBЉ and CЈϪCЉ between rotational constants
in excited and ground states, which leads to the formation of
a band head in the P branch. For iϾ3, the P and Q branches
are progressively blurred at higher excitation energy by the
increasing number of hot transitions.
1
2
k
j
␦
1
1
2
1
Db (i) and Db (i), iϭ0–5, with the same transition origin
and slightly different diagonal anharmonicities.
The spacing ⌬X (XϭF,D,C) between the members of a
given sequence is directly related to different xll and xlm
values, appearing in the standard anharmonic expansion.
for transitions in-
volving ␯␦1 and ␯␦2 provides a first estimate of x and xs␦2.
s␦
1
Ϫ1
The detailed interpretation which follows is based on the
Within the F band, ⌬FϷ9.6Ϯ0.3 cm
existence of couplings between ␯ and the intermolecular
s
modes ␯ , ␯ , and ␯ . The splitting of P(1) and P(2) into
1
1
j
␦
␦
␴
1
2
Within the Cb bands, ⌬Cb ϭϪx Ϫ2x
is lowered to
␦ ␦
j
j
s␦
j
j
two and three submaxima, respectively, seems to indicate
that the scenario to be considered in the present work is the
same as for (CH ) S-DF, i.e. as follows.
Ϫ1
7
.4Ϯ0.4 cm due to the positive values of x␦ . Within the
␦
j j
k
k
Ds bands, ⌬Ds is equal to (Ϫx ϩx␴␦j) and the band
s␦
j
2
2
1
2
origins of Ds (i) and Ds (i) are spaced by the quantity
Ϫx ϩ2x ) which provides precise values for x and
͑
i͒ Slightly different values of xs␦1 and xs␦2 imply the
(
s␴
␴␴
␴␦
i
presence of two overlapping hot band progressions for the
bending contribution. Their intensity envelope is of the form
1
j
1
j
x␴␴ . Finally, for the Db bands, ⌬Db is equal to (Ϫx
s␦
j
ϩ2x ). All the numerical values will be refined in the
(
v ϩ1)exp(Ϫv ␻ /k T ) ͑Ref. 33͒ originating from (v
␦ ␦
j j
␦
␦
␦
B
V
␦
ϩ1) nearby states provided that the dependence of the tran-
following.
sition moment on the excitation of the ␯ modes is weak.
␦
The width of each cluster of bending states varies as
v␦(xs␦1Ϫxs␦2) which causes the progressive overlap of the
V. SIMULATION OF CELL- AND JET-FTIR SPECTRA
A. Choice of the initial parameter set
hot transitions as v increases. With this coupling scheme the
␦
intensity distribution passes through a maximum for v␦F
The band contour simulation and fitting program already
Ϫ1
ϭ(k T /␻ )Ϫ1. With T ϭ248 K and ␻ Ϸ80 cm , v␦F
B
V
␦
V
␦
developed in Paper I has been used to reproduce the ␯ fun-
s
must be equal to 1 or 2, which is clearly observed in the cell
spectrum. The effective linewidths, albeit much larger than
for (CH ) S-DF, remain small enough for the appearance of
damental over a large range of temperatures from cell and jet
experiments, and then to analyze (␯ Ϯ␯ ) and (␯
s
␦
s
j
2
2
Ϫk␯␴)kϭ1,2 combination bands only observed in the cell
spectra. In the case of nonlinear least squares optimizations
including a high number of adjustable parameters, the ␹2
surfaces become extremely complicated and it is not unlikely
that only a local minimum, strongly dependent of the choice
of the initial parameter set, might be found. For this reason,
the simulations have been realized in two steps: first the ␯s
fundamental band alone is reproduced to determine a first set
of rovibrational and dynamical parameters. The rovibrational
partially resolved rovibrational branches up to v ϭ3,
␦
͑
ii͒ The occurrence of a third coupling with the stretch-
ing mode ␯ is suggested by the observation of two features
␴
Ϫ1
at 3517.1 and 3526.2 cm which do not belong to any bend-
ing mode progression.
On the grounds of the ␻␦1 and ␻␦2 ab initio harmonic
Ϫ1
frequencies at 77.4 and 83.4 cm , respectively, and by anal-
3
4–36
ogy with previous studies about (CH ) O-HCl and -HF,
3
2
for which at least one strong coupling between ␯ and ␯ has
X
s
␦
coupling constants ␣l ͑defined in Paper I͒ for lϭ␦ , ␦ ,
1
2
1
j
been proven, Cb components are assigned in a first step to
and ␴, as well as the harmonic frequencies ␻ cannot be
l
combination bands of the type
͉
0␯ 00
͘
→
͉1(␯ ϩ1)00
͘
␦
1
␦
1
estimated precisely from the ␯s fundamental alone but rather
from sum and difference combination bands composed of
two-quanta transitions. In a second step all the data are in-
troduced in the initial parameter set for each observed com-
and/or 00␯ 0 10(␯ ϩ1)0 . In a second step, the ques-
͉
͘
→
͉
͘
␦
␦
2
2
tion will be to validate this scenario and to determine if any
1
valuable information can be extracted from the Cbj band
X
analysis with the support of band contour simulations and of
bination band in order to refine the values of ␣l and to
the vibrational data derived from the ␯ fundamental band.
determine the values of ␻ , x , and x . The convergence
s
l
ll
lm
The observation of several difference combination bands
towards an unique parameter set which well reproduces the
on the low frequency side of the ␯ band gives us the oppor-
whole ␯ band region can be obtained after successive round
s
s
tunity to directly extract several values of ␯inter , x , and x
trips between the fundamental and the combination bands.
ll
lm
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J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
The complex (CH ) S-HF
5247
2
2
The construction of the synthetic spectrum of
(
CH ) S-HF rests on the assumptions which have proved to
2 2
be successful for (CH ) S-DF. The rotational constants in
2
2
the ground state are fixed at values obtained in microwave
experiments by Atkins et al.37 The band hybridization has
been computed from the projection of the HF dipole vector
onto the molecular inertial axes. In the absence of direct
experimental observations we fix the intermolecular modes
␻␦1
, ␻ , and ␻ to the ab initio harmonic frequencies and
␦ ␴
2
use only the anharmonicity constants as adjustable param-
eters.
As a first step only couplings between the HF stretch and
the two bending modes ␯␦1 and ␯␦2 are considered, which
results in overlapping hot band sequences of the type
͉
0v v 0
͘
→
͘
͉1v v 0 with all v , v combinations up
␦ ␦ ␦ ␦
1 2 1 2
␦
␦
FIG. 5. Enlarged portion of the ␯s band of (CH2)2S-HF at 248 K: ͑a͒
observed cell spectrum, ͑b͒ best simulated spectrum with the contribution of
1
2
to v ϭ3 and nearly equal values of x and xs␦2. This part
of the ␯ spectrum contains ten transitions and is represented
by 860 experimental points for a total of 34 parameters, i.e.,
nine rovibrational constants ␣ ͑with XϭA, B, C and lϭs,
␦
s␦
1
␯␴
, ͑c͒ best simulated spectrum without the contribution of ␯␴ , ͑d͒ ob-
s
served spectrum–simulated ͑b͒ spectrum, ͑e͒ observed spectrum–simulated
͑c͒ spectrum.
X
l
␦1
, ␦ ), one harmonic frequency ␻ , two anharmonicities
2
s
xs␦1 and xs␦2, two transition specific parameters ͑the effec-
tive width ␥ and the relative intensity I with respect to I
located at 3517.1 and 3526.2 cmϪ1. A second synthetic spec-
trum including ␯␴ ͓Fig. 5͑c͔͒ shows that this three mode-
i
i
1
ϭ1) per transition, and two global parameters, which are an
overall intensity scaling factor f and a base line offset f .
s
o
coupling model is best suited to reproduce all the resolved
Due to the increasing number of overlapping transitions from
Ϫ1
structures of the cell spectrum between 3485 and 3528 cm
.
v ϭ1 onward, all ␥ are constrained to a single parameter,
␦
i
Ϫ1
Beyond 3528 cm the number of transitions increases
sharply and 55 rovibrational bands with excitation energies
up to 500 cm must be considered to reproduce the entire ␯s
which reduces to 25, the number of adjustable parameters.
The fit operates by progressively increasing the quantum
Ϫ1
number v and adding the corresponding transitions at each
␦
Ϫ1
A,B,C
band contour between 3485 and 3580 cm . We have veri-
step. At v ϭ0, only ␣s
are involved in the modeling of
␦
fied that the parameter set in Table IV describes the entire
the fundamental transition. For v Ͼ0, the rotational contours
␦
A,B,C
A,B,C
A,B,C
A,B,C
spectrum of the ␯ fundamental ͑see Fig. 1͒ in good agree-
depend on ␣s
, ␣␦1 , and/or ␣␦2 , but the ␣␦i
s
ment with the experimental spectrum also beyond the region
shown in Fig. 5.
values have no direct influence on the rotational contour be-
cause v␦i does not change in these transitions.
Figure 3 displays the two synthetic spectra obtained
from the restricted and full adjustments O and O for each
As a consistency check two parameter optimizations OA
A
B
and O were performed with the jet spectra ͑Fig. 3͒: in the
B
of the jet spectra ͑a͒ and ͑b͒. The negligible difference be-
tween the two fitted spectra for all jet temperatures shows the
self consistency of the molecular parameter set and indicates
that a reliable parameter set has been found which correctly
first one, all molecular ͑rovibrational and transition specific͒
parameters were fixed at the values derived from the best fit
to the cell spectrum and only the global parameters, four of
them in the jet spectra ͑temperatures TR and T , scaling
v
describes the evolution of the ␯ band over a temperature
parameters f and f ) were treated as adjustable. In the sec-
s
s
o
range from 40 to 250 K. The small contribution of ␯␦1 and
ond one, all parameters were reoptimized, starting from ini-
tial values obtained from the best cell spectrum fit.
␯␦2 between 50 and 75 K leads to a large uncertainty for
A,B,C
A,B,C
␣
and ␣␦2
in the jet spectra and consequently only
␦
1
B. Results from simulated cell- and jet-FTIR spectra
A,B,C
␣s
͑but also ␻ and x ) are reported in the jet column in
s
s␦
i
1
. The v band
the upper part of Table IV. Because the standard analysis of
the curvature matrix38 provides too optimistic parameter er-
ror estimates, uncertainties for both molecular and individual
parameters ͑listed in the cell column of Table IV͒ have been
s
Figure 5 displays an expanded view of the experimental
and synthetic cell spectra of the ␯ band of (CH ) S-HF up
to v ϭ3. The excellent agreement between both spectra is an
evident proof for a coupling between ␯ and both bending
s
2 2
␦
2
evaluated by analyzing the shape of the ␹ surface around
s
the mathematically best point by defining the physically ac-
ceptable region of parameter space from the noise level of
the gas phase spectra ͑cf. Sec. D in Paper I͒.
modes ␯␦1 and ␯ . Table II summarizes the frequencies and
␦
2
assignments of transitions, Tables III and IV gather the tran-
sition specific parameters ␥ and I , and the molecular pa-
i
i
The rovibrational parameters derived precisely from the
rameters derived from the band contour analysis including
A,B,C
simulation of the ␯ band, i.e. x , xs␦2, xs␴ and ␣s
are
hot bands up to v ϭ3.
s
s␦
1
␦
In a second step, hot bands associated with ␯␴ were
introduced to test if this explains the additional structures
now introduced as initial parameters for the analysis of the
combination bands.
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5248
J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
Asselin et al.
TABLE II. Frequencies ͑cmϪ1͒ and assignments of the components of the ␯ band and of all combination bands
s
involving ␯ observed in the spectra of (CH ) S:HF. Except for the (␯ Ϯ␯ ) bands where the reported values
s
2
2
s
␦
1
correspond to the maxima of P branches, frequencies correspond to the maxima of Q branches.
Assignment
Name
Frequency
͉
vЉvЉ vЉ vЉ
͘
→
͉
vЈvЈ vЈ vЈ
͘
s
␦
␦
␴
s
␦
␦ ␴
2
1
2
1
1
Ds
Ds
3325.2, 3336.9, 3348.9
3355.5, 3367.3, 3379.6
3438.6, 3449.5, 3460.9
3469.9, 3479.4, 3487.8
͉
͉
0v␦1v␦21
0v␦1v␦22
͘
͘
͘
͘
→
→
→
→
͉
͉
͉
͉
1v␦1v␦2
1v␦1v␦2
1v␦1v␦2
0
1
0
0
͘v␦р2
͘v␦р2
͘v␦р5
2
1
Db
Db
͉
͉
0(v␦1ϩ1)v␦2
0
and
1
1
2
0v␦1(v␦2ϩ1)0
1v␦1v␦2
͘v␦р5
a
␯s͓F(0)͔
3497.3 , 3497.5
͉0000͘ → ͉1000͘
F
3506.1, 3514.5, 3523.2
͉
͉
0v␦100
00v␦20
͘
͘
͘
͘
͘
→
→
→
→
→
͉
͉
͉
͉
͉
1v␦100͘v␦
10v␦20
͘v␦
1ϭ1–3
2ϭ1–3
3
3
3
506.9, 3516.5, 3525.9
515.5, 3524.0, 3525.2
519.2, 3528.3, 3529.1
͉
͉
0v␦1v␦20
0v␦1v␦21
͉
1v␦1v␦2
1v␦1v␦2
0
1
͘v
␦ϭ2–3,v Þ0
͘v␦р1
␦
1
1
Cb
3568.1, 3575.0, 3582.4,
589.9, 3597.5
3570.4, 3576.4, 3584.4,
591.7, 3599.2
0v␦100
1(v␦1ϩ1)00
͘
1
v␦1ϭ2–6
v␦2ϭ2–6
3
1
2
Cb
͉
00v␦2
0
͘
→
͉
10(v␦2ϩ1)0
͘
3
aValue obtained from the jet-FTIR spectra.
1
2
. The „v Àkv …, kÄ1–2, bands
͑C͒ The assignment of the Cb sequences is validated
s
␴
j
The combination difference bands Ds and Ds2 have
1
after examining several approaches.
͑
i͒ Simulation with only one mode ␦ . Extensive at-
been simulated following the same scheme as for ␯ . As
indicated in Sec. IV, the value of ⌬Ds is j dependent. Con-
sequently the spacing of the hot sequence involving ␦1 is
selected to be slightly shifted from that involving ␦ in order
j
s
k
tempts to correctly simulate a rotational band contour with P
Ϫ1
and Q branches separated by 1.8 cm by adjustment of the
A,B,C
A,B,C
, ␣␦
A,B,C
coupling constants ␣s
, or ␣␦
were unsuc-
2
1
2
to account for the progressive overlap of bending states with
cessful. The scenario of a single combination band ␯sϩv␦j
increasing v . Figure 2͑b͒ displays the synthetic spectrum of
can be clearly dismissed.
␦
the (␯ Ϫk␯ )
bands of (CH ) S-HF. Reliable values of
͑ii͒ Introduction of all the combination sum transitions
s
␴
kϭ1,2
2 2
␻␴
, x␴␴ , x , and x
can be extracted by this way and
of the type
͉
0v v 0 →
͘ ͘
͉1(v ϩ1)v 0 and ͉0v v 0
␦ ␦ ␦ ␦
1 2 1 2
␦ ␴
␦ ␴
␦
␦
͘
1
2
1
2
are reported in the lower part of Table IV.
TABLE IV. Molecular parameters ͑cmϪ1͒ of (CH ) S-HF obtained in the
2
2
3
. The (␯ Áv ) bands
s
j
␦
upper part, from the contour fit of cell- and jet-FTIR spectra of the ␯ band,
s
in the lower part from the contour fit of the cell-FTIR of the (␯ Ϯ␯ ) and
s
␦
j
The simulation of the combination difference and sum
1
1
(␯ Ϫk␯ )
bands. Numbers in parentheses indicate estimated uncertain-
kϭ1,2
s
␴
bands Db and Cb is based on the following assumptions
j
j
ties in units of the last digit.
and observations.
͑
A͒ The harmonic frequencies ␻␦1 and ␻␦2 differ by
Cell
Jet
only a few wave numbers, as experimentally shown by Geor-
A
␣s
Ϫ0.000 12͑8͒
Ϫ0.003 48͑3͒
Ϫ0.002 75͑2͒
3 476.03͑10͒
Ϫ9.0͑1͒
¯
Ϫ1
B
giou et al. for (CH ) O-HF (␻ Ϫ␻ Ϸ3 cm ) ͑Ref. 39͒
␣s
Ϫ0.003 40͑7͒
Ϫ0.002 87͑6͒
3 476.03͑10͒
Ϫ9.0͑2͒
2
2
␦
␦
2
1
C
␣s
and found in ab initio calculations.
a
1
␻s
͑
B͒ The ⌬Dbj spacings are sufficiently close for the
xs␦1
xs␦2
xs␴
two sequences to be slightly shifted at low values of v␦
Ϫ10.0͑1͒
Ϫ23.2͑1͒
Ϫ10.0͑2͒
¯
͑broadening of the cluster of bending states͒ and superposed
at higher values up to v ϭ5 ͑narrowing of the cluster͒.
␦
A
␣
␦
Ϫ0.005͑2͒
ϩ0.000͑1͒
Ϫ0.005͑2͒
ϩ0.000͑1͒
62͑1͒
65͑1͒
171͑1͒
0.6͑1͒
0.5͑1͒
3.6͑1͒
2.7͑1͒
2.3͑1͒
1946͑80͒
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
1
B
C
␣
, ␣␦1
␦
1
A
TABLE III. Effective Lorentzian widths ␥ ͑values in parentheses in cmϪ1͒
␣␦
2
i
B
C
␣
, ␣␦2
␦
and relative intensities Ii for transitions
from the simulation of the cell-FTIR spectrum of (CH ) S-HF.
͉
0v␦1v␦20
͘
→
͉
1v␦1v␦20
͘
derived
2
␻␦1
␻␦2
␻␴
x␦
2
2
v␦1ϭ
0
1
2
3
␦
1
1
2
v␦2ϭ0
͑0.50͒
1
͑0.50͒
1
͑0.50͒
1.05
͑0.50͒
1
x␦
␦
2
x␴␴
x␦
v␦2ϭ1
v␦2ϭ2
v␦2ϭ3
͑0.50͒
͑0.50͒
0.9
͑0.50͒
1
͑0.50͒
0.5
␴
1
0
.9
͑0.50͒
.77
͑0.50͒
.7
x␦
␴
2
D0
0
a
Our fitting result for ␻ corresponds to the anharmonic transition frequency
␯sϭ␻sϪxs␦ /2Ϫxs␦ /2Ϫxs␴/2 with xss constrained to zero since we have
s
0
1
2
no independent information on ␻ and x
.
ss
s
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1

J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
The complex (CH ) S-HF
5249
2
2
→
͉
1v (v ϩ1)0
͘
are introduced. The relative position be-
͑d͒ Finally, the variations of the rotational constants in
␦
␦
2
1
A
the excited state are small, respectively, 0.1% for ␣ /A ,
tween these transitions, which depends on known parameters
s
0
B
C
3
.5% for ␣ /B , and 3.1% for ␣ /C , which suggests that
such as xs␦1, xs␦2 and on unknown parameters such as
s
0 0
s
the geometry of (CH ) S-HF varies little upon excitation of
(
␻ Ϫ␻ ), x
, x
, and x , appears difficult to de-
␦ ␦
1 2
2 2
␦
␦
␦ ␦
␦ ␦
2
1
1
1
2
2
␯s . The rotational constants in the excited state can now be
used to evaluate the structural changes of both complexes
termine precisely. However, we observe, whatever v , that
the paired combination transitions with v␦1 and/or v ϭ0
␦
␦
2
(
CH ) S-HF and -DF in the v ϭ1 state.
2 2 s
are well separated from the group of transitions with v␦1 and
v Þ0. As the number of transitions increases as 2v , over-
A. Determination of the geometry of „CH … S-H„D…F in
2
2
␦
␦
2
the v Ä1 state
s
lap between transitions close in energy should appear, but no
significant broadening is observed.
For the determination of the geometry of the two com-
͑
iii͒ The only possibility to explain the experimentally
plexes in the vsϭ1 state we dispose of only three observ-
observed series of doublets for all v is the assumption that
ables in each case, namely, the rotational constants X1 deter-
␦
X
the intensity of the transitions with v␦1 and v Þ0 is small
mined from the microwave X0 values and our ␣ data. The
␦
s
2
usual assumption of an unchanged geometry of the thiirane
monomer upon complexation and independent of the HF ex-
citation combined with the restriction that HF remains in the
compared to the doublet of transitions with v␦1 and/or v␦2
ϭ0. Each doublet would be the superposition of two hot
sequences and
͉
0v 00
͘
→
͉
1(v ϩ1)00
͘
͉00v 0
͘
␦
2
␦
␦
1
1
(
yz)-symmetry plane of the dimer leaves the four coordi-
1
→
͉
10(v ϩ1)0 with nearly equal values of the ⌬Cbj
͘
␦
2
nates y , z , y , z to be optimized. A meaningful fit to the
H
H
F
F
spacing.
three rotational constants requires the introduction of at least
one additional constraint which was chosen to be the HF
distance, fixed at its value in the ground state of (CH2)2S-HF
͑Ref. 37͒ and at a value computed by adding its change upon
excitation in the HF monomer.
Figure 2͑b͒ displays the synthetic spectrum of the (␯s
Ϫv ) band region of (CH ) S-HF. A set of parameters in-
␦
2 2
i
X
volving the ␦ modes, i.e., ␻ , ␻ , x
, x
, and ␣␦
j
␦
␦
␦ ␦
␦ ␦
1
2
1
1
2
2
j
1
1
can be extracted from the simulation of both Db and Cb
j
j
sequences. The good agreement between experimental and
synthetic spectra lends confidence to vibrational parameters
In practice we first determined a set of geometrical pa-
rameters for free thiirane which correctly reproduces the ro-
tational constants of its ground state from a microwave
study.40 Next the rotational constants of the ground state of
such as ␻ , ␻ , x
, and x
which are reported in the
␦ ␦
2
␦
␦
␦ ␦
1
2
1
1
2
lower part of Table IV. Table II summarizes the frequencies
and assignments of transitions identified for all the sum and
difference combination bands involving ␯s .
(
CH ) S-H͑D͒F ͑Ref. 37͒ are reproduced at best by adjust-
2 2
ing the position of HF. The results are gathered in Table V.
Several tests have been performed to establish the error mar-
gin of the data: variations of the position of H͑D͒ ͑Ϯ5% for
rH͑D͒F , Ϯ100% for ␣͒ give, as expected, only small varia-
tions of the rotational constants and lead to a large uncer-
tainty for rSH͑D) and ␣. The position of the center of mass of
HF or DF, respectively, and thus rSF and ␾ are, however,
well determined due to their strong influence on the moments
of inertia of the dimer.
VI. DISCUSSION
The excellent agreement between the synthetic and the
gas phase FTIR spectra of (CH ) S-HF in the temperature
2
2
range 40–250 K, has provided an unique and reliable set of
parameters including the rovibrational coupling constants
X
The variation of geometrical parameters between the
ground state and the v ϭ1 state is a 4% reduction of r and
␣s , the frequencies ␻ , and the anharmonicity constants x
l
ll
s
SF
and xlm for the three intermolecular coordinates ␦ , ␦ , and
1
2
a 1% change for ␾, which is consistent with an increase of
dipole moment related contributions to the intermolecular
interaction.33,4T1 his general trend in hydrogen bonded
␴, and relative oscillator strengths. Several general tenden-
cies in line with the study of (CH ) S-DF emerge from the
2
2
spectral analysis.
a͒ Important couplings exist between ␯ and the three
complexes
is consistent with the negative values of xsl
͑
s
which should therefore be a universal phenomenon.
low frequency intermolecular modes (xlm /␻ Ϸ10–12%)
l
and are reflected by blueshifted hot band progressions in-
dicative of a stiffening of the hydrogen bond upon HF exci-
tation.
B. Vibrational dynamics of „CH … S-H„D…F
2
2
The band contour of the observed transitions up to v
␦
Ϫ1
͑
b͒ The relative oscillator strengths ͑cf. Table III͒ for the
ϭ3 is correctly reproduced with a value of ␥ ϭ0.5 cm for
i
Ϫ1
hot progressions involving ␯␦1 and ␯␦2 modes exhibit small
HF and 0.06 cm for DF. The somewhat unrealistic attribu-
and regular variations with their corresponding vibrational
quantum number as expected for oscillators with a smooth
evolution of energy levels. This is consistent with all relevant
bending states remaining significantly below the adiabatic
tion of these observed widths exclusively to predissociation
establishes a lower lifetime limit around 10 ps for HF and 90
ps for DF. As proposed in Paper I, a second significant ho-
mogeneous contribution could arise from IVR, caused by
many small random couplings to a dense rovibrational back-
ground. To investigate the possible size of an IVR contribu-
tion we have estimated the vibrational density of states ␳vib
Ϫ1
barrier to inversion C →C →C ͑1088 cm ͒.
s
2v
s
͑
c͒ The ␥ values deduced from the simulations are
i
much larger for (CH ) S-HF than for (CH ) S-DF, which
2
2
2 2
will be discussed hereafter by considering the different con-
tributions to the effective line width.
for both complexes. For this purpose anharmonic state
counts4
2,43
were performed. In the absence of a full set of
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5250
J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
Asselin et al.
TABLE V. Geometrical parameters derived in the v ϭ1 state of (CH ) S-HF and (CH ) S-DF from the
s
2
2
2 2
experimental values of rotation-vibration coupling constants.
(
CH ) S-HF
(CH ) S-DF
2 2
2
2
vsϭ0
expt.a
calc.b
vsϭ1
c
vsϭ0
d
vsϭ1
c
A (cmϪ1)
0.271 90
0.271 70
0.271 85
0.27139
0.10161
0.08931
0.271 73
͑0.271 69͒
0.104 21
͑0.104 17͒
0.091 35
͑0.091 39͒
0.960e
2.084
3.043͑20͒
82.7͑2͒
v
͑
0.272 02͒
B (cmϪ1)
0.103 15
0.090 18
0.102 95
0.090 38
0.106 46
v
͑
0.106 63͒
C (cmϪ1)
0.093 10
v
͑
0.092 93͒
0.970e
rH͑D͒F ͑Å)
rSH͑D͒ ͑Å)
rSF ͑Å)
0.941
2.193
3.105
81.5
16.8
0.940e
2.155
3.083
82.9
11.0
0.940e
2.155
3.083
82.9
11.0
2.059
3.028͑10͒
82.6͑1͒
3.2
␾
͑deg͒
␣͑deg͒
3.2
a
Reference 40.
b
c
Best fitted geometry and corresponding rotational constants.
Values in parentheses correspond to the observables such as X ϭX Ϫ␣
Rotational constants of the ground state of (CH ) S-DF have been calculated from the geometry of
X
s
.
1
0
d
2
2
(
CH ) S-HF.
2 2
e
Fixed parameter used as a constraint, see text for details.
experimentally observed fundamental frequencies theoretical
harmonic frequencies have been slightly adjusted using
available monomer frequencies and combined with reason-
able models for the nature of the various oscillators ͑har-
monic for bending motions, Morse for stretches͒. This pro-
cedure yields vibrational density of states estimates of 140
the gas phase have been estimated from hot band sequences
and/or combination bands, the only exception being the di-
4
7
rect observation of the ␯ mode of (HF) .
6
2
For the (CH ) S-HF and -DF dimers, the only vibra-
2
2
tional data to be compared are the ␯ and ␯ modes and the
s
␴
xs␴ coefficient. The values are in good agreement for both
Ϫ1
Ϫ1
and 670 states per cm for (CH ) S-DF and -HF at the
complexes: for HF, ␯ ϭ3497.5 ͑gas͒ and 3456.0 cm
2
2
s
Ϫ1
respective excitation energies of the D͑H͒F stretch. An esti-
mation based on Fermi’s golden rule shows that even in the
complete absence of predissociation an average random
͑neon͒, ␯ ϭ171 ͑gas͒ and 183.0 cm ͑neon͒, x ϭϪ23.2
␴
s␴
Ϫ1
͑gas͒ and Ϫ24.2 cm ͑neon͒; for DF, ␯ ϭ2585.1 ͑gas͒ and
s
Ϫ1
Ϫ1
2556.8 cm ͑neon͒, x ϭϪ15.1 ͑gas͒ and Ϫ10.8 cm
s␴
Ϫ1
background coupling matrix element of only 0.01 cm
͑neon͒͒. An important difference remains to be explained: the
(␯ ϩ␯ ) combinations easily observable in the gas phase
would be sufficient to create a Lorentzian envelope with the
s
␦
j
observed ␥ values. Even though the fivefold increase of ␳
i
vib
͑Fig. 1͒ for (CH ) S-HF have not been found in the neon
2 2
does not quantitatively correlate with the ninefold increase of
the effective linewidth upon substitution of HF by DF, an
important IVR contribution to the observed band shapes ap-
pears therefore very likely.
matrix spectra. Although the density of intramolecular tran-
sitions of free and complexed (CH ) S is high in this spec-
2
2
tral range, the gas phase intensity ratio between ␯ and (␯s
s
ϩ␯ ) should be sufficient to allow the observation of this
␦
j
band in neon matrix. Conversely, the (␯ ϩ␯ ) combination
s
␴
band observed in the neon matrix has not been seen in the
gas phase. The failure to observe this band could be, how-
ever, due to a small cross section and its overlap with a
combination band of free (CH ) S, which cannot be easily
C. Comparison between gas phase, neon matrix
results, and ab initio calculations
The final proof for the internal coherence of our analysis
has to come from a comparison of some vibrational param-
eters which can be extracted independently from gas phase
experiments, neon matrix isolation studies, and ab initio cal-
culations. Recent studies of N -HF and (HF) trapped in
2 2
subtracted in the gas phase. Note that strong differences in
intensity ratios between fundamentals and two-quanta transi-
tions have been observed previously in gas phase and matrix
3
2
spectra of (HF)2 ,
indicating a remarkable matrix effect
2
2
3
1,32
aside from frequency shifts.
neon matrices
have allowed to quantify the matrix effects
The analysis of combination bands involving ␯ pro-
for these dimers whose spectra are very well known in the
s
4
4–46
vided precise harmonic values for the three lowest frequency
intermolecular modes ͑Table V͒. Comparison with the ab
gas phase.
The matrix shifts do not exceed 15% for the
low frequency intermolecular modes while the HF stretches,
their combination modes, and the intra-intermolecular anhar-
monicity coefficients xlm are very close to the gas phase
values. However, this comparison remains questionable be-
cause most intermolecular frequencies for these species in
initio values of ␻ , ␻ , and ␻ reveals an overestimate of
␦
␦
␴
1
2
theoretical values, up to 25% for the bending modes. This
discrepancy is however, not too surprising for a harmonic
approximation to large amplitude intermolecular modes.
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J. Chem. Phys., Vol. 121, No. 11, 15 September 2004
The complex (CH ) S-HF
5251
2
2
1
2
The combination band analysis has yielded values for
and x␴␴ which can be fruitfully exploited to estimate the
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3
4
Morse oscillator, use of the relationship D ϭ␻ /4x leads
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0
CP
Ϫ1
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͑
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The combined analysis of infrared spectra of thiirane-HF
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