Analysis of the Fourier transform infrared spectrum of the stannane species 116SnH4 in the region 1270-1600 cm-1

Article abstract of DOI:10.1140/epjd/e2004-00177-0

Monoisotopic stannane ¹¹⁶SnH₄ has been investigated at room temperature in the 600-850 cm^-1 and 1270-1600 cm^-1 regions by FTIR spectroscopy with an effective resolution of 2.1 × 10^-3 cm^-1 and 2.0 × 10^-3 cm^-1 respectively. The simultaneous analysis of infrared transitions of both the bending triad and the hot band {bending triad} minus {bending dyad}, enabled us to determine 26 parameters for the (2v₂) band and the combination band (v₂ + v₄). The standard deviation of the fit was about 1.5 × 10^-3 cm^-1. In this analysis, we have used, for the bending triad, a Hamiltonian developed to the fourth order of approximation. 163 observed transitions for the hot band and most observed transitions for the bending triad spectrum, were assigned to the two bands 2v₂ and (v₂ + v₄), up to J = 9. In the fit of the Hamiltonian parameters, we have used for the ground state and for the fundamentals v₂ and v₄, the parameters determined by Brunet, Pierre, and Bu?rger [J. Mol. Spectrosc. 140, 237 (1990)]. EDP Sciences, Societa? Italiana di Fisica, Springer-Verlag 2004.

Full text of DOI:10.1140/epjd/e2004-00177-0

Eur. Phys. J. D 32, 51–58 (2005)
DOI: 10.1140/epjd/e2004-00177-0
THE EUROPEAN
PHYSICAL JOURNAL D
Analysis of the Fourier transform infrared spectrum
of the stannane species 116SnH4 in the region 1270–1600 cm−1
A. Tabyaoui1,2,a, G. Pierre3, and H. Bu¨rger4
1
L.E.T.S., Facult´e des Sciences, avenue Ibn Batouta, B.P. 1014, Rabat, Maroc
Facult´e des Sciences et Techniques Settat, B.P. 577, 26000 Settat, Maroc
LPUB, CNRS, UMR 5027, Facult´e des Sciences Mirande, 9 rue Alain Savary, B.P. 47870, 21078 Dijon Cedex, France
Anorganische Chemie, FB C, Universit¨at-GH, Gauss-str. 20, 42097 Wuppertal, Germany
2
3
4
Received 10 August 2004
c
Published online 30 November 2004 – ꢀ EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2004
Abstract. Monoisotopic stannane 116SnH4 has been investigated at room temperature in the 600–850 cm−1
and 1270–1600 cm−1 regions by FTIR spectroscopy with an effective resolution of 2.1×10−3 cm−1 and 2.0×
10−3 cm−1 respectively. The simultaneous analysis of infrared transitions of both the bending triad and the
hot band {bending triad} minus {bending dyad}, enabled us to determine 26 parameters for the (2ν2) band
and the combination band (ν2 + ν4). The standard deviation of the fit was about 1.5 × 10−3 cm−1. In this
analysis, we have used, for the bending triad, a Hamiltonian developed to the fourth order of approximation.
163 observed transitions for the hot band and most observed transitions for the bending triad spectrum,
were assigned to the two bands 2ν2 and (ν2 +ν4), up to J = 9. In the fit of the Hamiltonian parameters, we
have used for the ground state and for the fundamentals ν2 and ν4, the parameters determined by Brunet,
Pierre, and Bu¨rger [J. Mol. Spectrosc. 140, 237 (1990)].
PACS. 33.20.Vq Vibration-rotation analysis – 33.20.Ea Infrared spectra
1 Introduction
determine simultaneously both ground and upper state
parameters of the Hamiltonian developed to the sixth or-
der approximation in the Amat-Nielsen classification.
The first vibration-rotation study of stannane SnH4, was
performed by Levin and Ziffer [2] who determined some
spectroscopic constants and showed that the two bend-
ing modes ν2 (E) and ν4 (F2) are strongly coupled by a
first order Coriolis interaction. This kind of interaction is
observed for all tetrahydride molecules XH4 like CH4 [3],
CD4 [4,5] and SiH4 [6]. Kattenberg and Oskam [7] mea-
sured the four fundamental bands using Raman and in-
frared (IR) spectroscopies.
The first high-resolution study of natural stannane
was performed by Ohshima et al. [8,9]. Their experi-
mental technique used IR-microwave (MW) double res-
onance employing a tuneable diode laser which allowed
them to observe three different types of transitions: rota-
tional transitions in the ground state [8] and in the ν2/ν4
dyad excited states [9], and rovibrational transitions of
the ν2 and ν4 bands between 640 and 850 cm−1. There-
after, Brunet et al. [1] made an analysis of the bending
dyad (ν2/ν4) of monoisotopic stannane 116SnH4 based on
FTIR high-resolution spectra. The very high precision of
the experimental IR spectrum and the very high accu-
racy of the model used in the analysis enabled them to
The stretching modes ν1 and ν3 were investigated, too,
by many authors. Birss [10] showed that the ν1 and the ν3
vibrational states are coupled by a second order rotation-
vibration interaction term. This interaction is generally
not strong but becomes very important when the wave
number difference of the two interacting states is within
a few reciprocal centimeters. In the IR, the formally for-
bidden ν1 transitions can therefore be observed. Such in-
teractions have been observed in SiH4 [11] and GeH4 [12].
Jo¨rissen et al. [13] have recorded and analysed the IR spec-
trum of the (ν1/ν3) dyad of stannane in natural isotopic
abundance. Their technique used IR-MW double reso-
nance employing a tuneable diode laser. They have de-
termined 17 constants for each of the five most abundant
isotopic species of stannane by fitting simultaneously the
IR and MW data. They have used for the ground state,
the parameters determined by Ohshima et al. [8,9]. The
Hamiltonian employed for the ground state and the v1 = 1
was that of Kirschner and Watson [14] and that for the
state v3 = 1 as given by Robiette [15]. Only one coupling
term between ν1 and ν3 given by Susskind in a tensorial
form [16] was taken into account.
a
e-mail: atabyaoui@yahoo.fr

52
The European Physical Journal D
Krivtsun et al. [17] made an analysis of the FTIR spec- was 2.3 × 10−3 cm−1 and 2.2 × 10−3 cm−1, respectively.
trum of 120SnH4 in the 1903–1960 cm−1 region. More than Trapezoidal apodization was employed. Calibration of the
230 transitions were used to analyse the ν1 and ν3 reso- former spectrum was done with N2O lines, reference [22],
nance states. These authors have determined 21 spectro- while H2O lines [22] were used to calibrate the latter spec-
scopic parameters of the upper states using a Hamiltonian trum. Wave number accuracy is better than 1×10−3 cm−1
.
developed to the fourth order of approximation, which ex-
plicitly takes into account the resonance interactions.
Tabyaoui et al. [18,19] have recorded and analysed the
3 Theorical section
FTIR and high-resolution stimulated Raman spectra of
monoisotopic stannane, 116SnH4. A simultaneous analy-
The transformed vibrational-rotational Hamiltonian for
tetrahedral molecules developed by Champion and
Pierre [23–25] is especially well adapted for vibrational ex-
trapolation. Vibrational operators are expressed in terms
of tensor products of creation and annihilation elementary
operators in such a way that each term of the Hamiltonian
expansion corresponds to a given vibrational state or set
of quasi-degenerate vibrational states. According to this
scheme, the completely transformed Hamiltonian for the
vibrational states taken into account in this work, can be
written as
sis of IR, Raman and MW [13,20] data with a Hamilto-
nian developed to sixth order for the (ν1/ν3) dyad enabled
them to determine 4 parameters of ν1, 17 parameters of ν3,
and 6 interaction parameters. Transitions were assigned
up to J = 14. For high J values (J > 14), they have
shown that the (ν1/ν3) dyad interacts with the bending
tetrad (v1v2v3v4) = (3ν2, 2ν2 + ν4, ν2 + 2ν4, 3ν4), as the
third harmonic of the bending modes ν2 and ν4 is close
to the stretching dyad (ν1/ν3). So, in order to analyse
completely the IR spectrum of 116SnH4 in the 1900 cm−1
region, the authors [18] propose that the full (ν1, ν3, 3ν2,
2ν2 + ν4, ν2+2ν4, 3ν4) polyad interaction scheme must be
considered. That needs the good knowledge of the bend-
ing triad (2ν2, ν2 + ν4, 2ν4) and the bending tetrad (3ν2,
2ν2 + ν4, ν2 + 2ν4, 3ν4) levels.
ꢀ
ꢀ
ꢀ
˜
˜
˜
˜
˜
H = H
+
H
+
H
+
H +...
{νs+νsꢀ }
{GS}
{νs}
{2νs}
s<sꢀ
s
s
(1)
˜
In this expansion, H
contains only pure rotational op-
{GS}
The present work is a first step toward this aim. It
consists of an analysis of the bending triad (2ν2, ν2 + ν4,
2ν4) of 116SnH4 in the 1400 cm−1 region, based on high-
resolution Fourier transform spectra. Moreover, use was
made of hot band {bending triad} minus {bending dyad}
transitions [21] occurring in the region of the bending dyad
and reaching the triad levels in their upper states. The
high precision of the experimental spectra and the high
accuracy of the Hamiltonian model used in the analysis
made it possible to determine 26 parameters correspond-
ing to the (2ν2) and (ν2 + ν4) bands.
erators of the type JΩ (J designating one component Jx,
Jy or Jz of the angular-momentum operator). In the no-
tation introduced in [23–25], its tensorial expression is
ꢀ
H
=
tΩ0 (K,A )TΩ0 (K,A )
(2)
1
1
˜
{GS}
gathers all terms of type rs2JΩ (rs designating qs
˜
H
or{pνss}) quadratic in the νs mode elementary operators. Its
tensorial expression [23–25] is
ꢀ
Ω(K,Γ ) Ω(K,Γ )
s,s
˜
Transitions were assigned up to J = 9.
H
=
t
Ts,s
(3)
{νs}
˜
ꢀ
H
gathers all term quartic in the νs and νs mode
{νs+νsꢀ
}
2 Experimental details
elementary operators of the type rs2rs2ꢀ JΩ. Its tensorial
expression [23–25] is
Monoisotopic stannane, 116SnH4, was prepared by re-
acting a solution containing SnCl26− (1 mg Sn/ml), ob-
tained by dissolving 116Sn (98% 116Sn, Oak Ridge) in
an aqueous HCl/HNO3 mixture, with an aqueous solu-
tion of NaBH4 (3%) in vacuum (50−80 mbar). Gaseous
116SnH4 evolved was collected at −196 ◦C and purified by
repeated fractional condensation using a standard vacu-
umline, yield ∼90%.
ꢀ
Ω(K,Γ )Γ1Γ2 Ω(K,Γ )Γ1Γ2
˜
H
=
}
t
Tssꢀ,ssꢀ
.
(4)
ssꢀ,ssꢀ
{νs+νsꢀ
˜
The expression for H
is quite similar and can be ob-
{2νs}
tained by setting sꢀ = s in equation (4).
In the above expressions and throughout this paper,
Ω(K,Γ )Γ1Γ2
T
s...,sꢀ...
is a rovibrational operator obtained by cou-
The FTIR spectra of 116SnH4 were recorded
at Giessen, Germany, in the 600−850 cm−1 and
1250−1600 cm−1 range at room temperature with a
Bruker 120 HR spectrometer equipped with a Ge/KBr
beam splitter. A Globar source was employed, and a liquid
He cooled Cu:Ge and MCT800 detector were used, respec-
tively. For the two spectra, pressures of 1 mbar and 7 mbar
and cells measuring 18.7 cm and 1.5 m respectively, were
used. The effective line widths of weak lines (FWHM)
were 2.1 × 10−3 cm−1 and 2 × 10−3 cm−1 respectively.
The resolution based on maximum optical path difference
pling rotational and vibrational operators:
Ω(K,Γ )Γ1Γ2
T
= βΩΓ1K(RΩ(K,Γ ) × VsΓ.1..Γ,s2ꢀ(.Γ..)
)
(5)
(A1)
s...,sꢀ...
where
βΩΓ1K = 1
if K = 0
if K = 0.
ꢂ
ꢃ
√
(Ω/2)
ꢁ
− 3
=
Γ1
4

A. Tabyaoui et al.: Analysis of the Fourier transform infrared spectrum of the stannane species 116SnH4
53
The rotational operator RΩ(K,Γ ) is obtained by tensorial
coupling of elementary rotational operator Ω, and the vi-
Γ1Γ2(Γ )
brational operator V
is obtained by tensorial cou-
s...,sꢀ...
pling of s. . . elementary creation operators and of sꢀ. . . el-
ementary annihilation operators. The value of [Γ1] is the
dimension of the representation. Details of the coupling of
different operators can be obtained in [25].
The rovibrational effective Hamiltonian for a set of in-
teracting states ꢁvꢂ is given by:
ꢁvꢂ
Hꢁvꢂ = PꢁvꢂHP
(6)
˜
where Pꢁvꢂ is the projector operator on the vibrational
Hilbert subspace.
The ground-state effective Hamiltonian contains terms
˜
from H
only:
{GS}
HꢁGSꢂ = PꢁGSꢂ
H
PꢁGSꢂ
˜
{GS}
1
Fig. 1. Schematic presentations of effective Hamiltonian
matrices.
ꢀ
Ω(K,A1)
=
tΩ0 (K,A )PꢁGSꢂT0
PꢁGSꢂ
(7)
where PꢁGSꢂTΩ0 (K,A1)PꢁGSꢂ denotes the projection of the
operator TΩ0 (K,A ). For simplicity, in all subsequent formu-
1
The effective Hamiltonian for the harmonic state ꢁ2νsꢂ ≡
{vs = 2} is similarly obtained by setting s = sꢀ in the
above expression. Its matrix representation can be ex-
pressed as a sum of three terms:
lae, the same symbol will be used for one operator and its
projections in all Hilbert subspaces. For instance, (7) will
be rewritten as
ꢀ
HꢁGSꢂ
=
tΩ0 (K,A )TΩ0 (K,A )
(8)
=
1
1
ꢁ2νsꢂ
ꢁ2νsꢂ
{2νs}
Hꢁ2ν ꢂ = H{GS} + H{ν }
ꢁ2ν ꢂ + H
.
(13)
s
s
s
Its matrix representation can be denoted by HꢁGSꢂ
In the general notation Hꢁ{Pp}ꢂ, ꢁPꢂ specifies the Hilbert
ꢁGSꢂ
H
.
{GS}
subspace (associated with the polyad P) on which H is
operating, whereas {p} specifies the type of the vibrational
operators involved (relating to the polyad p). The v quan-
tum numbers of the states included in polyad p are less
or equal to that included in the polyad P. In practice, ac-
cording to the so-called vibrational extrapolation scheme,
the parameters involved in all subsequent effective Hamil-
tonians HꢁP ꢂ are those of the unique transformed Hamil-
The effective Hamiltonian for the fundamental state
ꢁνsꢂ ≡ {vs = 1} contains terms from H
˜
˜
and H
{νs}
{GS}
only:
ꢄ
ꢅ
Hꢁν ꢂ = Pꢁν ꢂ
H
Pꢁν ꢂ
s
s
s
˜
˜
+ H
{νs}
{GS}
tΩ0 (K,A )TΩ0 (K,A )
ꢀ
ꢀ
1
1
Ω(K,Γ ) Ω(K,Γ )
s,s
=
+
t
Ts,s
.
(9)
˜
tonian H. In the cases considered in this work, three types
Its matrix representation can be expressed as the sum of
two terms:
of parameters can be distinguished:
ꢁνsꢂ
ꢁνsꢂ
Hꢁν ꢂ = H{GS} + H
.
(10)
tΩ0 (K,A )
so-called ground-state parameters;
1
s
{νs}
The effective Hamiltonian for the combination state ꢁνs +
Ω(K,Γ )
s,s
t
so-called νs parameters;
˜
˜
ꢀ
ꢀ
νs ꢂ ≡ {vs = vs = 1} contains terms from H
, H
,
{νs}
{GS}
˜
˜
Ω(K,Γ )Γ1Γ2
H
and H
only:
{νsꢀ
}
{νs+νsꢀ
}
ꢀ
t
so-called (νs + νs ) parameters
ssꢀ,ssꢀ
(or 2νs parameters if s = sꢀ).
ꢆ
ꢀ ꢂ
ꢀ ꢂ
Hꢁν +ν = Pꢁν +ν
H
+ H
Pꢁν +ν
+ H
{νsꢀ }
s
s
s
s
˜
˜
˜
{GS}
{νs}
ꢇ
ꢀ ꢂ
Figure 1 shows the Hamiltonian matrices in the three
states considered here.
Perevalov et al. [26–29] showed that different unitary
transformations of the effective Hamiltonian can be con-
sidered. These transformations change the eigenfunctions
of the Hamiltonian but do not change its eigenvalues:
s
˜
s
+ H
{νs+νsꢀ
}
1
ꢀ
ꢀ
1
Ω(K,Γ ) Ω(K,Γ )
s,s
=
tΩ0 (K,A )TΩ0 (K,A )
+
t
Ts,s
ꢀ
Ω(K,Γ ) Ω(K,Γ )
Tsꢀ,sꢀ
+
t
sꢀ,sꢀ
ꢀ
Ω(K,Γ )Γ1Γ2 Ω(K,Γ )Γ1Γ2
s,sꢀ
+
t
Ts,sꢀ
.
(11)
ꢀ
Ω(K,nΓ )Γ1Γ2
Ω(K,nΓ )Γ1Γ2
˜
˜
iS
−iS
˜
˜
H = e He
=
ts...,sꢀ...
× T
(14)
s...,sꢀ..
Its matrix representation can be expressed as sum of four
terms:
with
ꢁνs+νsꢀ
ꢁνs+νsꢀ
Hꢁν +ν = H{GS} ꢂ +H
ꢂ +Hꢁνs+νsꢀ ꢂ +Hꢁνs+νsꢀ ꢂ
.
ꢀ ꢂ
s
s
ꢄ
ꢅ
ꢀ
(A1)
{νs}
{νsꢀ
}
{νs+ν
}
ꢀ
(s12)
Ω(K,nΓ )Γ1Γ2
s...,sꢀ...
Γ1Γ2(Γ )
ε
S =
S
RΩ(K,Γ ) × Vs...,sꢀ...
. (15)

54
The European Physical Journal D
Table 1. Parameters of the 2ν2 and (ν2+ν4) bands of 116SnH4. state, dyad states, states connected by hot bands, etc.; by
fitting simultaneously several types of experimental data.
Ω(K,nΓ) s1s2 Γ1s3s4 Γ2
0(0,0A1) 0200A1 0200A1
2(0,0A1) 0200A1 0200A1
Value (cm−1
)
The whole package STDS is freely accessible through
ftp (user anonymous) at jupiter.u-bourgogne.fr
or through the World Wide Web site at
fttp://www.u-bourgogne.fr/LPUB/STDS.html.
The analysis is based on an iterative weighted least-
squares fitting procedure of the transition wave numbers.
In order to minimize a dimensionless Q number in the
least-squares procedure, the weight wi for each piece of
data fi is equal to the inverse of the square of the esti-
mated uncertainty ∆i:
−8.395(26) × 10−1
1.121(22) × 10−3
1.32550(62)
0(0,0A1)
2(0,0A1)
1(1,0F1)
1(1,0F1)
1(1,0F1)
0200 E 0200 E
0200 E 0200 E
2000A1 0101F1
0200 E 0101F1
0200 E 0101F2
−9.86(76) × 10−5
−4.237(24) × 10−2
4.060(28) × 10−2
−1.74(87) × 10−4
−3.17(55) × 10−2
6.17(66) × 10−4
4.71(34) × 10−2
−2.024(76) × 10−3
7.389(97) × 10−2
2.30605(23)
ꢆ
ꢇ
0(0,0A1) 0200A1 0002A1
2(0,0A1) 0200A1 0002A1
2
fiobs − fical
ꢀ
Q =
.
(17)
2
∆
i
i
0(0,0A1)
2(0,0A1)
1(1,0F1)
0(0,0A1)
1(1,0F1)
2(0,0A1)
1(1,0F1)
0(0,0A1)
1(1,0F1)
2(0,0A1)
1(1,0F1)
1(1,0F1)
1(1,0F1)
1(1,0F1)
0(0,0A1)
1(1,0F1)
2(0,0A1)
0200 E 0002 E
0200 E 0002 E
0200 E 0002F2
0101F1 0101F1
0101F1 0101F1
0101F1 0101F1
0101F1 0101F2 −1.24941(49) × 10−1
0101F2 0101F2
0101F2 0101F2 −3.39699(73) × 10−1
0101F2 0101F2
0101F1 0002A1
0101F1 0002 E
0101F1 0002F2
0101F2 0002 E
0101F2 0002F2
0101F2 0002F2
0101F2 0002F2
In practice, we assigned an uncertainty ∆i of 1 ×
10−3 cm−1 to unblended transitions for the bending triad
and of 0.3 × 10−3 cm−1 for the hot band {bending triad}
minus {bending dyad} transitions.
−4.589(10) × 10−2
Of the 575 calculated transitions assigned to observed
lines up to J = 9, 443 presumably unblended ones were
used in the fit. IR data corresponding to the 2ν2 and
(ν2 +ν4) bands and to the hot band {bending triad} minus
{bending dyad} [21] were combined to refine the Hamilto-
nian parameters. The ground state and the bending dyad
(ν2/ν4) parameters used in the fit were fixed to the values
determined by Brunet et al. [1]. Twenty-six parameters of
the Hamiltonian, corresponding to the 2ν2 and (ν2 + ν4)
bands, were determined with a standard deviation of the
fit of about 1.5×103 cm1. The results are given in Table 1.
Statistics of the fit are listed in Tables 2 and 3.
−1.1630(74) × 10−3
−7.6(1.1) × 10−4
−1.636(31) × 10−4
1.0544(49) × 10−1
−2.5247(51) × 10−1
−1.7923(41) × 10−1
−2.6628(47) × 10−1
−8.5484(47) × 10−1
1.4166(18) × 10−1
1.040(12) × 10−3
A graphical display of the quality of the present anal-
ysis is shown in Figure 2 in which the Obs-Cal residuals
are plotted as a function of the wave number (a) and as
a function of the rotational J number (b). This empha-
sizes the effect of neglected perturbations, which increases
with J.
* One standard deviation in parenthesis.
These transformations keep the operator form and eigen-
values unalterated but change the values of its parameters,
according to:
5 Rovibrational energy levels
The rovibrational energy levels are obtained by diagonal-
izing the effective Hamiltonian.
t = t + ∆t(s(1), s(2), ...)
˜
(16)
E
ꢁνꢂ(J, C, α) = ꢁJ, C, α| Hꢁνꢂ |J, C, αꢂ
(18)
Ω(K,nΓ )Γ1Γ2
Most of the t
terms cannot be determined
s...,sꢀ...
from observed lines in a unique way (for details, see
Refs. [26–30]), they are not spectroscopic constants.
where |J, C, αꢂ are the eigenfunctions of the effective rovi-
brational Hamiltonian, and α gives the energy levels of the
vibrational polyads having the same J and C values.
Reduced energies are obtained by subtracting the
scalar terms:
4 Data analysis
ꢀ
Eꢁrνeꢂd(J, C, α) = Eꢁνꢂ(J, C, α)−
tΩ0 (0,0A )(J(J + 1))Ω/2
.
1
A new set of programs, grouped in a software package
named STDS (Spherical Top Data System), was devel-
oped in the LPUB in Dijon [31]. These programs may be
Ω
(19)
used to study the vibrational polyads with J < 200, they Figure 3a shows all reduced calculated (0200) and (0101)
were adapted to refine at the same time several types of levels up to J = 9 while Figure 3b shows the reduced
vibrational parameters that can belong to the ground energy levels reached by the observed transitions.

A. Tabyaoui et al.: Analysis of the Fourier transform infrared spectrum of the stannane species 116SnH4
55
Table 2. Statistics on the fit of the infrared transitions of 116SnH4. Bending triad.
28 Data for the (0200) band.
J
number of cumulated number standard deviation cumulated St. Dev.
data
4
of data
(10−3 cm−1
)
(10−3 cm−1
)
6
7
8
9
4
1.127
1.127
9
13
24
28
0.964
1.017
11
4
1.012
1.015
0.724
0.978
280 Data for the (0101) band.
J
number of cumulated number standard deviation cumulated St. Dev.
data
1
of data
1
(10−3 cm−1
)
(10−3 cm−1
)
0
1
2
3
4
5
6
7
8
9
1.157
1.157
7
8
0.853
0.897
15
20
30
38
39
52
44
34
23
0.775
0.819
43
1.008
0.912
73
0.822
0.876
111
150
202
246
280
0.796
0.850
0.735
0.822
0.969
0.862
0.869
0.863
0.962
0.876
Table 3. Statistics on the fit of the infrared transitions of 116SnH4. Hot band {bending triad} minus {bending dyad} [21].
10 Data for the (0200) ← (0100) band.
J
number of cumulated number standard deviation cumulated St. Dev.
(10−3 cm−1
data
of data
(10−3 cm−1
)
)
6
7
8
9
2
3
3
2
2
5
0.310
0.310
0.709
0.583
8
0.403
0.523
10
0.098
0.470
124 Data for the (0101) ← (0100) band.
J
number of cumulated number standard deviation cumulated St. Dev.
data
1
of data
1
(10−3 cm−1
)
(10−3 cm−1
)
0
1
2
3
4
5
6
7
8
9
0.839
0.839
6
7
0.717
0.736
9
16
0.532
0.629
12
14
17
17
17
18
13
28
0.713
0.667
42
0.756
0.697
59
0.773
0.720
76
0.549
0.687
93
0.649
0.680
111
124
0.803
0.702
0.666
0.698
1 Data for the band (0101) ← (0001).
J
number of cumulated number standard deviation cumulated St. Dev.
data
1
of data
1
(10−3 cm−1
)
(10−3 cm−1
)
7
0.244
0.244

56
The European Physical Journal D
Fig. 4. Comparison of calculated (a) and experimen-
tal (b) spectra in the (ν2 + ν4) P branch of 116SnH4.
Fig. 2. Differences between experimental and calculated line
positions: (a) as a function of the wave number; (b) as a func-
tion of the quantum number J.
Fig. 5. Comparison of calculated (a) and experimen-
tal (b) spectra of P(8) in the (ν2 + ν4) P branch of 116SnH4.
a
b
A1
F1
+ F1
*
+
: R 0
: Q 3
: R 4
: R 1
+ F2
F1
* A1
+ A2
-1
-1
Fig. 3. Reduced energy level diagram: (a) All calculated levels.
(b) Levels reached by the observed lines.
1441.6 cm
1443.1 cm
Fig. 6. Comparison of calculated (a) and observed (b) spectra
in the (ν2 + ν4) P branch of 116SnH4.

A. Tabyaoui et al.: Analysis of the Fourier transform infrared spectrum of the stannane species 116SnH4
57
Fig. 7. Comparison of calculated (a) and observed (b) spectra
of P(9) In the (2ν2) P branch of 116SnH4.
Fig. 9. Observed (a) and calculated (b) {bending triad} minus
{bending dyad} hot band transitions of R(8) occurring in the
bending dyad region of 116SnH4.
Fig. 8. Comparison of calculated (a) and observed (b) spectra
of R(6) in the (2ν2) R branch of 116SnH4.
We could then start the analysis of the bending tetrad
(3ν2, 2ν2 + ν4, ν2 + 2ν4, 3ν4).
6 Discussion
The author A. Tabyaoui would like to thank Ch. Wenger for his
invaluable assistance. The “Conseil R´egional de Bourgogne” is
gratefully acknowledged for the financial support to the “Lab-
oratoire de Physique de l’Universit´e de Bourgogne”.
In the bending triad, the intensity of lines belonging to
the 2ν4 band is small. This made it so difficult to assign
any transitions corresponding to the 2ν4 band.
It is well-known that the 2ν2, (ν2 + ν4) and the 2ν4
levels belonging to the bending triad are perturbed by
resonance interactions. However, for relatively low values
of J (J < 10) the isolated-state model is still applicable.
With the aim to minimize the resonance interaction effect
between the (ν2 + ν4) and 2ν4 bands, we analysed the
infrared spectra up to J = 9.
Many lines corresponding to the 2ν2 and (ν2 + ν4)
bands were assigned and a first set of the Hamiltonian
parameters for these two bands has been determined. Al-
together 163 transitions corresponding to the hot band
{bending triad} minus {bending dyad} were assigned to
observed lines with J up to J = 9 [21].
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