Analysis of the hot band of stannane 116SnH4 in the 600-850 cm-1 range

Article abstract of DOI:10.1140/epjd/e2003-00283-5

The FTIR spectrum of monoisotopic stannane ¹¹⁶SnH₄ has been recorded in the 600-850 cm^-1range, with the Bruker 120 HR interferometer at Giessen, Germany. The resolution was 2.1 × 10 ^-3 cm^1-. The analysis of infrared transitions in this region enabled Brunet et al. to assign many lines to the bending dyad ν ₂/ν₄,. However, several lines in this spectrum were found to be unassigned. In a recent work, we have analysed the infrared spectrum of stannane in the bending triad region at 1400 cm^-1. The results obtained enabled us to assign directly, for the spectrum in the region 600-850 cm^-1, 163 of the observed transitions to the hot band {bending triad} minus {bending dyad} up to J = 9. These transitions were combined to the infrared data corresponding to the bending triad (2ν ₂, ν₂ + ν₄, 2ν₄), to refine a set of Hamiltonian parameters for the two bands 2ν₂ and (ν₂ + ν₄).

Full text of DOI:10.1140/epjd/e2003-00283-5

Eur. Phys. J. D 28, 49–57 (2004)
DOI: 10.1140/epjd/e2003-00283-5
THE EUROPEAN
PHYSICAL JOURNAL D
Analysis of the hot band of stannane 116SnH4
in the 600–850 cm−1 range
A. Tabyaoui1,2,a, G. Pierre3, and H. Bu¨rger4
1
FST Settat, km 3, B.P. 577, 26000 Settat, Morocco
LETS, Facult´e des sciences, avenue Ibn Batouta, B.P. 1014, Rabat, Morocco
LPUB, CNRS UMR 5027, Facult´e des sciences Mirande, 9 rue Alain Savary, B.P. 47870, 21078 Dijon, France
Anorganische Chemie, FB 9, Universit¨at-GH, Gauss-Str. 20, 5600 Wuppertal 1, Germany
2
3
4
Received 16 July 2003 / Received in final form 7 August 2003
c
Published online 8 October (2003) – ꢀ EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2004
Abstract. The FTIR spectrum of monoisotopic stannane 116SnH4 has been recorded in the 600–850 cm−1
range, with the Bruker 120 HR interferometer at Giessen, Germany. The resolution was 2.1 × 10−3 cm−1
.
The analysis of infrared transitions in this region enabled Brunet et al. [1] to assign many lines to the
bending dyad ν2/ν4. However, several lines in this spectrum were found to be unassigned. In a recent
work [2], we have analysed the infrared spectrum of stannane in the bending triad region at 1400 cm−1
.
The results obtained enabled us to assign directly, for the spectrum in the region 600–850 cm−1, 163 of the
observed transitions to the hot band {bending triad} minus {bending dyad} up to J = 9. These transitions
were combined to the infrared data corresponding to the bending triad (2ν2, ν2 + ν4, 2ν4), to refine a set
of Hamiltonian parameters for the two bands 2ν2 and (ν2 + ν4) [2].
PACS. 33.20.Vq Vibration-rotation analysis – 33.20.Ea Infrared spectra
1 Introduction
small induced dipole moment by excitation of a triply de-
generate vibration [8,9]. Pure rotational transitions result-
Many experimental and theoretical studies were de- ing from this induced dipole moment have been observed
voted to tetrahedral molecules generally and to the for several tetrahedral molecules [10–16].
stannane molecule SnH4 particularly, using Raman, in-
Jo¨rissen et al. [17] have recorded and analysed the in-
frared and microwave spectroscopy. The first work on
frared spectrum of the (ν1/ν3) dyad of stannane in nat-
stannane was done by Levin and Ziffer [3] who deter-
ural isotopic abundance. Their technique used infrared-
mined some molecular constants and showed that the
microwave double resonance employing a tunable diode
two bending modes ν2(E) and ν4(F2) are strongly cou-
laser. They have determined for each of the five most
abundant isotopic species of stannane seventeen constants
pled by a first order Coriolis interaction. Kattenberg
and Oskam [4] measured the four fundamental bands
by fitting simultaneously the infrared and microwave data
(ν1(A1), ν2(E), ν3(F2), ν4(F2)) using Raman and infrared
using for the ground state and the ν1 = 1 state the
spectroscopy and found that the infrared inactive ν1 band
Hamiltonian of Kirschner and Watson [18] and for the
ν3 = 1 state that of Robiette et al. [19]. Only one cou-
was only 2.5 cm−1 above the infrared active ν3 band.
Thereafter, Birss [5] showed that the ν1 and the ν3 vi-
pling term between ν1 and ν3 given by Cabana et al. [6]
brational states are coupled by a second order rotation-
and expressed by Susskind [20] in a tensorial form as
vibration interaction term. Generally this interaction
H(ν1/ν3) = d13T123 was used. The ground state param-
is not strong but becomes very important when the
eters used in their fit were those determined by Ohshima
wavenumber difference of the two bands is within a
et al. [21,22].
few cm−1. In the infrared, the formally forbidden ν1 tran-
Krivtsun et al. [23] recorded and analysed the FTIR
sitions can therefore borrow intensity from the allowed
spectrum of monoisotopic stannane 120SnH4 in the
ν3 transitions and be observed. Such interactions have
1903–1960 cm−1 region. More than 230 transitions of
been observed in SiH4 [6] and GeH4 [7].
the 120SnH4 isotopic specie were used for simultaneous
It is well-known that tetrahedral molecules, which are
analysis of the ν1, ν3 resonance states. They have de-
non polar in their equilibrium configuration, develop a
termined 21 spectroscopic parameters of the upper states
a
e-mail: atabyaoui@yahoo.fr
using a model Hamiltonian developed to the forth order

50
The European Physical Journal D
of approximation, which explicitly takes into account the
resonance interaction.
The (ν1/ν3) stretching dyad of stannane was reinves-
tigated by Tabyaoui et al. [24,25] near 1900 cm−1, em-
ploying a monoisotopic sample, 116SnH4, by which am-
biguities caused by mutual blending of lines, belonging
to different isotopic species could be circumvented. They
have recorded and analysed the FTIR and high-resolution
Stimulated Raman spectra. A simultaneous analysis of the
Raman, infrared and microwave data using a Hamiltonian
developed to the sixth order for the (ν1/ν3) dyad enabled
them to determine 4 parameters for the ν1 band, 17 pa-
rameters for the ν3 band and 6 interaction parameters.
The line transitions were assigned up to J = 14. They
have shown that for high J values (J > 14), a perturba-
tion appears due to an interaction between the stretching
dyad (ν1/ν3) and the second overtone of bending modes
(3ν2, 2ν2 + ν4, ν2 + 2ν4, 3ν4). In the fit of the Hamiltonian
parameters, the ground state parameters were fixed to the
values determined by Brunet et al. [1], where the tenso-
rial ones are close to the values determined by Ohshima
et al. [21,22].
Fig. 1. Experimental spectrum of monoisotopic stannane
116SnH4.
116SnH4 was investigated too by Brunet et al. [1] who
analysed the FTIR spectrum of the (ν2/ν4) dyad using a
sixth order Hamiltonian. The analysis of the infrared tran-
sitions allowed them to determine 10 ground state param-
eters, 9ν2 parameters, 17ν4 parameters and 18 interaction
parameters.
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 vacuum
line, yield ∼90%.
FTIR spectra were recorded at Giessen in the
490–980 cm−1 range with a Bruker 120 HR spectrome-
ter equipped with a Ge/KBr beam splitter and a Cu:Ge
detector. The resolution, trapezoidal apodization, was
2.0 × 10−3 cm−1; the Doppler width at 700 cm−1 is ap-
prox. 0.7 × 10−3 cm−1. The actual width of weak lines
(FWHM) was ∼2.1×10−3 cm−1. A cell of 18.7 cm length
equipped with KBr windows was employed, and a pres-
sure of 1 mbar chosen. A total of 50 scans were co added.
Calibration was performed with N2O lines [28]; relative to
Halonen et al. [26] have analysed the FTIR spectrum
of the (2000, A1/F2) stretching vibrational band system
of 116SnH4 up to J = 20 and refined 21 Hamiltonian pa-
rameters in a local mode model. Also, Halonen et al. [27]
have analysed the FTIR spectra of the (1000, A1/F2),
(2000, A1/F2), (3000, A1/F2) vibrational band systems
for 120SnD4. They have made a rotational analysis of the
spectra. The local mode relations obtained confirm that
vibrational energy localization takes place in the second
stretching vibrational overtone of deuterated stannane.
Recently, we have made an analysis of the FTIR spec-
trum of the monoisotopic stannane in the 1400 cm−1 re-
gion corresponding to the bending triad [2]. The results
obtained enabled us to assign directly most observed tran-
sitions to the hot band {bending triad} minus {bending
dyad} near 700 cm−1. We have then included these tran-
sitions in the fit of the Hamiltonian parameters. The
simultaneous analysis of infrared data corresponding to
both hot band and bending triad enabled us to deter-
mine 26 Hamiltonian parameters for the 2ν2 and (ν2 +
these lines it is better than 1.0 × 10−4 cm−1
.
The medium-resolution spectrum showed in Figure 1
was recorded with a Nicolet 7199 FTIR spectrometer em-
ploying a resolution of 0.05 cm−1
.
3 Theory
The transformed vibrational-rotational Hamiltonian for
tetrahedral molecules developed by Champion and
Pierre [29–31] 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
ν4) bands [2]. The standard deviation was 1.5×10−3 cm−1
.
In this work, we present for the hot band {bending
triad} minus {bending dyad}, the assignments realized up
to J = 9 and the results obtained for this hot band during
the analysis of the bending triad (2ν2, ν2 + ν4, 2ν4).
2 Experimental details
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
ꢁ
ꢁ
ꢁ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
H = H
+
H
+
H
+
H
. (1)
{νs+νsꢀ }
{GS}
{νs}
{2νs}
s<sꢀ
s
s

A. Tabyaoui et al.: Analysis of the hot band of stannane 116SnH4 in the 600–850 cm−1 range
51
where PꢁGSꢂTΩ0 (K,A1)PꢁGSꢂ denotes the projection of the
ꢀ
In this expansion, H
contains only pure rotational op-
{GS}
erators of the type JΩ (J designating one component Jx,
Jy or Jz of the angular-momentum operator). In the no-
tation introduced in [29–31] its tensorial expression is
operator TΩ0 (K,A ). For simplicity, in all subsequent for-
1
mulae, the same symbol will be used for one operator and
its projections in all Hilbert subspaces. For instance, (7)
will be rewritten as
ꢁ
H
=
tΩ0 (K,A ) TΩ0 (K,A )
.
(2)
1
1
ꢀ
ꢁ
{GS}
1
1
HꢁGSꢂ
=
tΩ0 (K,A )TΩ0 (K,A )
.
(8)
=
ꢀ
H
gathers all terms of type rs2JΩ (rs designating qs
or{pνss}) quadratic in the νs mode elementary operators. Its
Its matrix representation can be denoted by HꢁGSꢂ
ꢁGSꢂ
tensorial expression [29–31] is
H
.
{GS}
ꢁ
The effective Hamiltonian for the fundamental state
Ω(K,Γ ) Ω(K,Γ )
s,s
ꢀ
H
=
t
Ts,s
.
(3)
ꢀ
ꢀ
{νs}
ꢁνsꢂ ≡ {vs = 1} contains terms from H
and H
{GS}
{νs}
only:
ꢀ
ꢀ
H
gathers all term quartic in the νs and νs mode
ꢂ
ꢃ
{νs+νsꢀ
}
Hꢁν ꢂ = Pꢁν ꢂ
H
+ H
Pꢁν ꢂ
s
s
s
elementary operators of the type rs2rs2ꢀ JΩ. Its tensorial
ꢀ
ꢀ
{GS}
{νs}
expression [29–31] is
ꢁ
ꢁ
ꢁ
tΩ0 (K,A ) TΩ0 (K,A )
+
t
Ts,s
.
1
1
Ω(K,Γ ) Ω(K,Γ )
s,s
Ω(K,Γ )Γ1Γ2
H
=
}
t
TsΩs(ꢀK,s,sΓꢀ )Γ1Γ2
.
(4)
ꢀ
=
ssꢀ,ssꢀ
{νs+νsꢀ
(9)
ꢀ
The expression for H
is quite similar and can be ob-
{2νs}
Its matrix representation can be expressed as the sum of
two terms:
tained by setting sꢀ = s in (4).
In the above expressions and throughout this paper,
ꢁνsꢂ
ꢁνsꢂ
Hꢁν ꢂ = H{GS} + H
.
(10)
s
Ω(K,Γ )Γ1Γ2
{νs}
T
is a rovibrational operator obtained by cou-
s...,sꢀ...
pling rotational and vibrational operators:
The effective Hamiltonian for the combination state ꢁνs +
ꢀ
ꢀ
ꢀ
ꢀ
νs ꢂ ≡ {vs = vs = 1} contains terms from H
, H
,
{νs}
ꢂ
ꢃ
{GS}
(A1)
Ω(K,Γ )Γ1Γ2
T
= βΩΓ1K RΩ(K,Γ ) × VsΓ.1..Γ,s2ꢀ(.Γ..)
(5)
ꢀ
ꢀ
s...,sꢀ...
H
and H
only:
{νsꢀ
}
{νs+νsꢀ
}
ꢀ ꢂ
s
Hꢁν +ν
=
s
where
βΩΓ1K = 1
= [Γ1]1/2
if K = 0
if K = 0.
ꢀ ꢂ
ꢀ ꢂ
Pꢁν +ν (H
+ H
+ H
+ H
)Pꢁν +ν
s
s
ꢀ
ꢀ
ꢀ
ꢀ
s
s
{GS}
{νs}
{νsꢀ
}
{νs+νsꢀ
}
ꢄ
ꢅ
Ω/2
−31/2
ꢁ
ꢁ
tΩ0 (K,A ) TΩ0 (K,A )
+
t
Ts,s
1
1
Ω(K,Γ ) Ω(K,Γ )
s,s
=
+
4
The rotational operator is denoted by RΩ(K,Γ ) where Ω,
K and Γ designate respectively rotational degree, ten-
sor rank in the rotation group O(3), and symmetry in
the group Td. It is obtained by tensorial coupling of Ω
ꢁ
ꢁ
Ω(K,Γ ) Ω(K,Γ )
Tsꢀ,sꢀ
Ω(K,Γ )Γ1Γ2
t
+
t
TΩs,s(Kꢀ ,Γ )Γ1Γ2
.
sꢀ,sꢀ
s,sꢀ
(11)
elementary rotational operators, and the vibrational op-
Its matrix representation can be expressed as sum of four
terms:
Γ1Γ2(Γ )
erator V
is obtained by tensorial coupling of s...
s...,sꢀ...
elementary creation operators and of sꢀ... elementary an-
nihilation operators. The value of [Γ1] is the dimension
of the representation. Details of the coupling of different
operators can be obtained in [31].
Hꢁν +ν = H{GS} ꢂ + H
ꢁνs+νsꢀ
ꢁνs+νsꢀ ꢂ
{νs}
ꢀ ꢂ
s
s
ꢁνs+νsꢀ
+ H
ꢂ + Hꢁνs+νsꢀ ꢂ
.
(12)
{νsꢀ
}
{νs+νsꢀ }
The rovibrational effective Hamiltonian for a set of in-
teracting states ꢁνꢂ is given by:
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:
Hꢁνꢂ = PꢁνꢂHP
(6)
ꢁνꢂ
ꢀ
where Pꢁνꢂ is the projector operator on the vibrational
ꢁ2νsꢂ
ꢁ2νsꢂ
{2νs}
ꢁ2ν ꢂ + H
.
(13)
s
Hꢁ2ν ꢂ = H{GS} + H{ν }
Hilbert subspace.
s
s
The ground-state effective Hamiltonian contains terms
ꢀ
In the general notation Hꢁ{Pp}ꢂ, ꢁPꢂ specifies the Hilbert
from H
only:
{GS}
subspace (associated to the polyad P) on which H is oper-
ating, whereas {p} specifies the type of the vibrational op-
erators involved (relating to the polyad p). The v quantum
numbers of the states included in polyad p are less or equal
HꢁGSꢂ = PꢁGSꢂ
H
PꢁGSꢂ
{GS}
ꢀ
ꢁ
tΩ0 (K,A )PꢁGSꢂT0Ω(K,A1)PꢁGSꢂ
(7)
1
=

52
The European Physical Journal D
to that included in the polyad P. In practice, according Table 1. Hamiltonian parameters of the 2ν2 and (ν2 + ν4)
bands of 116SnH4.
to the so-called vibrational extrapolation scheme, the pa-
rameters involved in all subsequent effective Hamiltonian
Ω(K, nΓ )
0(0, 0A1)
2(0, 0A1)
0(0, 0A1)
2(0, 0A1)
1(1, 0F1)
1(1, 0F1)
1(1, 0F1)
0(0, 0A1)
2(0, 0A1)
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)
s1s2Γ1s3s4Γ2
0200A1 0200A1
0200A1 0200A1
0200 E 0200 E
0200 E 0200 E
2000A1 0101F1
0200 E 0101F1
0200 E 0101F2
0200A1 0002A1
0200A1 0002A1
0200 E 0002 E
0200 E 0002 E
0200 E 0002F2
0101F1 0101F1
0101F1 0101F1
0101F1 0101F1
0101F1 0101F2
0101F2 0101F2
0101F2 0101F2
0101F2 0101F2
0101F1 0002A1
0101F1 0002 E
0101F1 0002F2
0101F2 0002 E
0101F2 0002F2
0101F2 0002F2
0101F2 0002F2
Value (cm−1)*
−8.395(26) × 10−1
1.121(22) × 10−3
1.32550(62)
HꢁP ꢂ are those of the unique transformed Hamiltonian H
ꢀ
In the cases considered in this work, three types of param-
eters can be distinguished:
tΩ0 (K,A )
so-called ground-state parameters;
1
−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
Ω(K,Γ )
s,s
t
so-called νs parameters;
Ω(K,Γ )Γ1Γ2
ꢀ
t
so-called (νs + νs ) parameters
ssꢀ,ssꢀ
(or 2νs parameters if s = sꢀ).
Perevalov et al. [32–35] 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:
4.71(34) × 10−2
−2.024(76) × 10−3
7.389(97) × 10−2
2.30605(23)
ꢀ
iS
−iS
ꢀ
ꢀ
H = e He
ꢁ
Ω(K,nΓ )Γ1Γ2
ts...,sꢀ...
Ω(K,nΓ )Γ1Γ2
ꢀ
=
× T
(14)
s...,sꢀ...
−4.589(10) × 10−2
−1.1630(74) × 10−3
−1.24941(49) × 10−1
−7.6(1.1) × 10−4
−3.39699(73) × 10−1
−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
with
ꢂ
ꢃ
ꢁ
(A1)
Ω(K,nΓ )Γ1Γ2
s...,sꢀ...
Γ1Γ2(Γ )
ε
S =
S
RΩ(K,Γ ) × Vs...,sꢀ...
. (15)
These transformations keep the operator form and eigen-
values unalterated but change the values of its parameters,
according to:
ꢂ
ꢃ
t = t + ∆t s(1), s(2), ... .
(16)
ꢀ
Ω(K,nΓ )Γ1Γ2
s...,sꢀ...
Most of the t
terms cannot be determined
from observed lines in a unique way (for details, see
Refs. [32–36]), they are not spectroscopic constants.
*One standard deviation in paranthesis.
4 Data analysis
A new set of programs, grouped in a software package
named STDS (Spherical Top Data System), was devel-
oped in the LPUB in Dijon [37]. These programs may
be used to study the vibrational polyads with J < 200,
they were adapted to refine at the same time several
types of vibrational parameters that can belongs to the
ground state, dyad states, hot band states, etc.; by fitting
simultaneously several types of experimental data. 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.
fi is equal to the inverse of the square of the estimated
uncertainty ∆i:
ꢆ
ꢇ
2
fiobs − fical
ꢁ
Q =
·
(17)
2
∆
i
i
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.
The analysis is based on an iterative-weighted least
The analysis of the bending triad [2] enabled us to
squares fitting procedure of the transition wavenumbers. assign 163 observed lines to hot band transitions up
In order to minimize a dimensionless Q number in the least to J = 9. 135 presumably unblended lines were combined
squares procedure, the weight wi for each piece of data to infrared data corresponding to the bending triad to

A. Tabyaoui et al.: Analysis of the hot band of stannane 116SnH4 in the 600–850 cm−1 range
53
Table 2. Statistics on the fit of the hot band infrared transi-
tions of 116SnH4.
10 data for the (0200) ← (0100) band.
number cumulated
standard
deviation
(10−3 cm−1
cumulated
St. Dev.
(10−3 cm−1
)
J
of
data
number
of data
)
6
7
8
9
2
3
3
2
2
5
0.310
0.709
0.403
0.098
0.310
0.583
0.523
0.470
8
Fig. 2. Obs-Calc residuals as a function of the wavenumber.
10
124 data for the (0101) ← (0100) band.
number cumulated
number
of data
standard
deviation
(10−3 cm−1
cumulated
St. Dev.
(10−3 cm−1
J
of
data
)
)
0
1
2
3
4
5
6
7
8
9
1
1
7
0.839
0.717
0.532
0.713
0.756
0.773
0.549
0.649
0.803
0.666
0.839
6
0.736
9
16
28
42
59
76
93
111
124
0.629
12
14
17
17
17
18
13
0.667
0.697
Fig. 3. Obs-Calc residuals as a function of the rotational J
number.
0.720
0.687
0.680
5 Discussion
0.702
0.698
It’s well-known that the 2ν2, (ν2 + ν4) and the 2ν4 bands
of the bending triad are perturbed by resonance interac-
tion. However, for relatively low values of J (J < 10) the
isolated-state model is still applicable. As the line inten-
sity of vibrational levels of the 2ν4 band is small, it was
so difficult for us to assign the transitions corresponding
to this band. Thus, in the aim to minimize the resonance
interaction effect between the (ν2 + ν4) and 2ν4 bands,
we analysed the infrared spectra up to J = 9. Figure 2
shows the Obs-Calc residuals plotted as a function of the
wavenumber and Figure 3 shows them as a function of
the rotational J number. This emphasizes the effect of ne-
glected perturbations that increases as J value. One can
see that the calculations for the hot band transitions are
in good agreement with experimental data (Tab. 3). The
set of parameters determined for the two bands 2ν2 and
(ν2 + ν4) can be used to analyse completely the bending
triad using a spectrum more intense in this region and
with help of the hot band transitions assignments.
1 data for the (0101) ← (0001).
number cumulated standard
cumulated
St. Dev.
(10−3 cm−1
J
of
data
number
of data
deviation
(10−3 cm−1
)
)
7
1
1
0.244
0.244
determine the Hamiltonian parameters. The simultaneous
analysis of these data enabled us to determine 26 param-
eters for the two bands 2ν2 and (ν2 + ν4), using a Hamil-
tonian developed to the fourth order (Tab. 1). The RMS
for the hot band transitions used in the fit was about
2.26×10−3 cm−1 while the standards deviation for the fit
of the parameters was 1.5 × 10−3 cm−1. Statistics of the
fit are listed in Table 2. Table 3 regroups the assignments
made for the hot band transitions with the difference be-
tween observed and calculated frequencies.
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”.

54
The European Physical Journal D
Table 3. Assignments of the hot band infrared transitions of 116SnH4.
Obs
(cm−1
Calc
(cm−1
Obs–Calc
(10−3 cm−1
)
Assignments
)
)
654.5296
654.5437
654.6731
654.8776
655.2688
655.5852
656.8451
657.6139
657.6763
657.7052
657.9287
658.3189
659.2121
659.5672
660.1022
660.2566
660.3022
660.3855
660.6277
660.7599
660.8899
661.0806
661.6291
662.0653
662.1077
662.2349
663.5039
663.5922
663.6136
663.8588
663.8752
664.0518
664.1256
664.1361
664.3570
665.8020
666.0112
666.1770
666.2728
666.3897
666.5938
667.6507
667.7773
667.9616
668.8250
668.8250
668.8290
654.5297
654.5433
654.6737
654.8785
655.2691
655.5851
656.8456
657.6126
657.6761
657.7051
657.9283
658.3196
659.2124
659.5666
660.1004
660.2596
660.3051
660.3881
660.6278
660.7594
660.8891
661.0814
661.6292
662.0648
662.1088
662.2357
663.5040
663.5930
663.6136
663.8594
663.8737
664.0510
664.1253
664.1364
664.3571
665.8020
666.0108
666.1772
666.2730
666.3885
666.5943
667.6507
667.7772
667.9614
668.8247
668.8242
668.8300
−0.1124
0.3650
10
10
10
10
10
10
10
10
9
F1
A1
F2
A2
F2
E
11
4
9
9
9
9
9
9
9
9
8
8
8
8
8
8
8
9
9
9
7
7
7
7
7
7
8
8
6
6
6
7
6
7
F2
A2
F1
A1
F1
E
24
9
−0.5294
−0.8839
−0.3737
0.0939
11
4
25
8
13
9
28
18
27
29
22
15
21
25
17
24
9
−0.5257
1.3131
F1
F2
F1
E
13
12
10
7
F2
F1
F2
E
0.2029
0.0573
9
0.3990
9
F2
F1
E
10
11
8
F1
F2
E
−0.6169
−0.3089
0.5453
9
9
9
F2
A2
E
11
4
F1
A1
E
1.7537
9
−2.9483
−2.8574
−2.5479
−0.0878
0.4855
10
10
10
8
8
19
28
10
20
13
19
8
F1
A1
F2
E
12
5
F2
A2
F1
E
9
8
6
0.7888
8
F1
A1
F1
F2
F2
F1
F2
A2
F1
A2
A1
F2
E
9
F2
A2
F2
F1
F1
F2
F1
A1
F2
A1
A2
F1
E
−0.8360
−0.1213
0.4767
8
4
8
10
10
12
12
8
22
22
25
26
16
7
8
−1.1060
−0.8427
−0.1268
−0.7808
−0.0148
−0.6139
1.4702
9
9
7
7
3
7
8
17
7
8
4
7
3
6
0.8384
8
11
7
23
15
19
13
19
20
9
0.3587
8
−0.2809
−0.0602
−0.0152
0.3934
7
F1
E
9
6
6
6
6
5
5
5
5
5
5
5
4
4
4
F2
E
7
6
7
F2
F1
E
9
F1
F2
E
7
10
5
−0.1177
−0.1491
1.1768
6
6
F2
F1
F2
E
7
F1
F2
F1
E
15
14
17
11
16
6
6
7
−0.4424
−0.0177
0.1163
6
8
6
6
6
F1
A1
F2
E
8
F2
A2
F1
E
0.1695
6
3
0.3264
5
6
11
9
0.7565
5
4
−1.0147
5
F1
6
F2
12

A. Tabyaoui et al.: Analysis of the hot band of stannane 116SnH4 in the 600–850 cm−1 range
Table 3. Continued.
55
Obs
(cm−1
Calc
(cm−1
Obs–Calc
(10−3 cm−1
)
Assignments
)
)
668.8607
669.5131
669.6829
669.7277
671.1460
671.2460
671.4066
671.4759
671.5844
671.6278
673.3956
673.4523
673.4553
673.8574
673.9106
673.9935
674.8838
674.9227
674.9452
675.0845
675.3440
675.7386
675.8323
675.9326
676.3727
676.4718
676.5989
676.7378
676.7408
677.0906
677.1022
677.3570
677.4258
677.5252
677.5824
677.7834
677.8112
677.8175
677.8624
677.9282
677.9819
678.1180
678.3454
678.5627
678.5728
678.6429
678.7463
668.8611
669.5132
669.6789
669.7283
671.1458
671.2464
671.4061
671.4762
671.5848
671.6301
673.3964
673.4517
673.4558
673.8576
673.9102
673.9933
674.8839
674.9220
674.9456
675.0845
675.3439
675.7392
675.8336
675.9329
676.3738
676.4726
676.5995
676.7332
676.7407
677.0892
677.1030
677.3576
677.4258
677.5242
677.5831
677.7839
677.8214
677.8205
677.8632
677.9292
677.9814
678.1205
678.3461
678.5607
678.5733
678.6422
678.7459
−0.4011
−0.1292
3.9180
5
5
5
5
4
4
4
4
4
4
3
3
3
3
9
9
8
2
8
8
2
7
2
7
6
1
6
9
6
9
5
9
5
8
4
4
8
8
2
3
7
7
6
4
5
1
2
A2
F2
A1
F1
F2
F1
A2
F2
E
3
7
2
7
5
5
2
6
4
2
5
3
4
4
8
8
5
2
7
3
3
6
2
7
2
2
6
3
4
9
5
6
5
8
3
4
3
8
1
3
5
7
6
2
2
2
3
4
4
4
4
3
3
3
3
3
3
2
2
2
2
9
9
8
1
8
8
1
7
1
7
6
0
6
9
6
9
5
9
5
8
4
4
8
8
2
3
7
7
6
4
5
1
2
A1
F1
A2
F2
F1
F2
A1
F1
E
5
13
4
−0.5829
0.2586
14
10
9
−0.4015
0.4762
3
−0.2546
−0.4487
−2.3304
−0.7304
0.5904
11
7
A1
F1
E
A2
F2
E
4
8
5
−0.4739
−0.2273
0.3877
F2
F1
F2
F1
E
F1
F2
F1
F2
E
6
7
20
19
12
2
0.1886
−0.1228
0.6953
A1
F1
A1
F1
F2
E
A2
F2
A2
F2
F1
E
−0.3565
0.0299
18
6
0.0533
4
−0.6199
−1.3173
−0.2066
−1.1193
−0.8391
−0.5499
4.6244
16
3
F1
A2
F1
F2
A1
E
F2
A1
F2
F1
A2
E
15
6
2
13
8
0.0377
9
1.3398
F1
F2
E
F2
F1
E
20
12
13
11
19
7
−0.7311
−0.5759
−0.0036
0.9914
F1
F1
E
F2
F2
E
−0.6579
−0.4295
−10.2436
−2.9768
−0.8244
−1.0412
0.4553
F1
A2
F2
A2
F2
E
F2
A1
F1
A1
F1
E
10
7
17
3
8
11
17
14
3
−2.5292
−0.6579
2.0312
F2
F1
A1
A1
F2
F2
F1
F2
A2
A2
F1
F1
−0.5036
0.7279
5
4
0.4422
5

56
The European Physical Journal D
Table 3. Continued.
Obs
(cm−1
Calc
(cm−1
Obs–Calc
(10−3 cm−1
)
Assignments
)
678.7840
679.0969
679.2718
679.3318
679.3891
679.4161
679.4640
679.5159
679.5597
679.5860
679.6137
679.6753
679.7959
679.9453
680.0417
680.0564
680.0803
681.1905
682.8799
683.1731
684.5837
684.7743
685.0269
686.3234
686.4463
687.8439
687.9844
688.0429
688.1460
689.0403
689.4070
689.5121
689.5538
689.6250
689.6961
689.7519
691.1934
691.2106
691.2197
691.2635
691.3095
692.5395
692.5669
692.7186
692.7615
692.8849
692.8904
)
678.7822
679.1002
679.2929
679.3327
679.3914
679.4192
679.4638
679.5284
679.5612
679.5870
679.6137
679.6752
679.7953
679.9450
680.0385
680.0643
680.0802
681.1900
682.8792
683.1730
684.5830
684.7746
685.0274
686.3232
686.4463
687.8437
687.9843
688.0433
688.1438
689.0405
689.4063
689.5115
689.5532
689.6254
689.6969
689.7544
691.1940
691.2100
691.2202
691.2638
691.3110
692.5395
692.5663
692.7174
692.7576
692.8872
692.8898
1.7212
−3.3326
−21.0773
−0.8691
−2.2769
−3.0972
0.1247
3
6
9
5
5
6
4
9
5
4
4
3
3
1
3
9
2
0
1
1
2
2
2
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
F1
E
4
5
7
6
6
7
5
10
4
2
5
3
4
2
5
10
3
1
2
2
3
2
3
4
3
4
2
5
5
3
3
7
7
6
4
6
6
7
8
3
7
9
6
8
3
9
3
3
6
9
5
5
6
4
9
5
4
4
3
3
1
3
9
2
1
2
2
3
3
3
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
8
8
8
8
8
8
F2
E
7
10
14
12
13
14
11
23
8
E
E
F1
F2
F2
F1
F2
E
F2
F1
F1
F2
F1
E
−12.5433
−1.5051
−0.9945
0.0033
A2
F2
E
A1
F1
E
4
9
0.0636
5
0.5668
F2
F1
F1
F1
F1
E
F1
F2
F2
F2
F2
E
9
0.2324
3
3.2128
8
−7.9507
0.1071
22
6
0.5281
2
0.7113
F1
F2
F1
E
F2
F1
F2
E
5
0.025
4
0.7196
6
−0.3812
−0.5877
0.1359
4
F2
F2
E
F1
F1
E
7
7
−0.0006
0.2198
6
E
E
6
0.0713
A2
F2
F1
E
A1
F1
F2
E
3
−0.3642
2.1085
10
9
−0.2314
0.7178
7
A2
F2
F1
F2
E
A1
F1
F2
F1
E
5
0.5342
12
13
10
8
0.5264
−0.3712
−0.854
−2.4606
−0.6339
0.5884
F1
E
F2
E
11
10
12
14
5
F1
F1
A1
F2
F1
E
F2
F2
A2
F1
F2
E
−0.4805
−0.3495
−1.5560
0.0254
13
16
11
14
5
0.6198
1.2090
F1
A1
F2
A2
F2
A2
F1
A1
3.9614
−2.3530
0.5779
16
6

A. Tabyaoui et al.: Analysis of the hot band of stannane 116SnH4 in the 600–850 cm−1 range
Table 3. Continued.
57
Obs
(cm−1
Calc
(cm−1
Obs–Calc
(10−3 cm−1
)
Assignments
)
692.9361
693.9935
694.2150
694.2414
694.2468
694.5634
694.6120
694.6319
695.3501
716.0510
716.0786
716.5453
719.1787
719.2676
719.2676
719.2676
722.4808
722.5576
722.5819
724.7180
726.0105
726.2777
)
692.9376
693.9938
694.2029
694.2360
694.2415
694.5686
694.6157
694.6350
695.3457
716.0536
716.0785
716.5454
719.1815
719.2670
719.2678
719.2673
722.4820
722.5581
722.5818
724.7178
726.0107
726.2773
−1.5226
−0.2977
12.0247
5.3441
7
8
F1
A1
F1
F2
E
10
4
8
9
9
9
9
9
9
9
9
9
9
9
8
8
8
8
7
7
7
7
6
6
F2
A2
F2
F1
E
17
7
8
9
15
16
10
6
8
9
5.3199
8
6
−5.1996
−3.6570
−3.1246
4.3705
8
A2
F2
E
4
A1
F1
E
8
11
7
19
12
16
37
35
34
32
12
22
31
10
28
29
15
25
9
8
8
F1
F2
F1
F2
F1
A2
E
8
F2
F1
F2
F1
F2
A1
E
−2.6064
0.0746
10
10
10
9
13
13
10
11
4
−0.1174
−2.8326
0.5931
9
−0.2622
0.2604
9
8
9
F2
A1
F1
F2
F2
F1
A2
11
4
F1
A2
F2
F1
F1
F2
A1
−1.1440
−0.4443
0.0164
8
8
10
10
1
8
0.2442
8
−0.2024
0.3892
7
9
7
3
References
20. J. Susskind, J. Chem. Phys. 56, 5152 (1972)
21. Y. Ohshima et al., J. Chem. Phys. 85, 5519 (1986)
22. Y. Ohshima et al., J. Chem. Phys. 87, 5141 (1987)
1. F. Brunet, G. Pierre, H. Bu¨rger, J. Mol. Spectrosc. 140,
237 (1990)
23. V.M. Krivtsun et al., J. Mol. Spectrosc. 139, 107 (1990)
24. A. Tabyaoui et al., Phys. Chem. News 10, 106 (2003)
25. A. Tabyaoui et al., J. Mol. Spectrosc. 148, 100 (1991)
26. M. Halonen et al., J. Chem. Phys. 93, 1607 (1990)
27. M. Halonen, L. Halonen, J. Chem. Phys. 108, 9285 (1998)
28. G. Guelachvili, K. Narahari Rao, Handbook of Infrared
Standards (Academic Press, San Diego, 1986)
29. J.P. Champion, Can. J. Phys. 55, 1802 (1977)
30. J.P. Champion, G. Pierre, J. Mol. Spectrosc. 79, 255
(1980)
31. J.P. Champion, M. Lo¨ete, G. Pierre, in Spectroscopy of the
earth’s atmosphere and interstellar molecules, edited by
K.N. Rao, A. Weber (Academic Press, Inc. U.S.A., 1992),
p. 339
32. V.I. Perevalov, V.G. Tyuterev, B.I. Zhilinskii, Dokl. Acad.
Nauk SSSR 263, 868 (1982)
2. A. Tabyaoui, G. Pierre, H. Bu¨rger (in preparation)
3. I.W. Levin, H. Ziffer, J. Chem. Phys. 43, 4023 (1965)
4. I.W. Kattenberg, A. Oskam, J. Mol. Spectrosc. 51, 377
(1974)
5. F.W. Birss, Mol. Phys. 31, 491 (1976)
6. A. Cabana et al., Mol. Phys. 36, 1503 (1978)
7. P. Lepage, J.P. Champion, A.G. Robiette, J. Mol.
Spectrosc. 89, 440 (1981)
8. M. Mizushima, P. Venkateswarlu, J. Chem. Phys. 21, 705
(1953)
9. I.M. Mills, J.K.G. Watson, W.L. Smith, Mol. Phys. 16,
329 (1969)
10. M. Oldani et al., J. Mol. Spectrosc. 113, 229 (1985)
11. M. Oldani, A. Bauder, G. Pierre, J. Mol. Spectrosc. 117,
435 (1986)
12. M. Takami, J. Chem. Phys. 71, 4164 (1979)
13. M. Takami, J. Chem. Phys. 73, 2665 (1980)
14. M. Takami, J. Chem. Phys. 74, 4276 (1981)
15. M. Takami, J. Chem. Phys. 76, 1670 (1982)
16. M. Takami, J. Mol. Spectrosc. 93, 250 (1982)
17. L. J¨orissen et al., J. Chem. Phys. 90, 2109 (1989)
18. S.M. Kirschner, J.K.G. Watson, J. Mol. Spectrosc. 47, 347
(1973)
33. V.I. Perevalov, V.G. Tyuterev, B.I. Zhilinskii, J. Mol.
Spectrosc. 103, 147 (1984)
34. V.I. Perevalov, V.G. Tyuterev, B.I. Zhilinskii, Chem. Phys.
Lett. 104, 455 (1984)
35. V.I. Perevalov, V.G. Tyuterev, B.I. Zhilinskii, J. Mol.
Spectrosc. 111, 1 (1985)
36. C. Pierre, M. Lo¨ete, G. Pierre, Can. J. Phys. 65, 708 (1987)
37. M. Rey et al., J. Mol. Spectrosc. 219, 313 (2003)
19. A.G. Robiette, D.L. Gray, F.W. Birss, Mol. Phys. 32, 1591
(1976)