Fourier-transform microwave spectroscopy of InF, InCl, and InBr, prepared using laser ablation

Article abstract of DOI:10.1039/a607080i

High-resolution rotational spectra of InF, InCl, and InBr have been measured with a pulsed jet cavity Fourier-transform microwave spectrometer. Samples were prepared by vaporizing In with a pulsed Nd:YAG laser, and reacting the vapour with a precursor gas entrained in the Ne backing gas of the jet. Precise rotational and nuclear quadrupole coupling constants have been obtained for all these molecules, along with the first nuclear spin-rotation constants of InCl and InBr. The hyperfine coupling constants are discussed in terms of the electronic structures of the molecules.

Full text of DOI:10.1039/a607080i

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Fourier-transform microwave spectroscopy of InF, InCl, and InBr,
prepared using laser ablation
Kristine D. Hensel¤ and Michael C. L. Gerry*
Department of Chemistry, T he University of British Columbia, 2036 Main Mall, V ancouver, BC,
Canada V 6T 1Z1
High-resolution rotational spectra of InF, InCl, and InBr have been measured with a pulsed jet cavity Fourier-transform micro-
wave spectrometer. Samples were prepared by vaporizing In with a pulsed Nd : YAG laser, and reacting the vapour with a
precursor gas entrained in the Ne backing gas of the jet. Precise rotational and nuclear quadrupole coupling constants have been
obtained for all these molecules, along with the Ðrst nuclear spinÈrotation constants of InCl and InBr. The hyperÐne coupling
constants are discussed in terms of the electronic structures of the molecules.
Although the Ðrst description of a pulsed jet cavity Fourier-
transform microwave (FTMW) spectrometer appeared over 15
Experimental
Since the experiments were very similar to those described
earlier,6,7 only a brief description of the methods used will be
given here. The spectra were observed in the frequency range
years ago,1 these instruments are only now reaching their full
potential. Recent developments are due largely to improve-
ments in both instrumental design and microwave technology,
along with increased general awareness of the spectrometersÏ
capabilities. The earliest experiments were on van der Waals
complexes2 formed through intermolecular collisions in the
sample-injection nozzle, and stabilized in the largely collision-
free jet. Many recent experiments continue to be on such
systems. However, samples prepared by other means, such as
via an electric discharge or laser irradiation, can also be stabil-
ized and studied in the jet.3h8
6
È18 GHz, using the pulsed jet cavity FTMW spectrometer
described previously.6,22 The nozzle was mounted in one of
the cavity mirrors, so that each line was doubled by the
Doppler e†ect. Line widths were typically ca. 7 kHz, and fre-
quency measurement accuracies ca. ^1 kHz. For closely
spaced lines, accurate frequencies were obtained by Ðtting to
the time-domain signals.23
Samples were prepared via vaporization of an In metal rod
using the second harmonic (532 nm) of a pulsed Nd : YAG
laser. The In vapour was reacted with a second reagent con-
tained in the Ne backing gas. These reagents were SF , Cl ,
Use of the jet has further advantages. Rotational tem-
peratures are very low (near 1 K) and result in simpliÐcation
of the observed spectra, along with an increase in sensitivity.
Spectral lines are very narrow: widths of ca. 5 kHz FWHM
are routinely obtained, particularly when the nozzle is
mounted in one of the cavity mirrors.9 As a result, previously
measured molecular constants can be obtained with improved
precision, and the e†ect of smaller parameters can generally be
determined.
We have reported a series of experiments in which rotation-
al spectra of metal chlorides (AgCl, CuCl, AlCl6 and YCl7)
were measured with a cavity FTMW spectrometer. Samples
were prepared by vaporizing a metal using a pulsed Nd:YAG
laser, and reacting the vapour with a small amount of chlorine
contained in the Ne backing gas of the jet. Because of the high
resolution of the spectrometer it was possible to improve the
precision of several rotational and nuclear quadrupole coup-
ling constants, and to measure nuclear spinÈrotation param-
eters for the Ðrst time.
The present paper describes the extension of these experi-
ments to three indium halides, InF, InCl, and InBr. Rotational
spectra of all these compounds have been reported pre-
viously.10h21 These earlier experiments covered both the
microwave and millimetre-wave regions, and included a very
precise molecular beam electric resonance experiment on
InF.16 The results described here demonstrate the feasibility of
using other precursor gases besides chlorine in laser ablation
experiments, and, in the case of InCl and InBr, have produced
new values for several hyperÐne constants. Interpretation of
these constants has been carried out in terms of the electronic
structures of the molecules.
6
2
and Br to prepare InF, InCl, and InBr respectively. The pro-
2
portions of these gases were kept very low (0.1% SF and Cl ,
.05% Br ) to minimize production of compounds with higher
oxidation states of In (e.g., InCl , InBr .) Typical total static
6
2
0
2
3
3
gas pressures were 1È2 atm. The In rod was 1 cm long and 2
mm in diameter, held Ðxed inside a 40 mm3 chamber mounted
in front of the pulsed General Valve nozzle.6 This allowed for
stabilization of the samples before they were injected into the
microwave cavity through a 1 mm diameter exit channel.
Relative timing of the gas and microwave pulses was crucial
to the strengths of the signals observed, and much e†ort was
made to optimize this condition.
Results and analysis
Because spectra of InF, InCl and InBr had been reported pre-
viously, spectral searching was minimized, and assignments
were relatively straightforward. 115In (95.7% natural
abundance) has a large nuclear spin (I \ 9/2) which is strongly
coupled to the molecular rotation through its nuclear quadru-
pole moment. Since couplings of the halogen nuclei are much
weaker, the assignments were made in terms of the coupling
scheme
J ] I \ F
In
1
I ] F \ F
X
1
with X \ F, Cl, or Br, as appropriate. No spectra were
observed for isotopomers containing 113In (4.3% natural
abundance).
The only available transition of InF in the frequency range
of the spectrometer was J \ 1È0. The large In hyperÐne split-
ting was further resolved by nuclear spinÈrotation coupling of
¤
Present address: Research School of Chemistry, Australian
National University, Canberra ACT 0200, Australia.
J. Chem. Soc., Faraday T rans., 1997, 93(6), 1053È1059
1053

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The J \ 2È1 and 3È2 transitions have been measured for
15In79Br (48.5% natural abundance) and 115In81Br (47.2%).
1
Because of the large quadrupole moments of both the In and
Br nuclei, the hyperÐne components of this transition extend
over a wide frequency range and are overlapped for the two
isotopomers. The measurements and assignments are in Table
3.
The spectra were analysed using PickettÏs global least-
squares Ðtting program SPFIT.24 Rotational constants,
quartic centrifugal distortion constants, and nuclear quadru-
pole and spinÈrotation coupling constants were included
where appropriate; the e†ects of nuclear spinÈspin coupling
were too small to be determined. For InF, where only one
transition had been measured, the centrifugal distortion con-
stant D was Ðxed at a value obtained from a recent analysis
0
of the IR spectrum.25 The resulting constants are in Tables 4,
5
and 6 for InF, InCl and InBr, respectively.
Discussion
The present experiments represented the Ðrst time we used a
precursor gas other than Cl to prepare metal compounds.
2
Both SF and Br worked well and easily. Clearly they and
6
2
other precursors will provide good routes to further com-
pounds prepared for FTMW study by laser ablation. This
conclusion is conÐrmed by the recent reports of spectra of
CaNC4 and MgS,26 produced by similar procedures.
Fig. 1 The F \ 3.5È4.5 hyperÐne component of the J \ 1È0 rota-
1
tional transition of 115In19F, observed for both the ground vibra-
tional state (a) and the Ðrst excited vibrational state (b). Experimental
conditions (a): In rod; gas sample 0.1% SF in Ne; excitation fre-
6
quency 15738.701 MHz; sampling 4 K points at 50 ns interval; 8 K
The rotational constants determined in this work (Tables
FT; 80 averaging cycles. Experimental conditions (b): In rod; gas
4
È6) are in all cases more precise than those in the literature,
sample 0.1% SF in Ne; excitation frequency 15625.980 MHz; sam-
although they are not necessarily more accurate. Only very
few rotational transitions were measured, so the accuracies of
the rotational constants are probably rather nearer the mea-
surement accuracy (^1 kHz). This is especially so for InF, for
6
pling 4 K points at 50 ns interval; 2 K FT; 687 averaging cycles.
1
9F, shown in the spectrum of Fig. 1. The measured transition
frequencies are in Table 1; the 19F spinÈrotation constant C ,
which only J \ 1È0 was observed. In this case, B could only
F
0
be determined by Ðxing D , the uncertainty of whose liter-
0
as determined by molecular beam electric resonance,16 was
used to assign the hyperÐne components.
ature value25 contributed much less than our measurement
In addition, the F \ 3.5È4.5 hyperÐne component of the
uncertainties.
1
J \ 1È0 transition of InF has been observed in the Ðrst
On the other hand, the centrifugal distortion constants
which we could determine (Tables 5 and 6) are all less precise
than the literature values. This was not unexpected, as the
earlier values had been obtained by millimetre-wave spectros-
copy, in which the distortion e†ects can be very large and
easily measured to several signiÐcant Ðgures. Nevertheless, the
new values are very reasonable, and are an excellent indica-
tion of the resolution, precision, and accuracy obtainable by
FTMW spectroscopy. The maximum measured distortion
contribution was \50 kHz, yet it has still been possible to
obtain distortion constants accurate to two and three signiÐ-
cant Ðgures.
In the case of the hyperÐne constants, the new values for
InF represent no improvement over the earlier values. The
latter had been obtained by molecular beam electric reso-
nance;16 in terms of precision and accuracy, our FTMW
results do not compete. For InCl and InBr, on the other hand,
the new results are a signiÐcant improvement. The quadrupole
coupling constants are much more precise than the previous
values; the nuclear spinÈrotation constants are the Ðrst mea-
surements.
excited vibrational state (v \ 1, l ca. 530 cm~1.25) It is also
vib
shown in Fig. 1; with the much lower signal-to-noise ratio,
1
9F spin-rotation splittings could not be determined accu-
rately. By comparing the signal-to-noise ratios of the two
spectra in Fig. 1, and assuming a Boltzmann distribution over
vibrational levels, the vibrational temperature of the expan-
sion may be estimated to be ca. 300È400 K. For comparison,
a vibrational temperature of ca. 500 K was estimated for
MgCl produced in a similar laser ablation/FTMW experi-
ment.8
InCl has a large dipole moment [3.79(10)D,17 D B 3.335 64
C m], and is stable enough to be commercially available. Con-
sequently, very strong signals were observed for both
1
15In35Cl (72.5% natural abundance) and 115In37Cl (23.2%).
The J \ 1È0 and 2È1 transitions were measured; the line fre-
quencies and their assignments are in Table 2.
Table 1 Measured hyperÐne components of the J \ 1È0 transition
of 115In19F
frequency/
MHz
obs. [ calc./
F@
F@
FA
FA
kHz
1
1
Interpretation of hyperÐne constants
v \ 0
Both nuclear quadrupole and spinÈrotation coupling con-
stants depend on electronic structure. In order to interpret the
hyperÐne constants of the indium halides, we will consider the
valence molecular orbitals (MOs), shown schematically in the
energy level diagram of Fig. 2. This scheme parallels those
used for AlF and AlCl,27h29 with the addition of the inner 4d
atomic orbitals (AOs) on In. However, we will assume that the
5.5
5.5
3.5
3.5
4.5
4.5
5
6
3
4
4
5
4.5
4.5
4.5
4.5
4.5
4.5
4
5
4
5
4
5
15 708.6416a
15 708.6669
15 738.7072
15 738.6975
15 575.8635
15 575.8635
[2.7
2.7
[3.3
3.3
2.0
[1.7
v \ 1
3
.5
4.5
15 625.9667
4
d orbitals play little part in the bonding, as they are rela-
a Measurement accuracy better than ^1 kHz.
054 J. Chem. Soc., Faraday T rans., 1997, V ol. 93
tively small in radius and their charge distribution is spherical
1

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Table 2 Measured hyperÐne components of InCl
15In35Cl
obs. [ calc./kHz
1
115In37Cl
F@
F@
FA
FA
frequency/MHz
frequency/MHz
6165.3614
obs. [ calc./kHz
1
1
J \ 1È0
4.5
4.5
4.5
4.5
5.5
5.5
5.5
5.5
3.5
3.5
3.5
3.5
3
6
4
5
6
5
7
4
4
3
5
2
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
3
6
4
5
5
4
6
3
5
4
6
3
6434.1926a
6435.0110
6436.8213
6437.6728
6555.6403
6555.8488
6557.3901
6557.7150
6583.6770
6583.9029
6584.6868
6584.8274
0.8
[0.8
0.8
[0.3
[0.5
6167.4547
6285.9940
6286.1986
6287.3774
6287.6571
6313.8886
6314.0930
6314.6761
[1.5
0.6
0.4
0.3
0.7
[0.7
[0.1
0.5
0.1
0.2
[0.3
[0.6
[0.2
0.2
0.7
[0.4
J \ 2È1
4.5
4.5
4.5
4.5
5.5
4.5
5.5
4.5
5.5
5.5
4.5
4.5
3.5
3.5
3.5
3.5
3.5
6.5
6.5
6.5
6.5
6.5
6.5
2.5
2.5
2.5
2.5
4.5
5.5
5.5
4.5
5.5
5.5
5.5
4.5
4.5
6
3
5
4
4
6
7
6
5
6
5
4
2
5
5
3
4
7
7
6
8
5
5
3
4
2
1
6
5
6
5
4
7
6
4
3
3.5
3.5
3.5
3.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
3.5
3.5
3.5
3.5
3.5
5.5
5.5
5.5
5.5
5.5
5.5
3.5
3.5
3.5
3.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
5
2
4
3
4
7
7
6
5
6
6
5
2
5
4
3
4
7
6
5
7
4
5
4
5
3
2
5
4
5
5
3
6
6
4
3
12930.0468
12930.4296
12933.7853
12933.8542
12957.2001
12957.3449
12958.4523
12959.0634
12959.9006
12961.3212
12961.8234
12961.9076
12988.4497
12989.3760
12990.3551
12991.1514
12992.1008
13059.0279
13060.7454
13061.0634
13061.4214
13061.6656
13063.5033
13072.4186
13072.5800
13072.8460
13073.0441
13077.0284
13078.9285
13079.2904
13079.7908
[1.9
1.8
12390.7558
12391.0807
12393.7491
[1.2
1.4
1.5
[1.0
0.6
1.3
0.4
[0.0
[0.3
0.8
12417.8908
12418.0560
0.1
0.4
12419.9792
[0.5
[1.0
0.0
[0.1
0.6
[0.2
1.0
[0.7
[1.3
0.8
[1.0
[0.7
[0.3
[0.8
0.9
12521.0767
12521.2880
12521.6088
12521.7724
[0.4
[1.0
[0.4
[0.8
[1.2
12532.7690
12532.9003
12533.0786
12533.2370
[0.0
[0.9
0.4
0.6
[1.5
0.1
1.2
[2.2
0.6
12539.3888
12539.7208
[0.5
1.4
0.6
0.2
12540.8329
12540.8774
0.1
0.9
13080.8314
13081.9835
0.5
2.0
12541.0476
12541.1898
[0.3
[0.4
a Measurement accuracy better than ^1 kHz.
around the In nucleus. The Ad, Bn, and Cp MOs, assumed to
be constructed entirely from In 4d AOs, will be considered to
be occupied, non-bonding orbitals.
The bonding will thus be described in terms of 5s and 5p
orbitals on In, and of ns and np orbitals on the halogens
(
n \ 2, 3, 4 for F, Cl, Br, respectively). The relevant LCAO
MOs are written as follows:
o EpT \ e o In(5s)T ] e o In(5p )T
5pz
5s
z
[
e o X(ns)T ] e o X(np )T
ns npz
z
o DpT \ d o In(5s)T[d o In(5p )T
5s
5pz
z
[
d o X(ns)T[d o X(np )T
ns npz
z
o BpT \ b o In(5s)T[b o In(5p )T
5s
5pz
z
Fig. 2 Schematic diagram (not to scale) of the valence molecular
orbital energy levels for an indium(I) halide, InX
] b o X(ns)T]b o X(np )T
ns npz
z
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1055

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Table 3 Measured hyperÐne components of InBr
15In35Br
obs. [ calc./kHz
1
115In37Br
F@
F@
FA
FA
frequency/MHz
frequency/MHz
obs. [ calc./kHz
1
1
J \ 2È1
4.5
5.5
3.5
3.5
3.5
3.5
6.5
2.5
6.5
6.5
5.5
2.5
2.5
5.5
5.5
2.5
4.5
4.5
4.5
6.5
4.5
4.5
5.5
5.5
5.5
5.5
4.5
3.5
3.5
3.5
5
7
4
3
5
2
8
4
7
5
6
3
1
7
4
2
4
3
5
6
5
6
5
6
5
4
3
5
3
4
5.5
5.5
3.5
3.5
3.5
3.5
5.5
3.5
5.5
5.5
4.5
3.5
3.5
4.5
4.5
3.5
4.5
4.5
4.5
5.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
6
7
3
3
5
2
7
5
6
4
6
4
2
6
3
3
4
3
5
5
5
6
4
5
5
4
4
6
4
5
6470.3476a
6491.0736
[1.9
0.9
6604.1039
6607.9857
6612.0374
6628.7970
6680.5504
6683.4523
0.4
[2.4
0.8
[0.5
[1.4
[0.1
6511.7997
6515.8834
2.2
[1.6
6583.4056
6588.4788
6587.8420
6588.2380
[0.2
[1.2
[0.7
[0.4
6687.2419
6687.6085
6690.4708
6691.7346
6693.3651
6694.5730
6694.6634
6696.0571
6696.2324
1.5
5.3
0.4
[2.8
[0.8
[0.7
[3.9
1.4
6594.5962
6597.0359
6598.3234
[1
0.5
1.3
6599.3748
6599.5942
6606.6898
6597.3860
0.1
1.7
0.8
1.8
1.2
6698.7110
6704.4096
6705.5634
6707.7118
6708.5354
6713.0034
6717.4856
6719.1435
6758.8904
6762.8429
6764.2450
0
1.1
0.1
[2.0
[2.8
3.2
1.8
2.3
0.8
6607.2960
6609.1366
6609.6932
0.1
[2.1
[0.3
6660.6886
6664.1811
3.0
[3.0
[1.6
[1.3
J \ 3È2
5.5
3.5
7.5
7.5
7.5
7.5
6.5
1.5
6.5
1.5
6.5
7
5
6
9
7
8
6
2
8
3
7
5.5
3.5
6.5
6.5
6.5
6.5
5.5
2.5
5.5
2.5
5.5
7
5
5
8
6
7
5
3
7
4
6
9996.2778
10003.6364
10009.2192
10010.0396
10012.0460
10012.4468
10015.9650
10017.6481
10017.6940
10019.1348
10037.5968
2.6
1.5
0.8
[1.6
[0.2
[0.9
[4.3
1.1
9850.6363
9857.2374
9863.3901
9863.9498
9865.7220
9866.0036
2.3
0.2
0.3
[1.1
[0.1
[0.0
[1.1
9871.9570
9872.5022
9888.2025
[0.0
1.0
[2.7
2.6
[0.7
a Measurement accuracy is estimated to be better than ^1 kHz.
o ApT \ a o In(5s)T]a oIn(5p )T
bonding or antibonding character. As the In 5s/5p and
halogen ns/np AOs are not assumed to contribute to any
MOs apart from those given above, a2 ] b2 ] d2 ] e2 \ 1 in
5
s
5pz
z
]
a o X(ns)T[a o X(np )T
(1)
ns npz
z
j
j
j
j
The n orbitals have the form
eqn. 1 and a2 ] c2 \ 1 in eqn. (2), for each atomic orbital j.
j j
x
The nuclear quadrupole coupling constants may be used to
estimate values for some of the atomic orbital coefficients. For
o Cn T \ c o In(5p )T[c o X(np )T
5px npx
x
x
x
o An T \ a o In(5p )T]an o X(np )T
(2)
nucleus i, the coupling constant eQq is given by 30,31
x
5px
x
px
x
i
with analogous equations for the n orbitals. The coefficients
y
C
(ai )2 ] (ai )2
jx jy
D
in eqn. (1) and (2), which we will collectively refer to as a , are
j
eQq \ 2(eQq ) ; ; (ai )2 [
(3)
i
i 0
jz
2
taken to be positive, so the signs in eqn. (1) and (2) indicate
a
j
Table 4 Spectroscopic constants of 115In19F
where (eQq ) is the atomic nuclear quadrupole coupling con-
i 0
stant for nucleus i, resulting from a singly occupied valence p
this work
lit. value
ref.
orbital. Summation is carried out over all occupied MOs and
over all valence p orbitals j which are localized on nucleus i;
for example, eQq would depend on terms such as a ( 4
B /MHz
7836.135 02(24)a,b
7836.1376(17)
21
25
16
16
16
0
7836.1393(36)
In
5pz
eQq /MHz
[723.795(12)
17.47(10)
[723.7996(2)
aIn ) but not on a (4aX .) As s orbitals are spherical and
In
5pz
npz
npz
C /kHz
17.50(1)
therefore do not contribute to the nuclear quadrupole coup-
ling e†ect, the coupling constants are independent of the coef-
Ðcients of the In 5s and halogen ns orbitals.
In
C /KHz
18.3(10)
18.77(10)
F
a Numbers in parentheses are one standard deviation in units of the
last signiÐcant Ðgure. b The centrifugal distortion constant D
Ðxed at 0.00755 MHz25 in the least-squares analysis.
0 was
In our molecular orbital scheme, neither Ep nor Cn is
populated in the ground-state conÐguration. The expressions
1056
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

View Article Online
Table 5 Spectroscopic constants of InCl
15In35Cl
lit. value
1
115In37Cl
lit. value
this work
ref.
this work
ref.
B /MHz
3261.73321(20)a
1.548(26)
[657.8487(18)
[13.7575(15)
10.454(38)
3261.73242(53)b
1.54373(14)
[657.52(50)
[13.63(20)
È
19
19
15
15
3126.79399(23)
1.386(30)
[657.8913(23)
[10.8399(26)
9.980(46)
3126.79430(67)b
1.41872(17)
[657.20(45)
[10.11(45)
È
19
19
11
11
0
D /KHz
0
eQq /MHz
In
eQq /MHz
Cl
C /kHz
In
C /kHz
Cl
1.71(11)
È
1.19 (14)
È
a Numbers in parentheses are one standard deviation in units of the last signiÐcant Ðgure. b Calculated from the constants given in ref. 19.
Numbers in parentheses reÑect the error limits given here.
Table 6 Spectroscopic constants of InBr
1
15In79Br
115In81Br
lit. value
this work
lit. value
ref.
this work
ref.
B /MHz
1667.29199(11)a
0.4092(76)
[633.5756(35)
110.6501(22)
6.168(44)
1667.29062(90)b
0.41713(13)
[633.50(26)
110.63(27)
È
20
20
18
18
1642.90726(12)
0.3941(83)
[633.5731(34)
92.4367(28)
5.924(52)
1642.90394(90)b
0.40472(12)
[633.20(26)
92.33(26)
È
20
20
18
18
0
D /kHz
0
eQq /MHz
In
eQq /MHz
Br
C /kHz
In
C /kHz
Br
5.30(10)
È
5.36(11)
È
a Numbers in parentheses are one standard deviation in units of the last signiÐcant Ðgure. b Calculated from the constants given in ref. 20.
Numbers in parentheses reÑect the error limits given there.
for the quadrupole coupling constants are therefore
the sum of nuclear and electronic terms:33,34
C \ Cnucl] Cel
(8)
C
1
D
i
i
i
eQq \ 2(eQq ) a2 ] b2 ] d2 [ (a2 ] a2 ) (4)
In
In 0 5pz
5pz
5pz
2
5px
5py
Cnucl depends on the equilibrium internuclear separation R,
i
and can be approximated by34
C
1
D
eQq \ 2(eQq ) a2 ] b2 ] d2 [ (a2 ] a2 )
(5)
X
X 0 npz
npz
npz
2
npx
npy
2ek g B Z
Cinucl \
N i
+c
l
(9)
R
In order to determine any of the coefficients from the
experimental nuclear quadrupole coupling constants, we must
make several assumptions. The fundamental assumption is
that the In and halogen AOs remain highly localized upon
formation of the bond. Based on this, we assume the follow-
ing:
where e is the charge on the proton, k is the nuclear magne-
N
ton, g is the g-factor of nucleus i, B is the equilibrium rota-
i
tional constant, Z is the atomic number of the other nucleus l,
and c is the speed of light. The electronic term Cel depends on
ground and excited electronic state wavefunctions, and is
l
i
given by33,34
(
i) a \ a B 0
5
px
5py
Cel \ [ 2 N i
ek g B
+cm
a
\ a B 1
i
npx
npy
i.e. the An orbital is located entirely on the halogen atom;
S0 o L o kTSk o L r~3 o 0T ] S0 o L r~3 o kTSk o L o 0T
]
;
k
x
x
x
x
(10)
E [ E
(
ii) a B b B 0
0
k
5
pz 5pz
Here m is the electronic mass, L is a component of the total
i.e. Ap and Bp have very little In 5p character;
x
z
electronic orbital angular momentum L, and r~3 depends on
(
iii) d2 B e2
the positions of the electrons. o 0T and o kT are ground and
excited singlet states, at energies E and E , respectively.
npz npz
i.e. Dp and Ep have comparable amounts of halogen np char-
acter.
Given these approximations, eqn. (4) and (5) reduce to
0
k
z
Both Cnucl and Cel, and hence C , are proportional to the
i i i
product g B. In Table 8, the ratios of spinÈrotation constants
i
eQq \ 2(eQq ) d2
In In 0 5pz
(6)
Table 7 Molecular orbital coefficients of indium halides from
nuclear quadrupole coupling constants
eQq \ 2(eQq ) (a2 ] b2 ] d2 [ 1)
X
X 0 npz
npz
npz
Ina
Xb,c
eQq /MHz
\
\
[2(eQq ) e2
X 0 npz
[2(eQq ) d2
X 0 npz
eQq /MHz
d
d
d d
In
5pz
X
npz
(7)
1
15In19F
15In35Cl
[723.800
[657.849
[657.891
[633.576
[633.573
0.634
0.604
0.604
0.593
0.593
È
È
Using these equations, estimated values for d
were calculated from the experimental nuclear quadrupole
coupling constants and known atomic coupling constants
and d
1
[13.7575
[10.8399
110.6501
92.4367
0.251
0.251
0.268
0.268
5
pz
npz
115In37Cl
115In79Br
115In81Br
(
eQq ) ;30 the results are presented in Table 7. The small
i 0
values of d2 (\e2 ) support our model of highly localized
npz
atomic orbitals.
npz
a (eQq ) \ [899.10 MHz.32
b
X \ F, Cl, or Br. c (eQq ) \
In 0
Cl 0
]
109.74 MHz for 35Cl and ]86.51 MHz for 37Cl; (eQq ) \
Br 0
We now consider the spinÈrotation constants C . For a
[769.76 MHz for 79Br and [643.03 MHz for 81Br.32 d Using the
i
diatomic molecule, C (4C ) for nucleus i may be expressed as
assumptions made in the text.
i
M
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1057

View Article Online
Table 8 Comparison of spinÈrotation constants of InCl and InBr with rotational constants and nuclear g-factors
C /kHz
B /MHz
C /kHz
g B /MHza
In
0
X
X 0
1
15In35Cl
15In37Cl
10.454 (86)
9.980 (46)
1.047 (6)
6.168 (44)
5.924 (52)
1.041 (12)
3261.73321 (20)
3126.79439 (23)
1.043b
1667.29199 (11)
1642.90726 (12)
1.015b
1.71 (11)
1.19 (14)
1.44 (19)
5.30 (10)
5.36 (11)
0.99 (3)
1787.1565 (9)
1426.0759 (8)
1.253b
2341.323 (5)
2486.882 (5)
0.941b
1
isotopic ratio
1
15In79Br
1
15In81Br
isotopic ratio
a g is the g-factor for the halogen nucleus. b Uncertainties in the ratios of B and of g B
0 are three to four orders of magnitude smaller than the
X
0
X
number of digits given.
for di†erent isotopomers of the same compound are compared
above from the quadrupole coupling constants, and applying
the approximate method Ðrst presented by Cornwell to
account for the anomalous 19F shielding in ClF.31
BrieÑy, CornwellÏs method assumes that the molecular
orbitals are written using LCAO expansions of the type given
in eqn. (1) and (2). The approximation assumes that all contri-
butions to the paramagnetic shielding on a given nucleus i,
with ratios of g B for these isotopomers. One would expect
i
0
some discrepancy simply due to small di†erences between the
equilibrium and ground-state rotational constants, but there is
good general agreement between these two ratios. This reÑects
the similarity in structure and electronic states between iso-
topomers, and indicates a straightforward method of estimat-
ing spinÈrotation constants for di†erent isotopomers once the
hyperÐne structure for a particular isotopomer has been
examined.
p(i), come from valence-shell p orbitals, and some terms for
p
atomic orbitals not localized on nucleus i are dropped. The
paramagnetic shielding is then written as
The electronic part of the spinÈrotation constant is particu-
[
3
8k2
N
=
Ri( jk) É R( jk)
larly interesting because Cel is proportional to the paramagne-
B
p(i) \
Sr~3T
p,i
;
;
(15)
i
p
Ejk [ E
tic shielding, p(i), at nucleus i:33
j/1 k/N`1
0
p
where k is the Bohr magneton and Sr~3T is the average
e+
B
p,i
p(i) \ [
Ciel
(11)
value of r~3 for an electron in a valence-shell p orbital located
on atom i. The indices j and k refer to the occupied and
unoccupied molecular orbitals in the ground electronic state;
N orbitals are occupied. The denominator, E [ E , is the
p
6mck g B
N i
The diamagnetic shielding at nucleus i, p(i), depends on the
d
ground electronic state wavefunction:33
jk
0
energy change from the ground state to the singlet state corre-
sponding to the one-electron excitation o jT ] o kT. Ri( jk) and
R( jk) are vectors, deÐned by
e2
3mc2
p(i) \
S0 o ; r~1 o 0T
(12)
d
n
n
where summation is over all electrons n. The average mag-
Ri( jk) \ ai ] ai
j
k
netic shielding, p(i) , is given by
av
R( jk) \ ; Ri( jk)
p(i) \ p(i) ] p(i)
(13)
i
av
d
p
with ai and ai being vectors of the coefficients of the valence-
j
k
and it is this parameter which determines the chemical shift
obtained in NMR experiments.
shell p orbitals on atom i for molecular orbitals j and k,
respectively. The i summation is over all atoms in the mol-
ecule.
From recent values of the fundamental constants,35 if Cel is
i
in kHz and B is in MHz, then p(i) in ppm is given by
It can be seen from Fig. 2 that the lowest energy excitation
that can contribute to the indium halide shieldings is
o DpT ] o CnT. Using eqn. (15), and assuming that
o DpT ] o CnT is the dominant excitation, the paramagnetic
shieldings are found to be
p
Cel
p(i) \ [612050.90(58)
i
(14)
p
g B
i
For InF, InCl and InBr, the nuclear contributions Cnucl
i
were readily determined for both nuclei using eqn. (9). It was
p(In) \ [ 1 BSr~3T
6k2
3
C
c2 d2 [ c
5px 5pz
5px 5pz npx npz (16)
d
c
d
D
then straightforward to calculate the Cel using eqn. (10), and
i
p
p,In
*E(o DpT ] o CnT)
from them to obtain p(i) with eqn. (11) and (14). The results are
p
given in Table 9.
p(X) \ [ 1 BSr~3T
6k2
3
C
c2 d2 [ c
npx npz
5px 5pz npx npz
d
c
d
D
(17)
A proper theoretical accounting for the values of p(i)
p
p,X
*E(o DpT ] o CnT)
p
requires an accurate knowledge of the wavefunctions of the
ground and excited singlet states, as well as of the energy gaps
between them. Since these are unavailable, we have attempted
Values for Sr~3T may be obtained from the literature;37 the
energy gap *E(o DpT ] o CnT) corresponds to the lowest
energy 1% ^ 1& electronic transition, and experimental values
to account for the p(i) values using the wavefunctions deduced
p
Table 9 Nuclear and electronic contributions to the experimental spinÈrotation constants and corresponding paramagnetic shieldings in InF,
InCl, and InBr
In
Xa
C /kHz
Cnucl/kHz
Cel/kHz
p(In)(ppm)
C /kHz
Cnucl/kHz
Cel/kHz
p(X)(ppm)
In
In
In
p
X
X
X
p
1
1
1
1
1
15In19F
17.50
10.45
9.98
6.17
5.92
[0.67
[0.44
[0.42
[0.43
[0.43
18.17
10.89
10.40
6.60
[1153
[1660
[1653
[1968
[1921
18.77
1.71
1.19
5.30
5.36
[15.60
[0.56
[0.45
[0.69
[0.74
34.38
2.27
1.64
5.99
6.10
[510
[777
15In35Cl
15In37Cl
[704
15In79Br
15In81Br
[1566
[1501
6.35
a X \ F, Cl or Br.
058 J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1

View Article Online
Table 10 Observed and estimated 115In paramagnetic shieldings
pp(In)/ppm
*
E(o DpT ] o CnT)/cm~1
Sr~3Ta /a ~3
numeratorb
calc.c
exptl.d
p,In
0
InF
InCl
InBr
42 809e
37 568f
35 053g
6.051
6.051
6.051
0.402
0.365
0.352
[885
[916
[946
[1153
[1657
[1944
a Ref. 37. b Numerator in eqn. (16), calculated using orbital coefficients in Table 7. c Estimated using eqn. (16). d Values for the two isotopomers of
InCl and InBr have been averaged. e Ref. 36. f Ref. 38. g Ref. 39.
5
6
7
R. J. Low, T. D. Varberg, J. P. Connelly, A. R. Auty, B. J.
Howard and J. M. Brown, J. Mol. Spectrosc., 1993, 161, 499
K. D. Hensel, C. Styger, W. JaŽ ger, A. J. Merer and M. C. L.
are known for all three compounds. In order to estimate p(In)
p
we have used the values for Sr~3T and the energy gaps which
are shown in Table 10. We also use the estimated coefficients
Gerry, J. Chem. Phys., 1993, 99, 3320.
d
and d from Table 7, and we further let c (\c ) B 1
K. D. Hensel and M. C. L. Gerry, J. Mol. Spectrosc., 1994, 166,
5
pz npz 5px 5py
and c (\c ) B 0, consistent with the assumptions used to
account for the quadrupole coupling constants.
304.
npx
npy
8
9
Y. Ohshima and Y. Endo, Chem. Phys. L ett., 1993, 213, 95.
J-U. Grabow and W. Stahl, Z. Naturforsch., T eil A, 1990, 45,
The resulting values of p(In) , calculated from eqn. (16), are
p
1
043.
presented in Table 10. Even given the fairly severe approx-
10
11
12
A. H. Barrett and M. Mandel, Phys. Rev., 1958, 109, 1572.
imations involved, the agreement is only moderately satisfac-
tory for InF, and less so for InCl and InBr. The deÐciency of
the approximations is emphasized by the halogen shieldings
calculated from eqn. (17): with c \ c B 0, p(X) should be
J. Hoeft, Z. Phys., 1961, 163, 262.
G. A. L. Delvigne and H. W. de Wijn, J. Chem. Phys., 1996, 45,
3318.
13 F. J. Lovas and T. To
Ž
rring, Z. Naturforsch., T eil A, 1969, 24, 634.
J. Hoeft, F. J. Lovas, E. Tiemann and T. Torring, Z. Naturforsch.,
T eil A, 1970, 25, 1029.
B. Schenk, E. Tiemann and J. Hoeft, Z. Naturforsch., T eil A,
npx
npy
p
14
15
16
Ž
zero for all three compounds, in clear contradiction to experi-
ment. The obvious way to try to modify the model, by delo-
calizing the molecular orbitals to give o ApT, o BpT and o AnT a
little In character and the o CnT orbital some halogen charac-
ter (thus increasing the halogen character of o DpT and o EpT),
in fact makes the situation worse. The agreements among the
indium constants worsen considerably, and the calculated
halogen shieldings are positive.
1
971, 26, 240.
R. H. Hammerle, R. Van Ausdahl and J. C. Zorn, J. Chem. Phys.,
1972, 57, 4068.
17 E. Tiemann, J. Hoeft and T. To
Ž
rring, Z. Naturforsch., T eil A,
1
972, 27, 869.
E. Tiemann, U. Ko
977, 32, 6.
1
8
Ž hler and J. Hoeft, Z. Naturforsch., T eil A,
1
It is likely that other electronic excitations also contribute
1
2
9
0
J. Hoeft and K. P. R. Nair, Chem. Phys. L ett., 1989, 155, 273.
J. Hoeft and K. P. R. Nair, Chem. Phys. L ett., 1989, 164, 33.
to the p(i). Two possibilities are o BpT ] o CnT and
p
o AnT ] o EpT. Back-of-an-envelope-type estimates for both
21 J. Hoeft and K. P. R. Nair, Z. Phys. D: At. Mol. Clusters, 1994,
give trends in the correct direction for all shieldings, especially
for the cases where the molecular orbitals are slightly delocal-
ized. Unfortunately, the electronic structures of these mol-
ecules are not well characterized, and the energy gaps for the
excitations are unknown; quantitative comparisons are not
possible at this time. It is interesting that the lowest 1% state
of InCl is predissociated, presumably by another nearby 1%
state.40
29, 203.
2
2
Y. Xu, W. Ja
51, 206.
J. Haekel and H. MaŽ der, Z. Naturforsch., T eil A, 1988, 43, 203.
Ž ger and M. C. L. Gerry, J. Mol. Spectrosc., 1992,
1
23
24
25
H. M. Pickett, J. Mol. Spectrosc., 1991, 148, 371.
T. Karkanis, M. Dulick, Z. Morbi, J. B. White and P. F. Bernath,
Can. J. Phys., 1994, 72, 1213.
26 K. A. Walker and M. C. L. Gerry, J. Mol. Spectrosc., in the press.
27
28
29
S. P. So and W. G. Richards, J. Phys. B: At. Mol. Phys., 1974, 7,
1
973.
It must be remembered that there might be other contrib-
R. S. Ram, S. B. Rai, K. N. Upadhya and D. K. Rai, Phys. Scr.,
uting factors to p(i) . Excitations involving the In 4d electrons
p
1982, 26, 383.
might contribute, for example, as might e†ects of overlap.
S. R. Langho†, C. W. Bauschlicher Jr. and P. R. Taylor, J. Chem.
Phys., 1988, 88, 5715; erratum J. Chem. Phys., 1988, 89, 7650.
However, CornwellÏs fairly simple model, involving only p
electron excitations, has been found to give a convincing
picture in other situations.31,41,42 Better knowledge of wave-
functions and energy levels is needed to clarify the matter.
30 C. H. Townes and B. P. Dailey, J. Chem. Phys., 1949, 17, 782.
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3
1
2
C. D. Cornwell, J. Chem. Phys., 1966, 44, 874.
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3
3
4
W. H. Flygare, J. Chem. Phys., 1964, 41, 793.
The work was supported by the Natural Sciences and Engin-
eering Research Council (NSERC) of Canada, and by the
Network of Centres of Excellence in Molecular and Interfacial
Dynamics (CEMAID), administered by NSERC. K. D. H.
thanks NSERC for the award of a Postgraduate Scholarship.
3
C. Schlier, Fortschr. Phys., 1961, 9, 455.
35 I. Mills, T. Cvitas‘ , K. Homann, N. Kallay and K. Kuchitsu,
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7
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J. R. Morton and K. F. Preston, J. Magn. Reson., 1978, 30, 577.
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4
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Ž
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Paper 6/07080I; Received 17th October, 1996
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1059