Infrared emission spectra of BeH2 and BeD2

Article abstract of DOI:10.1063/1.1539850

Fourier transform spectrometer was used to record high resolution infrared spectra of beryllium dihydride (BeH₂) and dideuteride. The BeH₂ spectrum was recorded in the 1800-2900 cm^-1 spectral region at an instrumental resolution of 0.03 cm^-1 using a CaF₂ beamsplitter. The equilibrium rotational constant of BeH₂ was found to be 4.75366(2) cm^-1.

Full text of DOI:10.1063/1.1539850

Infrared emission spectra of BeH 2 and BeD 2
A. Shayesteh, K. Tereszchuk, P. F. Bernath, and R. Colin
Citation: The Journal of Chemical Physics 118, 3622 (2003); doi: 10.1063/1.1539850
View online: http://dx.doi.org/10.1063/1.1539850
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 8
22 FEBRUARY 2003
Infrared emission spectra of BeH2 and BeD2
A. Shayesteh, K. Tereszchuk, and P. F. Bernatha)
Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
R. Colin
´
´
Laboratoire de Chimie Physique Moleculaire, Universite Libre de Bruxelles, C.P. 160/09,
50 av. F. D. Roosevelt, 1050 Brussels, Belgium
͑Received 30 September 2002; accepted 2 December 2002͒
High resolution infrared emission spectra of beryllium dihydride and dideuteride have been
recorded with a Fourier transform spectrometer. The molecules were generated in a
discharge-furnace source, at 1500 °C and 333 mA discharge current, with beryllium metal and a
mixture of helium and hydrogen or deuterium gases. The antisymmetric stretching modes (␯3) of
BeH2 and BeD2, as well as several hot bands involving ␯1 , ␯2 , and ␯3 , were rotationally analyzed
and spectroscopic constants were determined. The equilibrium rotational constant (Be) of BeH2 was
found to be 4.753 66͑2͒ cmϪ1, and the equilibrium bond distance (Re) of 1.326 407͑3͒ Å was
determined for BeH2. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1539850͔
INTRODUCTION
the metal vapor and molecular hydrogen. FeH2 is the only
other metal dihydride known in the gas phase,18 except for a
comment about the electronic spectrum of AlH2 in an appen-
dix of Herzberg’s book on polyatomics.19 We report here the
BeH2 is a famous molecule. The chemical bonding in
BeH2 is discussed in many introductory chemistry textbooks,
in the context of the formation of sp hybrid orbitals.1 Since
BeH2 has only six electrons, it is a favorite target molecule
for quantum chemists to test their new ab initio methods.2–6
However, the high toxicity of beryllium-containing
compounds7 has inhibited experimental work. According to
Hinze et al.,8 the insertion of ground state Be atoms into the
H2 bond has a barrier of 203.5 kJ/mol ͑48.6 kcal/mol͒, and
the overall reaction
observation and detailed analysis of the ␯ antisymmetric
3
stretching fundamental bands and several hot bands of both
BeH2 and BeD2 .
EXPERIMENTAL DETAILS
The high resolution infrared emission spectra of BeH2
and BeD2 were recorded with a Bruker IFS 120 HR Fourier
transform spectrometer at the same time that we recorded the
BeH and BeD spectra.11 A new emission source with an elec-
trical discharge inside a high temperature furnace was used
to make the molecules. Powdered beryllium metal ͑about 5
g͒ was placed inside a zirconia boat in the center of an alu-
mina tube ͑5 cmϫ120 cm͒. The central part of the tube was
heated to 1500 °C by a CM Rapid Temp furnace, and the end
parts were cooled by water and sealed with CaF2 windows. A
slow flow of helium ͑about 20 Torr͒ and hydrogen or deute-
rium ͑a few Torr͒ was passed through the cell. Two stainless
steel tube electrodes were placed inside the cool ends of the
tube, and a dc discharge ͑2.5 kV, 333 mA͒ was struck be-
tween them. A CaF2 lens was used to focus the emitted light
from the source into the entrance aperture of the spectrom-
eter.
The BeH2 spectrum was recorded in the 1800–2900
cmϪ1 spectral region at an instrumental resolution of 0.03
cmϪ1 using a CaF2 beamsplitter. A liquid nitrogen-cooled
InSb detector was used, and 200 scans were co-added. The
spectral band pass was set by the detector and a 2900 cmϪ1
long-wave pass filter.
The BeD2 spectrum was recorded ͑200 scans͒ in the
spectral region of 1200–2200 cmϪ1 with the same instru-
mental resolution using a liquid nitrogen-cooled HgCdTe
͑MCT͒ detector. In this case the bandpass was set by the
CaF2 beamsplitter and a 2200 cmϪ1 long-wave pass filter.
Be g͒ϩH g͒→BeH g͒
͑
͑
͑
2
2
has been predicted9 to be exoergic by 157.3 kJ/mol ͑37.6
kcal/mol͒. BeH2 was calculated10 to be linear and to have an
equilibrium bond length of 1.3324 Å, close to the recently
observed value of 1.342 436 Å for the BeH free radical.11
In spite of this strong interest in BeH2, the molecule
remained unknown except for the detection12 of its infrared
spectrum in an argon matrix at 10 K, and in a silicon crystal
as an impurity.13 In the series of first row hydrides, LiH,
BeH2 , BH3 , CH4 , NH3 , OH2 , and FH, it was the only free
molecule remaining to be discovered. We recently reported
in a short note the first observation of gaseous BeH2 ͑Ref.
14͒ in a discharge-furnace emission source.
Solid BeH2 is well-known.15 The structure was assumed
to have linear polymeric chains of Be atoms joined together
by two bridging H atoms.16 This commonly accepted ‘‘fact’’
is in error. The observed crystal structure is based on a three-
dimensional arrangement of connected BeH4 tetrahedra.17
Heating solid BeH2 results in decomposition to the
elements,15 not the production of gaseous molecule. The
BeH2 molecule is, however, one of the few metal dihydrides
that is stable ͑in the thermodynamic sense͒ with respect to
a͒
Author to whom correspondence should be addressed; electronic mail:
bernath@uwaterloo.ca
0021-9606/2003/118(8)/3622/6/$20.00
3622
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 8, 22 February 2003
IR emission spectra of BeH2 and BeD2
FIG. 3. An overview of the infrared emission spectrum of BeD2 recorded
with the HgCdTe detector. All BeD lines are below 1680 cmϪ1, and the
weak emission lines near 1750 cmϪ1 are from the antisymmetric stretching
(␯3) fundamental band of BeD2 . The strong absorption of atmospheric H2O
can be seen.
FIG. 1. An overview of the infrared emission spectrum of BeH2 recorded
with the InSb detector. All BeH lines are below 2240 cmϪ1, and the strong
emission lines above 2240 cmϪ1 are from the antisymmetric stretching (␯3)
fundamental band of BeH2 . The absorption of atmospheric CO2 can be seen
near 2350 cmϪ1
.
by water absorption lines from the short atmospheric path
between the cell and the spectrometer. There are also a few
series of lines with alternating 2:1 intensities ͑Fig. 4͒ that
were assigned to BeD2 .
Atomic and molecular emission lines were present in the
spectra, as well as absorption lines from atmospheric CO2
and H2O. The signal-to-noise ratio for the strongest BeH2
lines was about 150.
Line positions in the spectra were determined using the
´
WSPECTRA program, from M. Carleer ͑Universite Libre de
RESULTS AND ANALYSIS
Bruxelles͒. The BeH2 spectrum was calibrated using impu-
rity CO emission lines, and the BeH2 lines have an absolute
accuracy of better than 0.001 cmϪ1. The calibration of BeD2
spectrum was based on five lines that were common with a
previously calibrated BeH spectrum in the 1200–2200 cmϪ1
region. Assignment of the bands was carried out with the aid
of a color Loomis–Wood program.
The strongest emission lines in the BeH2 spectrum ͑Fig.
1͒ are the R branch lines of the BeH ϭ1→0 band, and all
v
BeH lines are below 2240 cmϪ1. In addition, there are sev-
eral series of lines with alternating 3:1 intensities ͑Fig. 2͒
that were assigned to BeH2 transitions. This spectrum had
channeling in the baseline that we could not eliminate in
spite of our efforts. In the BeD2 spectrum ͑Fig. 3͒, the BeD
The strongest series of lines with intensity alternation in
both BeH2 and BeD2 spectra were assigned to the antisym-
ϭ1→0 band is the strongest series and all BeD lines are
v
below 1680 cmϪ1. This spectrum was unfortunately plagued
ϩ
metric stretching fundamental, 001–000, ͚ϩ – ͚ transi-
u
g
FIG. 2. An expanded view of the R branch of the 001→000 band of BeH2
with 3:1 intensity alternation. The absorption lines are from atmospheric
CO2 .
FIG. 4. An expanded view of the R branch of the 001→000 band of BeD2
with 2:1 intensity alternation. The strong absorption lines are from atmo-
spheric H2O.
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3624
J. Chem. Phys., Vol. 118, No. 8, 22 February 2003
Shayesteh et al.
The following bands ͑Fig. 5͒ were assigned for BeH2 :
ϩ
001–000
011–010
012–011
101–100
0201–0200 ͚ϩ – ͚
0202–0201 ͚ϩ – ͚
͚ϩ – ͚
,
u
g
u
g
ϩ
u
͟
–
–
͟
,
002–001
003–002
111–110
͚ϩ – ͚
,
,
g
g
ϩ
g
͟
͟
,
͚ϩ – ͚
u
u
ϩ
g
͚ϩ – ͚
,
,
,
͟ – ͟ ,
g u
u
ϩ
g
0221–0220 ⌬u –⌬g ,
0222–0221 ⌬g –⌬u ,
u
ϩ
u
g
0311–0310
͟
–
͟
,
u
0331–0330 ⌽g –⌽u .
g
In BeD2 we assigned five bands:
ϩ
g
001–000
011–010
͚ϩ – ͚
,
u
ϩ
u
͟
–
͟
,
002–001
͚ϩ – ͚
,
FIG. 5. An energy level diagram for BeH2 showing the observed emission
bands. The vibrational energies have been calculated with Eq. ͑4͒ using a
combination of experimental and theoretical constants ͑see the text͒.
g
u
g
ϩ
g
0201–0200 ͚ϩ – ͚
,
0221–0220 ⌬u –⌬g .
u
ϩ
g
We could not find the 110–000,
͟
u – ͚ combination band,
or any other combination bands in our spectra.
tions. The next intense series were assigned to the first bend-
The value of ␣2 in BeH2 is negative, and considerably
smaller in magnitude than the ␣1 and ␣3 values. The 011–
010 band of BeD2 was rotationally assigned so that it yielded
a reasonable ␣2 value compared to ␣2 in BeH2 . All the
ing mode hot band, 011–010,
͟ – ͟ transitions. All the hot
g u
bands are shifted to the lower wave numbers because of an-
harmonicity. The 3:1 intensity ratio of adjacent lines in BeH2
and the 2:1 ratio in BeD2 arise from the ortho–para nuclear
spin statistical weights with (Iϩ1)/I ratio.20
The rotational assignment of the fundamental band of
BeH2 was made based on the ‘‘missing line’’ at the band
͟
–
͟
transitions showed a large l-type doubling, and we
used the energy expression:
E
,
,
,J͒ϭG
,
,
͒ϩF J͒,
͑2͒
͑v1 v2 v3
͑v1 v2 v3
͑
origin, and a small perturbation at J ϭ22, which is due to an
Ј
with20
interaction between 001 (͚ϩu ) and 0310(
els. In the BeD2 fundamental band, we found the rotational
͟u) vibrational lev-
F J͒ϭBJ Jϩ1͒ϪDJ2 Jϩ1͒2ϩHJ3 Jϩ1͒
3
͑
͑
͑
͑
assignment from a small perturbation at J ϭ29, which is due
Ј
Ϯ 12 qJ Jϩ1͒ϩq J2 Jϩ1͒2ϩq J3 Jϩ1͒
3
͓
͑
͑
͑
͔
D
H
to the same interaction as in BeH2 . The absolute rotational
assignments of the hot bands were not easy, because the band
origins could not be predicted with the required accuracy.
For BeH2 we assigned the bands based on the Bv v v values,
͑3͒
in our least-squares fitting program. The observed line posi-
tions and the outputs of the least-squares fits for all the bands
have been placed in Electronic Physics Auxiliary Publication
Service ͑EPAPS͒.21 The band constants in Tables I and II
were determined for BeH2 and BeD2 using Eq. ͑3͒, in which
qϭqDϭqHϭ0 for ͚ states, and the plus ͑minus͒ sign refers
to e(f) parity. For a given J in ͟ states, the e parity lies
below the f parity in energy, and the l-type doubling param-
eter q is negative ͑rather than the traditional positive value͒
for the 010 vibrational level.
1
2 3
with20
Bv v v ϭBeϪ␣1 ϩ 12͒Ϫ␣2 2ϩ1͒Ϫ␣3 3ϩ 21͒. ͑1͒
͑v1 ͑v ͑v
1
2 3
We used the ab initio ␣1 and ␣2 values,9 as well as B000 and
from the ␯ fundamental band, to predict the Bv v v
␣
3
3
1
2 3
values for various vibrational levels. For each band we con-
sidered several rotational assignments, and we accepted the
one nearest to the predicted Bv v v value.
1
2 3
TABLE I. Spectroscopic constants ͑in cmϪ1͒ of BeH2 ͑all uncertainties are 1␴͒.
104
D
106 qD
Level
Gv-ZPE
B
109
H
102
q
1010 qH
ϩ
g
0.0
4.701 398 52͑747͒
4.632 187 25͑689͒
4.564 259 00͑684͒
4.497 254 3͑109͒
4.712 233 95͑599͒
4.642 962 78͑563͒
4.574 960 51͑584͒
4.644 418 1͑138͒
4.574 112 3͑130͒
4.654 705 5͑140͒
4.584 407 4͑132͒
1.049 985͑168͒
1.033 120͑145͒
1.017 027͑141͒
0.998 463͑506͒
1.090 965͑120͒
1.074 817͑110͒
1.059 394͑114͒
1.042 413͑274͒
1.026 031͑247͒
1.082 079͑436͒
1.066 978͑382͒
2.7175͑100͒
2.631 73͑820͒
2.571 71͑770͒
2.001 2͑728͒
3.048 59͑714͒
2.987 98͑620͒
2.947 92͑629͒
2.7895͑168͒
2.6557͑143͒
3.0902͑383͒
3.0546͑314͒
000 ͚
001 ͚
002 ͚
003 ͚
ϩ
u
2178.865 906͑205͒
4323.782 804͑295͒
6434.108 813͑474͒
a
aϩ2165.882 529͑162͒
aϩ4298.243 253͑256͒
b
bϩ2120.153 214͑256͒
c
cϩ2106.857 965͑242͒
ϩ
g
ϩ
u
010a
011
012
͟
Ϫ9.140 65͑116͒
Ϫ9.098 80͑112͒
Ϫ9.060 33͑114͒
8.1214͑234͒
8.0347͑219͒
7.9762͑222͒
Ϫ8.000͑139͒
Ϫ7.987͑124͒
Ϫ8.168͑122͒
u
g
͟
͟
u
ϩ
100a ͚
g
ϩ
101 ͚
u
110a
111
͟
Ϫ9.021 92͑274͒
Ϫ8.973 79͑264͒
8.6389͑850͒
8.5964͑761͒
Ϫ13.372͑749͒
Ϫ13.771͑624͒
u
͟
g
aThe estimated values of a, b, and c are 713, 1981, and 2696 cmϪ1, respectively ͑see the text͒.
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3625
J. Chem. Phys., Vol. 118, No. 8, 22 February 2003
IR emission spectra of BeH2 and BeD2
TABLE II. Spectroscopic constants ͑in cmϪ1͒ of BeD2 ͑all uncertainties are 1␴͒.
105
D
106 qD
Level
Gv-ZPE
B
1010
H
102
q
1010 qH
ϩ
0.0
2.360 987 2͑124͒
2.330 282 8͑127͒
2.299 905 9͑150͒
2.367 845 2͑177͒
2.337 135 2͑180͒
2.620 62͑262͒
2.589 97͑295͒
2.516 52͑380͒
2.693 39͑400͒
2.671 20͑428͒
3.213͑173͒
5.177͑212͒
2.883͑293͒
1.572͑275͒
5.191͑320͒
000 ͚
001 ͚
002 ͚
g
ϩ
u
1689.678 781͑334͒
3356.735 331͑589͒
ϩ
g
010a
011
͟
a
Ϫ3.017 54͑352͒
Ϫ3.029 90͑359͒
1.9011͑798͒
2.0133͑850͒
Ϫ4.711͑550͒
Ϫ6.211͑632͒
Ј
u
g
͟
a ϩ1680.588 327(369)
Ј
aThe value of a is aproximately 532 cmϪ1 ͑Ref. 12͒.
Ј
The following expression was used for the vibrational
energy:
and ⌬ ͑e͒ levels in fitting the 0201–0200, 0221–0220,
0202–0201, and 0222–0221 bands of BeH2 .
͑v ͑v ͑v
͒ϭ␻ 1ϩ 12͒ϩ␻ 2ϩ1͒ϩ␻ 3ϩ 21͒
ͱ2W
E⌬0
E0
G
,
,
͑v1 v2 v3
1
2
3
͚
20
Hϭ
.
͑5͒
ͩ
ͪ
1
2
ϩx11 1ϩ 2͒2ϩx22 2ϩ1͒
ͱ
2W20
͑v ͑v
ϩx33 3ϩ 12͒2ϩx12 ϩ 1͒ 2ϩ1͒
͑v ͑v1 ͑v
The diagonal matrix elements are the ordinary energy ex-
pressions for ͚ and ⌬ states:
2
ϩ
ϩx13 ϩ 1͒ 3ϩ 12͒ϩx23 2ϩ1͒
͑v1 ͑v ͑v
2
E0ϭG
,
,
͑v1 v2 v3
͑
͒ϩBJ Jϩ1͒
ϫ
3ϩ 12͒ϩg22l2.
͑4͒
In Tables I and II the vibrational energies are determined as
the difference between G( 3) and the zero point en-
͑v
2
ϪDJ2 Jϩ1͒2ϩHJ3 Jϩ1͒3,
͑6͒
͑
͑
while the off-diagonal term has the following form:
,
,
v
v1 v2
ergy ͑ZPE͒. We could not determine the absolute positions of
all of the observed energy levels and have called the un-
1
2
qϩq J Jϩ1͒ϩq J2 Jϩ1͒
W ϭͱ2
͓
͑
͑
͔
20
D
H
known values a, b, c, and a in Tables I and II. However,
Ј
1/2
ϫ J2 Jϩ1͒2Ϫ2J Jϩ1͒͒
.
͑7͒
some of the constants in Eq. ͑4͒ can be determined from
experimental data, and the ab initio values10 can be used for
undetermined constants. Using a combination of experimen-
tal and theoretical constants, the numerical values of a, b,
and c in Table I are roughly estimated to be 713, 1981, and
͑
͑
͑
No interaction affects the ⌬ state f levels and we used Eq. ͑6͒
for the f parity.
The constants of Table III were determined for BeH2
with an l-resonance fit of the corresponding bands. The value
of d in Table III is roughly estimated to be 1420 cmϪ1, and
2696 cmϪ1, respectively. The a value in Table II is approxi-
Ј
mately 532 cmϪ1 based on a matrix isolation experiment.12
ϩ
the difference between ͚ and ⌬ states origins is equal to
4g22 ͓Eq. ͑4͔͒. The ⌬ states vibrational energies in Table III
are higher than those of corresponding ͚ states, which is
l-TYPE RESONANCE
ϩ
Although the splitting between ⌬ state e/f parity levels
(l2ϭϮ2) should be very small and negligible, for both
BeH2 and BeD2 we observed a large splitting in all the vi-
brational levels with l2ϭ2 due to l-type resonance. The de-
consistent with a positive g22 predicted by ab initio
calculations.10 We found fitting errors ͑smaller than 0.1
cmϪ1͒ for the line positions of ⌬–⌬ transitions, but the
ϩ
͚ϩ – ͚ transitions fitted very well within the experimental
ϩ
tailed theory of l-type resonance between ͚ (l2ϭ0) and ⌬
uncertainty. This additional perturbation is caused by the 050
and 051 vibrational levels that are close to 021 and 022
levels, respectively. There are three states with l2ϭ1, 3, and
5 ͑͟, ⌽, and H͒ for the 050 and 051 levels, and we assume
that the ⌽ states (0530 and 0531) are perturbing the ⌬ states
(l2ϭ2) states was first derived by Amat and Nielsen,22 and
was expanded later.23–25 The ͚ state levels have e parity
ϩ
and they interact with ⌬ state e levels. Following Maki and
Lide,23 the Hamiltonian matrix ͓Eq. ͑5͔͒ was used for ͚ ͑e͒
ϩ
TABLE III. Spectroscopic constants ͑in cmϪ1͒ of BeH2 for levels involving l-type resonance ͑all uncertainties are 1␴͒.
104
D
106 qD
Level
020a
l
B
109
H
102
q
1010 qH
Gv-ZPE
0
d
4.723 696 6͑172͒
1.140 252͑405͒
3.7571͑278͒
Ϫ9.179 95͑132͒
Ϫ9.119 10͑429͒
Ϫ9.056 07͑864͒
8.2333͑254͒
Ϫ7.573͑157͒
2
0
dϩ8.200 88͑553͒
4.722 444 51͑995͒
4.653 428 5͑784͒
1.134 571͑234͒
1.109 73͑251͒
3.6242͑160͒
2.988͑225͒
021
022
dϩ2152.984 78͑146͒
7.852͑104͒
7.410͑345͒
Ϫ6.123͑603͒
Ϫ4.79͑295͒
2
0
dϩ2161.090 45͑772͒
dϩ4272.893 08͑249͒
4.653 488 5͑490͒
4.584 354͑154͒
1.124 32͑219͒
1.079 17͑646͒
3.806͑219͒
2.306͑586͒
2
dϩ4280.918 1͑115͒
4.585 760 4͑932͒
1.114 75͑363͒
4.024͑341͒
aThe estimated value of d is 1420 cmϪ1 ͑see text͒.
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3626
J. Chem. Phys., Vol. 118, No. 8, 22 February 2003
Shayesteh et al.
TABLE IV. Spectroscopic constants ͑in cmϪ1͒ of BeD2 for levels involving l-type resonance ͑all uncertainties are 1␴͒.
105
D
106 qD
Level
020a
l
B
1010
H
102
q
Gv-ZPE
0
d
2.375 102 0͑514͒
2.892 1͑130͒
10.312͑990͒
Ј
Ϫ2.971 45͑121͒
Ϫ2.978 27͑120͒
1.0799͑125͒
2
0
d ϩ0.598 33(987)
2.374 545 2͑315͒
2.344 428 3͑550͒
2.820 90͑788͒
2.873 0͑141͒
5.367͑577͒
13.52͑111͒
Ј
021
d ϩ1671.503 13(170)
Ј
1.0478͑124͒
2
d ϩ1672.161 1(104)
Ј
2.343 858 9͑314͒
2.820 00͑810͒
12.788͑628͒
aThe estimated value of d is 1064 cmϪ1 ͑obtained as 2 times ␯ from the matrix value reported in Ref. 12͒.
Ј
2
(0221 and 0222). We added the 0200 and 0220 states com-
bination differences in our fit ͑with 0.0015 cmϪ1 weight͒,
and deweighted the 0221–0220 and 0222–0221 lines to 0.1
cmϪ1. As a result, the 020 constants ͑Table III͒ were deter-
mined accurately, but the 021 and 022 constants have only
moderate precision and accuracy. A more complete analysis
of the various resonances was not attempted.
Using the origins of 001–000, 101–100, 011–010, and
002–001 bands with Eq. ͑4͒, some anharmonicity constants
(x13 , x23 , x33 of BeH2 and x23, x33 of BeD2) were obtained.
The equilibrium frequency of the antisymmetric stretching
mode ␻ was calculated for BeH2 using ␯3 , x13 , x23 , and
3
x33 . Our ␻ value of 2255.155͑1͒ cmϪ1 is close to the ab
3
initio value of 2249.4 cmϪ1. The l-type doubling constant q
The 0201–0200 and 0221–0220 bands of BeD2 were
fitted using the same l-resonance matrix elements, and the
corresponding constants were determined ͑Table IV͒. In this
case, we did not observe any perturbation in the 021 vibra-
tional level. However, the number of observed lines was
smaller and we had to fix qHϭ0 for the 020 and 021 levels
of BeD2 .
for the ͟ states is related to Be , ␻2 , and ␻ by19,23
3
2
Be2
4␻
2
qϭϪ
1ϩ
2ϩ1͒.
͑8͒
͑v
ͩ
ͪ
2
2
␻
␻23Ϫ␻
2
Using Be , ␻3 , and q010 values, the equilibrium bending
mode frequency (␻2) of BeH2 was calculated to be 716.5
cmϪ1, very close to the theoretical value of 717.7 cmϪ1. We
The 0311–0310,
͟ – ͟
g
u , and 0331–0330, ⌽g –⌽u
bands of BeH2 showed l-type resonance between ͟ and ⌽
states in both e and f parity levels. According to the positive
sign of g22 , the ⌽ states have higher energy than the ͟
states. There is also a large l-type doubling in the ͟ states,
which splits the e and f parity levels. The splitting increases
with J ͓Eq. ͑3͔͒, and the f parity levels of ͟ and ⌽ states
cross at JϷ13. Because of this crossing, we could not deter-
mine any reasonable constants for the 030 and 031 vibra-
tional levels.
TABLE V. Equilibrium constants of BeH2 and BeD2 ͑in cmϪ1͒.
BeH2
͑this work͒
BeH2
BeD2
Constant
͑Martin and Leea͒
͑this work͒
1.326 407͑3͒
1.333 758͑1͒
4.753 66͑2͒
1.021 2͑5͒
2.39͑3͒
1.332 4
1.339 7
4.711 17
1.007 9
2.5
¯
Re/Å
R0/Å
1.331 361͑4͒
Be
¯
Deϫ104
Heϫ109
¯
¯
␣
␣
␣
q010
0.056 98͑2͒
Ϫ0.010 84͑1͒
0.069 21͑1͒
Ϫ0.091 41͑1͒
¯
0.055 76
Ϫ0.011 83
0.069 96
͑Ϫ0.0896͒
1979.6
716.8
2167.2
2037.3
717.7
2249.4
Ϫ14.29
1.80
¯
1
Ϫ0.006 86͑2͒
0.030 70͑2͒
Ϫ0.030 18͑4͒
¯
2
DISCUSSION
3
b
The intensity alternation in both BeH2 and BeD2 lines is
consistent with a linear structure with Dϱh symmetry. The
equilibrium structure of BeH2 and some constants of BeD2
can be determined from the band constants of Tables I–IV.
The experimental constants of BeH2 are compared with the
ab initio values10 in Table V. We found bands involving all
three vibrational modes of BeH2 and ␣1 , ␣2 , ␣3 , and Be
were determined ͑Table V͒ using B000 , B100 , B010 , and B001
values and Eq. ͑1͒, but for BeD2 we could determine only ␣2
and ␣3 . The equilibrium rotational constant (Be) of BeH2
was found to be 4.753 66͑2͒ cmϪ1, in good agreement with
the theoretical value of Martin and Lee.10 The equilibrium
Be–H distance (Re) was calculated to be 1.326 407͑3͒ Å
using the Be value of Table V, while the ab initio value10 of
Re is 1.3324 Å. The 001–000 band origin (␯3) of BeH2 is
2178.8659͑2͒ cmϪ1, close to the theoretical value10 of 2167.2
cmϪ1 and to the matrix isolation value12 of 2159 cmϪ1. Our
␯
␯
␯
(␴g)
(␲u)
(␴u)
1
2
3
¯
¯
c
d
2178.865 9͑2͒
¯
1689.678 8͑3͒
␻
␻
␻
x11
x12
x13
x22
x23
x33
g22
¯
1
2
3
716.5e
¯
2255.155͑1͒
¯
¯
¯
¯
¯
Ϫ58.712 7͑3͒
¯
Ϫ61.84
¯
b
͑ϩ0.52͒
¯
Ϫ12.983 4͑3͒
Ϫ16.974 5͑3͒
2.050͑1͒
Ϫ11.68
Ϫ19.78
2.46
Ϫ9.090 5͑5͒
Ϫ11.311 1͑4͒
0.150͑2͒
aReference 10.
bThe value of Ϫ0.002 71 cmϪ1 for q010 is in error in Ref. 10. A more recent
value using the same approach but a slightly different basis set is Ϫ0.0896
cmϪ1, in excellent agreement with our data. In addition, the sign of x22 is
erroneous in Ref. 10, the value should be ϩ0.52 cmϪ1 ͑Ref. 27͒.
cThe matrix isolation values ͑Ref. 12͒ of ␯ and ␯ are 698 and 2159 cmϪ1
,
2
3
respectively.
␯ value of 1689.6788͑3͒ cmϪ1 for BeD2 is also in reason-
dThe matrix isolation values ͑Ref. 12͒ of ␯ and ␯ are 532 and 1674 cmϪ1
,
3
2
3
able agreement with the matrix isolation value12 of 1674
respectively.
eCalculated from the q010 value and Eq. ͑8͒.
cmϪ1
.
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3627
J. Chem. Phys., Vol. 118, No. 8, 22 February 2003
IR emission spectra of BeH2 and BeD2
5 R. Baer and D. Neuhauser, J. Chem. Phys. 112, 1679 ͑2000͒.
also determined g22 for both molecules from the l-type reso-
nance constants in Tables III and IV. Our g22 value of
2.050͑1͒ cmϪ1 for BeH2 is in reasonable agreement with the
6 Y. G. Khait and M. R. Hoffmann, J. Chem. Phys. 108, 8317 ͑1998͒.
7 S. Budavari, M. J. O’Neil, A. Smith, and P. E. Heckelman, The Merck
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8 J. Hinze, O. Friedrich, and A. Sundermann, Mol. Phys. 96, 711 ͑1999͒.
9 J. M. L. Martin, Chem. Phys. Lett. 273, 98 ͑1997͒.
10 J. M. L. Martin and T. J. Lee, Chem. Phys. Lett. 200, 502 ͑1992͒.
11 A. Shayesteh, K. Tereszchuk, P. F. Bernath, and R. Colin, J. Chem. Phys.
118, 1158 ͑2003͒. ͑in press͒.
ab initio value of 2.46 cmϪ1
.
CONCLUSION
The high resolution infrared emission spectra of BeH2
and BeD2 at 1500 °C were recorded with a Fourier transform
12 T. J. Tague, Jr. and L. Andrews, J. Am. Chem. Soc. 115, 12111 ͑1993͒.
13 R. Mori, N. Fukata, M. Suezawa, and A. Kasuya, Physica B 302-303, 206
͑2001͒.
spectrometer. The antisymmetric stretching modes ␯ of both
3
14 P. F. Bernath, A. Shayesteh, K. Tereszchuk, and R. Colin, Science 297,
1323 ͑2002͒.
molecules, as well as ten hot bands of BeH2 and four hot
bands of BeD2 were rotationally analyzed. From the equilib-
rium rotational constant (Be) of BeH2 , the equilibrium
Be–H distance (Re) was determined to be 1.326 407͑3͒ Å.
Our work represents the first complete rotational analysis
(Be and three ␣i’s͒ and equilibrium structure for a metal
dihydride. The discharge-furnace emission source and the
technique of high resolution infrared emission
spectroscopy26 are powerful tools for generating and study-
ing high temperature metal hydrides.
15 N. N. Greenwood and A. Earnshaw, Chemistry of the Elements ͑Perga-
mon, Oxford, 1984͒, p. 125.
16 G. J. Brendel, E. M. Marlett, and L. M. Niebylski, Inorg. Chem. 17, 3589
͑1978͒.
17 G. S. Smith, Q. C. Johnson, D. K. Smith, D. E. Cox, R. L. Snyder, R.-S.
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18
¨
H. Korsgen, W. Urban, and J. Brown, J. Chem. Phys. 110, 3861 ͑1999͒.
19 G. Herzberg, Electronic Spectra of Polyatomic Molecules ͑Van Nostrand
Reinhold, New York, 1966͒, p. 583.
20 P. F. Bernath, Spectra of Atoms and Molecules ͑Oxford University Press,
New York, 1995͒.
21 See EPAPS Document No. JCPSA6-118-016308 for the observed line
positions and the outputs of the least-squares fits for all the bands. A direct
link to this document may be found in the online article’s HTML reference
section. The document may also be reached via the EPAPS homepage
͑http://www.aip.org/pubservs/epaps.html͒ or from ftp.aip.org in the direc-
tory /epaps/. See the EPAPS homepage for more information.
22 G. Amat and H. H. Nielsen, J. Mol. Spectrosc. 2, 163 ͑1958͒.
ACKNOWLEDGMENTS
This work was supported by the Natural Sciences and
Engineering Research Council ͑NSERC͒ of Canada and by
the Fonds National de la Recherche Scientifique ͑FNRS͒ of
Belgium.
23 A. G. Maki, Jr. and D. R. Lide, Jr., J. Chem. Phys. 47, 3206 ͑1967͒.
24
1 For example, S. R. Radel and M. H. Navidi, Chemistry ͑West Publishing,
St. Paul, 1990͒, p. 390.
ˇ
D. Papousek and M. R. Aliev, Molecular Vibrational–Rotational Spectra
͑Elsevier, Amsterdam, 1982͒.
25 J. K. G. Watson, Can. J. Phys. 79, 521 ͑2001͒.
26 P. F. Bernath, Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 96, 177
͑2000͒.
2 P. G. Szalay and R. J. Bartlett, J. Chem. Phys. 103, 3600 ͑1995͒.
3 U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171
͑1999͒.
4 D. A. Mazziotti, Phys. Rev. A 60, 4396 ͑1999͒.
27 J. M. L. Martin and T. J. Lee ͑private communication͒.
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