Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen
We report high-resolution infrared absorption spectroscopic studies of the dopant-induced Q₁(0) vibron band in solid parahydrogen crystals doped with low concentrations of rare gas atoms. The frequency, lineshape, and integrated absorption coefficient for the rare gas atom-induced Q₁(0) vibron ban...
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irk-123456789-1217802017-06-17T03:02:56Z Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen Raston, P.L. Anderson, D.T. Quantum Crystals We report high-resolution infrared absorption spectroscopic studies of the dopant-induced Q₁(0) vibron band in solid parahydrogen crystals doped with low concentrations of rare gas atoms. The frequency, lineshape, and integrated absorption coefficient for the rare gas atom-induced Q₁(0) vibron band are measured for Ne, Ar, Kr, and Xe. The observed lineshapes and peak maxima frequencies are sensitive to the H₂ vibrational dependence of the dopant-H₂ isotropic intermolecular potential. Trends observed for Ar, Kr and Xe indicate the vibrational dependence is strong enough for Xe to trap the infrared-active vibron in its first solvation shell while for Ar the vibron remains delocalized. The Ne-induced feature displays a qualitatively different lineshape which is attributed to the weak intramolecular vibrational dependence of the Ne–H₂ intermolecular potential relative to the H₂–H₂ interaction. The lineshapes of the Ar, Kr, and Xe dopant-induced Q₁(0) pure vibrational features agree well with recent first principles calculations. 2007 Article Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen / P.L. Raston, D.T. Anderson // Физика низких температур. — 2007. — Т. 33, № 6-7. — С. 653-660. — Бібліогр.: 44 назв. — англ. 0132-6414 PACS: 33.20.Ea; 63.50.+x; 67.80.–s http://dspace.nbuv.gov.ua/handle/123456789/121780 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| topic |
Quantum Crystals Quantum Crystals |
| spellingShingle |
Quantum Crystals Quantum Crystals Raston, P.L. Anderson, D.T. Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen Физика низких температур |
| description |
We report high-resolution infrared absorption spectroscopic studies of the dopant-induced Q₁(0) vibron
band in solid parahydrogen crystals doped with low concentrations of rare gas atoms. The frequency,
lineshape, and integrated absorption coefficient for the rare gas atom-induced Q₁(0) vibron band are measured
for Ne, Ar, Kr, and Xe. The observed lineshapes and peak maxima frequencies are sensitive to the H₂
vibrational dependence of the dopant-H₂ isotropic intermolecular potential. Trends observed for Ar, Kr and
Xe indicate the vibrational dependence is strong enough for Xe to trap the infrared-active vibron in its first
solvation shell while for Ar the vibron remains delocalized. The Ne-induced feature displays a qualitatively
different lineshape which is attributed to the weak intramolecular vibrational dependence of the Ne–H₂
intermolecular potential relative to the H₂–H₂ interaction. The lineshapes of the Ar, Kr, and Xe dopant-induced
Q₁(0) pure vibrational features agree well with recent first principles calculations. |
| format |
Article |
| author |
Raston, P.L. Anderson, D.T. |
| author_facet |
Raston, P.L. Anderson, D.T. |
| author_sort |
Raston, P.L. |
| title |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| title_short |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| title_full |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| title_fullStr |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| title_full_unstemmed |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| title_sort |
infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2007 |
| topic_facet |
Quantum Crystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121780 |
| citation_txt |
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen / P.L. Raston, D.T. Anderson // Физика низких температур. — 2007. — Т. 33, № 6-7. — С. 653-660. — Бібліогр.: 44 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT rastonpl infraredactivevibronbandsassociatedwithraregasatomdopantsisolatedinsolidparahydrogen AT andersondt infraredactivevibronbandsassociatedwithraregasatomdopantsisolatedinsolidparahydrogen |
| first_indexed |
2025-07-08T20:30:45Z |
| last_indexed |
2025-07-08T20:30:45Z |
| _version_ |
1837112121834340352 |
| fulltext |
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7, p. 653–660
Infrared-active vibron bands associated with rare gas
atom dopants isolated in solid parahydrogen
P.L. Raston and D.T. Anderson
Department of Chemistry, University of Wyoming, Laramie, WY 82071–3838, USA
E-mail: danderso@uwyo.edu
Received February 7, 2007
We report high-resolution infrared absorption spectroscopic studies of the dopant-induced Q1(0) vibron
band in solid parahydrogen crystals doped with low concentrations of rare gas atoms. The frequency,
lineshape, and integrated absorption coefficient for the rare gas atom-induced Q1(0) vibron band are mea-
sured for Ne, Ar, Kr, and Xe. The observed lineshapes and peak maxima frequencies are sensitive to the H2
vibrational dependence of the dopant-H2 isotropic intermolecular potential. Trends observed for Ar, Kr and
Xe indicate the vibrational dependence is strong enough for Xe to trap the infrared-active vibron in its first
solvation shell while for Ar the vibron remains delocalized. The Ne-induced feature displays a qualitatively
different lineshape which is attributed to the weak intramolecular vibrational dependence of the Ne–H2
intermolecular potential relative to the H2–H2 interaction. The lineshapes of the Ar, Kr, and Xe dopant-in-
duced Q1(0) pure vibrational features agree well with recent first principles calculations.
PACS: 33.20.Ea Infrared spectra;
63.50.+x Vibrational states in disordered systems;
67.80.–s Solid helium and related quantum crystals.
Keywords: IR spectroscopic studies, fundamental vibrational transitions, vibron bands.
The distinguishing feature of quantum crystals, such
as solid helium and solid molecular hydrogen, is the large
amplitude zero-point motion of the constituent atoms or
molecules about their equilibrium positions in the crystal
lattice [1–5]. In solid parahydrogen (p-H2) the root-
mean-square deviation of the p-H2 molecule from its lat-
tice site is approximately 18% of the nearest-neighbor
spacing [3]. The presence of this zero-point energy dy-
namically inflates the molar volume of the crystal and
thus solid p-H2 has a molar volume (23.15 cm
3
·mol
–1
)
comparable to solid argon (22.42 cm
3
·mol
–1
) and signifi-
cantly greater than solid neon (13.31 cm
3
·mol
–1
) [4,6].
This molecular motion in solid p-H2 influences the rates
of intrinsically quantum relaxation processes such as
ortho–para conversion and quantum diffusion whose
rates are amplified by intimate short-range interactions
[4,7]. While these quantum mechanical zero-point effects
are more pronounced in low density solid helium com-
pared to solid p-H2, because hydrogen molecules have vi-
brational and rotational degrees of freedom, quantum
crystals of solid p-H2 have excitons (vibrons and rotons)
that have no analogy in solid helium and these excitons
can be used to spectroscopically probe the zero-point mo-
tion of the quantum solid [8].
Solid mixtures of p-H2 doped with low concentrations
of rare gas (Rg) atoms are of interest to investigate how
the heavy dopant species perturbs the zero-point motion
of the quantum crystal [4]. X-ray diffraction studies of
solid p-H2 doped with Ne, Ar, or Kr indicate that the mo-
lar volume of the doped solid increases and the c/a ratio of
the hexagonal close-packed (hcp) lattice decreases for Ne
and Ar and increases for Kr [6,9–11]. The increase in mo-
lar volume for the Ne and Ar doped solids is in violation
of Vegard’s law which holds that a linear relation exists
between the crystal lattice constant of an alloy and the
concentration of the constituent elements [12]. Since both
Ne and Ar have smaller molar volumes than solid p-H2,
one would expect the molar volume to decrease upon add-
ing the Rg atom to solid p-H2 instead of increase. This
paradoxical behavior for Ne and Ar doped p-H2 solids led
the researchers studying this effect to speculate that due
to the greater mass of Ne the first solvation shell around
the impurity is drawn inward toward the Ne atom as ex-
pected for a lower zero-point energy. The contraction of
the first solvation shell around the Rg atom impurity
© P.L. Raston and D.T. Anderson, 2007
weakens its interaction with the second solvation shell
such that the second solvation shell expands causing the
net increase in molar volume that is observed [6,9]. This
interpretation raises basic questions about the nature of
the solvent environment around the Rg atom in a quantum
solid. The infrared spectroscopic studies presented here
provide additional albeit indirect information on the
«quantum solvation» environment of Rg atoms in solid
p-H2 via detailed lineshape measurements of the solid
p-H2 fundamental vibrational transition.
Although infrared (IR) transitions of isolated H2 are
electric dipole forbidden, the solid possesses a rather
strong infrared absorption spectrum induced via weak
intermolecular interactions [13] that was first measured
in neat p-H2 solids by Soots et al. [14]. The IR spectrum
of solid hydrogen is therefore purely an induced spectrum
arising from the electric dipole moments caused by the
intermolecular forces between interacting molecules,
which obviously depends on the relative separation of the
H2 molecules within the solid. The infrared transition mo-
ments in solid hydrogen are induced mainly by
long-range electrostatic multipole interactions among the
molecules [13,15,16]. Doping solid p-H2 with low con-
centrations of closed-shell, neutral spherical dopants
which rigorously do not have electric multipole moments,
such as rare gas atoms, allows a qualitatively different IR
induction mechanism that originates from short-range
overlap interactions to be studied [17–19]. In contrast to
multipole induction, overlap induction is inherently
short-ranged and thus the intensity and lineshape of these
Rg atom-induced transitions are sensitive mainly to the
immediate solvation environment around the Rg impu-
rity.
In this paper, we consider the frequency, lineshape and
integrated absorption coefficients of the zero phonon
Q1(0) transition at ~ 4150 cm
–1
induced by the presence
of Rg atoms, corresponding to the H2 pure vibrational
transition (v = 1 0� , J = 0 0� ). This transition has en-
coded in its high-resolution IR absorption lineshape in-
formation about the configuration distribution function of
the Rg atom and the surrounding p-H2 solvation shell(s).
The Rg atom doped solid p-H2 system is also amenable to
first principles calculations and the present experimental
results will be compared to recent theoretical studies by
Hinde [19].
An important consideration in the study of the Q1(0)
transition is the nature of the excited state. In the absence
of any vibrational coupling between molecules, the Q1(0)
transition would produce a single v = 1, J = 0 p-H2 mole-
cule with an energy of 4152.2 cm
–1
. This energy differs
from the gas-phase value because the molecule is
solvated in the p-H2 crystal [15]. However, the weak
intermolecular forces between two adjacent p-H2 mole-
cules depend on the intramolecular stretching coordinate
of the two molecules and this dependence leads to a mech-
anism for vibrational coupling [20]. This vibrational
coupling delocalizes the v = 1 vibrational state such that
the v = 1 vibrational excitation can «hop» from p-H2 mol-
ecule to p-H2 molecule within the crystal. The v = 1 p-H2
vibrational state is broadened into a vibrational exciton
band which extends over approximately 4 cm
–1
and the
exciton is termed a vibron [13].
There have been two previous experimental reports of
the Rg atom-induced Q1(0) transition in solid p-H2. The
first was conducted by Fajardo and Tam who developed
the «rapid vapor deposition» technique utilized in this
study to grow chemically doped p-H2 crystals [21]. The
paper by Fajardo and Tam describes the rapid vapor depo-
sition technique and also presents the Xe atom-induced
Q1(0) absorption spectrum. In a later publication, Hinde
et al. present data in the Q1(0) region for N2 and Ar dop-
ant species [18]. Recently, Hinde has published a theoreti-
cal paper in which a model is developed for first princi-
ples calculation of the Rg atom-induced Q1(0) feature
[19]. These experiments [18,21] and calculations [19] are
the main motivation for the present work, along with the
x-ray diffraction studies of the structural changes pro-
duced by doping solid p-H2 with Rg atoms [6,9–11].
Experimental
A detailed description of the experimental apparatus
and sample preparation technique has been reported else-
where [22]. Rg atom doped solid p-H2 crystals are pre-
pared using rapid vapor deposition [21,23] of separate
gas streams of precooled p-H2 and room temperature Rg
onto a 1 inch diameter BaF2 substrate (T � 2.5 K) within a
liquid helium bath cryostat (Janis SSVT-100). High pu-
rity p-H2 gas (99.99%) is prepared by passing normal H2
(n-H2) gas through a low temperature catalytic converter
containing granular Fe(OH)3 (hydrous ferric oxide) just
prior to deposition. For most of these experiments the cat-
alytic converter was maintained at 14 K during deposi-
tion, which is the lowest temperature possible whilst
maintaining a significant gas flow through the converter.
Based on the integrated absorption of the o-H2 impu-
rity-induced Q1(0) transition, we estimate the o-H2 con-
centration to be ~100 parts per million (ppm) in the sam-
ples discussed in this paper [23]. Both Rg and p-H2 gas
streams impinge on the BaF2 substrate orthogonal to one
another and at an angle of 45° with respect to the sub-
strate. Thermal isolation vacuum is maintained during de-
position with the aid of a turbomolecular pump mounted
directly to the cryostat delivering a vacuum of less than
10
–4
Torr for the duration of each deposition. Sample
thickness is determined to within ±5% from the integrated
intensities of the Q1(0) + S0(0) or S1(0) + S0(0) double
transitions [24].
654 Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7
P.L. Raston and D.T. Anderson
In these studies the n-H2 flow rate was between 170 to
300 mmol·h
–1
, allowing samples from 1.6 mm to 2.8 mm
thick to be grown in under an hour. The Rg atom concen-
tration in these studies ranged from 140 to 1300 ppm,
however, most samples have approximately 1000 ppm Rg
atom concentrations since the induced features are rela-
tively weak. The Rg concentrations cited here are ratios
of the quantities of Rg and H2 entering the sample cham-
ber. These values may differ from the actual Rg concen-
trations in the solid (due to varying sticking efficiencies
of p-H2 and Rg atoms, among other reasons) but are esti-
mated to be within ±40% of the in situ concentrations
[18]. The Rg atoms investigated were Ne (Airgas, purity:
99.999%), Ar (Airgas, purity: 99.999%), Kr (Scott Spe-
cialty Gases, Inc., purity: 99.995%), and Xe (Scott Spe-
cialty Gases, Inc., purity: 99.995%), all of which were
used as received. As-deposited spectra are recorded im-
mediately after deposition at approximately 2 K and are
known to contain face-centered-cubic (fcc) and hexago-
nal close-packed (hcp) crystal domains [25]. Annealing
the sample involves raising the temperature to 4.3 K for
~40 minutes, and should to a certain extent convert the fcc
domains to the lower energy hcp crystal structures [25].
The IR absorption spectra of Rg atom doped solid
p-H2 are recorded at resolutions ranging from 0.008 cm
–1
to 0.02 cm
–1
(nominal with boxcar apodization). The
FTIR spectrometer (Bruker IFS 120HR) was equipp-
ed with a Tungsten source, either a KBr or CaF2 beam
splitter, and a liquid nitrogen cooled InSb detector
(1850–9000 cm
–1
). The optical path outside the spec-
trometer and cryostat was purged with dry N2 gas to re-
duce atmospheric absorptions.
Results and analysis
The o-H2 impurity-induced Q1(0) feature has been ex-
tensively studied both experimentally [26–29] and theo-
retically [13,15,16]. The dipole moment induced in p-H2
by an o-H2 molecule via intermolecular forces consists of
two main parts; the overlap dipole moment and the elec-
tric quadrupole-induced dipole moment due to the
rotationally averaged quadrupole moment of o-H2. For
o-H2–p-H2 pairs at the nominal 3.79 � nearest-neighbor
spacing in the crystal [3], the overlap dipole moment is
small compared to the quadrupole-induced moment and
therefore assumed not to contribute to the o-H2 induced
Q1(0) transition. An important distinction between the
two induction mechanisms is that overlap induction is
isotropic while quadrupole induction is anisotropic. In
addition, overlap induction falls off exponentially with
respect to distance, while quadrupole induction decays
rather slowly with increasing distance (1/R
4
) and thus ac-
tivates vibrons with substantial amplitude on non-nearest
neighbor p-H2 molecules [19]. The quadrupole induction
mechanism, IR selection rules, and the fact that the upper
state is a delocalized vibron results in the distinct broad
asymmetric lineshape observed for the o-H2 impurity-in-
duced Q1(0) transition where the IR absorption line pro-
file is similar to the calculated density of vibron Bloch
states [30].
The o-H2 induced Q1(0) transition is shown in Fig. 1
for a series of p-H2 solids with low concentrations of
o-H2. The spectra shown in Fig. 1 are all as-deposited
spectra recorded at 1.9 K with o-H2 concentrations as
follows: trace (a) ~100 ppm, trace (b) 1000 ppm, and
trace (c) 5200 ppm. The Q1(0) feature at 4153.1 cm
–1
exhibits the broad asymmetric lineshape which maps out
the subset of delocalized Q1(0) vibrons whose spatial
wave functions achieve nonzero overlap with the quadru-
polar electrostatic field of the o-H2 dopant. In contrast,
the Q1(1) transition (v = 1 0� , J = 0 0� ) of the o-H2
dopant itself is observed at 4146.55 cm
–1
with a narrow
linewidth, indicating the vibrational excitation is ex-
tensively localized on o-H2 [31]. The large vibra-
tion–rotation interaction in H2 shifts the Q1(1) transition
~6.6 cm
–1
to lower energy than the Q1(0) transition, thus
the o-H2 vibrational excited state is below the p-H2
vibron band which substantially localizes the vibrational
excitation on the o-H2 dopant.
To minimize the intensity of the o-H2 Q1(1) and o-H2
impurity-induced Q1(0) absorption features in the present
study, the crystals were grown with the lowest concentra-
tion of o-H2 that could be achieved (approximately
100 ppm), a representative spectrum at this o-H2 concen-
tration is shown in trace (a) of Fig. 1. Since the ortho to
para conversion rate in the solid at these low o-H2 con-
centrations is on the order of days, all the spectra reported
here in the Q1(0) region contain a small feature due to the
o-H2 impurity-induced Q1(0) absorption [3,32]. The fre-
quency and lineshape of this Q1(0) absorption feature are
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7 655
Wavenumber, cm
–1
4140 4145 4150 4155 4160
lg
(
)
I
/I
0
0
0.05
0.15
0.20
Q (1)1
Q (0)1
a
b
c
0.10
Fig. 1. Infrared absorption spectra in the 4140–4160 cm
–1
re-
gion recorded at 1.9 K for as-deposited neat p-H2 crystals with
o-H2 concentrations as follows: 100 ppm (a), 1000 ppm (b),
5200 ppm (c). The o-H2 Q1(1) and o-H2 impurity-induced
Q1(0) absorption features are labeled accordingly.
well-known and at these low o-H2 concentrations this
peak does not significantly mask the Rg atom-induced
Q1(0) feature.
A series of spectra in the Q1(0) region are shown in
Fig. 2 for p-H2 crystals doped with different Rg atoms.
The spectrum shown in trace (a) of Fig. 2 is for a
2.8(1) mm thick neat p-H2 crystal, no Rg atom dopant,
and illustrates the small o-H2 impurity-induced Q1(0) ab-
sorption feature that is present in all the spectra due to re-
sidual o-H2. Traces (b)–(e) are recorded at 2 K for as-de-
posited p-H2 samples containing Ne, Ar, Kr, and Xe,
respectively. Note that attempts to observe the He
atom-induced Q1(0) absorption were unsuccessful, even
for samples deposited with relatively high He gas flow
rates. Possible reasons for the lack of a He induced Q1(0)
feature could be the inability of the p-H2 crystals to trap
sufficient concentrations of He atoms and/or that the He
induced Q1(0) feature is extremely weak and below cur-
rent detection limits.
Examination of Fig. 2 illustrates the trend that the Rg
atom-induced Q1(0) absorption feature shifts to lower en-
ergy and narrows going from Ar to Kr to Xe. Note that the
Ne induced Q1(0) feature does not follow this trend, with
almost no induced signal except for a sharp absorption
feature right at the blue edge of the o-H2 impurity-in-
duced Q1(0) feature. The spectra shown in Fig. 2 were re-
corded for Rg atom concentrations ranging from 260 to
1300 ppm. To make comparison with solid p-H2 literature
values [27,33,34], integrated absorption coefficients (~�)
for the experimental decadic absorption spectra recorded
as a function of wavenumber are determined using the
equation,
~ .
~ lg ~�
�
��
� �
�
�
�
�
2 303 0c
N d
I
I
d
Rg
band
(1)
in which c is the speed of light, NRg is the number density
of Rg atoms (atoms cm
–3
), d is the optical path length of
the sample, and � �~� is the centroid of the absorption
band. The number density of Rg atoms is calculated using
the fractional dopant concentration and the number
density [4] of solid p-H2 at lHe temperatures (Np–H2
=
= 2.601·10
22
molecules·cm
–3
). The frequencies of the
peak maxima, the full width at half maximum (FWHM),
and the integrated absorption coefficients for these Rg
atom-induced Q1(0) features are given in Table 1.
Table 1. Measured Rg atom-induced Q1(0) transition frequency,
FWHM, centroid frequency, and integrated absorption coefficient
Rg ���max
cm–1
FWHM ,
cm–1
� �~�
cm–1
~� ,
cm3· s–1*
Ne 4153.20(1) 0.03(1) 4153.20(1) 1(2)·10–15
Ar 4151.6(1) 2.0(1) 4151.6(1) 5.1(4)·10–14
Kr 4150.5(1) 1.1(1) 4150.8(1) 1.0(1)·10–13
Xe 4149.82(1) 0.11(1) 4149.9(1) 1.7(2)·10–13
Notes: * reported uncertainties represent estimated statistical errors only
The Rg atom-induced Q1(0) spectra show no discern-
able temperature dependence over the 1.9 K to 4.5 K tem-
perature range studied. In addition, annealing the as-de-
posited samples at 4.3 K for ~1 hour had little if any effect
on the Rg atom-induced Q1(0) absorption features. Fi-
gure 3 shows the effects of annealing a 440 ppm Kr doped
p-H2 solid. Sharp features at 4149.02, 4149.61, and
4149.72 cm
–1
grow in upon annealing, indicating they
may be due to the presence of Kr atom dimers or clusters.
The main conclusion, however, is the Rg atom-induced
Q1(0) absorption lineshape is not temperature dependent
and shows little change upon annealing.
Discussion
The lineshape of the Rg atom-induced Q1(0) feature
can be modeled with a tight-binding-like Hamiltonian in
which nearest-neighbor p-H2 molecules are coupled by
off diagonal matrix elements that represent the «hopping»
of the vibrational excitation from one molecule to the
next [19,35]. The Hamiltonian can be written as
� | | | |
,
H E k k k nk
k nk
� �� � ���� � , (2)
656 Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7
P.L. Raston and D.T. Anderson
4140 4145 4150 4155 4160
0
0.04
0.08
0.12
0.16
a
b
c
d
e
Wavenumber, cm
–1
lg
(
)
I
/I
0
Fig. 2. Infrared absorption spectra in the 4140–4160 cm
–1
region displaying the Rg atom-induced Q1(0) absorption
features. All spectra are for as-deposited samples recorded at
2 K. Trace (a) is for a 2.8(1) mm thick neat p-H2 solid
containing ~100 ppm of o-H2. The other spectra are Rg atom
doped samples with thicknesses and Rg atom concentrations
as follows: 2.8(1) mm, 1000 ppm Ne (b), 1.8(1) mm, 1300 ppm
Ar (c), 1.6(1) mm, 790 ppm Kr (d), and 2.5(1) mm, 260 ppm
Xe (e).
where Ek is the Q1(0) transition energy for vibrational ex-
citation localized on molecule k and � represents the vi-
brational coupling between nearest-neighbor molecules.
Intermolecular interactions in the solid [16] reduce Ek
from its gas-phase value of Ek = 4161.1 cm
–1
to Ek =
= 4152.2 cm
–1
. The vibron hopping parameter � has been
determined from experiment [29,36] and theory [15,30]
to be � = –0.25 cm
–1
. The sign of the vibron coupling pa-
rameter indicates the out-of-phase (antisymmetric) com-
bination of vibrational states is higher in energy than the
in-phase (symmetric) combination. Since the equilibrium
intermolecular distance [4] in the crystal (3.783 �) is
much larger than the equilibrium distance [37] of the
intermolecular pair potential (3.41 �), molecules sense
mostly the attractive part of the intermolecular potential
due to the 1/R
6
dispersion term and thus the vibrational
coupling depends primarily on the intramolecular stretch-
ing dependence of the C6 dispersion coefficient [38].
In the Rg atom doped p-H2 crystal, the Q1(0) transition
energy Ek for p-H2 molecules that are nearest-neighbors
of the Rg atom will differ from p-H2 molecules distant
from the Rg atom. In model studies conducted by Hinde
[19], this perturbation of Ek caused by the presence of the
Rg atom dopants was taken into account by introducing a
parameter �E that quantifies the shift in the Q1(0) transi-
tion energy for p-H2 molecules that are nearest-neighbors
to the Rg atom. In the calculations, Ek = 4152.2 cm
–1
– �E
for nearest-neighbors, while Ek remains 4152.2 cm
–1
for
all other p-H2 molecules. The doped p-H2 crystal is
treated as a random close-packed solid consisting of a
randomly chosen sequence of close-packed planes of
p-H2 molecules. Hinde then studied how the line profile
of the dopant-induced Q1(0) vibron band depends on the
detuning parameter �E. At low values of �E, the dop-
ant-induced Q1(0) absorption feature shows substantial
IR intensity over the entire vibron band ranging from
4149.5 to 4153.1 cm
–1
. As �E increases, the dopant-in-
duced absorption feature shifts to the red and sharpens
(see Fig. 2 in Ref. 19).
The �E dependence of the lineshape predicted by the
calculations of Hinde reproduces the general trend ob-
served experimentally for Ar, Kr, and Xe. Based upon
measurements of the vibrational shifts of the Q1(0) transi-
tion in the isolated gas-phase van der Waals dimers
(Rg–p-H2) [39,40], one can roughly estimate the value of
the �E parameter in the p-H2 solid. The vibrational shifts,
�� = �gas��
vdw, for the Rg–p-H2 van der Waals dimers
are reproduced in Table 2 and can be used as estimates of
the �E values; that is, �E equals 1.09, 1.63, and 2.51 cm
–1
for Ar, Kr, and Xe, respectively. Comparison of Fig. 2 in
Ref. 19 with the experimental spectra in Fig. 2 illustrates
that the calculated lineshapes for �E parameters equal to
1, 1.5 and 2 cm
–1
nearly quantitatively reproduce the ex-
perimentally measured lineshapes and shifts for Ar, Kr,
and Xe. However, the van der Waals dimer Q1(0) red-
shifts can not be directly equated with the �E parameter,
because the vibrationally averaged distance between the
Rg atom and p-H2 molecule in the isolated van der Waals
dimer (see Table 2) will most likely differ from the aver-
age separation in the p-H2 solid. While �E was used as an
adjustable parameter in the published work by Hinde, cur-
rently these researchers are trying to calculate �E directly
using path integral Monte Carlo simulations and ab initio
calculations of the interaction-induced dipole moment
[41,42].
The evolution in the lineshape of the Rg atom-induced
Q1(0) feature going from Ar to Kr to Xe reflects a transi-
tion from a delocalized IR-active vibron for Ar to a
strongly localized IR-active vibron for Xe. As the magni-
tude of �E increases, it becomes more difficult for a vi-
brational excitation localized in the dopant’s first solva-
tion shell to hop to the next solvation shell and move
away from the dopant. Thus, as the interaction with the
Rg dopant shifts the vibrational frequency of the p-H2
molecules in the first solvation shell to lower energies,
these p-H2 molecules become effectively decoupled from
the bulk and the transition sharpens. Furthermore, the
Infrared-active vibron bands associated with rare gas atom dopants isolated in solid parahydrogen
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7 657
Table 2. The vibrational shifts of the Q1(0) transition for the iso-
lated Rg–p-H2 van der Waals dimer (Ref. 40). The intermolecular
spacing R0 determined from analysis of the rotational B constant
are also reported (Ref. 40)
Rg ����gas��
vdw , cm–1 R0 , �
Ne 0.02 3.99
Ar 1.09 3.94
Kr 1.63 4.07
Xe 2.51 4.25
4145 4147 4149 4151 4153 4155
0
0.005
0.010
0.015
0.020
0.025
a
b
Wavenumber, cm
–1
lg
(
)
I
/I
0
Fig. 3. Infrared absorption spectra in the 4145–4155 cm
–1
re-
gion of a 1.6(1) mm thick, 440 ppm Kr doped p-H2 solid.
Trace (a) is the as-deposited sample recorded at 2.1 K and
trace (b) is the annealed sample recorded at 2 K.
short-range nature of the overlap induction mechanism
only activates p-H2 molecules in the first solvation shell
of the Rg atom. Thus, the picture that emerges for the Xe
atom-induced Q1(0) vibron is a v = 1 excitation
delocalized on the first solvation shell of the Xe atom, but
trapped around the Xe atom with negligible amplitude on
non-nearest neighbors. In contrast, the vibron induced by
the Ar atom remains delocalized, with significant vibra-
tional amplitude on non-nearest neighbor p-H2 mole-
cules.
A comparison of Hinde’s lineshape calculations with
the spectra in Fig. 2 also supports overlap induction as the
operative induction mechanism. In the case of the o-H2
dopant, both quadrupole and overlap induction mecha-
nisms are operative, however quadrupole induction tends
to dominate at the relatively large nearest-neighbor spac-
ing of the solid and therefore masks the effects of overlap
induction. Quadrupole induction is anisotropic and falls
off as 1/R
4
, while overlap induction is isotropic and falls
off as exp (–R/R0). Both induction mechanisms generate
net transition dipole moments through sums of pairwise
induction and thus can suffer from cancellation effects. In
the high symmetry hcp environment of the solid, the iso-
tropic overlap induction mechanism relies on the symme-
try breaking due to the presence of the Rg atom to gener-
ate net transition dipole moments that differ from zero
since the induction mechanism is isotropic. Thus, the
lineshape of the Rg atom-induced Q1(0) feature is qualita-
tively different from the o-H2 induced Q1(0) feature.
As discussed in the results section, the Ne induced
Q1(0) lineshape does not follow the trend measured for
Ar, Kr, and Xe. If Ne did follow the trend, one would
expect a lineshape reminiscent of the Ar induced Q1(0)
feature since the detuning parameter �E for Ne would be
expected to be even smaller. While the Q1(0) absorption
induced by Ne is very weak, we assign the sharp feature at
the blue edge of the residual o-H2 induced Q1(0) feature
to Ne. Unlike Ar, Kr and Xe, the shallow attractive well of
the Ne–H2 intermolecular potential is comparable in mag-
nitude to the H2–H2 intermolecular potential well. The
corresponding Rg–H2 isotropic pair potentials [43,44] for
all the rare gases are plotted in Fig. 4. The Ar, Kr, and Xe
potentials all have significantly deeper wells compared to
the isotropic H2–H2 pair potential determined by Silvera
and Goldman [37] with equilibrium separation rm =
= 3.41 � and well depth � = 23.8 cm
–1
. Therefore, we sur-
mise that replacing one of the nearest-neighbor p-H2 mol-
ecules of a central p-H2 molecule with an Ar, Kr, or Xe
atom results in a redshift of that p-H2 molecule’s vibra-
tional frequency. However, since the Ne–H2 and H2–H2
potentials are very similar with near identical equilibrium
distances and well depths, it seems that replacing one of
the nearest-neighbors of a central p-H2 molecule with Ne
results in a net blue shift of the H2 vibrational frequency.
We speculate based on examination of the intermolecular
potentials that unlike the other Rg atoms, Ne shifts the
transition frequency of adjacent p-H2 molecules to higher
energies instead of lower relative to the pure p-H2 solid
vibron band. It would therefore be interesting to model
this transition by using a negative �E value in Eq. (2) to
see if the lineshape calculations reproduce the sharp Ne
induced Q1(0) absorption feature shown in Fig. 2.
The other experimental observable measured in these
studies is the integrated absorption strengths of the Rg
atom-induced Q1(0) absorption features. Overlap induc-
tion relies on the overlap of the charge clouds of the Rg
atom and p-H2 molecule. Overlap induction involves both
exchange and charge deformation terms [17]. Van
Kranendonk has shown that the magnitude of the induced
dipole moment when a vibrating-translating H2 interacts
with a impurity atom may be approximated empirically by
the relation �ind = � exp (–R/�), where � and � are param-
eters that represent the strength and range, respectively,
of the short-range induced moment [17]. The integrated
absorption strengths depend on the separation (R) be-
tween the p-H2 molecule and Rg atom sampled in the
solid at liquid helium temperatures, and on the strength of
the interaction as measured for example by the well depth
of the intermolecular potential. Thus, the integrated ab-
sorption strengths are strongly correlated to both the well
depth and equilibrium separation of the Rg–p-H2
intermolecular potential.
The greatest Rg atom-induced Q1(0) integrated ab-
sorption strength measured in this study for Xe is more
than an order of magnitude greater than the absorption
strength for the o-H2 impurity-induced Q1(0) feature. The
integrated absorption coefficient per single ortho-mole-
658 Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7
P.L. Raston and D.T. Anderson
3 4 5 6
–75
–50
–25
0
25
50
75
He
Ne
Ar
Kr
Xe
V
,
cm
–
1
R, �
Fig. 4. Plots of the isotropic Rg–H2 pair potentials for He, Ne,
Ar, Kr, and Xe. Note the Ne–H2 potential has a significantly
shallower well than Ar, Kr, or Xe. The Ne, Ar, Kr, and Xe po-
tentials are reproduced using parameters in Ref. 44 and the He
potential from Ref. 43.
cule per unit volume is measured [27] by Gush et al. to be
2.2·10
–14
cm
3
·s
–1
. Thus, the Rg atom-induced Q1(0) fea-
tures for Ar, Kr, and Xe all have greater absorption coeffi-
cients than the o-H2 impurity-induced Q1(0) feature and
can be used to quantify the concentration of Rg atom
down to approximately the 50 ppm level using infrared
absorption spectroscopy. Theoretical modeling of the in-
duced intensities can also be used to estimate <R>, the av-
erage value of the separation of the Rg atom and the first
solvation shell sampled in the solid, and thus by iterating
between experiment and simulation one may be able to
gain insight into how the heavy Rg atom perturbs the
zero-point motion of the p-H2 crystal.
Conclusions
In this paper we have presented IR spectroscopic stud-
ies of Rg atom impurity-induced Q1(0) fundamental vi-
brational transitions for solid p-H2 doped with Ne, Ar, Kr,
and Xe impurities. The impurities induce IR activity
through short-range overlap induction interactions. The
general trend in lineshape measured for Ar, Kr, and Xe are
well reproduced by the calculations of Hinde [19]. The Ar
induced Q1(0) vibron is a loosely bound IR-active vibron
with a broad lineshape while in contrast the Xe induced
Q1(0) vibron is tightly bound to the first solvation shell,
evident by the relatively sharp induced band. The
lineshape of the Ne atom-induced Q1(0) feature does not
follow the trend established for Ar, Kr and Xe and we
speculate that this difference is due to the subtle balance
between Ne–H2 and H2–H2 intermolecular interactions
within the solid. In contrast to Ar, Kr and Xe which
redshift the vibron band, doping with Ne results in a blue
shift of the vibron energy compared to the pure solid’s
vibron band. Interestingly, Hinde’s model calculations do
not predict an induced feature similar to the one measured
for Ne, and we believe this may be due to the fact that
Hinde did not consider blue-shifted vibrons in the pub-
lished work [19]. It is hoped that the spectroscopic data
presented here will motivate further theoretical studies so
that the information about the Rg–H2 pair distribution
function encoded in these spectroscopic data may be dis-
cerned and quantified. Understanding how the heavy Rg
atom perturbs the large amplitude zero-point motion of a
quantum solid is of general interest in many-body quan-
tum mechanics.
This work was funded in part by a grant from the Pe-
troleum Research Fund, administered by the American
Chemical Society, an award from the Research Corpora-
tion, and by a grant from the Chemistry Division of the
National Science Foundation (Grant No. CHE-0316268).
The authors would like to thank Dr. M.E. Fajardo for
making his IR spectral data available to us and acknowl-
edge helpful discussions throughout the course of this
work with Prof. R.J. Hinde.
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