Solvation of atomic fluorine in bulk superfluid ⁴He
Bosonic density functional theory calculations were carried out for fluorine atom solvated in superfluid ⁴He with an emphasis on the formation of dimeric species in the liquid. Atomic fluorine displays a relatively strong binding and anisotropic interaction with helium and hence the resulting solvat...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1185682017-05-31T03:08:15Z Solvation of atomic fluorine in bulk superfluid ⁴He Eloranta, J. 8th International Conference on Cryocrystals and Quantum Crystals Bosonic density functional theory calculations were carried out for fluorine atom solvated in superfluid ⁴He with an emphasis on the formation of dimeric species in the liquid. Atomic fluorine displays a relatively strong binding and anisotropic interaction with helium and hence the resulting solvation structure contains highly localized liquid helium layers. These solvent layers modify the gas phase dimer potentials by inclusion of a recombination barrier, which provides stabilization for the solvated fluorine atoms. At 0 K and saturated vapor pressure, the recombination barrier for the formation of molecular fluorine (²Σ⁺g) in superfluid helium is predicted to be 26.8 K. At temperatures below 1 K, this barrier prevents the F–F recombination as all the other electronic states correlating with the ground state atoms are essentially repulsive. It is concluded that it should be possible to stabilize fluorine atoms in superfluid helium below 1 K temperatures. 2011 Article Solvation of atomic fluorine in bulk superfluid ⁴He / J. Eloranta // Физика низких температур. — 2011. — Т. 37, № 5. — С. 491–493. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 36.40.Mr, 67.25.D– http://dspace.nbuv.gov.ua/handle/123456789/118568 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Eloranta, J. Solvation of atomic fluorine in bulk superfluid ⁴He Физика низких температур |
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Bosonic density functional theory calculations were carried out for fluorine atom solvated in superfluid ⁴He with an emphasis on the formation of dimeric species in the liquid. Atomic fluorine displays a relatively strong binding and anisotropic interaction with helium and hence the resulting solvation structure contains highly localized liquid helium layers. These solvent layers modify the gas phase dimer potentials by inclusion of a recombination barrier, which provides stabilization for the solvated fluorine atoms. At 0 K and saturated vapor pressure, the recombination barrier for the formation of molecular fluorine (²Σ⁺g) in superfluid helium is predicted to be 26.8 K. At temperatures below 1 K, this barrier prevents the F–F recombination as all the other electronic states correlating with the ground state atoms are essentially repulsive. It is concluded that it should be possible to stabilize fluorine atoms in superfluid helium below 1 K temperatures. |
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Article |
| author |
Eloranta, J. |
| author_facet |
Eloranta, J. |
| author_sort |
Eloranta, J. |
| title |
Solvation of atomic fluorine in bulk superfluid ⁴He |
| title_short |
Solvation of atomic fluorine in bulk superfluid ⁴He |
| title_full |
Solvation of atomic fluorine in bulk superfluid ⁴He |
| title_fullStr |
Solvation of atomic fluorine in bulk superfluid ⁴He |
| title_full_unstemmed |
Solvation of atomic fluorine in bulk superfluid ⁴He |
| title_sort |
solvation of atomic fluorine in bulk superfluid ⁴he |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| topic_facet |
8th International Conference on Cryocrystals and Quantum Crystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118568 |
| citation_txt |
Solvation of atomic fluorine in bulk superfluid ⁴He / J. Eloranta // Физика низких температур. — 2011. — Т. 37, № 5. — С. 491–493. — Бібліогр.: 18 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT elorantaj solvationofatomicfluorineinbulksuperfluid4he |
| first_indexed |
2025-07-08T14:15:10Z |
| last_indexed |
2025-07-08T14:15:10Z |
| _version_ |
1837088492282183680 |
| fulltext |
© J. Eloranta, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 491–493
Solvation of atomic fluorine in bulk superfluid 4He
J. Eloranta
Department of Chemistry and Biochemistry, California State University, Northridge
18111 Nordhoff St., Northridge, CA 91330, USA
E-mail: Jussi.Eloranta@csun.edu
Received December 1, 2010
Bosonic density functional theory calculations were carried out for fluorine atom solvated in superfluid 4He
with an emphasis on the formation of dimeric species in the liquid. Atomic fluorine displays a relatively strong
binding and anisotropic interaction with helium and hence the resulting solvation structure contains highly loca-
lized liquid helium layers. These solvent layers modify the gas phase dimer potentials by inclusion of a recombi-
nation barrier, which provides stabilization for the solvated fluorine atoms. At 0 K and saturated vapor pressure,
the recombination barrier for the formation of molecular fluorine ( 2
g
+Σ ) in superfluid helium is predicted to be
26.8 K. At temperatures below 1 K, this barrier prevents the F–F recombination as all the other electronic states
correlating with the ground state atoms are essentially repulsive. It is concluded that it should be possible to sta-
bilize fluorine atoms in superfluid helium below 1 K temperatures.
PACS: 36.40.Mr Spectroscopy and geometrical structure of clusters;
67.25.D– Superfluid phase.
Keywords: bulk superfluid helium, fluorine, quantum gel, solvation.
1. Introduction
Solvation of atomic and molecular impurities in bulk
superfluid 4He has been a subject to a number of experi-
mental and theoretical studies [1–5]. On the experimental
side absorption and fluorescence spectroscopy of solvated
atoms have provided detailed information about the solvent
structure surrounding the atomic impurities. Depending on
the characteristics of the impurity–helium interaction, the
resulting solvation structures can be classified according to
two different ideal limits. The “bubble” structure is ob-
served for impurities with mostly repulsive interaction with
helium (e.g., alkali metal atoms) whereas the “snowball”
structure forms around impurities exhibiting strongly
bound potentials towards helium (e.g., ions). The strongly
bound helium layer around the latter impurities often exhi-
bits helium densities that approach the solid helium densi-
ty. It was shown recently that such high-density solvent
layers around atomic impurities may have important impli-
cations for the impurity recombination processes in the
liquid [6]. As two impurities surrounded by high-density
helium approach each other in the liquid, the gas phase
interaction potential is altered mainly due to the repulsive
interaction between the solvent layers on the two different
centers. This effect was observed experimentally for the
first time for doubly doped Mg containing helium droplets
[7]. A theoretical investigation employing the bosonic den-
sity functional theory later confirmed the interpretation of
the experimental results [8]. In bulk superfluid helium ex-
periments, it is possible to accumulate a large number of
impurity centers in the sample, which may then lead to the
formation of macroscopic size quantum gel-type structures
[6]. It has been established that this type of structures are
not related to the well-known impurity helium solids dis-
covered by Gordon et al. [6,9,10]. Up to date no experi-
mental observation of such quantum gel formation in the
bulk has been published in the literature. To further eluci-
date the possible formation of quantum gel structures in the
bulk, this study explores the solvation of fluorine atoms in
bulk superfluid helium and provides estimates for the sol-
vent layer induced energy barrier for F–F molecular re-
combination.
2. Theory
The applied density functional theory (DFT) to model
bulk superfluid 4He and the numerical implementation has
been described previously [11–14]. The ground state solu-
tion was obtained by the imaginary time propagation me-
thod using variable time steps to speed up the convergence.
The DFT model also included the high density corrections
[12] to properly account for liquid localization in the
bound parts of the fluorine–helium potential. For calcula-
tions at nonzero temperatures, the thermal DFT approach
of Toigo et al. was used [15]. All calculations employed
J. Eloranta
492 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
pair potentials based on the published ab initio data [16–
18]. Since the calculations were carried out in a finite 3D
box, the number of helium atoms varied slightly depending
on the positions of the fluorine atoms and the surrounding
solvent layers. This was accounted for by normalizing the
system to a constant number of helium atoms and then
correcting the total energy appropriately. The zero-point
spread for the solvated fluorine was included in the calcu-
lation by first optimizing its nuclear wavefunction along-
side with the superfluid helium. The resulting fluorine
atom density was nearly Gaussian with a full width at half
height of 1.05 Bohr. In the subsequent calculations with
multiple fluorine atoms their nuclear wavefunctions were
kept fixed during the imaginary time propagation as the
atomic centers are located far away from each other ensur-
ing a minimal overlap between the nuclear wavefunctions.
3. Results and discussion
The formation of molecular fluorine in superfluid he-
lium presents an interesting system because the atomic
fluorine has a 2P ground state and as such it exhibits an
anisotropic interaction with the surrounding helium. Sub-
sequently the dynamic Jahn–Teller effect should lead to a
nonspherical solvation structure. It was recently discovered
that the F2 2
g
+Σ ground state potential has an unusual
hump around 7.3 Bohr with an approximate height of 12 K
in the gas phase [17,18]. When this molecular recombina-
tion barrier is augmented with the solvent layer induced
barrier, the effect becomes even more pronounced as de-
monstrated in Fig. 1. In superfluid helium ( < 2.17T K), a
barrier of 26.8 K is significant and should hinder thermally
induced recombination of fluorine atoms towards F2
2( )g
+Σ . Note that all the other states correlating with the
ground state atoms are essentially repulsive and therefore
only the ground state could lead to the formation of chemi-
cally bound F2.
By using the thermal DFT model, the effect of tempera-
ture on the solvent induced recombination barrier was cal-
culated. However, since the liquid structure is dominated
by the fluorine–helium pair potential, the thermal effects
up to 3 K were found to be very small (less than 3 K). On
the other hand, the effect of increased pressure is more
pronounced as the higher liquid density strongly amplifies
the structure of the bound solvent layers and consequently
the solvent layer induced recombination barrier becomes
higher (see Fig. 2). At bulk liquid densities higher than
02.5ρ , where 0ρ is the superfluid helium density at 0 K
(0.0218360 Å–3), a strongly inhomogeneous solid helium
structure forms around the fluorine atoms. Due to the li-
mited size of the simulation cube, it was not possible to
study this region in detail at present. Ideally the atomic
mobility would be greatly diminished in the limit of solid
helium.
To understand the dynamics of thermal diffusion in-
duced recombination of fluorine atoms in superfluid he-
lium better, it is instructive to provide estimates for the
second order rate constant for this process (i.e.,
[ ] [ ]22F / = Fd dt k− where [ ]F is the fluorine atom con-
centration and 2k is the 2nd order recombination rate con-
stant). For reactive collisions, this can be estimated from
( )2 = * 8 / exp /A ak kT N E RTσ πμ − where *σ is the re-
active cross-section (estimate 23·10−≈ m2 with a reactive
diameter of 3 Å and a steric factor of 1/9), k is the
Boltzmann constant, μ is the fluorine atomic mass, AN is
the Avogadro's constant, aE is the solvent layer barrier
height, and R is the gas constant. Under saturated vapor
pressure conditions, the resulting temperature dependency
for 2k is shown in Fig. 3. After the temperature exceeds
the lambda point, the exponential term leads to a rapid in-
crease in 2k as temperature increases. The fluorine atom
Fig. 1. F–F recombination potential in superfluid helium (1
g
+Σ ).
5 10 15
F–F distance, Bohr
–40
–20
0
20
E
,
K
Erc = 26.8 K
20
Fig. 2. F–F recombination potential barrier height as a function of
bulk liquid density. 0ρ represents the bulk liquid density at 0 K
(see text).
0.5 1.0 1.5 2.0 2.5
20
25
30
35
40
ρ0
B
ar
ri
er
h
ei
g
h
t,
K
Solvation of atomic fluorine in bulk superfluid 4He
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 493
concentration as a function of time at selected temperatures
are plotted in Fig. 4. Below approximately 1 K tempera-
ture, the recombination kinetics is very slow allowing for
fluorine atom buildup in bulk superfluid helium.
4. Conclusions
The present DFT calculations predict that the F–F mo-
lecular recombination barrier is sufficiently high so that
isolated fluorine atoms can be stabilized in bulk superfluid
helium below 1 K temperature.
Financial support from the National Science Foundation
grant CHE-0949057 is gratefully acknowledged.
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Fig. 3. Temperature dependence of the 2nd order recombination
rate constant 2k predicted by collision theory.
0
0.5
1.0
1.5
2.0
T, K
1 2 3 4
k
2
,
1
0
d
m
/(
m
o
l·
s)
6
3
Fig. 4. Concentration of fluorine atoms [ ]F as a function of time
at selected temperatures. The atoms are stabilized below 1 K
temperature.
0
0.2
0.4
0.6
0.8
1.0
2 4 6 8
0.4 K
0.6 K
0.8 K
1.0 K
1.2 K
[F
]
,
m
o
l/
d
m
3
Time, 10 s
3
10
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