Reversible hydrogen storage capacity of vanadium decorated small boron

Computational and Theoretical Chemistry 1217 (2022) 113899
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Computational and Theoretical Chemistry
journal homepage: www.elsevier.com/locate/comptc
Reversible hydrogen storage capacity of vanadium decorated small boron
clusters (BnV2, n = 6–10): A dispersion corrected density functional study
Shakti S Ray , Rakesh K Sahoo , Sridhar Sahu *
Computational Material Research Laboratory, Department of Physics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
A R T I C L E I N F O
A B S T R A C T
Keywords:
Hydrogen storage
Boron clusters
DFT calculation
QTAIM
ADMP-MD simulation
We present our theoretical investigation on hydrogen storage capacity of vanadium decorated small boron
clusters (BnV2, n = 6–10) employing dispersion-corrected density functional theory. Stabilities of the clusters
during H2 adsorption are confirmed from the global reactivity parameters. BnV2 clusters are found to adsorb up to
ten H2 molecules in quasi-molecular form via Kubas-Niu-Rao-Jena kind of interactions with average adsorption
energy in the range of 0.17–0.26 eV/H2. ADMP molecular dynamics simulation reveals the thermal stability,
structural integrity and reversibility of BnV2, n = 6–10 at room temperature (300 K). The maximum practical
hydrogen storage capacity at temperature up to 80 K and pressure ranges of 1–60 bar are found to store up to
8.75–10.78 wt% which is well above the target set by US-DOE (5.5 wt% by 2025). The results obtained from our
investigations assure the potential of vanadium decorated small boron clusters for reversible hydrogen storage.
1. Introduction
temperature of –40 to 80 ◦ C etc. [10–13].
In the recent past, nanostructured materials were studied extensively
for solid-state hydrogen storage purposes in view of their fast reaction
kinetics, stable thermodynamics and catalytic properties. Moreover,
nanostructured materials could adsorb a considerable amount of
hydrogen in molecular form due to their high surface to volume ratio
and the weak dispersive interaction, which would result in easy
desorption of adsorbed H2 molecules [14]. Extensive research work has
been done on carbon-based nanomaterial such as carbon nanotube,
fullerene, metal hydrides, metal–organic framework (MOFs), and co­
valent organic framework (COF) etc. for hydrogen storage purposes, but
none of the said material could meet the US-DOE target [15–19]. More
recently, boron-based clusters isovalent to carbonaceous compounds
received considerable attention for hydrogen storage material due to
their lightweight, catenation and suitable chemical and electronic
properties. Recent studies suggested that the boron cluster decorated
with suitable metal atoms could be a favourable storage medium due to
its higher binding ability, which prevents the clustering of the metal
atom over the host material [20,21]. Wu et al. showed that yttrium (Y)
decorated B80 fullerene could adsorb up to 6.85 wt% of H2 through
Dewar-Kubas interaction [22]. Dong et al. who theoretically predicted
the hydrogen adsorption behaviour of titanium decorated B40 fullerene
and found that the material showed excellent hydrogen binding capa­
bility up to 8.7 wt% with 0.2–0.4 eV/H2 adsorption energy [23].
During the last few decades, adequate use of fossil fuels for industrial
and automotive applications has not only led to their depletion but also
resulted in hazardous impacts on the global ecological system [1–3]. To
deal with the above problem, hydrogen has emerged as one of the major
alternative sources of energy because of its high abunduncy, high spe­
cific energy value and most importantly its carbon-free by-products. In
addition, as compared to the traditional fossil fuel such as gasoline and
diesel the efficiency of hydrogen is much more higher which further
promotes hydrogen as a most promising candidate for the future energy
need [4–8]. However, storage of hydrogen energy for automotive and
industrial applications has been a major hurdle due to the challenging
technology involved with it. Therefore, the major research focus in this
area has been given to successfully develop storage media which show
high gravimetric and volumetric density (5.5 wt% by 2025) and lenient
chemical process under favourable thermodynamic conditions as pro­
posed by the US Department of Energy (US-DOE) [9]. Furthermore,
there are some key parameters which should be maintained while
choosing a potential solid-state hydrogen storage material viz. (i) large
surface area of the host material under ambient conditions (ii) binding
energy should be in the intermediate between physisorption and
chemisorption mechanism (0.1–0.6 eV/H2) (iii) fast adsorption &
desorption kinetics (1.5 kg H2/min) (iv) reversible operation
* Corresponding author.
E-mail address: [email protected] (S. Sahu).
https://doi.org/10.1016/j.comptc.2022.113899
Received 14 June 2022; Received in revised form 9 September 2022; Accepted 26 September 2022
Available online 30 September 2022
2210-271X/© 2022 Elsevier B.V. All rights reserved.
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
Scandium decorated B38 fullerene was studied by Liu et al., who reported
that the B38 cluster could adsorb up to 7.57 wt% of H2 with average
adsorption energy of 0.0224 eV [24]. Juan et al. reported that the cal­
cium decorated B36 showed potential hydrogen adsorption up to 4.97 wt
% through an induced charge polarisation mechanism [25]. Moreover,
other researchers have also widely reported numerous theoretical
studies related to hydrogen adsorption in metal decorated boron clusters
[25–29].
Besides, metal decorated small and medium-sized boron clusters (n
< 20) have also shown better hydrogen storage capacity under ambient
conditions than the larger boron clusters [30–33]. For instance, Ojha
et al. predicted the hydrogen adsorption capacity of magnesium (Mg)
decorated boron clusters and reported that there existed a closed shell
type of interaction between Mg and H2 molecules, resulting in adsorp­
tion of 8.10 wt% of H2 molecules with an average adsorption energy
range of 0.13–0.22 eV/H2 at ambient temperature and pressure [34].
Zhai et al. reported the hydrogen storage capacity of inverse sandwich
like B6Ca2 and B8Ca2 clusters by performing Born-Oppenheimer mo­
lecular dynamics simulation and found that the these clusters could
reversibly store and release maximum up to 14.2 wt% of H2 molecules
with 0.13–0.15 eV/H2 adsorption energy at room temperature by
satisfying the US DOE targets [35]. A similar kind of investigation was
also done on the aromatic Ca2B8 complex by Du et al., and the results
showed that 10.6 wt% of molecular hydrogen could be adsorbed on the
complex (77 K), which could be efficiently released at ambient tem­
perature (300 K) as confirmed by ab initio molecular dynamics simu­
lations [36]. The hydrogen adsorption capacity of titanium (Ti)
decorated B8 clusters was theoretically investigated by Liu et al., who
reported up to 6 wt% of molecular hydrogen could be adsorbed on the
complex with 0.24–0.35 eV/H2 of adsorption energy via Dewar-Kubas
effects [37]. In our previous investigation, we reported the hydrogen
adsorbing properties of scandium decorated small boron clusters
employing molecular dynamics simulations, and we found that KubasNiu interaction attributed for adsorption of 9.43 wt% of H2 molecules
with moderate average adsorption energy in the range 0.08–0.10 eV/H2
satisfying the US-DOE target for room temperature adsorption [38].
Wang et al. theoretically predicted the H2 adsorption in beryllium
decorated small boron clusters, and they showed that these clusters
could store up to 25 wt% of H2 via Dewar and van der Waals interactions
with 0.10–0.50 eV/H2 adsorption energy [39]. However, hydrogen
storage properties of small-sized boron clusters are scarcely reported,
and there exist a considerable amount of small-sized boron clusters yet
to be explored for hydrogen storage. Notwithstanding, experimental
realization of hydrogen storage materials for commercial uses has been a
challenging task for the researchers. Major issues such as poor thermo­
dynamics, metal clustering, desorption at extreme temperatures,
reversibility and high-cost mechanisms are yet to be solved for vehicular
or domestic use of hydrogen energy [1,40–41].
Previously, the electronic properties of the vanadium decorated
small-sized boron clusters have been theoretically predicted. The
structures are reported to be thermodynamically stable and possess bipyramidal geometry [42]. Because vanadium decorated clusters have
been reported earlier to be potential candidates for hydrogen storage,
therefore, in the present work we conducted a theoretical investigation
on the performance of vanadium decorated small boron clusters (BnV2,
n = 6–10) for hydrogen adsorption by employing dispersion corrected
density functional theory [43,44]. Thermal stability, reversibility, and
the desorption mechanism was examined by means of molecular dy­
namics simulation and van’t Hoff’s equation, respectively.
used electronic structure calculation within the framework of density
functional theory (DFT) to explore these properties. The detailed theory
is discussed below.
The conceptual density functional theory (C-DFT) was used to verify
the thermodynamical stability and the reactivity of the optimized ge­
ometries upon calculating the global chemical reactivity descriptors
(GCRDs) i. e hardness (η), and electrophilicity index (ω) [45–52].
Now, the chemical hardness (η) is computed by the ionization po­
tential (I) and electron affinity (A) using Koopmaan’s Theorem [53].
Now, the expression for chemical hardness is,
η=
I− A
2
(1)
Similarly, the electrophilicity index can be expressed as.
ω=
χ2
(2)
2η
χ=
where
I+A
2
Further, the kinetic stabilities of the studied geometries were
confirmed by computing the energy gap (Eg) between their highest
occupied molecular orbitals (HOMOs) and lowest unoccupied molecular
orbitals (LUMOs).
The average adsorption energy (Eads) and sequential desorption en­
ergy (Edes) for all hydrogen adsorbed structures can be defined by the
following equations,
1
Eads = [{EHost + nEH2 } − EHost+nH 2 ]
n
Edes =
1 [{
2EH2 + EHost+(n−
2
}
2)H2
− EHost+nH 2
(3)
]
(4)
Here EHost+nH2, EH2 and EHost are the total electronic energies of hy­
drogenated complex (BnV2-nH2), hydrogen molecule (H2) and host
cluster (BnV2), respectively. The parameter n represents the total num­
ber of hydrogen molecules that are absorbed on the clusters. In addition,
the term EHost+(n− 2)H2 represents the energy of the previous H2 molecule
adsorbed, and n-2 represents two H2 molecules desorbed
simultaneously.
The gravimetric density is an important parameter which quantifies
the capacity of a storage system. The hydrogen storage gravimetric
density can be deduced using the following equation.
H2 (wt%) =
MH2
× 100
MH2 + MHost
(5)
Where MH2 indicates the mass of total number of adsorbed H2 mol­
ecules and MHost indicates the total mass of vanadium decorated boron
clusters (BnV2, n = 6–10).
The number of H2 molecules adsorbed on each vanadium atom of
BnV2 cluster is determined by calculating the occupation number using
the equation [54–56].
]
[
n(μ− Eads )
∑Nmax
kB T
ngn e
]
[
f = n=0
(6)
n(μ− Eads )
∑Nmax
kB T
n=0 gn e
Where Nmax is the maximum binding number of H2 molecules to each
V atom, n is the number of H2 molecules adsorbed, gn is the configura­
tional degeneracy for a given n, kB is the Boltzmann constant, Eads is the
adsorption energy, and μ is the H2 gas-phase chemical potential at a
given T and P obtained using the following equation [57].
( )
P
(7)
μ = H 0 (T) − H 0 (0) − TS0 (T) + kB Tln
P0
2. Computational details
To investigate the characteristics of a potential hydrogen storage
system, essential properties such as stability, energy and storage ca­
pacity of the host cluster are, in general, calculated along with addi­
tional thermodynamical properties to justify its practical usability. We
Here H0, S0 are the enthalpy and entropy of H2 at pressure P0 = 1 bar
obtained from Reference [58].
2
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
Table 1
Average bond lengths between Boron-Boron (dB-B), Boron-Vanadium (dB-V),
Vanadium-Vanadium (dV-V), Vanadium-Hydrogen (dV-H), Hydrogen-Hydrogen
(dH-H) in Å.
Cluster
dB-B (Å)
dB-V (Å)
dV-V (Å)
B6Ti2
B6V2-10H2
B7V2
B7V2-10H2
B8V2
B8V2-10H2
B9V2
B9V2-10H2
B10V2
B10V2-10H2
1.579
1.591
1.547
1.556
1.533
1.533
1.587
1.574
1.604
1.612
2.099
2.112
2.208
2.244
2.309
2.381
2.260
2.284
2.432
2.554
2.768
2.782
2.605
2.703
2.298
2.579
2.560
2.706
2.211
2.634
dV-H (Å)
dH-H (Å)
2.853
0.77
2.731
0.78
2.851
0.78
2.871
0.78
2.970
0.78
[65]. Bader’s Quantum Theory of Atoms in Molecules (QTAIM) was used
to analyse the nature of the interaction between the hydrogen molecules
and sorption centres [66].
Thermodynamics reversibility of adsorbed hydrogen molecules on
the vanadium decorated boron clusters (BnV2, n = 6–10) were deter­
mined by performing molecular dynamics simulation using Atomcentered Density Matrix Propagation (ADMP). The time steps for the
simulation are set to one femtosecond (△t = 1 fs), and the step size has
been specified to a maximum of 1000 steps for each trajectory. The
temperature is maintained for thermostatic simulations by applying the
velocity scaling method during the simulation [67–69]. We used
Gaussian 09 program suit to perform all the DFT calculations [70].
Fig. 1. Optimized geometry of bare and hydrogenated B6V2 cluster (a) B6V2,
(b) B6V2-2H2, (c) B6V2-4H2,(d) B6V2-6H2, (e) B6V2-8H2, and (e) B6V2-10H2.
3. Results & discussion
3.1. Geometry & stability
Generally, the hydrogen adsorption mechanism is governed by noncovalent weak interactions such as van der Waals forces. Therefore to
get a stable geometry and reliable adsorption energy, all the geometries
and frequency calculations were carried out using exchange correla­
tional functional Perdew–Burke-Ernzerhof (PBE) based on generalised
gradient approximation (GGA) and adding Grimme’s dispersion
correction method to density functional theory (DFT-D3) [59–60]. PBED3, which includes empirical dispersion and long-range corrections, has
been proven as a reliable method to study the weak non-covalent
interaction [61–63]. So the bare and hydrogen adsorbed structures
were optimized using the PBE-D3 method along with the standard splitvalence basis set with diffuse and polarization function 6–311++G(d,p)
[64]. The nature of the bonding between the adsorbed hydrogen and the
metal atom are explored by computing the NBO charges on each atom
In order to examine the hydrogen adsorption and storage capacity of
vanadium decorated small boron clusters (BnV2, n-6–10), we reoptimize
the host clusters with reference to the previous report using the density
functional theory (DFT) in conjunction with Grimme’s dispersion
correction and PBE-D3/6–311++G(d,p) basis set to. The results of
optimized geometries are found in good agreement with previous report
[42]. Then hydrogen molecules are sequentially added to host clusters,
and the complexes are re-optimized at the same level of theory.
The stable geometries of hydrogenated B6V2 clusters and BnV2-10H2,
n = 7–10 are illustrated in Figs. 1 and 2 respectively, and the other
optimized hydrogenated complexes are presented in the Figure S1
(Supplementary Information). The calculated geometrical parameters
Fig. 2. Optimized geometry of hydrogenated BnV2 cluster (a) B6V2,-10H2 (b) B7V2-10H2, (c) B8V2-10H2,(d) B9V2-10H2, and (e) B10V2-10H2.
3
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
length is found in the range of 2.58–2.78 Å which is larger than the ionic
radius of V which inhibits any clustering over the complexes. The H2
molecules are found to be adsorbed on the sorption site (V) in the quasimolecular form at an average distance in the range of 2.731 Å-2.970 Å
which is recommended by US-DOE for molecular adsorption. It is
evident form the Table 1 the structures of the host clusters remain almost
undistorted throughout the adsorption process indicating their chemical
stabilities.
Stability and the reactivity of the clusters can also be explained in
terms of conceptual DFT based global chemical reactivity descriptors
(GCRDs) i. e hardness (η) and electrophilicity index (ω). The GCRD pa­
rameters are computed using Equations (1) and (2) and are recorded in
Table 2. For the studied clusters, the hardness values are found to in­
crease while the electrophilicity values decrease upon gradual addition
of H2 molecules. For example, in B6V2 cluster the hardness increases by
15 % upon addition of 10H2 molecules while the value of ω decreases
almost by 11 %. Similarly, hardness of B10V2 increases by 57 % upon
hydrogenation whereas its electrophilicity decreases by 66 %. This im­
plies the chemical stability of the studied clusters following the principle
of maximum hardness (MHP) and minimum electrophilicity principle
Table 2
Calculated hardness (η), electrophilicity index (ω), and HOMO-LUMO energy
gap (Eg) of vanadium doped boron clusters (BnV2, n = 6–10) as well as hydro­
genated clusters.
Cluster
η (eV)
ω (eV)
Eg (eV)
B6V2
B6V2-10H2
B7V2
B7V2-10H2
B8V2
B8V2-10H2
B9V2
B9V2-10H2
B10V2
B10V2-10H2
0.65
0.77
0.56
0.56
0.39
0.37
0.39
0.41
0.17
0.40
10.58
9.39
16.70
18.17
31.54
30.21
27.25
25.69
76.40
25.53
1.31
1.55
1.12
1.12
0.78
0.74
0.79
0.83
0.34
0.81
are shown in Table 1. It is found that maximum of five numbers H2
molecules were adsorbed on each vanadium atom with H–H bond
length in the range of 0.75–0.85 Å, which is slightly elongated as
compared to that of the bare H2 molecule. In addition, the V-V bond
Fig. 3. Average adsorption energy and sequential desorption energies of hydrogenated BnV2, n = 6–10 clusters.
Fig. 4. Partial density of states on V and H atoms of B6V2-nH2 (n-2,10), (a) B6V2-2H2 and (b) B6V2-10H2.
4
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
energy per H2 molecule is found to reduce approximately to 0.04 eV
with a maximum number of H2 adsorption, and with the release of the
H2 molecules, the geometries of the host clusters almost remain intact,
which implies the reversibility of the studied system.
Table 3
Average NBO charges on each atom of BnV2 (n = 6–10) clusters before and after
H2 adsorption.
Cluster
B6V2
B7V2
B8V2
B9V2
B10V2
Before H2 adsorption
After H2 adsorption
Charge on
B
Charge on
V
Charge on
B
Charge on
V
0.10
− 0.06
0.19
0.15
0.11
0.16
0.03
0.06
0.01
0.05
−
−
−
−
−
−
−
−
−
−
0.03
0.05
0.04
0.03
0.02
1.19
0.83
1.12
0.77
1.21
Charge on
H
3.3. Partial density of state (PDOS) analysis
0.06
0.04
0.08
0.04
0.09
Partial density of state (PDOS) plots for vanadium and hydrogen
atoms of hydrogenated B6V2, clusters with firsts and last hydrogen
molecules adsorbed on each vanadium atom are presented in the Fig. 4
and PDOS of other hydrogenated clusters are provided in Figure S3-S6
(Supplementary Information). From PDOS plot it is observed that upon
adsorption of the 1st H2 molecule on each vanadium atom of B6V2, the σ
orbital of the hydrogen molecule overlap with the 3d orbital of V atom at
− 12.6 eV below the Fermi level and the σ * orbital of H2 interacts with
orbital of V above the Fermi level (Fig. 4(a)) indicating Kubas type of
interaction between hydrogen and V atom. According to the Kubas
mechanism, the occupied orbital of the H2 interacts with the vacant 3d
orbital of the V atom and a small charge transfer occurs from H2 mole­
cule with back donation of charge from partially filled 3d orbitals of V
atom to the unfilled σ * orbital of H2 molecules [74,75].
However, with increase in the hydrogen content over each vanadium
atom (5H2) the intensity of the σ orbital increases and move closer to the
Fermi level (Fig. 4b) and splits in to number of intense peaks near − 13.3
eV to − 9 eV implying the interaction getting weaker. This weak inter­
action can be explained through Niu-Rao-Jena mechanism in which
induced dipole develops in the H2 molecule due to the charge polar­
isation [76,77]. Similar kinds of observation were found for all other
studied clusters.
(MEP) [71,72]. In addition to that, the computed HOMO-LUMO energy
gap (Eg) also shows a gradual increase upon addition of the H2 molecules
(Figure. S2) during the adsorption process also indicating the molecular
stability of the complexes.
3.2. Adsorption energy
The energetic of the adsorption process in the studied clusters is
discussed through the average hydrogen adsorption energy and suc­
cessive desorption energies calculated using Equations (3) and (4),
respectively. We add H2 molecules sequentially over the sorption sites of
BnV2 n = 6–10 clusters and find that 10 H2 molecules get adsorbed on
both V atoms of the clusters with an average adsorption energy range of
0.17–0.26 eV/H2, which implies the adsorption process to be phys­
isorptive in nature. The variation of Eads with the number of adsorbed H2
molecules is depicted in Fig. 3. It can be noted that as the number of H2
molecules increases, the value of Eads follows a decreasing trend. For
instance, when two H2 molecules are adsorbed on the B6V2 clusters, Eads
value is computed to be 0.33 eV/H2. When the number of H2 molecules
gradually increases, the Eads value reduces to 0.17 eV/H2 with an
increasing V-H2 distance due to steric hindrance [73].
For practical use of hydrogen storage, delivery of H2 gas necessarily
depends on the efficient desorption of hydrogen molecules. The suc­
cessive desorption energy (Edes) (Fig. 3) is also found to show the same
pattern with the number of H2 molecules as Eads dose. The desorption
3.4. Interactions & bonding mechanism
We calculated the average natural bond orbital (NBO) charges before
and after adsorption to understand the bonding mechanism in the
studied complexes. The average NBO charges on B, V and H atoms are
listed in Table 3. During the adsorption process, about 0.05–0.20 eu of
positive NBO charges are transferred from the V atom to the B atom
resulting in an electric field around the former. This electric field
Fig. 5. Electrostatic potential (ESP) plots of bare and hydrogen adsorbed B6V2 cluster. (a) B6V2, (b) B6V2-2H2, (c) B6V2-4H2, (d) B6V2-6H2,(e) B6V2-8H2, and (f)
B6V2-10H2.
5
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
induces polarization in H2 molecules, causing them to bind to the va­
nadium atom via charge polarization mechanism as proposed by NiuRao-Jena [76,77]. The fact is also supported by the electrostatic po­
tential maps (ESP) analysis discussed below.
The ESP plots for B6V2 and BnV2, n-7–10, and their hydrogen
adsorbed derivatives, are presented in Fig. 5 and Figure S7 (Supple­
mentary Information), respectively. In the ESP map, the red colour at­
tributes to the accumulation of electron density while the blue colour
Table 4
Calculated electron density in (ρ) a.u.and ∇2 ρ in a.u at BCP of (B,V) and (V, H).
Cluster
ρV−
B6V2-10H2
B7V2-10H2
B8V2-10H2
B9V2-10H2
B10V2-10H2
0.0884
0.0719
0.0584
0.0756
0.0718
B
∇2 ρV−
B
0.1206
0.1050
0.0975
0.0893
0.0923
ρV−
H
0.0364
0.0483
0.0618
0.0570
0.0601
∇2 ρV−
H
0.1433
0.2030
0.2497
0.2276
0.2449
Fig. 6. Potential energy trajectories BnV2-10H2, n = 6–10 clusters at 0 K, 77 K, 300 K and TD[max] temperatures respectively.
6
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
attributes to electron density depletion. From Fig. 4, it can be noted that
the region over each vanadium atom is marked by dark blue colour,
signifying the electron depletion region as compared to the boron cluster
as pointed out from the NBO analysis. On adsorption of the first and
second H2 molecules, the colour changes from dark blue to light blue.
This comes about due to the electron density variation at the adsorption
sites leading to the Kubas-type bonding. Upon further adding H2 mole­
cules to the system, we do not observe any significant colour variation
except the ESP of H2 changes from light-blue to bluish-green, which
signifies that these H2 molecules are physisorbed due to the charge
polarization mechanism (Niu-Rao-Jena interaction) [76,77]. A similar
observation is also found for all the other studied clusters.
Further, the nature of interaction between the sorption centre (V
atom) and the adsorbed H2 molecules is characterized by analyzing the
topological parameters from the outcomes of Bader’s quantum theory of
atom in molecules calculation (QTAIM) [66]. The parameters such as
electron density (ρ) and Laplacian of electron density (∇2ρ) at the bond
critical point (BCP) are computed and presented in Table 4. The calcu­
lated value of ρ < 0.20 with a positive value of ∇2ρ at BCP of V-H2
bespeaks a closed shell type (weak non-covalent) interaction between
the metal atom (V) and adsorbed H2 molecule [78–80]. This noncovalent interaction is mainly due to the charge polarization mecha­
nism as confirmed from the NBO charge distribution and ESP analysis.
During the interaction, the interatomic distance of adsorbed H2 mole­
cules is found to be slightly elongated (up to 0.78 Å). However, the
average values of ρ over the H–H in all the hydrogenated clusters are
found to be almost same as that over the H–H in the isolated hydrogen
molecules which implies that the adsorbed hydrogens are in molecular
form (Table S1). The values of ρ and ∇2ρ are found in the range of
0.058–0.088 a.u and 0.089–0.120 a.u, respectively, suggesting all the
studied clusters can bind the H2 molecules via non-covalent interactions.
Table 5
Thermodynamically usable hydrogen capacity. NTheory is the number of adsor­
bed H2 molecules in calculation. Nads and Ndes the number of H2 molecules
adsorbed at (100 K − 60 bar) and desorbed (300 K − 1 bar) respectively. Nuse
(=Nads - Ndes) represents the usable number of H2 molecules. GTheory and
G100k− 60bar represents the theoretical and practical hydrogen wt% at adsorption
conditions respectively.
Cluster
NTheory
Nads
Ndes
Nuse
GTheory
G100K-60bar
B6V2-10H2
B7V2-10H2
B8V2-10H2
B9V2-10H2
B10V2-10H2
10
10
10
10
10
9.07
9.62
6.01
7.92
7.56
0.05
0.83
0.51
1.64
2.59
9.02
8.79
5.50
6.28
4.97
10.78
10.19
9.66
9.19
8.75
9.88
9.84
6.04
7.42
6.76
Equation (6) by employing the empirical value of the chemical potential
of H2 gas. We chose 100 K/60 bar for adsorption and 400 K/3 bar for the
desorption condition for all the clusters to estimate the usable number of
H2 molecules, and the values are presented in Table 5. The variations of
H2 occupation number with a finite range of temperatures and pressures
are shown in Fig. 7. It is observed that the adsorption occurs at high
pressure, whereas the desorption occurs at a lower pressure as the
chemical potential of the H2 gas increases with pressure. Therefore, the
H2 molecules are released at a constant temperature with lower pressure
[46]. It is found that, at a temperature of 80 K and a pressure range of
1–60 bar, all the studied clusters possess 10H2 molecules leading to a
maximum H2 storage capacity of 8.75 wt% − 10.78 wt%, which are well
above the target set by US-DOE (5.5 wt% by 2025). As temperature rises
beyond 80 K, the H2 molecules start desorbing from the host clusters,
and at 400 K in the pressure range of 1–3 bar, almost all the hydrogen
molecules desorbed from the host cluster. At the storage condition (100
K and 60 bar) all the studied cluster shows a gravimetric storage ca­
pacity up 6.76–9.88 wt%. Moreover, we find that the gravimetric stor­
age capacity of all the studied clusters at a temperature and pressure
range of 120 K-160 K and 30–60 bar are closed to the target set by USDOE.
The computed average adsorption energy, average desorption tem­
perature and hydrogen gravimetric density for the studied clusters can
be found suitable for a practical hydrogen storage system. We have also
compared these parameters with the previously reported work on
similar system and the data are presented in the Table 6.
Practical desorption temperature (TD) for vanadium decorated boron
clusters is estimated using the van’t Hoffs equation (Equation (8)) for the
range of pressure (1–5 atm) with an increment of 0.5.
)− 1
(
)(
Eads
ΔS
− lnP
TD =
(8)
R
kB
3.5. Molecular dynamics simulations
We examine the thermal stability and reversibility of the studied
clusters at different thermodynamic conditions for feasible hydrogen
storage using ADMP-molecular dynamics (MD) simulations. The simu­
lation is carried out at four different temperatures i.e 0 K, 77 K, 300 K
and maximum desorption temperature (TD[max]), for 1 ps time scale
employing the velocity scaling method. The variation of potential en­
ergy with time is depicted in Fig. 6 and the snapshots of BnV2-10 H2, n =
6–10 systems at different temperatures are presented in Figure S8-S12
(Supplementary Information).
The MD simulations reveal that at low temperatures (0 & 77 K), the
system can hold almost all the adsorbed H2 molecules. For example, at
77 K, nearly-two H2 molecules move away from the sorption centres
while all others are retained on the surface, resulting in hydrogen uptake
capacity of up to 10 wt%. On the other hand, while we increase the
temperature to 300 K, the hydrogen molecules start desorbing from the
host clusters, and at the end of the simulation, a maximum number of H2
molecules gets desorbed from the host clusters without distorting the
parent clusters. For instance, at 300 K, only three H2 molecules remain
adsorbed to the B6V2 clusters.
To examine the thermal stability of the host clusters, we analyse the
variation of bond distance between the two atoms of the host clusters. In
Figure S13 (Supplementary Information), we depict variations 〈dB − B〉,
〈dB− V〉, and 〈dV− V〉 bond distances at 300 K temperature. It is observed
that the host clusters remain stable with minimal fluctuation in all the
bond distances, which assures the thermal stability and reversibility of
the host clusters during the desorption process.
Where Eads is the calculated H2 adsorption energy, kB is the Boltz­
mann Constant, △S is the change in hydrogen entropy from gas to the
liquid phase. R is the gas constant, and P is the pressure (1 atm).
The variation of desorption temperature with equilibrium pressures
is presented in Fig. 8 and Figure S14 (Supplementary Information),
respectively. It is observed that the average value of TD fall in a range of
319.8 K-582.1 K under standard atmospheric pressure. For all the
studied clusters, the TD[avg] is found to be higher than the room tem­
perature, which implies that H2 molecules do not dissociate at small
thermal fluctuations. It can also be noted that the calculated values of
desorption temperature follow an increasing trend with increasing
pressure. The molecular dynamics simulations also support the
computed results for the practical desorption temperature.
4. Conclusion
3.6. Thermodynamically usable hydrogen storage
This study theoretically predicted the reversible hydrogen storage
capacity of vanadium decorated small boron clusters (BnV2, n = 6–10),
employing dispersion corrected density functional study and molecular
To determine the practical usable hydrogen capacities at ambient
thermodynamic conditions, the occupation number (f) is calculated at
various ranges of temperature and pressure (40–400 K & 1–60 bar) using
7
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
Fig. 7. Occupation number of H2 molecules as a function of the pressure and temperature on hydrogenated BnV2, n = 6–10 clusters.
Table 6
Hydrogen storage par ameters comparison for various nanomaterials.
System
Total
number of
adsorbed
hydrogen
molecule
Average
adsorption
energy per
H2 (eV)
Average
desorption
temperature
(K)
Gravimetric
density(%)
TiBn Clusters
[28]
Mg2Bn, n = 4–14
[34]
B8Ti Cluster [37]
BnSc2, n-3–10
[38]
Mx–B6H6
Complexes (M
= Y − Mo, Ru
− Ag, x = 1–2
[81]
Y + B40 [82]
Sc2–C6H6 [83]
Experimental
Graphene
based Nano
composite
[84]
CNT + Pd [85]
Present work
4
0.31
700 K
6.12
5
0.19
300 K
8.10
6
8
0.24
0.10
300 K
300 K
6.22
9.43
12
0.25
>300 K
8.86
5
8
–
0.21
0.35
–
281
300 K
–
5.8
8.76
>5
10
0.26
300 K
Fig. 8. Variation of desorption temperature with equilibrium pressure for B6V210H2 clusters. The black, red and blue lines represent minimum, average and
maximum temperatures respectively. (For interpretation of the references to
colour in this figure legend, the reader is referred to the web version of
this article.)
6
10.78
Topological analysis revealed the interaction between the host clusters
and vanadium atoms to be weak non-covalent. ADMP-MD simulations
suggested that clusters could adsorb a considerable amount of H2 at low
temperature (77 K), giving rise to storage capacity up to 10 wt% which
was well above the target of US-DOE. At 300 K, most of the hydrogen
molecules got desorbed without distorting the host clusters, implying
their thermal stability and reversibility. The H2 occupation number
dynamics simulations. The stabilities of the hydrogenated clusters were
confirmed by their enhanced chemical hardness and HOMO-LUMO
gaps. The H2 molecules were found to adsorb on BnV2, n = 6–10 via
Kubas-Niu interaction with an average adsorption energy range of
0.17–0.26 eV/H2 inferring the adsorption process to be physisortive and
quasi-molecular. The fact was supported by NBO and ESP analyses.
8
S.S. Ray et al.
Computational and Theoretical Chemistry 1217 (2022) 113899
calculation indicated that, at a temperature of 80 K and a pressure range
of 1–60 bar, all the studied clusters possessed 10H2 molecules leading to
a maximum H2 storage capacity of 8.75 wt% − 10.78 wt%, and at a
temperature and pressure range of 120 K-160 K and 30–60 bar the
storage capacities were close to 5.5 wt%. The average desorption tem­
perature (TD ) of all the studied clusters were found in a range of 319.8 K582.1 K under standard atmospheric pressure. Based on our result, we
can predict that BnV2, n = 6–10 clusters can be considered as promising
candidates for the reversible hydrogen storage medium under ambient
thermodynamic conditions.
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CRediT authorship contribution statement
Shakti S Ray: Conceptualization, Methodology, Software, Valida­
tion, Formal analysis, Investigation, Data curation, Writing – original
draft, Writing – review & editing. Rakesh K Sahoo: Conceptualization,
Investigation, Data curation, Validation. Sridhar Sahu: Conceptualiza­
tion, Resources, Formal analysis, Validation, Supervision, Project
administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgement
We acknowledge the financial support from Science & Engineering
Research Board (SERB), DST, India under grant no. EMR/2014/000141.
The Technical Education Quality Improvement Programme-III, Gov­
ernment of India is also acknowledged for the partial financial support.
The authors also acknowledge the Indian Institute of Technology (Indian
School of Mines), Dhanbad for providing support and other research
facilities.
Appendix A. Supplementary material
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.comptc.2022.113899.
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