# Feasibility of Li decorated Si6C14 and Si8C12 nanocages as promising
hydrogen storage media: A computational study

Ankita Jaiswal  Computational Materials Research Lab, Dept. of Physics, Indian
Institute of Technology (Indian School of Mines) Dhanbad, Jharkhand, 826004,
India  Rakesh K. Sahoo  Department of Physics, Karpagam Academy of Higher
Education, Eachanari, Coimbatore, Tamil Nadu, 641021, India  Department of
Materials Science and Engineering, Technion-Israel Institute of Technology,
Haifa, 3600003, Israel  Sridhar Sahu

###### Abstract

This article presents the reversible hydrogen storage capacities of Li
decorated Si6C14 and Si8C12 using Density Functional Theory (DFT). The
chemical stabilities of the designed Si6C14Li6 and Si8C12Li4 nanocages are
investigated using HOMO-LUMO gaps and various global reactivity descriptors
such as chemical hardness and electrophilicity index. Our study reveals that
each Li atom decorated over the designed Si6C14 and Si8C12 nanocages can hold
up to 5H2 molecules with adsorption energy lying in the optimum range of
0.14-0.085 eV, thereby yielding to an overall gravimetric density of 13.8% and
9.2% respectively. The interaction between adsorbed H2 molecules and the Li
metal sites are found to occur via non-covalent and closed shell type of
interaction. The H2 molecules are adsorbed in quasi-molecular fashion with
elongated bond length. The molecular dynamics study reveals that most of the
H2 molecules get desorbed from the designed host nanocages at 300K without
causing any significant structural changes, which confirmed their
reversibility. When the adsorption and desorption conditions are set at
100K/60bar and 240K/1bar respectively, the practical storage gravimetric
densities of Si6C14Li6 and Si8C12Li4 cages are estimated to be 13.73 wt% and
9.08 wt%, which are relatively high in comparison to the US-DOE target of 5.5
wt% by the year 2020. Hence, the computationally designed Si6C14Li6 and
Si8C12Li4 nanocages can be regarded as prospective systems for hydrogen
storage applications.

##  1 Introduction

The rapid depletion of fossil fuels and associated negative environmental
repercussions, such as pollution and global warming, have heightened interest
in developing alternative energy sources [1, 2]. Hydrogen is widely
acknowledged as the most promising energy carrier because of its abundancy,
maximum mass energy density and clean combustion [3, 4]. In comparison to
gasoline, hydrogen produces at least three times as much chemical energy per
unit mass. But from the standpoint of using hydrogen energy, its storage and
production are the two significant challenges [5]. Hydrogen can be produced
artificially using environmental-friendly processes like water electrolysis,
photocatalysis and thermo-chemical cycles. The main constraint in the
establishment and growth of a hydrogen-centric economy lies in the development
and practical use of hydrogen storage materials capable of storing hydrogen
with a substantial gravimetric and volumetric density. These materials should
also be feasible to implement under conditions close to normal atmospheric
conditions in order to ensure optimal efficiency, safety, reliability, and
cost-effectiveness in transportation systems [6]. According to the target
defined by the United States-Department of Energy (US-DoE), a hydrogen storage
material can be deemed suitable for practical applications if it can achieve
gravimetric density greater than 5.5 wt% by the year 2020. This should be
achievable within an optimal temperature range spanning from -40°C to 85°C,
while also allowing for a maximum delivery pressure of 12 bar [7]. The
conventional hydrogen storage technologies currently in use, which include
storing hydrogen gas compressed under high-pressure ($\sim$700-800 bar) or as
a cryogenic liquid ($\sim$20 K), are associated with notable drawbacks like
substantial energy losses, maintenance challenges, limited storage capacity,
and safety hazards. This has incited scientific community to investigate
material-based methods for storing hydrogen, wherein H2 molecules are securely
retained through the process of adsorption [8]. Chemisorption of atomic
hydrogens on a storage material with a high adsorption energy of (2-4 eV) has
the potential to generate a high gravimetric density. The high desorption
temperature, however, severely restricts its performance and practical
application. In contrast, in the context of physisorption, H2 molecules
exhibit adsorption onto the host material with very low adsorption energy
($\sim$meV), enabling for simple desorption at lower temperature [6]. However,
research has shown that at near-ambient temperatures, a hydrogen storage
material is considered to be ideal when it effectively stores hydrogen through
weak non-covalent interactions in a quasi-molecular fashion, with an
intermediate binding energy that lies between the chemisorbed and physisorbed
states. According to recent studies, it has been determined that the ideal
adsorption energy for H2 adsorption in near-ambient applications should fall
within the range of 0.1-0.2 eV [9]. As a result, storage materials such as
nanoclusters [10, 11], fullerenes [12, 13], and nanocages [14, 15] have
kindled a lot of research interest recently. For material-based hydrogen
storage systems, a variety of materials are already being investigated which
include, metal hydrides [16], complex chemical hydrides [17], metal organic
and inorganic frameworks [18], nanotubes [19], graphene sheet [20] etc.
However, due to slow kinetics, limited storage capacity, poor reversibility,
high desorption temperatures, a lack of feasible realization, and inefficient
application, most of the materials investigated have not been successfully put
into practical applications with high efficiency. As a result, it has led
researchers to either tailor and tune materials for efficient applications or
to design, test and manufacture new materials that can fulfill the US-DoE
criteria and technical challenges for hydrogen storage applications [21].

Extensive research has been conducted on carbon-based structures as
prospective materials for hydrogen storage, owing to their advantageous
characteristics such as low weight, significant porosity, and substantial
surface-to-volume ratio. However, the H2 molecules adsorbed onto the surface
of carbon-based structures exhibit a remarkably weak binding energy, leading
to suboptimal adsorption [22, 23]. According to reports, the overall
electronic properties of pristine nanostructures can be modified and rendered
more favorable for H2 adsorption through the use of different techniques, such
as the substitution of foreign atoms like B, N, and Si [24, 25]. For instance,
Si doped single-walled carbon nanotubes (SWNTs) and graphene are capable of
adsorbing significant number H2 molecules with enhanced binding energy than
their pristine counterparts [26]. According to recent research report Si doped
C60 fullerene can adsorb multiple molecular hydrogen resulting to a
gravimetric density of 7.5wt% [27]. The presence of active metal centers,
which produce a differential charge gradient on the surface and thus enhance
the dipole interactions, has also been shown to enhance the adsorption of H2
molecules in pure carbon-based structures through the decoration of metal
atoms. This has been the subject of both experimental and theoretical research
[28, 29]. A research report by Ammar et al. demonstrated that a single Ti atom
functionalized over C20 fullerene could adsorb 6H2 molecules [30]. However,
investigations reveals that H2 storage capacity of the transition metal
functionalized cages is greatly reduced due to metal clustering. This occurs
due to the exceptionally high cohesive energy of transition metals [31, 32].
In such instances, alkali metals such as Li are a superior alternative because
of their relatively low cohesive energies, which reduces the potential of
metal clustering [33, 34]. For example, Sun et al. studied that because of low
cohesive energy, Li atoms decorated over C60 fullerene does not undergo
aggregation and can adsorb H2 molecules with an average binding energy of
about 0.075 eV/H2 [35]. Further research also shows that H2 molecules adsorbed
over Li6C60 desorb at low temperatures [36]. Recent work by us has shown that
pure C20 fullerene when decorated with Li and Na can store 20H2 molecules and
thereby achieving a high gravimetric density of 13.08% and 10.82%,
respectively [37]. Metin et al. studied the encapsulation of molecular
hydrogen inside C20, Si- doped C20 fullerenes and reported that C15Si5 was the
most sensitive to the presence of H2 molecules [38]. W. Huang and his group
have studied that chain terminated C20 fullerene can adsorb multiple H2
molecules with average adsorption energy lying in the range of 0.30 eV-1.18 eV
[39]. Further, our recent study demonstrates the high H2 storage capacity of
Li decorated Si2C18 and Si4C16 nanocages [40].

In this article, we present the viability of Li decorated Si6C14 and Si8C12
nanocages as potential hydrogen storage materials. The Si6C14 and Si8C12
nanocages chosen for the study have been extensively investigated in
literature [41] but have not yet been experimentally produced in the
laboratory. However, based on the successful experimental synthesis of C20
fullerene and Si-doped heterofullerenes, it is possible that the experimental
synthesis of Si6C14 and Si8C12 nanocages will become viable in the near
future.

##  2 Theory and computation

In electronic structure calculations, the frontier molecular orbital energies
are vital inputs which are extensively used to estimate various reactivity
descriptors like ionization potential (I), electron affinity (A), HOMO-LUMO
gap (Eg) [42].

In conceptual density functional theory (CDFT) [43], electron donation or
acceptance induces an appreciable change in energy, which is measured by the
finite differences (FD) between the energies of the neutral system and its
corresponding cationic and anionic systems with N, N-1, and N+1 electrons,
respectively. Therefore, using Koopman’s theorem [44], I and A can be
qualitatively expressed as

$I=E(N-1)-E(N)\approx-E_{HOMO}$ (1)

$A=E(N)-E(N+1)\approx-E_{LUMO}$ (2)

The structural stability and chemical reactivity of the studied complexes are
described in terms of their binding energies (Eb), HOMO-LUMO gap (Eg) and
global reactivity descriptors like hardness ($\eta$), electrophilicity
($\omega$) and electronegativity ($\chi$).

Chemical hardness ($\eta$) for a given system is expressed as

$\eta=\frac{I-A}{2}\approx\frac{E_{g}}{2}$ (3)

Therefore, we can conclude that chemically hard complexes will have higher
Egvalues and vice versa. Similarly, for a given system, electronegativity
($\chi$) and eletrophilicity ($\omega$) can be expressed by the following
relations

$\chi=\frac{I+A}{2}$ (4)

$\omega=\frac{\chi^{2}}{2\eta}$ (5)

The average binding energy ($E_{b}$) of the Li decorated over Si6C14 and
Si8C12 nanocages are determined using the following relation

$E_{b}=\frac{E_{mLi+nanocage}-E_{nanocage}-mE_{Li}}{m}$ (6)

where $E_{mLi+nanocage}$, $E_{nanocage}$ and $E_{Li}$ are the total energy
with m number of Li atoms adsorbed on heterofullerene, the global minimum
energies of heterofullerene and an isolated Li atom, respectively.

The average adsorption energy $(E_{ads}$) of the H2 molecules adsorbed over
the nanocages is given by

$E_{ads}=\frac{\left[\left\\{E_{Host}+nE{}_{H_{2}}\right\\}-E_{Complex}\right]}{n}$
(7)

In the above Eq.(7), $E_{H_{2}}$, $E_{Host}$ and $E_{Complex}$ are the minimum
energies of the H2 molecule adsorbed over the system, Li decorated Si6C14 and
Si8C12 nanocages and their hydrogenated complexes respectively. The term $n$
signifies the number of H2 molecules adsorbed over the designed nanocages.

The occupation number $(f)$ or the practical hydrogen storage capacity
signifies the number of H2 molecules remain adsorbed over the designed
nanocages at a given temperature and pressure. Using grand canonical ensemble,
it can be shown that the occupation number $(f)$ and grand canonical partition
function ($Z$) are correlated as $f=k_{B}T\frac{\partial logZ}{\partial\mu}$
[46]. Therefore, the average occupation number $(f)$ can be expressed as

$f=\frac{\sum_{n=0}^{n=n_{max}}ng_{n}exp(\frac{n(\mu-
E_{ads})}{k_{B}T})}{\sum_{n=0}^{n=n_{max}}g_{n}exp(\frac{n(\mu-
E_{ads})}{k_{B}T})}$ (8)

where, $k_{B}$, $T$ and $\mu$ indicate Boltzmann constant, temperature in
Absolute scale and chemical potential of molecular hydrogen in gaseous phase
respectively. The degeneracy term $g_{n}$ is taken as 1 after neglecting
phonon contribution [47]. Further, chemical potential ($\mu$) can be expressed
in terms of other thermodynamic parameters as

$\mu=H^{0}(T)-H^{0}(0)-TS^{0}(T)+k_{B}Tln(\frac{P}{P_{0}})$ (9)

In the above Eq. (9) $H^{0}$ and $S^{0}$ denote the enthalpy and entropy of
molecular hydrogen gas at $1bar$ pressure. The reference pressure $P_{0}$ is
usually considered as $1bar$. The data required for the estimation of $\mu$ at
various temperature and pressure are taken from the Ref. [48].

For a given hydrogen storage complex, the gravimetric density (wt%) can be
calculated using the following relation:

$H_{2}\left(wt\%\right)=\left[\frac{M_{H_{2}}}{\left(M_{H_{2}}+M_{Host}\right)}\right]\times
100$ (10)

where $M_{H_{2}}$ and $M_{Host}$ are the total atomic weight of the adsorbed
H2 molecules and the bare complex respectively.

The density functional theory (DFT) based computations are performed with
6-311+G(d,p) basis set and Hybrid meta-GGA functional m06-2x functional.
M06-2x functional consists of 54% HF exchange and is nowadays widely used
functional for the adsorption related studies involving non-covalent
interactions in main group clusters [51] All these computation were carried
out using Gaussian 09 software [49]. The geometry optimizations of the
pristine nanocages, Li functionalized complexes and their hydrogenated systems
are done without any symmetry constraint. The density of states and partial
density of states calculation are carried out using Gaussum software packages
[52]. Further, the bonding mechanism and the related interaction among
different constituents of the complexes are understood in detail using quantum
theory of atoms in molecules (QTAIM) [53] using AIMALL software package [54].

##  3 Results and discussions

###  3.1 Design of Li decorated Si6C14 and Si8C12 nanocages

Si6C14 and Si8C12 are Si substituted analogs of the smallest carbon fullerene
C20 which are theoretically well explored [41]. The optimized geometry of
Si6C14 nanocage depicted in Figure 1, shows that it consists of twelve
pentagons, These twelve pentagons forms two types of pentagonal rings; in
type1 six pentagonal rings consists of five carbon atoms and one Si atom
whereas in type2- the other six pentagonal rings contains two Si atoms and
four carbon atoms. However, Si8C14 nanocage as shown in Figure 1, consists of
four tetragonal rings with alternate C-Si bonds, four pentagonal rings
containing one Si and four carbon atoms and four hexagonal rings containing
two Si atoms and four carbon atoms. To explore the potential of Si6C14 and
Si8C12 nanocages as hydrogen storage candidates, it is necessary to achieve
uniform functionalization of these cages with metal atoms. To computationally
design the Li functionalization of Si6C14 and Si8C12 nanocages, it is
necessary to identify the optimal site for Li binding, which is characterized
by the lowest and maximum Li binding energies. This is modeled by minima
hopping method [55, 56] in which a single Li atom is placed at each of the
possible metal adsorption site and the resultant geometry is then allowed to
relax. In case of Si6C14 cage, there can be four possible ways of Li atom
decoration- on the C-C bridge, on the C-Si bridge, atop of the pentagonal ring
of type1 and atop of the pentagonal ring of type2. Using minima hopping
method, it is found that the Li atom prefers to bind at the top of the
pentagonal ring of type1 with maximum binding energy of 3.94 eV. Therefore,
six Li atoms are decorated at the top of each type1 pentagonal ring and the
resultant structure is optimized to get our first computationally designed
host structure Si6C14Li6. Similar process is followed to decorate Li atoms
over Si8C12 nanocage. As earlier revealed from the optimized geometry of
Si8C12 cage that along with pentagonal rings and hexagonal rings, it also
contains tetragonal rings with alternate C-Si bonds. Thus, in case of Si8C12
nanocage, there can be five possible ways of Li decoration- on the C-C bridge,
on the C-Si bridge, on the top of the tetragonal ring, on the top of the
pentagonal ring and at the top of the hexagonal ring. Li atom is
regioselectively placed at each of the five possible sites of metal decoration
and the resultant structures are allowed to relax. The global minimum energies
of the optimized geometries of single Li atom decorated at different possible
sites are then compared and it is found that Li atom prefers to bind at the
top of the pentagonal sites with maximum binding energy of 3.05 eV. Therefore,
four Li atoms are uniformly decorated at the top of each pentagons and the
resultant structure is optimized to get our second designed host cage
Si8C12Li4. The functionalization of Li has no significant effect on the bond
distances and the structural geometry of the hosts, as evident from Table 2.

Figure 1: Optimized geometries of Si6C14, Si8C12, Si6C14Li6 and Si8C12Li4
nanocages.

As the average binding energy of the Li atoms in both the designed Si6C14Li6
and Si8C12Li4 cages are found to be higher than the cohesive energy of Li in
Li2 dimer as well as in bulk phase, no metal clustering can be expected.
Minimum energy and frequency associated with all the possible Li decoration
sites of Si6C14 and Si8C12 nanocages are tabulated in Table 1.

Table 1: Energetically favourable site search for Li decoration over Si6C14 and Si8C12 nanocages using minima hopping method. Cluster | Possible Site | Minimum Energy (eV) | Min Frequency (cm-1)
---|---|---|---
Li@Si6C14 | C-C bridge | 0.06 | 70.1340
C-Si bridge | 0.02 | 101.6228
Pentagonal Ring1 | 0.0 | 71.2104
Pentagonal Ring2 | 0.25 | 94.4917
Li@Si8C12 | C-C bridge | 0.28 | 159.5063
C-Si bridge | 0.04 | 99.6283
Tetragonal Ring | 0.38 | 67.3742
Pentagonal Ring | 0.0 | 158.9867
Hexagonal Ring | 0.04 | 108.7690

####  3.1.1 Mechanism of Li functionalization

The binding mechanism of Li over Si6C14 and Si8C12 nanocages can be understood
in terms of orbital interactions and charge transfer. This can be analysed by
comparing the variation in the density of states of each constituent caused as
a result of Li functionalization. The partial density of states plots of
Si6C14 and Si8C12 nanocages and their corresponding Li functionalized
derivatives are shown in Figure 2(a) & Figure 2(b) respectively. Li
functionalization over the nanocages is found to enhances the charge
delocalization and can be easily understood by the appearence of new peaks in
the density of states plot. No strong orbital overlap between Li, Si and C
orbitals are observed which indicates there is no bond formation between Li
and Si6C14 and Si8C12 nanocages. Due to Li functionalization, the density of
states for Si enhances whereas for C the density of states reduces. This
result is more prominent in Si8C12 and its Li decorated nanocages.

(a)

fig

(b)

Figure 2: Variation in PDOS due to Li functionalization over (a) Si6C14 and
(b) Si8C12 nanocages.

To understand the binding mechanism of Li atom with Si6C14 and Si8C12
nanocages, electrostatic potential maps of nanocages before and after Li
functionalization are plotted. The ESP maps of pristine Si6C14 and Si8C12
nanocages and their Li functionalized counterparts are depicted in terms of
R-G-B colour codes which varies from red to blue as shown in Figure 3. Red
indicates the accumulation of electrons and, thus, a region of high electron
density, whereas blue represents electron-deficient regions caused by electron
depletion. Green colour lying in between them indicates region with moderate
electron density. Unfunctionalized Si6C14 and Si8C12 nanocages are initially
greenish in colour, indicating their neutrality. However, Li functionalization
causes an electron density shift from the decorated Li atoms to the Si6C14 and
Si8C12 nanocages. As a result, the middle region turns crimson, while the
outside regions turn bluish. The difference in colour coding caused by Li
functionalization implies that electron density has been redistributed,
allowing the intended systems to adsorb additional H2 molecules. To quantify
the amount of charge transfer associated with electron density shift,
Hirshfeld charge analysis has been carried out which indicates that initially,
the bare cage Si6C14 carried a small negative charge of approximately -0.0005
a.u. However, Li functionalization over the cage causes charge transfer from
the decorated Li atoms to the cage. This charge transfer leads to charge gain
of -2.025 a.u by the cage whereas each Li atoms decorated undergoes a charge
loss of 0.34 a.u. In case of Si8C12 cage, the initial charge carried by the
cage is measured to be -0.00016 a.u. However, upon Li functionalization over
the Si8C12 cage causes it to gain a charge of -1.35 a.u and the decorated Li
atoms undergoes a charge loss of 0.34 a.u. Upon functionalization, Li atoms
undergo charge loss which make them cationic in nature. As compared to neutral
Li atom, the ionic Li atom is capable of adsorbing more H2 molecules via
charge polarization mechanism as proposed by Niu et al [59]. This finding is
in good consistent with the results of DOS analysis.

Figure 3: ESP maps of Si6C14, Si6C14Li6, Si8C12 and Si8C12Li4 nanocages.

####  3.1.2 Thermal Stability of the host cages

To gain insight into the structural integrity and thermodynamic stability of
the designed Si6C14Li6 and Si8C12Li4 nanocages, we carried out the ADMP-MD
simulation at 300K for 500fs with time step of 0.5 fs. In both the designed
nanocages, we found that the decorated Li atoms undergoes negligible changes
and remain bonded to the surface of the designed cages which indicate the
solidity and thermostability of the designed host cages. The variation of
nearest neighbour bond distances C-Si and Si-Li for both the designed
Si6C14Li6 and Si8C12Li4 nanocages are found to undergo a negligible change
which further remarks the structural stability of the designed nanocages.
Further, the potential energy vs. time graph shown in Figure 4 converges with
time which further confirms the thermal stability of the designed nanocages.

(a)

(b)

Figure 4: Potential energy vs. time graph for (a) Si6C14Li6 and (b) Si8C12Li4
nanocages.

###  3.2 H2 adsorption over Si6C14Li6 and Si8C12Li4 nanocages

To determine the hydrogen storage capacities of the designed Si6C14Li6 and
Si8C12Li6 cages, we have studied the sequential adsorption of H2 molecules
over them. We introduced the first sequence of H2 molecules over Li decorated
Si6C14 nanocage at a distance of about 2.1 Å and the structure is allowed to
relax. It is observed that the first sequence of H2 molecules are adsorbed at
a distance of 2.34 Å. The adsorption energy thus obtained is higher than the
some of the previously reported results in similar systems. In a similar
manner, more H2 molecules are introduced in second, third, fourth and fifth
sequential step. The optimized geometries of the sequentially hydrogen
adsorbed Si6C14Li6 and Si8C12Li6 complexes are presented in Figure 6.

Figure 5: Variation of average adsorption energy with sequential H2 adsorption
over Si6C14Li6 and Si8C12Li4 nanocages.

(a)

(b)

Figure 6: Successive adsorption of H2 molecules over (a) Si6C14Li6 and (b)
Si8C12Li4 nanocages.

For Si6C14Li6 cage, the first H2 molecule gets adsorb with an adsorption
energy of 0.13 eV with an elongated H-H bond length of 0.75 Å. The average
adsorption energy per H2 molecule calculated using Eq. (7) is found to lie in
the range of 0.13-0.095 eV. Further, the repulsion among the nearby H2
molecules also causes adsorption at slightly larger distances. The average
distance between the sorption centers and the adsorbed H2 molecules are found
to be in the range of 2.05-2.92 Å. For Si8C12Li4, the first sequential
adsorption of H2 molecules occur with a binding energy of 0.14 eV at an
average distance of 2.04 Å from the Li center. Each Li in Si6C14Li6 and
Si8C12Li4 cage can adsorb up to 5H2 molecules, thereby achieving a gravimetric
density of 13.8% and 9.2% respectively. The variation of adsorption energy
with sequential addition of H2 molecules over the surface of Si6C14Li6 and
Si8C12Li6 cages is depicted in Figure 5. Successive adsorption shows that with
the increase in H2 adsorption over both the cages, the H2 molecules are
adsorbed slightly at larger distances and with lower binding energy because of
space constraint and steric hindrance. In addition, the BSSE corrected
adsorption energies are found little bit lower. However, the change in
adsorption energies due to BSSE consideration is not very significant, which
is consistent with our earlier report [13]. The variation of various
geometrical parameters as a result of Li functionalization and sequential H2
adsorption over the cages are given in Table 2. In both the host cages, the
range of adsorption energy and the distances between the Li sorption center
and the adsorbed H2 indicates quasi-molecular adsorption.

Table 2: Average bond lengths of C-C, C-Si, H-H, distance of Li from the center of the ring (Li-ring) and from the adsorbed H2 molecules (Li-H2) in Å. Cluster | C-C | C-Si | Li-ring | Li-H2 | H-H
---|---|---|---|---|---
Si6C14 | 1.418 | 1.869 | - | - | -
Si6C14Li6 | 1.437 | 1.839 | 1.790 | - | -
Si6C14Li6-6H2 | 1.436 | 1.843 | 1.821 | 2.335 | 0.747
Si6C14Li6-12H2 | 1.437 | 1.965 | 1.811 | 2.052 | 0.748
Si6C14Li6-18H2 | 1.436 | 1.965 | 1.835 | 2.399 | 0.747
Si6C14Li6-24H2 | 1.436 | 1.964 | 1.860 | 2.661 | 0.746
Si6C14Li6-30H2 | 1.434 | 1.962 | 1.970 | 2.922 | 0.746
Si8C12 | 1.293 | 1.979 | - | - | -
Si8C12Li4 | 1.325 | 1.952 | 1.960 | - | -
Si8C12Li4-4H2 | 1.325 | 1.952 | 1.967 | 2.036 | 0.747
Si8C12Li4-8H2 | 1.324 | 1.954 | 1.977 | 2.176 | 0.745
Si8C12Li4-12H2 | 1.327 | 1.952 | 2.039 | 2.199 | 0.746
Si8C12Li4-16H2 | 1.327 | 1.953 | 2.036 | 2.660 | 0.746
Si8C12Li4-20H2 | 1.327 | 1.954 | 2.043 | 2.952 | 0.745

The stability of the hydrogen adsorbed systems are analyzed using HOMO-LUMO
gap (Eg), global reactivity descriptors like hardness ($\eta$) and
electrophilicity index ($\omega$). A larger Eg signifies that a greater amount
of energy will be needed by an electron to move from HOMO to LUMO level. The
HOMO-LUMO gap, hardness and electrophilicity index of the studied systems are
tabulated in Table 3. From the tabulated data, we can observe negligible
change in HOMO-LUMO gap and chemical hardness values increases due to Li
functionalization and sequential H2 adsorption. As the sequential $H_{2}$
adsorption process approaches saturation, there is an evident decrease in the
values of Eg. We can therefore argue that the maximum hardness concept is
being obeyed to some extent [60]. However, the electrophilicity values follow
a decreasing trend, demonstrating that the minimal electrophilicity principle
[61] is adhered to as a result of Li functionalization and successive $H_{2}$
adsorption across Si6C14Li6 and Si8C12Li4 nanocages. Thus, following the
principle of maximum hardness and minimal electrophilicity ensures the
stability of the studied systems.

Table 3: Eg, $\eta$ and $\omega$ of the studied systems in eV. Cluster | Eg | $\eta$ | $\omega$
---|---|---|---
Si6C14 | 2.66 | 1.328 | 4.142
Si6C14Li6 | 2.69 | 1.346 | 1.942
Si6C14Li6-6H2 | 2.73 | 1.364 | 1.773
Si6C14Li6-12H2 | 2.77 | 1.383 | 1.627
Si6C14Li6-18H2 | 2.74 | 1.371 | 1.622
Si6C14Li6-24H2 | 2.71 | 1.357 | 1.626
Si6C14Li6-30H2 | 2.62 | 1.312 | 1.571
Si8C12 | 2.78 | 1.388 | 3.929
Si8C12Li4 | 3.21 | 1.604 | 2.417
Si8C12Li4-4H2 | 3.2 | 1.601 | 2.325
Si8C12Li4-8H2 | 3.15 | 1.577 | 2.219
Si8C12Li4-12H2 | 3.13 | 1.564 | 2.162
Si8C12Li4-16H2 | 3.14 | 1.570 | 2.188
Si8C12Li4-20H2 | 3.17 | 1.585 | 2.186

####  3.2.1 ESP and Hirshfeld charge analysis

Surface mapping of electrostatic potential over total electron density is used
to study the electron density distribution that occurs as a result of
sequential H2 adsorption. As discussed earlier, in ESP maps, the change in
electron density can be visualized in terms of changing colour codes. The ESP
maps of the successive hydrogenated systems of Si6C14Li6 and Si8C12Li4 are
depicted in Figure 7.

Figure 7: ESP maps of sequential hydrogen adsorbed Si6C14Li6 and Si8C12Li4
systems.

Obviously successive adsorption of H2 molecules over Si6C14Li6 and Si8C12Li4
causes redistribution of the total electron density over the whole system, and
it can be seen that the central portion of Si6C14 and Si8C12 nanocages become
more reddish (gain of electron density) after H2 adsorption. On the other
hand, the color over Li atoms appears to fade after H2 adsorption. The color
shifts from red to yellowish-green, indicating that the electron density over
these atoms drops, resulting in positive polarity. When the first sequential
hydrogen adsorbed systems are compared with the saturated ones, we observe
that the colour over H2 molecules changes from blue to green, indicating
transfer of electron density from Li atoms to H2 molecules and thereby
triggering the adsorption process. The shifting of electron density in ESP
maps clearly indicates that charge transfer may be accompanied in the
adsorption process. The variation of electron density as a result of H2
adsorption is associated with charge transfer. In order to understand the
charge transfer caused due to H2 adsorption process over the Si6C14Li6 and
Si8C12Li4 nanocages, we calculated average Hirshfeld charges over the adsorbed
H2 molecules, decorated Li atoms and the pristine Si6C14 and Si8C12 nanocages.
Initially, the Hirshfeld charge over the Si6C14Li6 heterofullerene is found to
be 0.0003 a.u. But introduction of first sequence of H2 molecules over the Li
centers of Si6C14 cage, the total Hirshfeld charge on Si6C14Li6 becomes -0.51
a.u which clearly indicates accumulation of electron density over the host
cage and is marked by the reddish colour in Figure 7. As more and more number
of H2 molecules are adsorbed over the Si6C14Li6 and Si8C12Li4, the Hirshfeld
charge over Li goes on decreasing. Before hydrogenation, the Hirshfeld charge
of each Li functionalized over Si6C14 heterofullerene carried is 0.337 a.u.
However, in saturated hydrogen adsorbed system, the Hirshfeld charge of Li has
significantly decreased to 0.181 a.u. which is about 53.7% of the initial
charge. Further, for the sequential H2 adsorbed Si6C14Li6 nanocages, the
Hirsheld charge over the heterofullerenes decreases from -2.025 a.u to -1.865
a.u. Therefore, till H2 adsorption reaches saturation, the Si6C14Li6 loses
about 16% of charge. In addition, the average Hirshfeld charge over the
adsorbed H2 molecules goes on slight decreasing due to polarization as a
result of sequential adsorption. Similar change is also observed in
Si8C12Li4-nH2 complexes. However, Li and H continues to loose charge upon
sequential H2 adsorption. For example, successive hydrogen adsorption over
Si8C12Li4 causes total Hirshfeld charge of Li decreasing from 1.35-0.78 a.u
which is about 42.2% of the initial charge. Likewise, with successive
adsorption, the average Hirshfeld charge of the adsorbed H2 decreases
drastically because of polarization. Therefore Hirshfeld charge analysis gives
a qualitative as well as quantitative insight how Li atom donates charge to
the Si6C14(Si8C12) cages, resulting to the formation of a dipole. The dipole
formed because of polarization generates electrostatic field that helps to
adsorb H2 molecules through polarization which is also noticed form the above
ESP studies.

####  3.2.2 PDOS analysis

Partial density of states (PDOS) of constituent elements Li and H in
Si6C14Li6-nH2 and Si8C12Li4-nH2 complexes are plotted using convolution of
spectra to get insight into the binding mechanism and orbital hybridization.
The graph for the PDOS of Si6C14Li6-nH2 and Si8C12Li4-nH2 are depicted in
Figure 8. Figure 8(a) & Figure 8(b) demonstrates that the LUMO level and the
other unoccupied molecular orbitals have major contribution in bonding. After
H2 adsorption over Li centers of the Si6C14Li6 and Si8C12Li4 nanocages, the
density of states contribution of Li and H are found to undergo a significant
change. With sequential adsorption of H2 molecules over Si6C14Li6 nanocage,
the density of states of Li goes on decreasing whereas the density of states
of the adsorbed H2 molecules goes on increasing. As previously demonstrated by
ESP maps and Hirshfed charge analyses, the reduction in density of Li states
is linked with charge loss. However, the increase in density of states of the
adsorbed hydrogen is associated to charge gain. Initially, the density of
state peak of bare H2 at -15 eV is sharply oriented. But due to multiple H2
adsorption, the density of states distribution widens over the energy axis
with a few short peaks which signifies weakening of interaction with
successive adsorption. In addition, the degeneration and shifting of peaks of
H in adsorbed H2 molecules Si6C14Li6-30H2 denotes the charge polarization
effect between Li centers and molecular hydrogen, resulting to efficient H2
adsorption [52]. In addition, partial overlapping of the electronic states of
adsorbed hydrogen and Li in Si6C14Li6-30H2 indicate absence of strong orbital
overlap between them, which confirms that H2 molecules are held via weak Van
der Waals interaction. A similar trend for variation of electronic states of
the decorated Li atom and the adsorbed H2 molecules over Si8C12Li4 nanocages
is observed.

(a)

(b)

Figure 8: PDOS for sequential hydrogen adsorbed (a) Si6C14Li6 and (b)
Si8C12Li4 systems.

####  3.2.3 Topological analysis

In principle, the macroscopic behavior of materials is determined by the
interactions between constituent atoms at the microscopic level. Therefore, we
conducted Bader’s topological studies [46] to study the type of interaction
between the Si6C14Li6 and Si8C12Li4 nanocages and the adsorbed H2 molecules
over them. The interpretation of electron density ($\rho(r)$), Laplacian of
electron density ($\nabla^{2}\rho$) and total energy density $H(r)$ at various
bond critical points (BCPs) reveals the nature of atomic interactions. The
$\rho(r)$, $\nabla^{2}\rho(r)$, $H(r)$ and bond degree (BD) at various BCPs
are tabulated in the Table 4. The negative value of $\nabla^{2}\rho(r)$ at a
given BCP implies electrons sharing, and hence it characterizes a covalent
type of interaction. A relative depletion of electrons along a given bond
path, as indicated by a positive $\nabla^{2}\rho(r)$, demonstrates a closed-
shell type of noncovalent interactions [55]. In the context of weak
interactions, it is necessary to consider not only the variation in electron
density $\rho(r)$ and its Laplacian $\nabla^{2}\rho(r)$ at different BCPs, but
also the variation in total local energy density $H(r)$. The total local
energy density is defined as the sum of the local potential energy density
$V(r)$ and the local kinetic energy $G(r)$ at the corresponding BCP. At a
given BCP, negative values of $H(r)$ indicates bonds formed by sharing of
electrons and thus contains covalent component. Positive $H(r)$ values at a
certain BCP signifies closed shell type of interaction [56]. Additionally, the
characterization of interaction may be comprehended by considering bond degree
(BD), which is defined as the overall local energy density per electron at a
specific BCP. Mathematically, it can be represented as $BD=H/\rho{(r)}$.

Table 4: Topological parameters $\rho(r)$, $\nabla^{2}\rho(r)$ and $H(r)$ at all BCPs of the systems. Species | BCP |  $\rho(r)$ (a.u) | $\nabla^{2}\rho(r)$ |  $H(r)$ (a.u) | Bond degree (BD)
---|---|---|---|---|---
H2 | H-H | 0.257316 | -1.01865 | -0.254663 | -1
Si6C14 | C-C | 0.277374 | -0.668508 | -0.258539 | -0.9
C-Si | 0.116673 | 0.263295 | -0.070425 | -0.6
Si6C14Li6 | C-C | 0.247713 | -0.513906 | -0.20788 | -0.8
C-Si | 0.084015 | 0.122324 | -0.046665 | -0.6
C-Li | 0.022687 | 0.115333 | 0.003342 | 0.1
Si6C14Li6-30H2 | C-C | 0.248382 | -0.519464 | -0.208909 | -0.8
C-Si | 0.081904 | 0.105188 | -0.045559 | -0.6
C-Li | 0.02356 | 0.131348 | 0.003836 | 0.2
Li-H2 | 0.009148 | 0.051375 | 0.002563 | 0.3
H-H | 0.260958 | -1.063504 | -0.266436 | -1
Si8C12 | C-C | 0.353642 | -1.018858 | -0.426445 | -1.2
C-Si | 0.100182 | 0.198428 | -0.057756 | -0.6
Si8C12Li4 | C-C | 0.319298 | -0.838761 | -0.348065 | -1.1
C-Si | 0.106616 | 0.19604 | -0.063803 | -0.6
C-Li | 0.024209 | 0.141691 | 0.004636 | 0.2
Si8C12Li4-20H2 | C-C | 0.319649 | -0.840835 | -0.348774 | -1.1
C-Si | 0.106301 | 0.1945 | -0.063546 | -0.6
C-Li | 0.022379 | 0.127829 | 0.004346 | 0.2
Li-H2 | 0.008194 | 0.044993 | 0.002215 | 0.3
H-H | 0.26193 | -1.071127 | -0.268151 | -1

Positive BD, also known as softening degree (SD), refers to a non-covalent
interaction of the closed shell type. On the other hand, the covalent degree
(CD), which is a negative BD, represents covalent interactions that involve
shared and intermediate types. The stronger the covalent interaction will be,
the greater the magnitude of CD [57]. The tabulated data in Table 4 reveals
that bonding nature in the hosts hardly undergoes any change during Li
functionalization and successive H2 adsorption. For the saturated hydrogen
adsorbed Si6C14Li6 nanocage, the $\rho(r)$ value over the H-H bond in the
adsorbed H2 molecule is 0.26 a.u, which is nearly same as the $\rho(r)$ value
in the isolated H2 molecule. This clearly demonstrates that H2 molecules are
molecularly adsorbed onto the designed nanocages, which is in agreement with
the results reported by Jiguang et al. [58]. The sign of $\nabla^{2}\rho(r)$
and $H(r)$ in C-C and C-Si are the same in Si6C14, Si6C14Li6, and saturated
hydrogen adsorbed Si6C14Li6 systems, implying that the nature of bonding
hardly undergoes any significant change due to Li functionalization and
successive H2 adsorption. The positive signatures of $\nabla^{2}\rho(r)$ and
$H(r)$ at the BCPs of Li-H2 in the hydrogenated systems demonstrate that H2
molecules are adsorbed via weak non-covalent interaction. In addition, the
negative sign of $\nabla^{2}\rho(r)$ and $H(r)$ suggests that the H-H bond
remains intact following the adsorption process. A Similar trend is observed
in case of Si8C12 cage.

###  3.3 MD Simulation

We have performed the atom centered molecular dynamics (ADMP) simulation to
understand the thermal stability as well as the structural integrity of the
saturated H2 adsorbed systems. ADMP is an expanded Lagrangian method for MD
that employs the Gaussian basis function and propagates the density matrix.
During simulations, the temperature (kinetic energy thermostat) is maintained
by the velocity scaling method. For the saturated hydrogen adsorbed
Si6C14Li6-30H2 and Si8C12Li4-20H2 nanocages, ADMP simulations are performed at
a temperatures of 100K, 200K and 300K at 1 bar pressure for 400fs with a time
step of 0.5fs. The potential energy vs time graph for both the saturated
hydrogen adsorbed systems at100K, 200K and 300K are shown in Figure 9.

(a) Si6C14Li6-30H2

(b) Si8C12Li4-20H2

Figure 9: Potential energy vs. time graph for the saturated hydrogen adsorbed
nanocages at various temperature.

The potential energy at higher temperature is higher because of enhanced
molecular movements. At 100K, about 12H2 molecules got desorbed from the
saturated hydrogen adsorbed Si6C14Li6-30H2 system. When the temperature is
increased to 200K, almost 19H2 molecules got desorbed. Further, at 300K, 25H2
(83.3%) molecules get completely desorbed from the system. Similarly, for
Si8C12Li4-20H2 nanocage, 12H2 molecules are found to get desorb from the
system. When the temperature is increased to 300K, complete desorption of H2
molecules is achieved. From the Figure 9, we find that molecular movements is
higher at higher temperature, leading to easy and fast desorption. Therefore,
at 1 bar atmospheric pressure, Si6C14Li6 and Si8C12Li4 adsorb H2 molecules at
temperatures below 100K and undergo complete desorption at room temperature.
Additionally, it can be observed that the hydrogen molecules begin to shift
away from the complex, and as time passes, they move away from the vicinity of
the Li atoms. After complete desorption of H2 molecules, the designed host
complex endures minimal changes and remains stable. This indicates the on-
board reversibility of the system at the investigated temperatures. The
desorption pattern changes as the temperature varies. These results are
essential for further investigation of the on-board reversible storage
capacity of the designed complexes, as temperature variation causes the
desorption of hydrogen molecules, thereby maintaining the stability of the
host complex.

###  3.4 Practical hydrogen storage

At a given temperature and pressure, the maximum number of usable H2 molecules
that remain adsorbed in a storage system marks the practical storage capacity
of a hydrogen storage material. The practical H2 storage capacity of the
designed Si6C14Li6 and Si8C12Li4 nanocages clusters are investigated
thoroughly using the concept of grand canonical ensemble as explained in the
theoretical section. The phonon contribution in the entropy is neglected and
hence the degeneracy gn value is taken as 1. The occupation number ($f$)
denotes the number of usable H2 molecules remain adsorbed over each sorption
center of the Si6C14Li6 and Si8C12Li4 nanocages at a given temperature and
pressure. Consequently, for $N$ sorption sites, the total number of usable H2
molecules can be given by $fN$. Here, in our study, $N=4,6$ for Si6C14Li6 and
Si8C12Li4 nanocages respectively. The variation of fN for the saturated
hydrogen adsorbed Si6C14Li6 and Si8C12Li4 nanocages with temperature (T) and
pressure (P) is shown in Figure 10. In case of Si6C14Li6-30H2 (Ref. Figure
10), we can observe that for the temperature lying in the range of 40-80K all
30H2 molecules remain adsorbed at all pressure range of 1-60bar. When the
temperature is increased to 100K at 1 bar pressure, only 17 H2 molecules are
found to remain adsorb over the system. However, at the same temperature
pressure is increased, occupation number increases and in the pressure range
of 20-60 bar, almost all 30H2 molecules are found remain adsorb over the
system. Beyond this temperature, high occupation number of H2 molecules is
achieved only at higher pressure range of 40-60 bar. At 180K/60 bar, only 12
H2 molecules are found to remain adsorbed over the temperature. Further
increase in temperature allows more H2 molecules to get desorbed from the
system. A similar trend of desorption is also followed in case of saturated
hydrogen adsorbed Si8C12Li4 nanocage as shown in the Figure 10(b). After
thorough analysis of the adsorption-desorption pattern at various temperature
and pressure for both the designed hosts, it can be estimated that 100K/60bar
and 240K/1bar can be set as adsorption and desorption condition respectively.
The practical gravimetric densities for the saturated hydrogen adsorbed
Si6C14Li6 and Si8C12Li4 nanocages at the set adsorption-desorption conditions
are found to be 13.73 wt% and 9.08 wt%.

(a)

(b)

Figure 10: Practical hydrogen capacities of (a) Si6C14Li6 and (b) Si8C12Li4 nanocages at various temperature and pressure. Table 5: Practical hydrogen storage capacity obtained by setting 100K/60bar and 240K/1bar as adsorption and desorption condition respectively. Nads and Ndes are the occupation number of H2 molecules at 100K/60bar and 240K/1bar. Nuse indicates number of usable hydrogen molecules and is calculated by the difference of Nads and Ndes Complex | $N_{th}$ | $N_{ads}$ | $N_{des}$ | $N_{use}$ | $G_{th}(wt\%)$ | $G_{prac}(wt\%)$
---|---|---|---|---|---|---
Si6C14Li6-30H2 | 30 | 29.9 | 0.03 | 29.87 | 13.78 | 13.73
Si8C12Li4-20H2 | 20 | 19.7 | 0.03 | 19.67 | 9.22 | 9.08

##  4 Conclusions

In conclusion, we proposed Li decorated Si6C14 and Si8C12 nanocages as an
effective hydrogen storage media using density functional theory. The Li atoms
were found to get adsorb over the pentagonal ring with one Si atom and
tetragonal rings of Si6C14 and Si8C12 nanocages respectively. Global
reactivity descriptors and MD simulation confirm the structural stability and
integrity of the designed complexes without any clustering. Each Li atom
decorated over the designed Si6C14 and Si8C12 nanocages can adsorb about 5H2
molecules with optimum adsorption energy, thereby achieving a gravimetric
density of 13.8% and 9.2% respectively. The gravimetric density obtained is
well above the target set by US-DoE. The major cause of multiple H2 adsorption
over Si6C14Li6 and Si8C12Li4 nanocages are found to be due to charge transfer
and orbital hybridization as confirmed by ESP maps and PDOS analyses. The
nature of interaction between the decorated Li centers and the adsorbed H2
molecules are found to be weak noncovalent type, as confirmed by the Badar’s
topological analysis. Hence, the computationally designed Si6C14Li6 and
Si8C12Li4 nanocages can be regarded as promising template for hydrogen storage
materials.

## Acknowledgements

We acknowledge our institute Indian Institute of Technology (Indian School of
Mines) for providing research facilities.

## References

  * [1] Shafiee, Shahriar, and Erkan Topal. ” When will fossil fuel reserves be diminished?.” Energy policy 37.1 (2009): 181-189.
  * [2] Johnsson, F., Kjärstad, J., & Rootzén, J. (2019). The threat to climate change mitigation posed by the abundance of fossil fuels. Climate Policy, 19(2), 258-274.
  * [3] Züttel, A., Remhof, A., Borgschulte, A., & Friedrichs, O. (2010). Hydrogen: the future energy carrier. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1923), 3329-3342.
  * [4] Singh, S., Jain, S., Venkateswaran, P. S., Tiwari, A. K., Nouni, M. R., Pandey, J. K., & Goel, S. (2015). Hydrogen: A sustainable fuel for future of the transport sector. Renewable and sustainable energy reviews, 51, 623-633.
  * [5] Schlapbach, L., & Züttel, A. (2011). Hydrogen-storage materials for mobile applications. Materials for sustainable energy: a collection of peer-reviewed research and review articles from nature publishing group, 265-270.
  * [6] Jena, P. (2011). Materials for hydrogen storage: past, present, and future. The Journal of Physical Chemistry Letters, 2(3), 206-211.
  * [7] U.S. Department of Energy’s Energy Efficiency and Renewable Energy Website. https://www1.eere.energy.gov/hydrogen-and fuelcells/storage/current_technology.html (2010).
  * [8] Züttel, A. (2003). Materials for hydrogen storage. Materials today, 6(9), 24-33.
  * [9] Bhatia, S. K., & Myers, A. L. (2006). Optimum conditions for adsorptive storage. Langmuir, 22(4), 1688-1700.
  * [10] Mehboob, M. Y., Hussain, R., Younas, F., Jamil, S., Iqbal, M. M. A., Ayub, K., … & Janjua, M. R. S. A. (2023). Computation assisted design and prediction of alkali-metal-centered B12N12 nanoclusters for efficient H2 adsorption: new hydrogen storage materials. Journal of Cluster Science, 34(3), 1237-1247.
  * [11] Jaiswal, A., Sahoo, R. K., Ray, S. S., & Sahu, S. (2022). Alkali metals decorated silicon clusters (SinMn, n= 6, 10; M= Li, Na) as potential hydrogen storage materials: A DFT study. International Journal of Hydrogen Energy, 47(3), 1775-1789.
  * [12] Dong, H., Hou, T., Lee, S. T., & Li, Y. (2015). New Ti-decorated B40 fullerene as a promising hydrogen storage material. Scientific reports, 5(1), 9952.
  * [13] Jaiswal, A., Chakraborty, B., & Sahu, S. (2023). A computational insight on the effect of encapsulation and Li functionalization on Si12C12 heterofullerene for H2 adsorption: a strategy for effective hydrogen storage. ACS Applied Energy Materials, 6(6), 3374-3389.
  * [14] Ahangari, M. G., & Mashhadzadeh, A. H. (2020). Density functional theory based molecular dynamics study on hydrogen storage capacity of C24, B12N12, Al12 N12, Be12O12, Mg12O12, and Zn12O12 nanocages. International Journal of Hydrogen Energy, 45(11), 6745-6756.
  * [15] Guo, L., Li, Y., Ma, Y., Liu, Y., Peng, D., Zhang, L., & Han, S. (2017). Enhanced hydrogen storage capacity and reversibility of LiBH4 encapsulated in carbon nanocages. International Journal of Hydrogen Energy, 42(4), 2215-2222.
  * [16] Schneemann, A., White, J. L., Kang, S., Jeong, S., Wan, L. F., Cho, E. S., … & Stavila, V. (2018). Nanostructured metal hydrides for hydrogen storage. Chemical reviews, 118(22), 10775-10839.
  * [17] Orimo, S. I., Nakamori, Y., Eliseo, J. R., Züttel, A., & Jensen, C. M. (2007). Complex hydrides for hydrogen storage. Chemical reviews, 107(10), 4111-4132.
  * [18] Langmi, H. W., Ren, J., North, B., Mathe, M., & Bessarabov, D. (2014). Hydrogen storage in metal-organic frameworks: a review. Electrochimica Acta, 128, 368-392.
  * [19] Froudakis, G. E. (2011). Hydrogen storage in nanotubes & nanostructures. Materials Today, 14(7-8), 324-328.
  * [20] Jain, V., & Kandasubramanian, B. (2020). Functionalized graphene materials for hydrogen storage. Journal of Materials Science, 55(5), 1865-1903.
  * [21] Basic Research Needs for the Hydrogen Economy. www.sc.doe. gov/bes/hydrogen.pdf (2004).
  * [22] Chen, G., Gong, X. G., & Chan, C. T. (2005). Theoretical study of the adsorption of H 2 on (3, 3) carbon nanotubes. Physical Review B, 72(4), 045444.
  * [23] Okamoto, Y., & Miyamoto, Y. (2001). Ab initio investigation of physisorption of molecular hydrogen on planar and curved graphenes. The journal of physical chemistry B, 105(17), 3470-3474.
  * [24] Srinivasu, K., & Ghosh, S. K. (2011). Tuning the metal binding energy and hydrogen storage in alkali metal decorated MOF-5 through boron doping: A theoretical investigation. The Journal of Physical Chemistry C, 115(34), 16984-16991.
  * [25] Qiu, N. X., Zhang, C. H., & Xue, Y. (2014). Tuning Hydrogen Storage in Lithium-Functionalized BC2N Sheets by Doping with Boron and Carbon. ChemPhysChem, 15(14), 3015-3025.
  * [26] Cho, J. H., Yang, S. J., Lee, K., & Park, C. R. (2011). Si doping effect on the enhanced hydrogen storage of single walled carbon nanotubes and graphene. International journal of hydrogen energy, 36(19), 12286- 12295
  * [27] Ganji, M. D., Ahmadian, N., Goodarzi, M., & Khorrami, H. A. (2011). Molecular hydrogen interacting with Si-, S-and P-doped C60 fullerenes and carbon nanotube. Journal of Computational and Theoretical Nanoscience, 8(8), 1392-1399.
  * [28] Ward PA, Teprovich JA Jr, Compton RN, Schwartz V, Veith GM, Zidan R. Evaluation of the physi-and chemisorption of hydrogen in alkali (Na, Li) doped fullerenes. Int J Hydrogen Energy. 2015;40(6):2710-2716.
  * [29] Ataca, C., Aktürk, E., Ciraci, S. A. L. İ. M., & Ustunel, H. A. N. D. E. (2008). High-capacity hydrogen storage by metallized graphene. Applied Physics Letters, 93(4), 043123.
  * [30] Ammar HY, Badran HM. Ti deposited C20 and Si20 fullerenes for hydrogen storage application, DFT study. Int J Hydrogen Energy. 2021;46(27):14565-14580.
  * [31] Sun Q, Wang Q, Jena P, Kawazoe Y. Clustering of Ti on a C60 surface and its effect on hydrogen storage. J Am Chem Soc. 2005;127(42):14582-14583.
  * [32] Krasnov PO, Ding F, Singh AK, Yakobson BI. Clustering of Sc on SWNT and reduction of hydrogen uptake: ab-initio allelectron calculations. J Phys Chem C. 2007;111
  * [33] Huang, J., Zhou, C., & Duan, X. (2021). Li decorated C9N4 monolayer as a potential material for hydrogen storage. International Journal of Hydrogen Energy, 46(65), 32929-32935.
  * [34] Guo, Y., Jiang, K., Xu, B., Xia, Y., Yin, J., & Liu, Z. (2012). Remarkable hydrogen storage capacity in Li-decorated graphyne: theoretical predication. The Journal of Physical Chemistry C, 116(26), 13837-13841.
  * [35] Sun Q, Jena P, Wang Q, Marquez M. First-principles study of hydrogen storage on Li12C60. J Am Chem Soc. 2006;128(30): 9741-9745.
  * [36] Wang Q, Jena P. Density functional theory study of the interaction of hydrogen with Li6C60. J Phys Chem Lett. 2012;3(9): 1084-1088.
  * [37] Sahoo RK, Chakraborty B, Sahu S. Reversible hydrogen storage on alkali metal (Li and Na) decorated C20 fullerene: a density functional study. Int J Hydrogen Energy. 2021;46(80):40251- 40261.
  * [38] Metin T, Parlak C, Alver Ö, Tepe M. Hydrogen storage and electronic properties of C20, C15M5 and H2@ C15M5 (M = Al, Si, Ga, Ge) nanoclusters. J Mol Struct. 2022;1247:131272.
  * [39] Huang W, Shi M, Song H, et al. Hydrogen storage on chainsterminated fullerene C20 with density functional theory. Chem Phys Lett. 2020;758:137940
  * [40] Jaiswal, A., Chakraborty, B., & Sahu, S. (2022). High capacity reversible hydrogen storage in Si substituted and Li decorated C20 fullerene: Acumen from density functional theory simulations. International Journal of Energy Research, 46(14), 19521-19537.
  * [41] Koohi, M., Amiri, S. S., & Shariati, M. (2017). Silicon impacts on structure, stability and aromaticity of C20-nSin heterofullerenes (n= 1–10): A density functional perspective. Journal of Molecular Structure, 1127, 522-531.
  * [42] Chattaraj, P. K., Nath, S., & Maiti, B. (2003). Reactivity descriptors (pp. 295-322). Marcel Dekker: New York.
  * [43] Geerlings, P., De Proft, F., & Langenaeker, W. (2003). Conceptual density functional theory. Chemical reviews, 103(5), 1793-1874.
  * [44] Koopmans, T. (1934). Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. physica, 1(1-6), 104-113.
  * [45] Boys, S. F., & Bernardi, F. J. M. P. (1970). The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Molecular Physics, 19(4), 553-566.
  * [46] Combinatorial search for optimal hydrogen-storage nanomaterials based on polymers. Physical review letters, 97(5), 056104
  * [47] Lee, H., Choi, W. I., Nguyen, M. C., Cha, M. H., Moon, E., & Ihm, J. (2007). Ab initio study of dihydrogen binding in metal-decorated polyacetylene for hydrogen storage. Physical Review B, 76(19), 195110.
  * [48] Lide, D. R. (Ed.). (2004). CRC handbook of chemistry and physics (Vol. 85). CRC press.
  * [49] Gaussian 09, Revision E.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2016.
  * [50] Szabo, A., & Ostlund, N. S. (2012). Modern quantum chemistry: introduction to advanced electronic structure theory. Courier Corporation.
  * [51] Zhao, Y., & Truhlar, D. G. (2008). The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theoretical chemistry accounts, 120(1), 215-241.Lee, H., Choi, W. I., & Ihm, J. (2006)
  * [52] Tenderholt, A. L., & Langner, K. M. (2008). Cclib: A library for package-independent computational chemistry algorithms. Journal of Computational Chemistry, 29(5), 839-845.
  * [53] Bader, R. F. (1991). A quantum theory of molecular structure and its applications. Chemical Reviews, 91(5), 893-928.Keith TA.
  * [54] AIMALL (version 11.02.27, standard). Overland Park,KS, USA: TK Gristmill Software; 2011.
  * [55] B. Schaefer, S. Alireza Ghasemi, S. Roy, S. Goedecker, Stabilized quasinewton optimization of noisy potential energy surfaces, The Journal of chemical physics 142 (3) (2015) 034112.
  * [56] S. Goedecker, W. Hellmann, T. Lenosky, Global minimum determination of the born-oppenheimer surface within density functional theory, Physical review letters 95 (5) (2005) 055
  * [57] Korabel’nikov, D. V., & Zhuravlev, Y. N. (2019). The nature of the chemical bond in oxyanionic crystals based on QTAIM topological analysis of electron densities. RSC advances, 9(21), 12020-12033.
  * [58] Du, J., Sun, X., Zhang, L., Zhang, C., & Jiang, G. (2018). Hydrogen storage of Li4&B36 cluster. Scientific Reports, 8(1), 1940.
  * [59] Niu, J., Rao, B. K., & Jena, P. (1992). Binding of hydrogen molecules by a transition-metal ion. Physical review letters, 68(15), 2277..
  * [60] Pearson, R. G. The principle of maximum hardness. Acc. Chem. Res. 1993, 26 (5), 250−255.
  * [61] Chattaraj, P. K., & Poddar, A. (1999). Molecular reactivity in the ground and excited electronic states through density-dependent local and global reactivity parameters. The Journal of Physical Chemistry A, 103(43), 8691-8699.
  * [62] Bader, R. F. W., Nguyen-Dang, T. T., & Tal, Y. (1981). A topological theory of molecular structure. Reports on Progress in Physics, 44(8), 893.
  * [63] Espinosa, E.; Alkorta, I.; Elguero, J.; Molins, E. From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X− H···F−Y systems. J. Chem. Phys. 2002, 117 (12), 5529−5542.
  * [64] Du, J.; Sun, X.; Zhang, L.; Zhang, C.; Jiang, G. Hydrogen storage of Li4&B36 cluster. Sci. Rep. 2018, 8 (1), 1−7.
  * [65] Korabel nikov, D. V.; Zhuravlev, Y. N. The nature of the chemical bond in oxyanionic crystals based on QTAIM topological analysis of electron densities. RSC Adv. 2019, 9 (21), 12020−12033.