A DFT study of the hydrogen storage potentials and properties on Ca, Fe, and Ti deposited NaSi 20 fullerenes

doi:10.21203/rs.3.rs-2374317/v1

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A DFT study of the hydrogen storage potentials and properties on Ca, Fe, and Ti deposited NaSi 20 fullerenes

https://doi.org/10.21203/rs.3.rs-2374317/v1

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In this work, the hydrogen storage materials of Ca, Fe, and Ti deposited NaSi₂₀ clusters have been investigated utilizing DFT methods (B3LYP and M06-2X) at the 6-311G(d, p) level. The orbital analysis and thermodynamic analysis were carried out and the adsorption capacity of H₂ molecules by hydrogen storage materials are predicted. The results show that the encapsulated Na atoms in the Si₂₀ cluster provide a relatively regular shape for the NaSi₂₀ fullerene cluster. And Ca, Fe, and Ti atoms tend to bind with two adjacent Si atoms of NaSi₂₀ cluster. The Ca@NaSi₂₀, Fe@NaSi_20, and Ti@NaSi₂₀ can adsorb up to three, four, and six hydrogen molecules, respectively. The adsorption energy (E_ads) per hydrogen molecule meets the United States Department of Energy (DOE) target for hydrogen storage materials for nH₂-Ti@NaSi₂₀ (n = 2–6) and nH₂-Fe@NaSi₂₀ (n = 1–4), implying that Fe and Ti deposited NaSi₂₀ fullerene may be a potentially suitable material for hydrogen storage.

NaSi20 fullerenes

DFT methods

Hydrogen storage

With the growth of the world population and the rapid development of the economy, all kinds of the social life of development have actively responded to the slogan of low-carbon and environmental protection, as well as the shortage of fossil fuels and global environmental problems, which threaten the peaceful survival of mankind and stimulate people's determination to find new energy sources [1, 2]. After the 1974 global energy crisis, the idea of hydrogen as an energy carrier came into public view [3]. As a renewable and clean energy source, hydrogen has several ideal characteristics, for example, it contains the largest energy weight of per unit, abundant in the natural environment and its combustion products do not pollute the environment like sulfur oxidation and aromatic hydrocarbon oxides [4]. The U.S Department of Energy (DOE) system has fixed the targets for hydrogen storage materials such as the operating pressure and temperature should be in the range of 0.3–1.2 MPa and 233.15-378.15 K, respectively and the average adsorption energy of each H₂ (average adsorption energy per H₂, E_ad/H₂) in an ideal hydrogen storage material should be between chemisorption and physical adsorption (0.1–0.8 eV) to meet the reversibility of the hydrogen storage material [5].

At present, there are many types of hydrogen storage materials. Carbon-based and chemically active hydrogen storage materials include fullerene, graphene, carbon nanotubes, etc. Nano-structured magnesium and magnesium-based hydrides can also store hydrogen molecules through adsorption [6]. Yoon et al. have found that the Ca atom can bind strongly to the C₆₀ surface and Ca₃₂C₆₀ can bind at least 92 H₂ molecules (8.4 wt %) [7]. Wu et al. have discovered that an isolated cluster Ca₁₂B₈₀ can bind up to 66 H₂ molecules (9.0 wt %) with an average binding energy of 0.096 eV/H₂ [8]. Wang et al. have modified the fullerene C₂₀ with metal atom M (M = Li, Ti, and Fe) and have found that its average adsorption energy was in the range of 0.25 and 0.80 eV, which was between physical adsorption and chemical adsorption and reversible adsorption of H₂ could be achieved [9]. Guo et al. have proved that by doping one Ti atom at the double bond position of C₆₀ it can adsorb six H₂ molecules [10]. Wang et al. have modified C₆₀ fullerene with 32 Ca atoms in the kinetic simulation, which not only has good stability but also can adsorb up to 62 H₂ molecules, and its weight density of hydrogen storage reaches 6.2 wt% [11].

In recent years, the semiconductor cluster has become one of the research objects in cluster science and the silicon cluster is the most widely used technology in the semiconductor cluster. And its interaction with hydrogen makes it become an outstanding candidate material for hydrogen storage. Silicon is not only rich in content, but also one of the most important materials in modern industry. Its use is popular in various fields of life, such as metallurgy, electronic manufacturing, the military industry, the medical and pharmaceutical industry, and the machinery manufacturing, etc. At the same time, the disadvantages of silicon materials are also very obvious. For example, the hollow structure of silicon and the unsaturated bonds with a lack of sp² hybridization in the silicon valence electrons deliver unstable fullerene cages, such as silicon nanotubes and silfullerene [12]. However, studies over the years have shown that their structure can be improved by various chemical modifications, such as encapsulating metal atoms in clusters [13] or using H adsorption to enhance sp³ bonding between Si atoms to improve stability [14]. At the same time, Ryou et al. have found that the binding energy between hydrogen molecules and silicon nanotubes was less than 0.1 eV even in stable structures through DFT calculation, and then pure silicon nanotubes were not suitable for hydrogen storage [15]. However, in recent years, through experimental and theoretical research on silicon, it has been found that doped hybrid carbon-silicon nanomaterials can be designed to improve their hydrogen storage performance [16]. Lan et al. used DFT to design Li₁₀Si₆₀H₆₀ composite material, and Li atom doping can improve the stability of Si₆₀H₆₀ and Li atoms adsorbed on the group are not as easy to gather together as other metals, which is a promising hydrogen storage material [17]. Barman et al. confirmed that Si₆₀H₆₀ doped with P atoms (P₁₀Si₅₀H₅₀) is a symmetric and stable fullerene structure that can avoid aggregation of Ti atoms. P₁₀Si₅₀H₅₀ modified with Ti atoms can be used for hydrogen storage and its hydrogen storage capacity is up to 5.23 wt% [18]. Kumar et al. have found that metal doping enhanced the stability and size selectivity of elemental clusters [19]. Ohara et al. proved experimentally that a transition metal atom M (M = Ti, Hf, Mo and W) could be encapsulated in a cage with Si_n (n = 15) by adsorption reaction and photoelectron spectroscopy [20]. Kumar and Kawazoe investigated the encapsulation of metal M (M = Hf, Zr, Fe, Ru, Os) in a cage-like Si_n (n = 14, 16). It was found that the size or compactness of the encapsulated silicon cage depended on the size of the doping atoms[21]. Sporea et al. have stabilized silicon clusters by encapsulating alkali metal atoms Na, K, and Li inside Si₂₀, and alkali metal atoms could provide regular shapes to Si₂₀ clusters [22]. Moreover, Ammar et al. have used DFT-based B3YLP and M06-2X methods to study the hydrogen storage properties of KSi₂₀ and Ti@KSi₂₀. The adsorption energy values per hydrogen molecule (E_ads) satisfy the United States Department of Energy (DOE) target for hydrogen storage materials and one Ti atom modified on the cluster could adsorb five hydrogen molecules at the same time [23].

In addition, Ca, Fe and Ti metal atoms are often considered and performed well in the previous studies of modified carbon and boron based hydrogen storage materials [7, 9, 19]. At the same time, Ca atom is the most active of the alkaline earth metals, Fe atom is the transition metal atom with more outer electrons, and Ti atom is the transition metal atom with fewer outer electrons. To the best of our knowledge, the deposition of NaSi₂₀ by Ca, Fe, and Ti atoms as hydrogen storage materials have not been investigated previously. In this work, the structures and property of new hydrogen storage materials Ca@NaSi₂₀, Fe@NaSi₂₀ and Ti@NaSi₂₀ were investigated by DFT B3LYP and M06-2X using the 6-311G(d, p) basis set. The orbital analysis and thermodynamic analysis were carried out and the adsorption capacity of H₂ molecules by these hydrogen storage materials are predicted. It is shown that Fe and Ti deposited NaSi₂₀ fullerene may be a potentially suitable materials for hydrogen storage and will have very important role for hydrogen storage.

To investigate the storage properties of H₂ molecules on Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ fullerenes, DFT methods [24] were performed at B3LYP/6-311G(d,p) and M06-2X/6-311G(d,p) levels of theory for the non-metallic atoms (H, Si) and an effective pseudo potential basis set LANL2DZ for Na, Ca, Fe, and Ti atoms. Full geometric optimizations were carried out for free H₂ molecules, Si₂₀, NaSi₂₀, Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ substrates as well as nH₂-Ca@NaSi₂₀ (n = 1–3), nH₂-Fe@NaSi₂₀ (n = 1–4), and nH₂-Ti@NaSi₂₀ (n = 1–6) complexes at B3LYP/6-311G(d,p) level. And the optimized structures were further used in the single-point energy calculations using M06-2X/6-311G(d,p) method. All calculations are finished using the Gaussian 09 suite of the program [25].

The ionization potential (IP), electron affinity (EA), and chemical hardness (η) can be expressed in terms of HOMO and LUMO,

$$\text{IP}\approx \text{-}{\text{E}}_{\text{HOMO}}$$

$$\text{EA}\approx -{E}_{\text{LUMO}}$$

$${\eta }\approx \frac{1}{2}\left(\text{IP-EA}\right)$$

The binding energies E_b of per atom for Si₂₀, NaSi₂₀, Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ are calculated from the Eq. (4),

$${E}_{b}=\frac{{E}_{\text{cluster}}-\sum {E}_{\text{atom}}}{\text{total EquationNumber of the cluster atoms}}$$

where E_atom is the sum of the atomic energies of the cluster free atoms and E_cluster is the energy of the optimized cluster. The most stable spin state is considered for the Si, Na, Ca, Fe, and Ti free atoms. The binding energies (E_bind) of Ca, Fe, and Ti atoms on NaSi₂₀ substrate clusters are calculated from the Eq. (5). The adsorption energies (E_ads) for nH₂ molecule (n = 1–6) and the average adsorption energy per hydrogen molecule ($\stackrel{-}{E}$_ads) on M@NaSi₂₀ (Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀) fullerenes are calculated from equations (6) and (7), respectively.

$${E}_{\text{bind}}=\text{ }{\text{E}}_{M@\text{NaS}{\text{i}}_{20}}-\left({E}_{\text{NaS}{\text{i}}_{20}}+{E}_{M}\right)$$

$${E}_{\text{ads}}={E}_{\text{n}{\text{H}}_{2}/M@\text{NaS}{\text{i}}_{20}}-\left(\text{n}{\text{E}}_{{H}_{2}}+{E}_{M@\text{NaS}{\text{i}}_{20}}\right)$$

$${\stackrel{̄}{E}}_{\text{ads}}=\frac{1}{n}\left[{E}_{\text{n}{\text{H}}_{2}/M@\text{NaS}{\text{i}}_{20}}-\left(\text{n}{\text{E}}_{{H}_{2}}+{E}_{M@\text{NaS}{\text{i}}_{20}}\right)\right]$$

where ${{\text{E}}_{{\text{M}}@{\text{NaS}}{{\text{i}}_{{\text{2}}0}}}}$ is the energy of the optimized Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ complexes, ${{\text{E}}_{{\text{M}}@{\text{NaS}}{{\text{i}}_{{\text{2}}0}}}}$ is the energy of the corresponding optimized NaSi₂₀ substrate clusters, and E_M is the atomic energy of the free M (M = Ca, Fe, and Ti) atom, ${{\text{E}}_{{\text{n}}{{\text{H}}_{\text{2}}}/{\text{M}}@{\text{NaS}}{{\text{i}}_{{\text{2}}0}}}}$ is the total energy of the optimized nH₂-M@NaSi₂₀ (M = Ca, Fe, and Ti).

Enthalpy difference (ΔH^Ɵ) and Gibbs free energy difference (ΔG^Ɵ) for nH₂-M@NaSi₂₀ (M = Ca, Fe, Ti) complexes are calculated from equations (8) and (9) [26], respectively.

$${\Delta }{\text{H}}^{{\Theta }}=\left[{{\text{H}}^{{\Theta }}}_{\text{n}{\text{H}}_{2}-\text{M}@\text{NaS}{\text{i}}_{20}}-\left(\text{n}{{\text{H}}^{{\Theta }}}_{{\text{H}}_{2}}+{{\text{H}}^{{\Theta }}}_{\text{M}@\text{NaS}{\text{i}}_{20}}\right)\right]/\text{n}$$

where, H^Ɵ_{nH2−M@NaSi20}, H^Ɵ_M@NaSi20, and H^Ɵ_H2 are the enthalpies for nH₂-M@NaSi₂₀, M@NaSi₂₀ and H₂ molecule, respectively.

$${\Delta }{\text{G}}^{{\Theta }}=\left[{{\text{G}}^{{\Theta }}}_{\text{n}{\text{H}}_{2}-\text{M}@\text{NaS}{\text{i}}_{20}}-\left(\text{n}{{\text{G}}^{{\Theta }}}_{{\text{H}}_{2}}+{{\text{G}}^{{\Theta }}}_{\text{M}@\text{NaS}{\text{i}}_{20}}\right)\right]/\text{n}$$

where, ${G^\theta }_{{{\text{n}}{{\text{H}}_{\text{2}}} - {\text{M}}@{\text{NaS}}{{\text{i}}_{{\text{2}}0}}}}$, ${G^\theta }_{{{\text{M}}@{\text{NaS}}{{\text{i}}_{{\text{2}}0}}}}$ and ${G^\theta }_{{{{\text{H}}_{\text{2}}}}}$ are the free energies for nH₂-M@NaSi₂₀, M@NaSi₂₀ and H₂ molecule, respectively.

Geometric structures and electronic properties of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters

The optimized structures of Si₂₀ and NaSi₂₀ fullerenes as well as Ca, Fe, and Ti deposited NaSi₂₀ fullerenes, named Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters are shown in Fig. 1. The geometric and electronic properties of the investigated clusters are listed in Table 1. As can be seen from Fig. 1(a), the Si₂₀ fullerene cluster is a distorted cage with the shortest silicon-silicon bond lengths (d_Si−Si) of 2.279 Å and the dipole moments of 1.198 Debye at B3LYP level. In addition, the encapsulated Na atom into the Si₂₀ cluster has delivered the regular shape to the NaSi₂₀ cluster was shown in Fig. 1(b). Compared with the pure silicon cage without encapsulated metal atoms, the NaSi₂₀ shape has become more uniform and the d_Si−Si bond length is increased to 2.777 Å at the B3LYP level, which is similar to the previous report by Borshch et al. [27]. Moreover, the Na encapsulation into Si₂₀ clusters at the B3LYP and M06-2X level resulted in an increase in electron affinity (EA) values from 3.616 and 3.095 eV to 3.926 and 3.410 eV, while the HOMO-LUMO gaps (E_g) decreased from 2.163 and 3.486 eV to 1.329 and 2.512 eV, respectively. The chemical hardness (η) value decreased by 38.63% and 27.94% and the binding energies per atom (E_b) increased by 4.5% and 5.2% at B3LYP and M06-2X level, respectively.

Table 1

Ionization potential (IP, eV), electron affinity (EA, eV), hardness (η, eV), HOMO and LUMO energy gap (E_g, eV), binding energy per atom (E_b, eV), dipole moment (D, Debye), bond length (d, Å), binding energy (E_bind, eV) of Si₂₀, NaSi₂₀, Ca@NaSi₂₀, Fe@NaSi₂₀ and Ti@NaSi₂₀ as well as Mulliken charges (Q, e) of Ca, Fe, Ti atoms in the clusters.
	Si₂₀		NaSi₂₀		Ca@NaSi₂₀		Fe@NaSi₂₀		Ti@NaSi₂₀
	B3LYP	M06-2X	B3LYP	M06-2X	B3LYP	M06-2X	B3LYP	M06-2X	B3LYP	M06-2X
IP	5.780	6.581	5.255	5.922	4.761	5.485	5.372	5.656	5.209	5.391
EA	3.616	3.095	3.926	3.410	3.776	3.303	3.911	3.831	3.795	3.432
η	1.082	1.743	0.664	1.256	0.493	1.091	0.730	0.913	0.707	0.979
E_g	2.163	3.486	1.329	2.512	0.986	2.182	1.460	1.825	1.414	1.959
E_b	-4.285	-4.540	-4.091	-4.306	-3.955	-4.155	-4.137	-4.286	-4.103	-4.250
D	1.198	1.215	0.163	0.259	11.843	11.489	2.966	1.597	8.502	9.983
d_Si−Si/d_M−Si	2.279	-	2.777	-	3.013	-	2.367	-	2.502	-
E_bind					-1.091	-0.992	-5.109	-3.877	-4.348	-3.069
Q_M					1.266	1.042	-0.184	-0.123	0.398	0.466

The deposition of Ca, Fe, and Ti atoms at different sites of NaSi₂₀ fullerene was tested. The most energetic stable structures after the optimizations are shown in Fig. 1(c, d, and e). Ammar et al. [23] have explored that Ti atoms deposited on KSi₂₀ are also connected with two adjacent silicon atoms, and our results showed that Ca, Fe, and Ti were connected to NaSi₂₀ in the same manner. As shown in Table 1, the ionization potential (IP) of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters compared with Si₂₀ are reduced by about 17.63%, 7.05% and 9.88% at B3LYP and 16.65%, 14.06%, and 18.08% at M06-2X, respectively. This indicates that the clusters Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ are less stable than the pure Si₂₀. According to Baei's reports [28], the energy gap (E_g) is associated with chemical reactivity and stability. In our research, the deposition-enabling gap (E_g) of Fe and Ti on NaSi₂₀ is larger than that of NaSi₂₀, while the deposition-enabling gap (E_g) of Ca on NaSi₂₀ is smaller than that of NaSi₂₀ at the theory level of B3LYP. Similarly, the chemical hardness (η) of Fe@NaSi₂₀ and Ti@NaSi₂₀ increased by 9.93% and 6.48%, and that of Ca@NaSi₂₀ decreased by 25.75% at B3LYP level. When using the M06-2X method, the enabling gap (E_g) of Ca, Fe, and Ti deposited on NaSi₂₀ is smaller than that of NaSi₂₀, so the chemical hardness of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ is smaller than that of NaSi₂₀. The chemical hardness (η) of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ decreased by 22.05%, 27.31%, and 13.14% using the M06-2X method, respectively. Because the weak interaction system is considered in the fitting parameters of M06-2X, the weak interaction can be well described. At the same time, the accuracy of M06-2X in calculating thermodynamic quantities such as reaction energy, isomerization energy, and the energy barrier is one of its significant advantages. From the calculations, it can be concluded that the stability of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ is lower than that of the NaSi₂₀ cluster. Moreover, the E_b values of Ca, Fe, and Ti deposited on NaSi₂₀ increased by about 3.51%, 0.47%, and 1.31% compared with that of NaSi₂₀ at the M06-2X method, while the E_b values of Fe and Ti deposited on NaSi₂₀ decreased slightly by about 1.12% and 1.20% at B3LYP method. After Ca deposition on NaSi₂₀, the binding energy increased by about 3.61%, which was the same as the binding energy change of Ti deposition on C₂₀ and KSi₂₀ reported by Ammar et al [23]. Then, the deposition of Ca, Fe, and Ti on NaSi₂₀ decreased the stability of NaSi₂₀ and at the same time increased the reaction reactivity.

Interaction of H₂ on Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀

The adsorptions of n hydrogen molecules on Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ have been carried out in this work to identify the hydrogen storage materials. The optimized structures of nH₂-Ca@NaSi₂₀, nH₂-Fe@NaSi₂₀, and nH₂-Ti@NaSi₂₀ are shown in Fig. 2. It can be seen from Fig. 2, all structures of hydrogen molecules are not broken and are adsorbed as molecules by metal atoms. The adsorption properties are listed in Table 2–4. Equations (6) and (7) are used to calculate the adsorption energies and average adsorption energy per hydrogen molecule, as shown in Fig. 3 (a, b), respectively. The H-H bond length of free H₂ molecular is calculated to be 0.744 and 0.740 Å using the B3LYP and M06-2X methods.

Table 2

The dipole moment (D, Debye), bond length (d, Å), adsorption energy (E_ads, eV) and Mulliken charges (Q, e) of Ca@NaSi₂₀.
	D	d_Ca−Si	d_Ca−H	d_H−H	E_ads			$\stackrel{-}{\mathbf{E}}$_ads		Q_Na	Q_Ca	${\mathbf{Q}}_{{\mathbf{H}}_{2}}$
	B3LYP	B3LYP	B3LYP	B3LYP	B3LYP		M06-2X	B3LYP	M06-2X	B3LYP	B3LYP	B3LYP
H₂-Ca@NaSi₂₀	11.881	3.012	4.054	0.745	0.023	-0.040		0.023	-0.040	-0.311	1.020	-0.017
2H₂-Ca@NaSi₂₀	11.816	3.009	4.133	0.745	0.048	-0.041		0.024	-0.021	-0.323	1.029	0.005
			5.552	0.745								-0.019
3H₂-Ca@NaSi₂₀	11.857	3.009	4.107	0.745	0.057	-0.042		0.019	-0.014	-0.321	1.030	0.005
			5.411	0.745								-0.021
			6.259	0.744								-0.001

Adsorption of H₂ on Ca@NaSi₂₀

The interactions between H₂ and Ca@NaSi₂₀ have been discussed in this section. It can be seen from Table 2 that a single H₂ molecule has interacted with the Ca@NaSi₂₀ cluster leading to the change of adsorption energy with + 0.023 eV at the B3LYP method and the change of adsorption energy with − 0.040 eV at M06-2X method, respectively. The hydrogen bond lengths d_H−H of the hydrogen molecule adsorbed to Ca@NaSi₂₀ are 0.745 Å. And the distance between the Ca and the adsorbed H atom (d_Ca−H) is 4.054 Å at the B3LYP methods. By comparing the hydrogen bond lengths of free hydrogen molecules, it can also be seen from Fig. 2 that the chemical bond of the first H₂ adsorbed to Ca@NaSi₂₀ is not broken and H₂ has adsorbed in the form of molecules. Throughout the Mulliken charge analysis, it can be found that the H₂ molecule gained a negative charge of 0.017 e at the B3LYP level. This indicates that the charge transfer from Ca@NaSi₂₀ to the H₂ molecule has occurred. In addition, the positive charge on the Ca atom decreased by 0.246 e at the B3LYP level. The average adsorption energy of the nH₂-Ca@NaSi₂₀ is in the range of 0.019–0.024 eV using the B3LYP method, and the differences from the average adsorption energy of the first H₂ molecule to that of the third H₂ molecule are small and negligible from Fig. 3. It is from − 0.040 to -0.014 eV using M06-2X, and the absolute average adsorption energy from the first H₂ molecule to the third H₂ molecule decreased gradually. It can be seen from Table 2 that when adsorbing the second H₂ molecule both the distances d_Ca−Si between Ca and Si atom is 3.009 Å using B3LYP methods, and the d_Ca−Si value is the same as that of adsorbing the third H₂. In contrast, when the third H₂ molecule was adsorbed at B3LYP level, the distance between the H₂ molecule and Ca@NaSi₂₀ is 6.259 Å as shown in Table 2. However, the bond length of the H₂ molecule was similar to that of the free H₂ molecule (0.744 Å), and the adsorption energy change is lower, which means that the third H₂ molecule is not bonded to Ca@NaSi₂₀. In other words, the Ca@NaSi₂₀ cluster is saturated with only two hydrogen molecules. It can be also seen from Table 2 and Fig. 3 that for the nH₂-Ca@NaSi₂₀ clusters, with the increasing of H₂ molecule the E_ads of the cluster increased and changed very slightly. When the third H₂ molecule was adsorbed, E_ads becomes smaller than that of the second hydrogen molecule, indicating that the adsorption reaches saturation. Then although the hydrogen storage capacity of the NaSi₂₀ cluster modified by the Ca atom is much weak, which was lower than the minimum value of 0.1 eV for reversible adsorption, it could still adsorb up to three H₂ molecules effectively, hence it is not an ideal hydrogen storage material because it is unstable after adsorption.

Adsorption of H₂ on Fe@NaSi₂₀

This section concerns the interaction of the H₂ molecules with the Fe@NaSi₂₀ cluster. As can be seen from Table 3, when a single H₂ molecule is close to the Fe@NaSi₂₀ cluster, the adsorption energy of 0.175 and 0.291 eV is released as calculated by B3LYP and M06-2X method, respectively. The bond length of the H₂ molecule dilated to 0.802 Å instead of 0.744 Å for the free H₂ molecule and after adsorbing one H₂, the distance between the Si and Fe atom (d_Fe−Si) is 2.320 Å at B3LYP level. In addition, it can be seen from Fig. 2 that the first H₂ hydrogen bond adsorbed by Fe@NaSi₂₀ has not been broken and adsorbed in molecular form. Meanwhile, the bond length of the H₂ molecule is in the range of 0.8-1.0 Å [29], so the H₂ molecule formed a true ligand with Fe@NaSi₂₀. Seen from the Mulliken charge analysis, the H₂ molecule (${\text{Q}}_{{\text{H}}_{2}}$) gained a positive charge of 0.119 e, while the negative charge on the Fe atom changed by 0.114 e at B3LYP level. When the number of the adsorbed H₂ molecules increased from one to four molecules, the absolute value of the adsorption energy changed from 0.291 to 0.508 eV at M06-2X level and from 0.175 to 0.067 eV at B3LYP level from Table 3. As can be seen from Fig. 4, as the number of adsorbed H₂ increased, the negative E_g value of the complex became larger from the first to fourth H₂ and the E_g reached saturation value when the fourth H₂ molecule was adsorbed. However, the E_g value increased from − 2.689 eV to -1.348 eV when the Fe@NaSi₂₀ system adsorbed the fifth H₂ molecule. It is shown that it could not adsorb the fifth H₂ molecule effectively. According to the calculation of B3LYP, the average adsorption energy of hydrogen is in the range of -0.175 to 0.017 eV. According to M06-2X calculation, the average adsorption energy range of hydrogen is from − 0.125 to -0.291 eV, and the average adsorption energy of all hydrogen molecules adsorbed is higher than 0.1 eV, which is within the range of reversible adsorption. Therefore, nH₂-Fe@NaSi₂₀ (n = 4) can realize reversible adsorption of H₂ and can adsorb up to 4 hydrogen molecules. And the adsorption capacity of Fe@NaSi₂₀ for H₂ is greater than that of Ca@NaSi₂₀.

Table 3

The dipole moment (D, Debye), bond length (d, Å), adsorption energy (E_ads, eV) and Mulliken charges (Q, e) of Fe@NaSi₂₀.
	D	d_Fe−Si	d_Fe−H	d_H−H	E_ads		$\stackrel{-}{\mathbf{E}}$_ads		Q_Na	Q_Fe	${\mathbf{Q}}_{{\mathbf{H}}_{2}}$
	B3LYP	B3LYP	B3LYP	B3LYP	B3LYP	M06-2X	B3LYP	M06-2X	B3LYP	B3LYP	B3LYP
H₂-Fe@NaSi₂₀	3.359	2.320	1.771	0.802	-0.175	-0.291	-0.175	-0.291	-0.408	-0.298	0.119
2H₂-Fe@NaSi₂₀	3.397	2.260	1.629	0.851	0.156	-0.345	0.078	-0.172	-0.346	-0.434	0.296
			1.635	0.845							0.265
3H₂-Fe@NaSi₂₀	3.020	2.275	1.637	0.838	0.076	-0.374	0.025	-0.125	-0.344	-0.614	0.250
			1.635	0.842							0.230
			1.756	0.796							0.126
4H₂-Fe@NaSi₂₀	3.083	2.289	1.636	0.843	0.067	-0.508	0.017	-0.127	-0.368	-0.630	0.257
			1.637	0.839							0.255
			1.769	0.793							0.005
			3.387	0.744							-0.023

Table 4

The dipole moment (D, Debye), bond length (d, Å), adsorption energy (E_ads, eV) and Mulliken charges (Q, e) of Ti@NaSi₂₀.
	D	d_Ti−Si	d_Ti−H	d_H−H	E_ads		$\stackrel{-}{\mathbf{E}}$_ads		Q_Na	Q_Ti	${\mathbf{Q}}_{{\mathbf{H}}_{2}}$
	B3LYP	B3LYP	B3LYP	B3LYP	B3LYP	M06-2X	B3LYP	M06-2X	B3LYP	B3LYP	B3LYP
H₂-Ti@NaSi₂₀	8.252	2.465	1.957	0.791	0.185	-0.925	0.185	-0.925	-0.344	0.353	-0.155
2H₂-Ti@NaSi₂₀	7.850	2.452	1.870	0.824	0.261	-0.966	0.130	-0.483	-0.347	0.297	-0.131
			1.855	0.825							-0.118
3H₂-Ti@NaSi₂₀	6.133	2.470	1.856	0.826	-0.270	-0.694	-0.090	-0.231	-0.353	0.252	-0.026
			1.855	0.840							-0.007
			1.866	0.826							0.095
4H₂-Ti@NaSi₂₀	9.268	2.546	2.020	0.776	-0.512	-2.091	-0.128	-0.523	-0.366	0.279	-0.036
			2.120	0.768							-0.054
			2.028	0.775							0.094
			1.980	0.798							0.305
5H₂-Ti@NaSi₂₀	6.426	2.535	1.912	0.814	-0.413	-1.552	-0.083	-0.311	-0.404	0.220	-0.021
			1.907	0.816							0.008
			2.014	0.793							0.101
			1.875	0.818							0.149
			1.844	0.836							0.190
6H₂-Ti@NaSi₂₀	7.089	2.656	1.818	0.846	-0.279	-1.580	-0.047	-0.263	-0.390	0.240	-0.020
			1.916	0.811							0.041
			1.970	0.803							0.103
			1.917	0.803							0.204
			1.995	0.796							0.191
			1.921	0.810							0.161

Adsorption of H₂ on Ti@NaSi₂₀

The optimized geometrical parameters of the adsorbed H₂ molecules complexes nH₂-Ti@NaSi₂₀ are given in Table 4. When a single H₂ molecule interacted with the Ti@NaSi₂₀ cluster, the absolute value of the adsorption energy E_ads is 0.185 and 0.925 eV at B3LYP and M06-2X level, respectively. Moreover, the distance between the Ti atom and NaSi₂₀ cluster (d_Ti−Si) has no significant change, however, a bond length stretch of the H₂ molecule (d_H−H) is observed to be 0.791 Å instead of 0.744 Å for the free H₂ molecule. And the d_Ti−H is 1.957 Å at B3LYP. Compared with the hydrogen bond lengths in free H₂ molecules, it can be seen from Fig. 2 that the first H₂ hydrogen bond in the complex H₂-Ti@NaSi₂₀ is not broken and adsorbed in molecular form. Compared with that of Ti@NaSi_20, the Mulliken charge analysis result shows that the positive charge on the Ti atom in H₂-Ti@NaSi₂₀ decreased by 0.045 e at B3LYP level. Because of the charge redistribution, the dipole moment of H₂-Ti@NaSi₂₀ is less than that of Ti@NaSi₂₀ by 0.250 Debye at B3LYP level. According to Ref. [29–30], if the average adsorption energy of H₂ is between 0.1–0.8 eV, the adsorption and desorption reactions maybe occur easily. With the number increasing of H₂ molecules from two to six molecules, the absolute value of adsorption energy increased first and then decreased. When the fourth hydrogen molecule was adsorbed, the adsorption energy reached a minimum of -0.512eV at B3LYP level and − 2.091eV at M06-2X level, as shown in Table 4 and Fig. 3(a). With the increase in the number of adsorbed hydrogen molecules, the average adsorption energy and the energy gap of the system increased from one to three H₂ increasing and then decreasing from three to six H₂. While the sixth hydrogen molecule was adsorbed, the distance d_Ti−Si gradually dilated up to 2.656 Å at B3LYP. Furthermore, a decrease is noticed for the charge on the Ti atom to reach 0.240 e at B3LYP level, while a low charge of -0.020 e is observed on the H₂ molecules at B3LYP level. Additionally, the values of the H₂ bond lengths are in the range from 0.775 Å to 0.846 Å at B3LYP level, indicating that hydrogen molecules are adsorbed on the clusters. This implies that according to B3LYP and M06-2X calculations, the capability of the Ti@NaSi₂₀ cluster to adsorb a large number of hydrogen molecules is more than that of the Ca@NaSi₂₀ and Fe@NaSi₂₀ clusters. Consequently, the average adsorption energy per molecule ($\stackrel{-}{E}$_ads) for all the considered nH₂-Ti@NaSi₂₀ complexes beyond n = 1 at M06-2X level encounters the decisive boards of DOE for physisorption (0.1–0.8 eV) as shown in Fig. 3 (b).

Orbital analysis

The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) distributions are illustrated in Fig. 5 for Fe@NaSi₂₀, Ti@NaSi₂₀, 4H₂-Fe@NaSi₂₀, and 4H₂-Ti@NaSi₂₀ clusters. The active point is the region with high local charge density, pink and purple represent positive and negative wave functions, respectively. As can be seen from Fig. 5, the LUMO of Fe@NaSi₂₀ is mainly delocalized in the Si atoms near the Fe atoms, and nearly no contributions could be seen from the bottom Si atoms located far from the Fe atom, however, the HOMO of Fe@NaSi₂₀ is mainly located on Si atoms. In Ti@NaSi₂₀, both the LUMO and HOMO electrons are mainly localized in the Si and Ti atoms.

When the Fe@NaSi₂₀ cluster adsorbs four H₂ molecules, it is obvious that the HOMO electrons of the Fe and Si atoms in 4H₂-Fe@NaSi₂₀ increased and the delocalized electrons of LUMO orbitals decreased, which is in agreement with the lowest energy gap E_g in nH₂-Fe@NaSi₂₀ clusters. When the Ti@NaSi₂₀ cluster adsorbs four H₂ molecules, it is also obvious that the HOMO electrons of Si atoms in 4H₂-Ti@NaSi₂₀ increased and the delocalized electrons of LUMO orbitals decreased, implying that the stability of 4H₂-Ti@NaSi₂₀ increased, which is in agreement with the lower adsorption energy E_adv in nH₂-Fe@NaSi₂₀ clusters. Compared HOMO and LUMO of 4H₂-Ti@NaSi₂₀ with 4H₂-Fe@NaSi₂₀ clusters, it is found that for 4H₂-Ti @NaSi₂₀ cluster, the distribution of frontier orbitals increased on HOMO orbitals and decreased on LUMO orbitals, which explains that the 4H₂-Ti@NaSi₂₀ is more stable than 4H₂-Fe@NaSi₂₀, which is the good agreement with the E_adv prediction above.

Adsorbed H₂ predication

Theoretically, the Effective Atomic Number Rule (EAN) can be used to calculate the maximum adsorption capacity of hydrogen atoms of hydrogen storage materials doped with metal atoms on the surface [31]. The equation is as follows,

${{\text{n}}_{\text{H}}}={\text{18}} - {\text{n}}_{v}^{{\text{e}}} - {\text{n}}_{s}^{e} - {\text{n}}_{m}^{e}$

Where, ${\text{n}}_{v}^{{\text{e}}}$ is the number of valence electrons of metal atoms, ${\text{n}}_{s}^{e}$ is the number of bonds the metal has with the base, and ${\text{n}}_{m}^{e}$ is the number of bonds between neighboring metal atoms. Considering the 3d orbitals of transition metal atoms Ti and Fe, the number of valence electrons (${\text{n}}_{v}^{{\text{e}}}$) of Ca, Fe, and Ti atoms is 2, 8, and 4, respectively. Since M is adsorbed above the Si-Si bond, ${\text{n}}_{s}^{e}$ =2, the n_H of M@NaSi₂₀ (M = Ca, Fe, and Ti) is calculated to be 14, 8, and 12, respectively, which means that the maximum adsorption numbers of hydrogen molecules are 7, 4, and 6. Compared with the calculation results, it can be seen that the hydrogen storage property of Ca@NaSi₂₀ is less than the theoretical results, so the hydrogen storage performance is poor. The maximum hydrogen storage number of M@NaSi₂₀ (M = Fe, Ti) conforms to the theoretical expectation, that is, the number of H₂ molecules that can be adsorbed conforms to the EAN. At the same time, we tried to adsorb the 4th, 5th, and 7th H₂ molecules to Ca@NaSi₂₀, Fe@NaSi_20, and Ti@NaSi₂₀, respectively, and all the results failed to converge, which further means that Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ can adsorb at most 3, 4, and 6 H₂ molecules.

Thermodynamic analysis

Enthalpy difference (ΔH^Ɵ) can express the strength of the interaction and free energy difference (ΔG^Ɵ) is a measure of the spontaneity of the reaction, which are the key thermodynamic parameters for the interaction between hydrogen and the sorbent materials. ΔH^Ɵ and ΔG^Ɵ are graphed in Fig. 6 as a function of the number of hydrogen molecules for nH₂-Ca@NaSi₂₀, nH₂-Fe@NaSi₂₀, and nH₂-Ti@NaSi₂₀ complexes. As shown in Fig. 6 (a), ΔH^Ɵ values for all the considered structures are negative values indicating exothermic reactions. Furthermore, Ti@NaSi₂₀ shows the higher exothermicity towards the hydrogen compared to Ca@NaSi₂₀ and Fe@NaSi₂₀. The greatest negative ΔH^Ɵ value is 20.45 kcal/mol recorded for Ti@NaSi₂₀ at n = 1. As the number of H₂ molecules increased from n = 2–6, the negative ΔH^Ɵ values decreased. This emphasizes the physisorption of hydrogen molecules on the investigated clusters. Figure 6 (b) shows that the ΔG^Ɵ of 3H₂-Ca@NaSi₂₀ is the largest among all complexes, which is 10.50 kcal/mol, while those of 1H₂-Ti@NaSi₂₀, 2H₂-Ti@NaSi₂₀, 4H₂-Ti@NaSi₂₀, and 5H₂-Ti@NaSi₂₀ in nH₂-Ti@NaSi₂₀ complex are all negative (ΔG^Ɵ < 0), which show that they are spontaneous reactions. Because the more negative ΔH^Ɵ values point to more stability and the less negative ΔG^Ɵ values point to a high ability to reverse the reaction [32–34], therefore as the number of hydrogen molecules increased the stability decreased, and the ability to retrieve the stored hydrogen molecules increased.

In this study, the DFT methods are performed at B3LYP and M06-2X levels of theory to investigate the storage characteristics of H₂ molecules on Ca, Fe, and Ti deposited NaSi₂₀ fullerenes. The results show that the encapsulated Na atom into the Si₂₀ cluster delivers the regular shape to the NaSi₂₀. The deposition of the Ca, Fe and Ti atom on NaSi₂₀ clusters decreases the ionization potential (IP), HOMO-LUMO energy gap (E_g), and hardness (η), as well as increases the dipole moment (D), which confirms the less stability and consequently high reactivity of Ca@NaSi₂₀, Fe@NaSi₂₀ and Ti@NaSi₂₀ clusters than those of NaSi₂₀ clusters. Additionally, the Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters are saturated with three, four, and six H₂ molecules. The adsorption energy values (E_ads) per hydrogen molecule meet the United States Department of Energy (DOE) target for hydrogen storage materials for nH₂-Ti@NaSi₂₀ (n = 2–6) and nH₂-Fe@NaSi₂₀ (n = 1–4), implying that NaSi₂₀ fullerene may be a potentially suitable material for hydrogen storage. The calculated enthalpy difference emphasizes the physisorption of hydrogen on the investigated clusters for some hydrogen molecules greater than one.

Acknowledgments

The present work was conducted under the help of the Youth Innovation Team of Shaanxi Universities (Environmental Pollution Monitoring and Control Innovation Team, 51). We acknowledge financial support by Natural Science Basic Research Plan in Shaanxi Province of China [grant number 2022JM-075 ] and the Three-year action plan project of Xi'an University [grant number 21XJZZ0001-11 ].

Author contribution

Huixi Yang: Conceptualization, Data curation, Investigation, Methodology, Visualization, Writing - original draft, Writing - review & editing. Bin Liu: Data curation, Methodology, Visualization, Investigation, Writing - review & editing. Hongjiang Ren: Supervision, Formal analysis, Funding acquisition, Resources, Writing - review & editing.

Code availability Gaussian 09 package program

Funding Declaration

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.

Competing interests The authors declare no competing interests.

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A DFT study of the hydrogen storage potentials and properties on Ca, Fe, and Ti deposited NaSi 20 fullerenes

Status:

Version 1

Abstract

Figures

Introduction

Computational Methods

Results And Discussion

Geometric structures and electronic properties of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters

Interaction of H₂ on Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀

Adsorption of H₂ on Ca@NaSi₂₀

Adsorption of H₂ on Fe@NaSi₂₀

Adsorption of H₂ on Ti@NaSi₂₀

Orbital analysis

Adsorbed H₂ predication

Thermodynamic analysis

Conclusion

Declarations

References

Additional Declarations

Status:

Version 1

A DFT study of the hydrogen storage potentials and properties on Ca, Fe, and Ti deposited NaSi 20 fullerenes

Status:

Version 1

Abstract

Figures

Introduction

Computational Methods

Results And Discussion

Geometric structures and electronic properties of Ca@NaSi20, Fe@NaSi20, and Ti@NaSi20 clusters

Interaction of H2 on Ca@NaSi20, Fe@NaSi20, and Ti@NaSi20

Adsorption of H2 on Ca@NaSi20

Adsorption of H2 on Fe@NaSi20

Adsorption of H2 on Ti@NaSi20

Orbital analysis

Adsorbed H2 predication

Thermodynamic analysis

Conclusion

Declarations

References

Additional Declarations

Status:

Version 1

Geometric structures and electronic properties of Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀ clusters

Interaction of H₂ on Ca@NaSi₂₀, Fe@NaSi₂₀, and Ti@NaSi₂₀

Adsorption of H₂ on Ca@NaSi₂₀

Adsorption of H₂ on Fe@NaSi₂₀

Adsorption of H₂ on Ti@NaSi₂₀

Adsorbed H₂ predication