A Comparative Density Functional Theory Study of Hydrogen Storage in Cellulose and Chitosan Functionalized by Transition Metals (Ti, Mg, and Nb)

The focus of this work is hydrogen storage in pristine cellulose, chitosan, and cellulose. Chitosan doped with magnesium, titanium, and niobium is analyzed using spin unrestricted plane-wave density functional theory implemented in the Dmol3 module. The results of this study demonstrate that hydrogen interaction with pure cellulose and chitosan occurred in the gas phase, with an adsorption energy of Eb = 0.095 eV and 0.090 eV for cellulose and chitosan, respectively. Additionally, their chemical stability was determined as Eb= 4.63 eV and Eb = 4.720 eV for pure cellulose and chitosan, respectively, by evaluating their band gap. Furthermore, the presence of magnesium, titanium, and niobium on cellulose and chitosan implied the transfer of an electron from metal to cellulose and chitosan. Moreover, our calculations predict that cellulose doped with niobium is the most favorable medium where 6H2 molecules are stored compared with molecules stored in niobium-doped chitosan with Tmax = 818 K to release all H2 molecules. Furthermore, our findings showed that titanium-doped cellulose has a storage capacity of five H2 molecules, compared to a storage capacity of four H2 molecules in titanium-doped chitosan. However, magnesium-doped cellulose and chitosan have insufficient hydrogen storage capacity, with only two H2 molecules physisorbed in the gas phase. These results suggest that niobium-doped cellulose and chitosan may play a crucial role in the search for efficient and inexpensive hydrogen storage media.


Introduction
The increase in greenhouse gas emissions in the atmosphere accelerates global warming that threatens life on earth [1].Therefore, a smooth transition from fossil fuels to clean and sustainable fuels is required. Owing to its high energy content per mass (142 KJ/g) compared to petroleum (47 KJ/g), hydrogen is an optimum clean fuel; when used in fuel cells to generate electricity, it produces water [2,3]. However, the use of H 2 in the future clean economy will still face many obstacles and require various problems to be addressed. When generated, hydrogen has to be stored, and finding a safe and efficient hydrogen storage medium is important for the future hydrogen-based economy. Many hydrogen storage methods have been proposed to date. The most well-known method involves storing gas H 2 in high-pressure tanks [4,5]. However, compressing gaseous hydrogen in the pressure range of 70-80 MPa in a tank creates an additional risk of hydrogen-related embrittlement of the tank walls. Hydrogen can also be stored in cryogenic tanks, although this method requires thermal insulation and cooling of hydrogen below the critical temperature of 33 K. Significant energy is required to liquify H 2 , coupled with continuous boil-off. Therefore, to find an alternative way of storing hydrogen, the U.S. Department of Energy (DOE) initiated support for the extensive search for the materials for H 2 storage media in 2003. The criteria set by the DOE for materials for onboard hydrogen storage were specified as (i) high storage capability, that is, 5.5 wt% and 40 g/L at ambient temperatures; basis set, included the vdW interaction (DFT-D), as proposed by Grimme [38]. Energy minimization was achieved with a convergence tolerance energy of 10 −5 Ha. The atomic positions were relaxed such that the force acting on each atom was less than 0.002 Ha/Å.

Results and Discussion
We investigated the interaction between pure cellulose and transition metals (T.M.s), such as titanium (Ti), magnesium (Mg), and niobium (Nb). Similar calculations were performed for chitosan with the same metals. The strength of the interaction was measured using the following equation: where E (A) is the total energy of transition metals in an isolated cubic cell of lattice (a = b = c = 25 Å), E (B) is the ground energy of cellulose or chitosan, and E (AB) is the total energy of cellulose or chitosan doped with the mentioned TMs. The optimized structures of cellulose and chitosan are displayed in Figure 1.
We performed a first-principles calculation using spin unrestricted plane-wave density functional theory with the self-consistent field method implemented in the Dmol 3 module [34,35]. We used generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) [36] to approximate the exchange-correlation effects on electron−electron interactions. The semi-core-pseudopotentials represent the core electrons as a single effective potential [37]. Double-numerical plus polarization (DNP) used as a basis set, included the vdW interaction (DFT-D), as proposed by Grimme [38]. Energy minimization was achieved with a convergence tolerance energy of 10 −5 Ha. The atomic positions were relaxed such that the force acting on each atom was less than 0.002 Ha/Å.

Results and Discussion
We investigated the interaction between pure cellulose and transition metals (T.M.s), such as titanium (Ti), magnesium (Mg), and niobium (Nb). Similar calculations were performed for chitosan with the same metals. The strength of the interaction was measured using the following equation: where ( ) is the total energy of transition metals in an isolated cubic cell of lattice (a = b = c = 25 Å), ( ) is the ground energy of cellulose or chitosan, and ( ) is the total energy of cellulose or chitosan doped with the mentioned TMs. The optimized structures of cellulose and chitosan are displayed in Figure 1. We also studied the frontier molecular orbitals to gain insight into the interaction of pristine cellulose and chitosan with additives such as niobium, titanium, and magnesium. Figure 2 depicts the highest occupied molecular orbital (HOMO) ( Figure  2A) and the lowest unoccupied molecular orbital (LUMO) ( Figure 2B) for pristine cellulose. The same analysis was performed on pristine chitosan, the highest occupied molecular orbital (HOMO) ( Figure 2C) and the lowest unoccupied molecular orbital (LUMO) ( Figure 2D) or which are also plotted in Figure 2. Furthermore, the energy band gap was determined according to Equation (2).
where is the energy of the lowest unoccupied molecular orbital (LUMO), and is the energy of the highest occupied molecular orbital (HOMO). We also studied the frontier molecular orbitals to gain insight into the interaction of pristine cellulose and chitosan with additives such as niobium, titanium, and magnesium. Figure 2 depicts the highest occupied molecular orbital (HOMO) (Figure 2A) and the lowest unoccupied molecular orbital (LUMO) ( Figure 2B) for pristine cellulose. The same analysis was performed on pristine chitosan, the highest occupied molecular orbital (HOMO) ( Figure 2C) and the lowest unoccupied molecular orbital (LUMO) ( Figure 2D) or which are also plotted in Figure 2. Furthermore, the energy band gap was determined according to Equation (2).
where E LUMO is the energy of the lowest unoccupied molecular orbital (LUMO), and E HOMO is the energy of the highest occupied molecular orbital (HOMO). The energy difference between HOMO and LUMO orbitals determines the chemical stability of a molecule. These molecular frontiers were calculated using Dmol 3 implemented in the material studio.
In Equation (2), a low E g value indicates the ability to donate electrons to the additive atoms. Furthermore, the global chemical activity, hardness, and softness parameters were investigated. The ionization energy is defined as I = −E HOMO , which is the minimum energy required to remove an electron from a molecule in the gas phase. The electron affinity is defined as A = −E LUMO , which is the energy increase that occurs when an electron is added to a molecule in the gas phase. The chemical hardness (α) is α = (I − A)/2, measuring the inhibition activity of charge transfer within the molecule. The chemical softness is represented by S = 1/2α. In addition, Mulliken electronegativity is defined as (I + A)/2, which represents the ability of an atom in a molecule to attract electrons. Finally, the chemical potential and the maximum charge transfer parameter are defined as µ= − (I + A)/2 and Dn = (I + A)/2(I − A), respectively. These chemical parameters are summarized in Table 1. The energy difference between HOMO and LUMO orbitals determines the chemical stability of a molecule. These molecular frontiers were calculated using Dmol 3 implemented in the material studio.
In Equation (2), a low value indicates the ability to donate electrons to the additive atoms.
Furthermore, the global chemical activity, hardness, and softness parameters were investigated. The ionization energy is defined as I = − , which is the minimum energy required to remove an electron from a molecule in the gas phase. The electron affinity is defined as A = − , which is the energy increase that occurs when an electron is added to a molecule in the gas phase. The chemical hardness (α) is α = (I − A)/2, measuring the inhibition activity of charge transfer within the molecule. The chemical softness is represented by S = 1/2α. In addition, Mulliken electronegativity is defined as ((I + A)/2, which represents the ability of an atom in a molecule to attract electrons. Finally, the chemical potential and the maximum charge transfer parameter are defined as µ= − (I + A)/2 and Dn = (I + A)/2(I − A), respectively. These chemical parameters are summarized in Table 1. The HOMO and LUMO energy levels are −16.899 eV and −12.269 eV, respectively, for pristine cellulose compared to −5.918 eV and −1.196 eV for chitosan, as displayed in Table 1. Moreover, the ionization energy, electronegativity, chemical potential, chemical hardness, and chemical softness ranging between −14.584 eV and 16.899 eV for cellulose compared to −3.557 eV to 5.918 eV for chitosan, as shown in Table 1. The maximum charge transfer (Dn) is 3.149 eV and 1.507 eV for cellulose and chitosan, respectively. These results indicate that cellulose and chitosan are highly stable. Because cellulose presents with six carbon asymmetric and three oxygen atoms in a different state, it is important to search for the most favorable adsorption site of magnesium, titanium, and niobium on cellulose. Equation (1) shows that the most favorable site is the oxygen in the bridge position, as shown in Figure 3, with an adsorption energy of 1.890 eV, 3.720 eV, and 3.726 eV for Mg, Ti, and Nb, respectively. A similar investigation was performed on chitosan, with five asymmetric carbons, four oxygens in different states, and one nitrogen type, as shown in Figure 1. The favorable adsorption site of magnesium and titanium is the O_Bridge position, with a binding energy of 1.547 eV and 5.450 eV for Mg and Ti, respectively. However, for the niobium atom, the most favorable site is the N_Top site, as shown in Figure 3, with a binding energy equal to 8.185 eV ( Table 2). These high symmetry points are displayed in Figure 3.  The calculated enthalpy energy is summarized in Table 2. The interaction of pristine cellulose with titanium is the most stable, with a binding energy of = 3.720 eV and an optimized distance of d_CelTi = 2.340 Å, followed by interaction between cellulose and niobium, with = 3.572 eV and a final distance of d_CelNb = 2.312 Å. The lowest binding energy is associated with the interaction of cellulose with magnesium, with = 1.890 eV and a minimum distance of d_CelMg = 2.35 Å. A comparative study was also performed on chitosan, for which the most favorable interaction occurs between chitosan and niobium, with an adsorption energy of ℎ = 7.180 eV and a critical distance of d_ChNb = 2.110 Å for the nearest atom of The calculated enthalpy energy is summarized in Table 2. The interaction of pristine cellulose with titanium is the most stable, with a binding energy of E bTC =3.720 eV and an optimized distance of d_CelTi = 2.340 Å, followed by interaction between cellulose and niobium, with E bNbCel = 3.572 eV and a final distance of d_CelNb = 2.312 Å. The lowest binding energy is associated with the interaction of cellulose with magnesium, with E bMg = 1.890 eV and a minimum distance of d_CelMg = 2.35 Å. A comparative study was also performed on chitosan, for which the most favorable interaction occurs between Materials 2022, 15, 7573 6 of 15 chitosan and niobium, with an adsorption energy of E b Nbch = 7.180 eV and a critical distance of d_ChNb = 2.110 Å for the nearest atom of chitosan. The enthalpy reaction of titanium with chitosan is E b Tich = 5.450 eV, with a required length of 3.225 Å compared to 3.720 eV in the case of titanium-doped cellulose (d_CelTi= 2.32 Å). Finally, magnesium adsorption energy on chitosan is 1.547 eV, with an adsorption distance of 3.666 Å compared to 1.890 eV and d_CelMg = 2.544 Å in the case of magnesium-doped cellulose. Binding energy and bandgap energy were computed using Equations (1) and (2). These results are summarized in Table 2. Table 2. Equilibrium parameters (binding energy (E b ) and critical distance (d_F (Å))) and the bandgap (E g (eV)) of the interaction between pristine cellulose and chitosan with magnesium, titanium, and niobium. To investigate the binding process between pure cellulose or chitosan with magnesium, titanium, and niobium, we studied the fluctuation of cellulose's bandgap energy and chitosan's bandgap energy in the presence of the mentioned transition metals. We defined the bandgap of the investigated materials using Equation (2).
The calculated values of the bandgap energy are presented in Table 2. Analysis of the results reveals that the bandgaps of pure cellulose and chitosan are 4.630 and 4.720 eV, respectively, in agreement with results reported in the literature [27,[39][40][41].
When we doped cellulose with magnesium, titanium, and niobium, the energy gap decreased from E g = 4.630 eV to 1.250 eV. The same phenomenon was observed for chitosan coated with Mg, Ti, and Nb, for which the bandgap changed from 4.720 eV pristine chitosan to the lowest value of 1.570 eV. These results suggest that the decrease in the cellulose and chitosan bandgap in the coated system could be related to a charge transfer from the transition metal to the cellulose and chitosan. The same phenomenon was previously observed by Mahmood et al. [42][43][44][45][46]. A similar phenomenon was observed in copperdecorated, nitrogen-doped defective graphene nanoribbons, in which the presence of copper decreased the bandgap from 3.399 eV to 3.352 eV [47].

Interaction of Hydrogen with Pristine Cellulose and Chitosan
To test the hydrogen storage capacity of cellulose and chitosan, we first investigated the interaction of clean cellulose and chitosan with hydrogen. The strength of the interaction of H 2 with cellulose and chitosan was measured using the following equation: where E (S) is the total energy of the substrate (cellulose or chitosan), E (H2) is the total energy of isolated hydrogen, and E (S+H2) is the total interaction energy of cellulose or chitosan with H 2 .
The interaction of hydrogen with cellulose and chitosan was determined using Equation (3); the equilibrium parameters are summarized in Table 3. The results presented in Table 2 reveal a weak interaction (physisorption) between hydrogen and cellulose and between H 2 and chitosan. The calculated binding energy between H 2 and cellulose is 0.095 eV, compared to 0.090 eV for chitosan. These results align with results previously reported in the literature [48]. Furthermore, by increasing the number of H 2 molecules in pure cellulose and chitosan to two, a decrease in the binding energy is observed: E b = 0.083 eV and E b = 0.050 eV, for cellulose and chitosan, respectively. The optimized structures are displayed in Figure 4.
of the interaction of H2 with cellulose and chitosan was measured using the following equation: where ( ) is the total energy of the substrate (cellulose or chitosan), ( ) is the total energy of isolated hydrogen, and ( ) is the total interaction energy of cellulose or chitosan with H2.
The interaction of hydrogen with cellulose and chitosan was determined using Equation (3); the equilibrium parameters are summarized in Table 3. The results presented in Table 2 reveal a weak interaction (physisorption) between hydrogen and cellulose and between H2 and chitosan. The calculated binding energy between H2 and cellulose is 0.095 eV, compared to 0.090 eV for chitosan. These results align with results previously reported in the literature [48]. Furthermore, by increasing the number of H2 molecules in pure cellulose and chitosan to two, a decrease in the binding energy is observed: = 0.083 eV and = 0.050 eV, for cellulose and chitosan, respectively. The optimized structures are displayed in Figure 4.  These results show that pure cellulose and pure chitosan are not favorable storage media alone. Therefore, to increase their adsorption capacity, we doped them with magnesium, titanium, and niobium; these results are described in the following section.

Hydrogen Storage of Cellulose Coated with Magnesium, Niobium, and Titanium
Our hydrogen interaction results with pure cellulose and chitosan show that these new materials are not efficient for hydrogen storage under ambient conditions. Therefore, to enhance the hydrogen storage capacity, we functionalized the materials to increase the active site of hydrogen adsorption. We investigated hydrogen storage on cellulose functionalized with magnesium, niobium, and titanium. The optimized structures are depicted in Figure 5. These results show that pure cellulose and pure chitosan are not favorable storage media alone. Therefore, to increase their adsorption capacity, we doped them with magnesium, titanium, and niobium; these results are described in the following section.

Hydrogen Storage of Cellulose Coated with Magnesium, Niobium, and Titanium
Our hydrogen interaction results with pure cellulose and chitosan show that these new materials are not efficient for hydrogen storage under ambient conditions. Therefore, to enhance the hydrogen storage capacity, we functionalized the materials to increase the active site of hydrogen adsorption. We investigated hydrogen storage on cellulose functionalized with magnesium, niobium, and titanium. The optimized structures are depicted in Figure 5.  The strength of the binding between hydrogen and cellulose was calculated as follows: where E (Cel+TMs) is the total energy of cellulose doped with transition metals (TMs = Mg, Nb, and Ti); E (nH2) is the total energy of nH 2 molecules; and E ((Cel+TMs)+nH2) is the total energy of cellulose doped with Mg, Nb, and Ti with n H 2 molecules adsorbed on its surface, where n indicates the number of adsorbed H 2 molecules. The adsorption energy was computed using Equation (4); the equilibrium parameters are summarized in Table 4. Table 4. Equilibrium parameters: binding energy (E b ), critical distance (d_TM-H (Å)), distance between hydrogen atoms, and desorption temperature (T D. ) between cellulose doped with magnesium, titanium, and niobium.

Number of H 2 Molecules E b (eV) d_H-H (Å) d_TM-H (Å) T D (K)
Cell Cellulose coated with Nb atoms can store six H 2 molecules in the quasi-molecular form with a distance between H atoms in the range of 0.789 to 0.896 Å and a corresponding binding distance in the range of 1.900 to 2.250 Å. Their corresponding adsorption energy fluctuates in the range of 0.198-0.765 eV before reaching saturation, as shown in Table 4. To better visualize the successive adsorption of hydrogen, Figure 6a shows the variation in hydrogen binding energy with niobium-doped cellulose with varying numbers of adsorbed hydrogen molecules. The change in adsorption energy with the number of hydrogen molecules in titanium-doped cellulose is presented in Figure 6b. Figure 6a shows that the binding energy decreases as the number of added H 2 molecules increases. However, in cellulose doped with titanium, the maximum storage capacity is five H 2 Table 3. These results for cellulose are in agreement with previously reported results reported in the literature [49]. Furthermore, their corresponding binding energy varies in the range of 0.120 eV to 0.640 eV. Magnesium-doped cellulose is not displayed in Figure 4 because its storage capacity is poor. It can only adsorb two H2 molecules with the following equilibrium parameters: d_H-H= [0.757-0.758 Å], d_TM-H = [3.050-3.125 Å], and binding energy in the range of 0.086-0.112 eV, as shown in Table 3. These results for cellulose are in agreement with previously reported results reported in the literature [49]. Case (a) represents the variation in the binding energy with respect to the number of hydrogen molecules (cellulose + Nb), case (b) represents the variation in the binding energy with respect to the number of H 2 molecules (cellulose + Ti), case (c) represents the variation in the desorption temperature with respect to the adsorption energy (cellulose + Nb), and case (d) represents the variation in the desorption temperature with respect the adsorption energy of H 2 (cellulose + Ti).
To study the desorption process, we used the van't Hoff equation [2,48,49], as expressed below, to evaluate the desorption temperature (T D ): where E ads is the binding energy, K B represents Boltzmann's constant (8.61733 × 10 −5 eV/K), P denotes the pressure (reference pressure Po = 1 atm), R is the universal gas constant (8.314 JK −1 mol −1 ), and ∆S is the entropy change as H 2 moves from the gas to the liquid phase. Assume that P = 1 is the atmospheric pressure, and ∆S = 130.7 JK −1 mol −1 [49,50]. The variation in the binding energy with respect to absorbed H 2 in cellulose-doped titanium is displayed in Figure 6c.
We determine the desorption temperature for the successive addition of H 2 on cellulose doped with niobium, titanium, and magnesium using Equation (5); the results are summarized in Table 4. Cellulose-doped niobium and titanium are the most favorable for hydrogen storage, as shown in Table 4. Therefore, to better understand the correlation between the desorption temperature (T D ) and the adsorption energy, Figure 6c,d shows the desorption temperature as a function of the binding energy for the two most favorable composites (cellulose doped with niobium and cellulose doped with titanium). Figure 6c,d shows a linear relationship between the desorption temperature and the binding energy. The temperature variation in titanium-doped cellulose is expressed as by T D = 1277 × E b + 0.55. In niobium-doped cellulose, the temperature varies: T D = 1277 × E b − 0.071. The desorption temperature of the successive hydrogen addition in niobium-doped cellulose is in the interval of 253-978 K, where the maximum temperature is (T D = 978 K) to release all the adsorbed hydrogen at a atmospheric pressure of 1. However, in the case of titaniumdoped cellulose, the desorption temperature is within the range of 153-818 K, where T D = 818 K is the maximum temperature required to release all the adsorbed hydrogen at the standard pressure.

Hydrogen Storage on Chitosan Coated with Magnesium, Niobium, and Titanium
A comparative study was also performed on chitosan doped with magnesium, niobium, and titanium as a hydrogen storage medium. The optimized structure of the chitosan doped with magnesium, titanium, and niobium with the maximum H 2 storage capacity is shown in Figure 7. The first H 2 molecule dissociation is noticeable in titanium-and niobium-doped chitosan, with a binding energy of 0.615 eV for niobium-doped chitosan (Ch_Nb) and 0.405 eV for titanium-doped chitosan (Ch_Ti). However, in magnesium-doped chitosan (Ch_Mg), the first Ch_Mg adsorption energy is 0.142 eV. The successive adsorption energy of hydrogen with chitosan functionalized with the metals was determined using Equation (3). The calculation results for the subsequent H2 additions are summarized in Table 5. Table 5. Successive hydrogen adsorption on chitosan coated with magnesium, titanium, and niobium, along with their corresponding binding distance (d_H-M), the distance between hydrogen atoms (d_H-H), and the desorption temperature (TD).  The successive adsorption energy of hydrogen with chitosan functionalized with the metals was determined using Equation (3). The calculation results for the subsequent H 2 additions are summarized in Table 5. Table 5. Successive hydrogen adsorption on chitosan coated with magnesium, titanium, and niobium, along with their corresponding binding distance (d_H-M), the distance between hydrogen atoms (d_H-H), and the desorption temperature (T D ).  Table 5 shows that H 2 interacted with magnesium-coated chitosan in the gas phase, with an adsorption energy of 0.142 eV for the first adsorbed H 2 molecule, decreasing to 0.078 eV for the second H 2 molecule. In the case of magnesium-coated cellulose, the first adsorption energy of the first H 2 molecule is E b = 0.112 eV and 0.086 eV for the second adsorption. Moreover, the corresponding equilibrium parameters of chitosan are as follow: critical distance (d_H-Mg): 3.141 Å for the first H 2 molecule and 3.304 Å for the last added H 2 molecule. The results can be compared to the equilibrium parameters for magnesium-doped cellulose, where d_H-Mg = 3.050 Å for the first adsorption and d_H-Mg = 3.125 Å for the second adsorption. The desorption temperature (T D ) for these two successive adsorptions is T D = 181 K and T D = 99 K, respectively, compared with T D = 143 K and T D = 109 K in magnesium-doped cellulose.

Number of H 2 Molecules Binding Energy d_H-H (Å) d_H-M (Å) T D (K)
To better, observe the correlation between the adsorption energy and the number of added H 2 molecules. The maximum hydrogen storage capacity for niobium-coated chitosan is five hydrogen molecules, as shown in Figure 8, and the addition of the six H 2 molecules is not stable. This result indicates that niobium-doped chitosan can store five H 2 molecules in the quasi-molecular form before reaching saturation. Figure 8a,c shows the binding energy for the successive H 2 additions. The desorption temperature (T D ) of successive H 2 adsorption varies in the energy interval of 136-786 K. However, in the case of titanium-doped chitosan, the maximum storage capacity is three H 2 molecules in the quasi-molecular form, with binding energy in the range of 0.132-0.405 eV. A fourth H 2 molecule is in an unstable configuration, with an adsorption energy of 0.099 eV. The corresponding desorption temperature for the successive addition of molecules varies in the range of 168-517 K. To better understand the correlation between the adsorption energy and the corresponding desorption temperature, Figure 8c shows the desorption temperature changes (T D ) with respect to the hydrogen binding energy for niobium-doped chitosan. Figure 8d also displays the desorption temperature (T D ) for different hydrogen adsorption energy for titanium-doped chitosan. Furthermore, the relation between the desorption temperature (T D ) and the binding energy (E b ) is expressed by T D = 1290 × E b − 1.46 in niobium-doped chitosan and T D = 1280 × E b − 0.3 in the case of titanium-doped chitosan. energy and the corresponding desorption temperature, Figure 8c shows the desorption temperature changes (TD) with respect to the hydrogen binding energy for niobiumdoped chitosan. Figure 8d also displays the desorption temperature (TD) for different hydrogen adsorption energy for titanium-doped chitosan. Furthermore, the relation between the desorption temperature (TD) and the binding energy (Eb) is expressed by TD = 1290 × Eb − 1.46 in niobium-doped chitosan and TD = 1280 × Eb − 0.3 in the case of titanium-doped chitosan.  Case (a) represents the variation in the binding energy with respect to the number of hydrogen molecules (chitosan + Nb), case (b) represents the variation in the binding energy with respect to the number of H 2 molecules (chitosan + Ti), case (c) represents the variation in the desorption temperature with respect to the adsorption energy (chitosan + Nb), and case (d) represents the variation in the desorption temperature with respect to the adsorption energy of H 2 (chitosan + Ti).

Conclusions
In summary, the present study of hydrogen storage in pure cellulose and chitosan, as well as cellulose and chitosan doped with magnesium, titanium, and niobium using density functional theory highlights the mechanism of hydrogen storage. The results of this investigation show that the interaction between hydrogen and pure cellulose and chitosan takes place in the gas phase (physisorption). Additionally cellulose and chitosan coated with magnesium, titanium, and niobium show exciting results. Our calculations predict that cellulose doped with niobium is the most favorable medium, with a storage capacity of six H 2 molecules, adsorption energy in the range of 0.198-0.765 eV, with system release of all the hydrogen at 978 K. Niobium-doped chitosan can accommodate five H 2 molecules, with binding energy in the range of 0.107-0.615 eV, whereas titanium-doped cellulose has a storage capacity of four H 2 molecules, with binding energy in the range of 0.120-0.640 eV and a maximum desorption temperature of T max = 818 K, compared to a storage capacity of four H 2 molecules in the case of titanium-doped chitosan, with an adsorption range of 0.099-0.405 eV and a maximum desorption temperature of T max = 517 K. However, magnesium-doped cellulose and chitosan show an insufficient hydrogen storage capacity of two H 2 molecules physisorbed. These results demonstrate that niobium-doped cellulose and chitosan might play an important role in the search for efficient and inexpensive hydrogen storage media.