A theoretical modeling of NaBr(H2)n clusters as a unique approach in hydrogen gas storage

doi:10.21203/rs.3.rs-3312121/v1

Adsorption of H₂ molecules on a bed of NaBr unit for the formation of NaBr(H₂)_n(n = 1-8)aggregates is reported here theoretically. Second-order Moller-Plesset perturbation calculations were carried out using the MP2/aug-cc-pVDZ level for predictions of adsorption energies and Gibbs free energy changes for these aggregates. The NaBr(H₂)_n aggregates are predicted to steadily increase in H₂saving capacity and energy efficiency as n increases from 1 to 8, relative to free H₂ molecules under identical conditions. The low activation energies for H₂desorption from the NaBr(H₂)_n adducts resulting in high amounts of H₂molecules desorbed at low temperatures. The Natural Bond Orbital (NBO) calculations were used to investigate the nature of interactions in NaBrH_2(n) complexes. Furthermore, cooperativite effects were investigated for optimized complexes. Results are dealing with diminutive interactions in the NaBr(H₂)_n complexes. Finally, electronic properties of the NaBr(H₂)_n clusters were obtained by the Density Of States (DOS) calcalcuation.

hydrogen storage

intermolecular interactions

cooperativity

hydrogen adducts

diminutive effects

Hydrogen is known to be an important and clean energy carrier [1–2] that can be readily produced in large quantities from renewable resources [3]. In addition, hydrogen produces more energy than either gasoline or natural gas on weight basis [4]. However, the lower density of the hydrogen make its compression under high pressure and lower temperatures, which is not presently suitable as an effectiveness and efficiency energy source. Hydrogen must be safely stored for transportation, which is a major challege. Therefore, strategies to secure and efficient H₂ storage technology and H₂ storage materials are important and are can potentially improve the hydrogen storage capacity and stability of hydrogen storage materials further [5].

Because of the generation of electricity from hydrogen, a facet with the most energy density per unit mass, depends on the development of materials that can be utilized in its storage [6]. One of the major challenges for applications of hydrogen as an energy carrier is the lack of suitable storage materials [7]. However, how to improve the hydrogen storage capacity is the substantial and hot subject [8]. Chemisorption refers to a kind of absorption that occurs when the surface and the absorbent have a chemical reaction with each other. As a sense which is quite different from chemisorption, physisorption makes no variations in chemical species of the adsorbent and surface [9]. The defect of hydrogen physisorption is that the energy of gas-solid interaction is usually low; hence, considerable hydrogen storage only happens at very high pressures or at extremely low temperatures. As a consequence, in the effort for improved hydrogen storage; a primary target is obtaining materials with more adsorption energy for H₂ [10]. According to the agreed contracts, the desirable adsorption energy should be in the range of (-0.2) – (-0.7) eV/H₂ [11]. This area of energy is intermediate among the physisorbed and chemisorbed states. It is favorable for hydrogen storage under ambient pressure and temperature. To achieve this, a diversity of materials about hydrogen storage have been studied by several theoretical and experimental studies [12]. Hydrogen can be stored as a pressurized gas, cryogenic liquid, or solid fuel via physisorption or chemisorption onto (or into) solid materials [13].

Many metals like Li, Na, Mg, B, Al, Zn are directly or indirectly able to absorbing great amounts of hydrogen [14]. There is a main problem that no material so far has been successful in combining high volumetric and gravimetric density and the capability to reversibly absorb and desorb hydrogen with kinetics and thermodynamics [15]. Therefore, introducing new idea which make help to solve hydrogen storage problems is necessary. Storage (physically or chemically) of hydrogen adducts of light salts (MX(H₂)_n) instead of isolated molecular H₂ might be a good subject for investigation. Because these adducts under same condition (pressure and temperature) which applied for compression of H₂ molecules would store greater number of H₂ molecules per volume of vessel. In the present work, we investigate the H₂ adsorption on the NaBr and structural and energetic properties such as bond lengths, vibrational stretching frequencies, adsorption energies (E_ads) and Gibbs free energy changes (∆G) of NaBr(H₂)_n aggregates were investigated. Beside to Natural Bond Orbital (NBO) analysis [16], the Mulliken charge analysis is carried out for NaBr(H₂)_n to confirm the results. The cooperativity of noncovalent interactions in NaBr(H₂)_n complexes were analyzed and discussed [17]. The electronic properties of the complexes were investigated by calculating the Density Of States (DOS) [18–19].

The primary aim of this research is focusing on simple MX(H₂)_n, n = 1–8, complexes to understand the fundamental nature and strength of hydrogen binding interactions. Results of this work might provide beneficial guidance for designing novel hydrogen storage methods based on its adducts.

All geometry optimizations were performed at MP2/aug-ccpVDZ level of theory by GAUSSIAN 03 software [20]. The frequency calculations were done at the same level of theory to prove minimum energy nature of the complexes. In addition, the frequency analyses at the optimized structures were carried out to calculate the Gibbs free energy changes. The NBO analyses were carried out using the NBO computational package [16]. The interaction energy was calculated as the difference of the entire energy of the complexes and the sum of the energies of free monomers. With the optimized structures, the adsorption energy (E_ads) of H₂ on the NaBr monomers is obtained using the following formula:

E_ads= E[NaBr(H₂)_n] - E[(NaBr) + (n-1)H₂] - E(H₂) (1)

Where the first and second terms illustrate the total energies of NaBr monomer loaded with n and (n–1) H₂ molecules respectively, and the last one is the total energy of free H₂ molecule. Strong binding of NaBr (due to the difference between their electronegativity amounts) is required for reversible hydrogen storage utilizations and we can sure the NaBr structure is stable. The Basis Set Superposition Error (BSSE) was obtained for all complexes by using the counterpoise procedure [21]. In the present study, the cooperative energies of clusters were calculated using Eq. (2), in which SE_Complex is the stabilization energy of complex and ∑SE_dimmers is the sum of the energies of dimers forming the complex [19].

E_Coop = SE_complex - ∑SE_dimmers (2)

3.1. The structure optimization and adsorption of H₂

To begin with, we put H₂ molecule one by one at the top of Na and Br atoms on the NaBr surface and subsequently optimized the resulting structures to obtain the most stable geometries. After full relaxation, we continued to 8H₂ molecules are adsorbed molecularly around NaBr as shown in Fig. 1. This molecular adsorption is preferred for practical hydrogen storage applications. It is significant to note that adsorption of H₂ molecules on Na and Br atoms have different characteristics. As illustrated in Fig. 1, H₂ molecules interact by sides with Na atoms, while their interaction with Br atoms occurs through H₂ tails. In the first case, when hydrogen is adsorbed on the NaBr, the electron density from the σ bond of H₂ molecule transferred to σ* orbital (σ hole) of NaBr which has be located on the Na head of this salt. On the other tail, Br atom as an electron donor has interaction with σ* orbital (σ hole) of H₂ molecule. However, when there are several H₂ molecules adsorbed on each Br atom, the orbitals of the Br atom and the adsorbed H₂ molecules can be significantly overlapped, which leads to enhance orbital interactions. According to data given in Table 1, the electron rich orbital of H₂ as an electron donor should be preferably interacted with the electron poor Na atom of NaBr that this interaction is energetically more desirable than interaction of H₂ as an electron acceptor with Br as an electron donor.

Table 1

The number of adsorbed H₂ molecules (n), the adsorption energy of H₂ (E_ads), the Gibbs free energy changes (∆G), the basis-set superposition error values (BSSE), the cooperative effects (CE) and HOMO –LUMO energy gap (E_g) in the NaBr(H₂)_n complexes. E_ads, ∆G, and CE are related to the last absorbed H₂ at the MP2/aug-ccpVDZ level of theory.
System	nH₂	E_ads	∆G	BSSE	CE	E_g
NaBr	—	—	—	—	—	8.28
S1(NaBr···H₂)	1	-0.046	0.295	0.023	—	8.32
S2(NaBr···H₂)	1	-0.083	0.167	0.023	—	8.39
S3(NaBr···H₂)	1	-0.076	0.126	0.019	—	8.76
S4(NaBr···2H₂)	2	-0.046	0.128	0.045	0.08	8.43
S5(NaBr···2H₂)	2	-0.086	0.177	0.042	0.08	8.53
S6 (NaBr···2H₂)	2	-0.080	0.133	0.044	0.08	8.81
S7(NaBr···2H₂)	2	-0.091	0.208	0.051	0.08	8.49
S8(NaBr···2H₂)	2	-0.057	0.180	0.044	0.07	8.51
S9(NaBr···2H₂)	2	-0.047	0.144	0.042	0.08	8.81
S10(NaBr···3H₂)	3	-0.098	0.190	0.078	0.15	8.60
S11(NaBr···3H₂)	3	-0.085	0.188	0.070	0.16	8.85
S12(NaBr···3H₂)	3	-0.047	0.136	0.067	0.16	8.57
S13(NaBr···3H₂)	3	-0.085	0.133	0.077	0.16	8.85
S14(NaBr···3H₂)	3	-0.061	0.211	0.070	0.15	8.66
S15(NaBr···3H₂)	3	-0.058	0.184	0.072	0.15	8.54
S16(NaBr···3H₂)	3	-0.047	0.124	0.066	0.16	8.86
S17(NaBr···3H₂)	3	-0.057	0.207	0.066	0.15	8.87
S18(NaBr···3H₂)	3	-0.047	0.120	0.066	0.13	8.56
S19(NaBr···4H₂)	4	-0.091	0.170	0.109	0.24	8.79
S20(NaBr···4H₂)	4	-0.102	0.205	0.112	0.23	8.69
S21(NaBr···4H₂)	4	-0.104	0.228	0.110	0.22	8.81
S22(NaBr···4H₂)	4	-0.058	0.198	0.099	0.23	8.88
S23(NaBr···4H₂)	4	-0.059	0.225	0.100	0.23	8.89
S24(NaBr···4H₂)	4	-0.057	0.188	0.095	0.23	8.90
S25(NaBr···4H₂)	4	-0.058	0.211	0.095	0.23	8.75
Values of E_ads, ∆G, BSSE, CE and E_g are given in eV.

Table 1

(continued)
System	nH₂	E_ads	∆G	BSSE	CE	E_g
S26(NaBr···4H₂)	4	-0.046	0.150	0.097	0.24	8.88
S27(NaBr···4H₂)	4	-0.055	0.178	0.088	0.20	8.91
S28(NaBr···4H₂)	4	-0.092	0.228	0.092	0.20	8.89
S29(NaBr···5H₂)	5	-0.107	0.209	0.146	0.26	8.88
S30(NaBr···5H₂)	5	-0.078	0.318	0.146	0.34	8.75
S31(NaBr···5H₂)	5	-0.060	0.226	0.132	0.31	8.92
S32(NaBr···5H₂)	5	-0.059	0.190	0.133	0.31	8.91
S33(NaBr···5H₂)	5	-0.055	0.181	0.117	0.28	8.95
S34(NaBr···5H₂)	5	-0.111	0.298	0.123	0.22	8.94
S35(NaBr···6H₂)	6	-0.085	0.253	0.182	0.41	8.93
S36(NaBr···6H₂)	6	-0.058	0.190	0.169	0.40	8.79
S37(NaBr···6H₂)	6	-0.065	0.230	0.159	0.35	8.95
S38(NaBr···6H₂)	6	-0.065	0.205	0.159	0.35	8.95
S39(NaBr···6H₂)	6	-0.107	0.150	0.171	0.35	8.93
S40(NaBr···7H₂)	7	-0.062	0.263	0.213	0.48	8.97
S41(NaBr···7H₂)	7	-0.062	0.219	0.193	0.45	8.85
S42(NaBr···8H₂)	8	-0.059	0.195	0.237	0.53	9.02
S43(NaBr···8H₂)	8	-0.058	0.172	0.237	0.53	9.02
S44(NaBr···8H₂)	8	-0.061	0.215	0.233	0.52	9.02
S45(NaBr···8H₂)	8	-0.058	0.193	0.217	0.50	8.90
S46(NaBr···8H₂)	8	-0.051	0.195	0.216	0.50	8.90
S47(NaBr···8H₂)	8	-0.062	0.234	0.219	0.49	8.93
Values of E_ads, ∆G, BSSE, CE and E_g are given in eV.

3.2. Adsorption energies of H₂ and Gibbs free energy changes

In the following, we considered the adsorption energy (E_ads) of H₂ on the NaBr monomers. The E_ads values were calculated according to Eq. (1) and the results are summarized in Table 1. The negative amounts of E_ads indicate that the adsorption is exothermic and is thermodynamically favorable. As shown in Table 1, the range of the adsorption energy is from − 0.0462 to -0.1114 eV and this is appropriate for hydrogen molecules to store at ambient condition. The average adsorption energy of H₂ on the NaBr(H₂)_n (n = 1–8) complexes as a function of the number of adsorbed H₂ molecules is given in Fig. 2. To further examine the thermodynamic possibility of H₂ adsorption on NaBr we calculated Gibbs free energy (∆G) changes. The computed values of ∆G are given in Table 1. The results show that the ∆G varies from 0.1196 to 0.3183 eV for NaBr(H₂)_n (n = 1–8) complexes. The minimum and maximum amounts of ∆G are seen in the S18 and S30 states, respectively. Figure 3 shows the average Gibbs free energy changes of NaBr(H₂)_n complexes as a function of the number of adsorbed H₂ molecules.

3.3. Bond lengths and vibration frequencies

Here, we obtained the bond lengths and vibration frequencies for Na–Br and H–H bonds in the NaBr(H₂)_n complexes. In addition, the binding distances (distances between NaBr and H₂) were determined in these cases, Table 2. The NaBr bond shows elongation in the NaBr(H₂)_n complexes. The largest elongation of the Na–Br bond is found in the S42 (NaBr(H₂)₈, 0.0517 Å), whereas the smallest elongation of the Na–Br bond is seen in the S1(NaBr(H₂), 0.0028 Å). Based on the results, the largest elongation of the H–H bond is found in the S2 (NaBr(H₂), 0.0048 Å), whereas the smallest elongation of the H–H bond is seen in the S19 (NaBr(H₂)₄, 0.0005 Å). The elongation of the Na–Br and H–H bonds means that they become weakening due to the formation of NaBr(H₂)_n complexes. Moreover, the average H–H bond length result (0.7581 Å gathered in Table 2) is close to the original H–H bond distance of 0.7549 Å, which indicates weak bonding. Upon formation of the complexes, the distances between NaBr and H₂ (the binding distances) are calculated for all states, Table 2. The binding distance is 2.4970 Å in the S39 complex that it means a stronger NaBr···H₂ bond in this complex.

Table 2

The number of adsorbed H₂ molecules (n), the bond length of optimized geometries of Na–Br, H–H and NaBr···H₂ complexes. Unscaled vibrational frequencies with corresponding absorption intensities (values given in parenthesis, km mol^− 1) for ν(NaBr···H₂), ν(H–H), and ν(Na–Br) at the MP2/aug-ccpVDZ level of theory.
System	nH₂	d(Na–Br)	d(H–H)	d(NaBr···H₂)	ν(Na–Br)	ν(H–H)
NaBr		2.5753	—	—	282(43)	—
H₂	—	—	0.7549	—	—	4464
S1(NaBr···H₂)	1	2.5781	0.7570	3.0900	280(45)	4418(37)
S2(NaBr···H₂)	1	2.5844	0.7597	2.5658	278(42)	4369(29)
S3(NaBr···H₂)	1	2.5786	0.7565	2.6090	294(46)	4430(14)
S4(NaBr···2H₂)	2	2.5873	0.7572	3.0890	277(43)	4416(38)
S5(NaBr···2H₂)	2	2.5901	0.7589	2.5297	274(40)	4381(28)
S6(NaBr···2H₂)	2	2.5876	0.7562	2.5982	292(43)	4431(12)
S7(NaBr···2H₂)	2	2.5945	0.7596	2.5455	275(40)	4370(59)
S8(NaBr···2H₂)	2	2.5837	0.7586	3.0694	279(42)	4384(53)
S9(NaBr···2H₂)	2	2.5813	0.7572	3.0889	293(47)	4415(39)
S10(NaBr···3H₂)	3	2.6040	0.7596	2.5251	271(38)	4366(19)
S11(NaBr···3H₂)	3	2.5960	0.7559	2.5902	290(38)	4431(10)
S12(NaBr···3H₂)	3	2.5955	0.7572	3.0879	272(42)	4415(39)
S13(NaBr···3H₂)	3	2.5973	0.7560	2.5858	291(39)	4432(11)
S14(NaBr···3H₂)	3	2.5926	0.7587	3.0756	280(36)	4382(54)
S15(NaBr···3H₂)	3	2.5956	0.7583	3.0656	273(40)	4392(46)
S16(NaBr···3H₂)	3	2.5902	0.7572	3.0894	291(44)	4416(39)
S17(NaBr···3H₂)	3	2.5869	0.7585	3.0581	290(43)	4385(54)
S18(NaBr···3H₂)	3	2.5860	0.7572	3.0837	278(44)	4416(37)
S19(NaBr···4H₂)	4	2.6067	0.7554	2.5715	292(34)	4436(10)
S20(NaBr···4H₂)	4	2.6142	0.7592	2.5044	269(36)	4371(5)
S21(NaBr···4H₂)	4	2.6068	0.7590	2.5160	291(36)	4369(3)
S22(NaBr···4H₂)	4	2.5980	0.7583	3.0611	290(38)	4391(47)
S23(NaBr···4H₂)	4	2.5959	0.7587	3.0516	290(39)	4382(56)
Values of d and ν are given in Å and cm^− 1 respectively.

Table 2

(continued)
System	nH₂	d(Na–Br)	d(H–H)	d(NaBr···H₂)	ν(Na–Br)	ν(H–H)
S24(NaBr···4H₂)	4	2.5979	0.7560	2.5934	289(39)	4430(8)
S25(NaBr···4H₂)	4	2.5924	0.7585	3.0635	275(40)	4386(9)
S26(NaBr···4H₂)	4	2.5996	0.7592	2.5410	290(40)	4371(12)
S27(NaBr···4H₂)	4	2.5914	0.7586	3.0716	290(44)	4390(46)
S28(NaBr···4H₂)	4	2.5985	0.7592	2.5274	290(39)	4373(56)
S29(NaBr···5H₂)	5	2.6165	0.7588	2.5029	291(31)	4374(4)
S30(NaBr···5H₂)	5	2.6204	0.7589	2.5693	267(36)	4374(14)
S31(NaBr···5H₂)	5	2.6072	0.7591	2.5194	291(32)	4370(27)
S32(NaBr···5H₂)	5	2.6081	0.7591	2.5280	290(35)	4372(23)
S33(NaBr···5H₂)	5	2.5993	0.7580	3.0713	287(39)	4397(37)
S34(NaBr···5H₂)	5	2.5963	0.7577	2.5490	289(38)	4399(19)
S35(NaBr···6H₂)	6	2.6198	0.7585	2.5485	301(26)	4378(10)
S36(NaBr···6H₂)	6	2.6219	0.7582	3.0574	266(36)	4394(44)
S37(NaBr···6H₂)	6	2.6060	0.7586	3.0629	289(32)	4383(23)
S38(NaBr···6H₂)	6	2.6074	0.7586	3.0602	287(33)	4383(30)
S39(NaBr···6H₂)	6	2.6188	0.7590	2.4970	291(29)	4369(16)
S40(NaBr···7H₂)	7	2.6254	0.7587	3.0450	288(31)	4380(61)
S41(NaBr···7H₂)	7	2.6218	0.7581	3.0603	264(35)	4392(21)
S42(NaBr···8H₂)	8	2.6270	0.7581	3.0604	287(30)	4394(40)
S43(NaBr···8H₂)	8	2.6267	0.7581	3.0601	287(29)	4395(42)
S44(NaBr···8H₂)	8	2.6229	0.7581	3.0627	297(25)	4392(64)
S45(NaBr···8H₂)	8	2.6236	0.7581	3.0615	263(35)	4396(3)
S46(NaBr···8H₂)	8	2.6233	0.7574	3.0768	264(36)	4410(39)
S47(NaBr···8H₂)	8	2.6205	0.7582	3.0729	264(34)	4388(4)
Values of d and ν are given in Å and cm^− 1 respectively.

Table 2 presents the unscaled vibrational frequencies of the Na–Br and H–H bonds in the NaBr···nH₂ (n = 1–8) complexes. In each case, the frequencies are all real and no negative frequency was observed. Table 2 is showing that, NaBr···H₂ bond formation is commonly accompanied with shifts in the stretching frequency of the Na-Br bonds. These shifts are compatible with the change of the bond length variation. As presented in Table 2, the H–H stretch mode shows a red shift, which is consistent with the bond elongation. The vibrational stretching frequency of free H₂ molecule is 4464 cm^− 1.

3.4. The natural bond orbital Analysis

The NBO analysis indicates the role of intermolecular orbital interaction, particularly Charge Transfer (CT), in the complex formation. We hence performed a NBO analysis for the NaBr···nH₂ complexes. The E⁽²⁾, Table 3, second-order perturbation energy, might be considered as a factor to evaluate the strength of intermolecular interactions. Charge transfer results from the orbital interaction between the electron donor and acceptor species. Generally, the interaction between the bonding orbital (σ) in the electron donor and the antibonding orbital (σ*) in the electron acceptor is a main participation to the charge transfer in NaBr···H₂ bonding. The amount of second-order perturbation energy (E⁽²⁾) due to the interaction of donor and acceptor orbital, lets us to quantitatively check out the CT involving the formation of the NaBr···nH₂ complexes. These results indicate that the charge transfer from σ bond of H₂ to anti-bond orbital on Na atom is larger and more plausible than the charge transfer from lone pair on Br atom to σ* orbital of H₂.

Table 3

The values of the NBO analysis for the NaBr···nH₂ systems with geometries determined at the MP2/aug-ccpVDZ level of theory.
Complexes	n	Donor → Acceptor	E^{(2) a}	Complex	n	Donor → Acceptor	E^{(2) a}
S1(NaBr···H₂)	1	lp(Br) → σ*(H-H)	0.06	S25(NaBr···4H₂)	4	lp(Br) → σ*(H-H)	0.12
S2(NaBr···H₂)	1	lp(Br) → σ*(H-H)	0.06	S26(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.11
S3(NaBr···H₂)	1	σ(H-H) → lp*(Na)	0.10	S27(NaBr···4H₂)	4	lp(Br) → σ*(H-H)	0.12
S4(NaBr···2H₂)	2	lp(Br) → σ*(H-H)	0.07	S28(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.13
S5(NaBr···2H₂)	2	lp(Br) → σ*(H-H)	0.04	S29(NaBr···5H₂)	5	σ(H-H) → lp*(Na)	0.21
S6(NaBr···2H₂)	2	σ(H-H) → lp*(Na)	0.16	S30(NaBr···5H₂)	5	σ(H-H) → lp*(Na)	0.23
S7(NaBr···2H₂)	2	σ(H-H) → lp*(Na)	0.04	S31(NaBr···5H₂)	5	σ(H-H) → lp*(Na)	0.22
S8(NaBr···2H₂)	2	lp(Br) → σ*(H-H)	0.12	S32(NaBr···5H₂)	5	σ(H-H) → lp*(Na)	0.24
S9(NaBr···2H₂)	2	lp(Br) → σ*(H-H)	0.07	S33(NaBr···5H₂)	5	lp(Br) → σ*(H–H)	0.11
S10(NaBr···3H₂)	3	σ(H-H) → lp*(Na)	0.16	S34(NaBr···5H₂)	5	σ(H-H) → lp*(Na)	0.19
S11(NaBr···3H₂)	3	σ(H-H) → lp*(Na)	0.25	S35(NaBr···6H₂)	6	σ(H-H) → lp*(Na)	0.36
S12(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.07	S36(NaBr···6H₂)	6	lp(Br) → σ*(H–H)	0.12
S13(NaBr···3H₂)	3	σ(H-H) → lp*(Na)	0.23	S37(NaBr···6H₂)	6	lp(Br) → σ*(H–H)	0.08
S14(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.11	S38(NaBr···6H₂)	6	lp(Br) → σ*(H–H)	0.08
S15(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.12	S39(NaBr···6H₂)	6	σ(H-H) → lp*(Na)	0.28
S16(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.07	S40(NaBr···7H₂)	7	lp(Br) → σ*(H–H)	0.11
S17(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.12	S41(NaBr···7H₂)	7	lp(Br) → σ*(H–H)	0.09
S18(NaBr···3H₂)	3	lp(Br) → σ*(H–H)	0.06	S42(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.12
S19(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.19	S43(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.07
S20(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.16	S44(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.08
S21(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.25	S45(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.11
S22(NaBr···4H₂)	4	lp(Br) → σ*(H–H)	0.12	S46(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.06
S23(NaBr···4H₂)	4	lp(Br) → σ*(H–H)	0.12	S47(NaBr···8H₂)	8	lp(Br) → σ*(H–H)	0.11
S24(NaBr···4H₂)	4	σ(H-H) → lp*(Na)	0.24
^aThe second order perturbation energy (related to the last absorbed H₂ whose E⁽²⁾ values are given in eV).

3.5. The Mulliken charge analysis

The Mulliken charge analysis is carried out for the NaBr and adsorbed H₂ molecules to prove the above results (Fig. 4). From the Mulliken charge analysis can understand that charge transferred from H₂ molecules to Na atom, which illustrates these hydrogen molecules have an interaction with Na–Br. Due to the charge transfer, an electric field is created, which can be reason for polarization of H₂ molecules. The positive charges in Na atoms can polarize the electron clouds in hydrogen molecules and cause to persuade the electrostatic interaction. In the other cases, the presence of negative charges on the H₂ molecule in the NaBr···nH₂ complexes indicates that the charge is transferred from the Br atom to the H₂ molecule.

3.6. Cooperative and diminutive effects

The Cooperative Effects (CE) are interesting characteristics of intermolecular interactions. These effects can regulate the strength of each interaction and make the clusters more stable [22]. The CE plays different roles in stability of various complexes. Therefore, in this study we investigate various degrees of cooperativities which might observe during interactions of NaBr with H₂ molecules in different directions. As previously defined, the cooperative energy E_coop is calculated by subtraction the sum of stabilization energies of dimmers from the total stabilization energy of the complex [19, 23]. In the all studied systems, the intermolecular interaction in these clusters makes negative contributions to the cooperativity, and it is called the anti-cooperative or diminutive effect, Table 1. As shown, the cooperative effect ranges from 0.07 to 0.53 eV. The positive values of ∆E_CE are indicating diminutive energies for corresponding complexes and on the basis of these results, the CE does not have a significant role in their stabilities. As a result, no significant correlation found between the cooperative values and stabilities. Indeed, the cooperative and diminutive effects are mainly attributed to the charge transfer.

3.7. DOS

Due to quasi-degenerate energy levels of the neighboring orbitals in the frontier, considering only HOMO and LUMO cannot give an accurate explanation of the boundary orbitals. Hence, the DOS spectrum for the NaBr and NaBr(H₂)_n molecules were obtained by using the Gauss Sum 3.0 program. The total DOS, alpha, and beta DOS of the molecules are plotted in Fig. 5. The spectrum of DOS explains the contribution of electrons to the chemical bonding and it shows how many density states are available at various energy levels. As demonstrated by the calculated DOS and the energy gaps (E_g) between the HOMO and LUMO, the E_g of NaBr is computed as 8.28 eV. DOS plots in Fig. 5 show that NaBr···nH₂ complexes has greater energy gap (Eg = 8.32–8.90 eV) relative to NaBr molecule. It also shows the combination of electronic states of H₂ molecules with NaBr. Therefore, the electrical conductivity of NaBr is decreased with the adsorption of H₂ molecules which can be attributed to the following equation [24].

$${\sigma }=\text{A}{\text{T}}^{\frac{3}{2}}2{\text{e}}^{\left(\frac{-{\text{E}}_{\text{g}}}{2\text{k}\text{T}}\right)}$$

3

Where the electrical conductivity is denoted by σ, A is the material constant (electrons/m³K^3/2), Eg is the bandgap width, k is Boltzman’s constant and T is the temperature. According to Eq. (3), when the bandgap width increases, the value of electrical conductivity decreases.

We investigated interactions between NaBr and 1–8 molecules of H₂ using MP2 computational step with aug-ccpVDZ basis set. The NaBr forms weak interactions with H₂ molecules to reach NaBr···nH₂ (n = 1–8) complexes. The computed results predict hydrogen adsorption on NaBr based not only on charge-induced dipole (electrostatic efficacy) interactions, but also orbital interactions and vdW interactions. Geometrical structures and absorption energies (E_ads) were obtained for the NaBr···nH₂ (n = 1–8) complexes. The range of the adsorption energies were from − 0.0462 to -0.1114 eV, suggesting a potentially appropriate method for hydrogen storage at ambient condition. Furthermore, the negative sign of E_ads indicates an exothermic and thermodynamically desirable adsorption mechanism.

To examine the thermodynamic potential for H₂ adsorption in NaBr···nH₂, we calculated the change in Gibbs free energy (∆G). The results show that the ∆G varies from 0.1196 to 0.3183 eV for all complexes. The elongation of the X–Y bond is observed in the XY···nH₂ complexes. With increasing the number of adsorbed H₂ in the XY···nH₂ complexes, the length of the X–Y bond changes. The elongation of the X–Y and H–H bonds means that they become weakening due to the formation of XY···nH₂ bonding. Moreover, the H–H bond length results (0.7554–0.7597 Å) are close to the original H–H bond distance of 0.7549 Å, which indicates weak bonding. It is found that the XY (X = Na and Y = Br) complexes display red and blue shifts of the X–Y stretching frequency. the H-H stretch mode shows a red shift, which is consistent with the bond elongation. Also, we accomplished a NBO analysis for the XY···nH₂ complexes. The results show that the charge transfer from σ orbital of H₂ to anti-bond pair orbital of X atom is larger and more plausible than the charge transfers from lone pair orbital of Y atom to σ* orbital of H₂. Finally, in this study we investigate various degrees of cooperativities which might observe during interactions of NaBr with H₂ molecules in different directions. In the studied NaBr···nH₂ complexes, diminutive effects are observed in all configurations. Lastly, DOS diagrams show that the changes in electronic properties of the studied complexes are insignificantly. We anticipate that these results will provide a beneficial reference for the design of hydrogen storage materials in the laboratory.

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No competing interests reported.

A theoretical modeling of NaBr(H2)n clusters as a unique approach in hydrogen gas storage

Status:

Version 1

Abstract

Figures

1. Introduction

2. Computational details

3. Results and discussion

3.1. The structure optimization and adsorption of H₂

3.2. Adsorption energies of H₂ and Gibbs free energy changes

3.3. Bond lengths and vibration frequencies

3.4. The natural bond orbital Analysis

3.5. The Mulliken charge analysis

3.6. Cooperative and diminutive effects

3.7. DOS

4. Conclusions

Declarations

References

Additional Declarations

Status:

Version 1

A theoretical modeling of NaBr(H2)n clusters as a unique approach in hydrogen gas storage

Status:

Version 1

Abstract

Figures

1. Introduction

2. Computational details

3. Results and discussion

3.1. The structure optimization and adsorption of H2

3.2. Adsorption energies of H2 and Gibbs free energy changes

3.3. Bond lengths and vibration frequencies

3.4. The natural bond orbital Analysis

3.5. The Mulliken charge analysis

3.6. Cooperative and diminutive effects

3.7. DOS

4. Conclusions

Declarations

References

Additional Declarations

Status:

Version 1

3.1. The structure optimization and adsorption of H₂

3.2. Adsorption energies of H₂ and Gibbs free energy changes