DFT calculations for Adsorption of H2S and other natural gas compounds on M-BTC MOF clusters

Desulfurization is a necessary process to reduce the corrosiveness of natural gas. In this regard, H 2 S adsorption on porous materials is the focus of study for development of new eco-friendly technologies. Although there are many experimental and theoretical studies about gas adsorption on MOFs, so far, there has been no theoretical work about desulfurization of natural gas or biogas through H 2 S adsorption on MOF BTC. Therefore, the objective of this study is to preselect which metal center, M 2+ = Co 2+ , Ni 2+ , Cu 2+ , or Zn 2+ , has the highest potential for selective desulfurization of natural gas. DFT calculations were performed at B3LYP ‐ D3/6 ‐ 311++G(2d,p)+LanL2DZ level for H 2 O, H 2 S, COS, CO 2 , and CH 4 adsorption on M-BTC MOF clusters in order to obtain equilibrium geometries of adsorption complex, adsorption energies and thermodynamic properties. It was found that Zn-BTC MOF cluster has the highest potential for selective H 2 S removal from dry natural gas streams, as it has an adsorption energy of ‐ 79.4 kJ mol ‐ 1 , which is 2.4 times higher than CH 4 . Furthermore, it is an exothermic and thermodynamically favorable process. Through NBO and EDA analyses, it was found that d electrons transfer from adsorbate to unoccupied orbitals of metal center contributes mainly to H 2 S chemisorption on Zn-BTC and Co-BTC, while for CO 2 and CH 4 adsorption, non-bonded interactions predominate. Most of the gases coordinate to coordinatively unsaturated site of BTC MOF cluster at axial position, indicating a stronger interaction with metal center compared to linkers.


INTRODUCTION
Natural gas consumption and production have increased in recent years, reaching an annual production of roughly 4.04 10 9 m 3 in 2021, which is likely to increase in the next years (BPstats 2022).In this view, natural gas is critical in the global energy matrix since it is less polluting than fossil fuels such as oil and coal, producing less carbon dioxide (CO 2 ) ) (Santos et al. 2021;Santos et al. 2017).Natural gas in raw form is a mixture of methane (CH 4 ) and light hydrocarbons that contains undesirable compounds such as water (H 2 O), hydrogen sul de (H 2 S), carbon dioxide (CO 2 ), and carbonyl sul de (COS) (Faramawy et al. 2016).
H 2 S is a toxic and acid gas that can corrode equipment and steel pipelines (Li et al. 2012).CO 2 reduces natural gas net calori c value and, in presence of water, produces carbonic acid (H 2 CO 3 ) (Farag et al. 2011).COS is a toxic and corrosive substance produced by the reaction between H 2 S and CO 2 in natural gas pipelines (Bartholomaeus and Haritos 2005;Guo et al. 2016;Li et al. 2010;Zhao et al. 2013).
Considering the problems caused by these compounds, there are regulatory restrictions on their maximum concentrations.For example, the Brazilian National Agency of Petroleum, Natural Gas, and Biofuels (ANP) speci es that the concentrations of H 2 S and CO 2 in natural gas must be less than 10 ppm and 3 mol %, respectively (National Agency of Petroleum Natural Gas and Biofuels 2008).In this regard, it is vital to purify raw natural gas by eliminating these unwanted compounds in order to meet the requisite quality criteria.
The use of hollow ber membranes for CO 2 separation from natural gas streams is an e cient industrial process point due to its high selectivity in CO 2 /CH 4 removal.However, before reducing CO 2 concentrations, it is necessary to desulphurize natural gas in order to prevent corrosion and damage to membranes caused by H 2 S (Buonomenna 2017).
Several classes of adsorbent materials have already been tested and applied for the removal of acid gases from natural gas or biogas streams, among them metal oxides (Zhang et  The BTC MOF structure is made up of dimeric metal units of Cr 2+ , Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ or Ru 2+ connected by linker molecules of benzene-1,3,5-tricarboxylate (Ketrat et al. 2017;Kozachuk et al. 2011).BTC MOF in hydrated state contains water molecules coordinated to metal atoms in axial position, but after an activation process with heating and vacuum, these molecules are removed from the structure, forming a coordinatively unsaturated site that can be accessed by other molecules in the dehydrated state (Hu et al. 2019).
The adsorption energy of H 2 S on Cu-BTC MOF clusters was determined by Zhang et al., through DFT calculations using PBE-D2 method, considering different positions of the adsorbate molecule on the cluster structure.They found that the strongest interaction occurs between the sulfur atoms of gas and the Cu 2+ cation, while interaction between gas and linkers is weaker (Zhang et al. 2018).
On the other hand, the study by Belmabkhout et al. used the uorinated MOF AlFFIVE-1-Ni.They studied the simultaneous and similarly selective removal of H 2 S and CO 2 from CH 4 rich stream in a single adsorption step.The authors argue that this material incorporates favorable sites that can adsorb both acid gases (Belmabkhout et al. 2018).
More recently, Zn-MOF/ ZnO nanocomposites were manufactured by Gupta et al., to test them in a desulfurization process aimed at regenerating the adsorbent material.Through spectroscopic studies, the authors con rmed that Zn is the adsorption site for H 2 S molecules via interactions between Zn 2+ ions and sulfur atoms (Gupta et al. 2021).
However, so far no theoretical work has been found that investigates the effect of the nature of the metal cation on the adsorption of acid molecules and methane in MOF BTC using ab initio calculations.The cluster used for DFT calculations was paddlewheel unit of the BTC structure in the dehydrated state.
It is built up of four benzene-1,3,5-tricarboxylate linkers molecules, which bridge two metal atoms (M 2+ ) as shown in Fig. 1.They are obtained by cutting out the periodic structure and introducing hydrogen atoms to saturate the unsaturated oxygen atoms, keeping the overall charge zero, as commonly found in literature (Fellah 2016;Gomes et al. 2019).The different types of MOF BTC clusters were obtained by simply replacing the two transition metals of the structure with Co 2+ , Ni 2+ , Cu 2+ and Zn 2+ atoms.
The H 2 O, H 2 S, COS, CO 2 , and CH 4 molecules were generated utilizing the Avogadro software (Hanwell et al. 2012).Prior to that, optimization of these molecules was carried out using the Merck molecular force eld (MMFF94) (Halgren 1996).

Computational Methods
The method used for theoretical calculations was the B3LYP-D3, which combines B3LYP hybrid functional with Grimme's D3 empirical dispersion correction.This method allows a better description of long-range electron interactions (Baker et al. 1996;Grimme et al. 2010).

Adsorption energy and thermodynamic properties
The detailed computational steps for adsorption energy calculations are as follows: rstly, the initial con guration of adsorption complex is built by positioning adsorbate molecule next to metal cation at axial position of paddlewheel unit.Secondly, the geometric optimizations of M-BTC MOF cluster, adsorbates and adsorption complexes were carried out separately by equilibrium geometry calculations at B3LYPD3/6-31 + G(2d,p) + LanL2DZ level.Then, adsorption complex energy , adsorbate energy and M-BTC MOF cluster energy are obtained by single point energy calculations at B3LYPD3/6-311 + + G(2d,p) + LanL2DZ level with Counterpoise corrections to minimize basis set superposition error (BSSE).Finally, the adsorption energy ( ) was calculated by the following equation: where is the gas constant and is the system temperature.Entropy ( ) was calculated by statistical thermodynamic methods at 298.15 K using scaled frequencies and approximations of ideal gas, rigid rotor and harmonic oscillator.Gibbs free energy of adsorption ( ) was calculated by (Sandler 2006): 3

Natural bond orbital and energy decomposition analysis
Partial charges of adsorbate molecules, metal cations, and the MOF organic framework (benzene-1,3,5tricarboxylate linker molecules) were calculated through population analysis.Additionally, the electron con gurations of metal cations (ECMC) were obtained using Natural Bond Orbital (NBO) analysis (Pounds 2007;Reed et al. 1988).The calculation of atomic partial charges is crucial for understanding the distribution of electrons, charge transfer, and polarization within the adsorption complexes.
To determine the nature of the interaction between the adsorbate molecules and CoBTC and ZnBTC MOF clusters, Energy Decomposition Analysis (EDA) based on Absolutely Localized Molecular Orbitals (ALMO-EDA) (Khaliullin et al. 2008;Khaliullin et al. 2007) was employed.This analysis allowed for quantifying the contribution of energy terms with physical signi cance to the adsorption energy, as demonstrated in the following equation: In this study, an Energy Decomposition Analysis (EDA) was conducted to determine the contributions of different energy components to adsorption energies, which can vary depending on the adsorbate molecule and metal cation.The EDA involved evaluating various energy terms, including ΔE FRZ , which represents the frozen energy referent permanent electrostatic and steric repulsion, ΔE DISP , which corresponds to the dispersion energy, ΔE POL , which represents the polarization energy, ΔE CT , which denotes the charge transfer energy, and ΔE GD , which accounts for the energy penalty associated with the distortion of isolated fragments to their geometries in the complex.
To simplify the representation of results, the frozen and dispersion energy terms were combined, considering the application of an effective core potential as done in this study.The ALMO-EDA calculations were performed using Q-Chem software (Shao et al. 2015), while all other calculations were conducted using Gaussian 09 software (Schlegel et al. 2016).
By conducting this EDA, the study aimed to provide a comprehensive understanding of the different energy components contributing to adsorption energies, with consideration for the speci c adsorbate molecule and metal cation under investigation.4 and 5.

Adsorption Complex Equilibrium Geometry
The measured distances between atom with a partial negative charge and metal cation, as well as the distances between atom with a partial positive charge and oxygen of MOF cluster, were found to be greater than 2.3 Å.This observation suggests that these adsorption complexes do not form chemical bonds, as such bonds typically fall within the range of 1-2 Å (Williams 1996).

Natural Bond Orbital and Energy Decomposition Analysis
Natural bond orbital results are shown in Table 2. Thermodynamic properties calculated at 298 K and 1 atm indicated that all the studied adsorption systems were exothermic, while only a few systems exhibited spontaneity (exergonic process, ΔG < 0).
Positive and relatively small Gibbs free energies implied favorable desorption and regenerability.
In conclusion, the theoretical ndings presented in this study contribute to a better understanding of the energetics underlying the adsorption of major natural gas contaminants on different M-BTC MOF clusters.These results highlight Zn-BTC MOF as a promising adsorbent material for selective natural gas desulfurization.

Figure 1 M
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Figure 2 Top
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Figure 3 Top
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Figure 4 Top
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Figure 5 Top
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Figure 7 Figure 8 .
Figure 7 Therefore, this work aimed to theoretically describe of H 2 O, H 2 S, COS, CO 2 and CH 4 adsorption on coordinatively unsaturated site of CoBTC, NiBTC, CuBTC and ZnBTC MOF through DFT calculations using the adsorption energy, thermodynamic properties, NBO and EDA analysis, to pre-select which BTC MOF has the greatest potential for selective natural gas desulfurization.
no change in the lengths and internal bond angles of gases evidencing that the interactions involved in these adsorption systems are unable to modify lengths and angles bond.The adsorption of these molecules does not signi cantly change clusters geometry.Note that atoms with partial negative charges ( ) such as oxygen in H 2 O, sulfur in H 2 S, sulfur in COS, oxygen in CO 2 and carbon in CH 4 coordinate with metal cation (M 2+ ) of BTC MOF clusters.This points out that coordinatively unsaturated site is important for H 2 O, H 2 S, COS, CO 2 and CH 4 adsorption on M-= (ΔE F RZ + ΔE DI SP ) + ΔE P OL + ΔE C T + ΔE GD δ − charge ( ) and interact with oxygen atoms of M-BTC MOF framework.The COS and CO 2 adsorption on Cu-BTC and Zn-BTC MOF clusters occurs in a similar way, S and O atoms of adsorbates coordinate to metal cation of MOF framework.C atom of these gases interacted with the two O atoms of MOF, illustrated in Figs.
Adsorption complexes equilibrium geometries are shown in Figs. 2 to 5 for CoBTC, NiBTC, CuBTC and ZnBTC MOF clusters, respectively.Analyzing adsorption complexes equilibrium geometries, it is veri ed that there is no breakage or formation of new chemical bonds between M-BTC MOF clusters and adsorbates, practically there is BTC MOF, having little interaction with benzene-1,3,5-tricarboxylate linkers molecules as also observed by Zhang et al. for H 2 S adsorption on Cu-BTC (Zhang et al. 2018).The H 2 O, H 2 S and CH 4 molecules are stabilized with their O, S and C atoms closer to metal cation (M 2+ ) at axial position of the paddlewheel unit.The hydrogen atoms of these adsorbates have a partial positiveΔE

Table 1
(Do 1998) al. 2018reported similar results for H 2 S adsorption on Cu-BTC cluster(Zhang et al. 2018).3.2.Adsorption EnergyFollowing the geometric optimization, adsorption energies on the coordinatively unsaturated site were calculated by utilizing energies of M-BTC MOF clusters, adsorbates, and obtained adsorption complexes through SP energy calculations.The energies for H 2 O, H 2 S, COS, CO 2 , and CH 4 adsorption on Co-BTC, Ni-presents the thermodynamic properties at 298 K and 1 atm for H 2 O, H 2 S, COS, CO 2 , and CH 4 adsorption on M-BTC MOF.The enthalpy of adsorption data suggests that these gases adsorption on M-BTC MOF is an exothermic process, which is a characteristic feature of adsorption phenomenon(Do 1998).Although enthalpies of adsorption are comparatively lower than adsorption energies, they exhibit similar behavior in relation to the adsorbate and M-BTC MOF clusters.Speci cally, for H 2 O and H 2 S adsorption on Zn-BTC, enthalpies of adsorption exceed 70 and 90 kJ mol − 1 , respectively, indicating chemisorption from a thermodynamic perspective, where electron transfer plays a dominant role.Conversely, for CO 2 and CH 4 adsorption on all BTC, Cu-BTC, and Zn-BTC MOF clusters, as calculated by Eq. 1, are exhibited in Fig.8.The ndings presented inFig.8demonstratethatadsorptionenergies of H 2 O, H 2 S, and COS on M-BTC MOF clusters follow the order Zn > Co > Cu > Ni.Conversely, adsorption energies of CO 2 and CH 4 on M-BTC MOF clusters follow the order Zn > Cu > Co > Ni.These results align with the study conducted by Pnevskaya and Bugaev (Pnevskaya and Bugaev 2023), who also observed the same order for H 2 O adsorption on M-BTC MOF clusters.Figure 8 further reveals that adsorption energies of H 2 O and H 2 S on Zn-BTC and Co-BTC exceed 50 kJ mol − 1 , indicating a typical chemisorption phenomenon observed in literature (Castellan 1986).Based on a comparison of the adsorption energies, it can be inferred that Zn-BTC MOF exhibits the highest a nity for selective desulfurization of natural gas, as it demonstrates the strongest interaction with H 2 S molecules and potentially greater selectivity.The adsorption energies of H 2 S on Zn-BTC MOF are at least 45% higher than those of COS, CO 2 , and CH 4 .However, it should be noted that Zn-BTC MOF is prone to H 2 O adsorption.In this regard, Co-BTC MOF can serve as an alternative material, as its adsorption energy for H 2 O is only 10% higher compared to H 2 S. MOF clusters, enthalpies of adsorption are below 40 kJ mol − 1 , indicating physisorption, where nonbonded interactions such as Van der Waals and Coulomb interactions prevail.In order to gain deeper insights into the nature of these interactions involved in adsorption processes, energy decomposition analysis can be utilized.The examination of Gibbs free energy of adsorption allows us to deduce that H 2 O and H 2 S adsorption onZn-BTC and Co-BTC MOF clusters is thermodynamically favorable, as the values of Gibbs free energy are negative.Conversely, gases with positive and small Gibbs free energy values (below 25 kJ mol − 1 ) indicate thermodynamically unfavorable adsorption, suggesting that adsorption occurs in equilibrium with desorption.Additionally, among the studied gases, H 2 O adsorption exhibits the highest favorability, characterized by the lowest Gibbs free energy values, followed by H 2 S adsorption.

Table 2
Partial charges of adsorbate molecules, metal cations, MOF framework and the electron con gurations of metal cations obtained from NBO analysis (values are in units of Coulomb).2 O, H 2 S, COS, CO 2 , and CH 4 adsorption leads to electron recovery in the 4p orbital of all cations.Additionally, H 2 S adsorption promotes greater electron recovery in the 4s orbital and 4p orbital of all cations compared to other adsorbate molecules.Similar results have been reported by Braga et al. for H 2 S, COS, CO 2 , and CH 4 adsorption on transition metal-exchanged Y zeolite (Braga et al. 2022).Therefore, transfer of electrons between cation and adsorbate, speci cally donation of d electrons and acceptance of electrons in cation's unoccupied orbitals, plays a crucial role in determining adsorption energy.The charge transfer in complexes with transition metals follows a clear trend, as also depicted by Sung et al. (Sung et al. 2013).However, a more precise interpretation of adsorption energy in terms of charge transfer requires further investigation.The EDA results, illustrated in Fig. 8, present the values of (ΔE FRZ + ΔE DISP ), ΔE POL , and ΔE CT for different systems studied in this work.The results presented in Fig. 9 provide a decomposition of the adsorption energy reported in Fig. 8, shedding light on the contributions of different energy terms.For H 2 S adsorption on Co-BTC and Zn-BTC MOF clusters, both the charge transfer and polarization energy contributions (ΔE CT + ΔE POL ) dominate, indicating the occurrence of electron transfer from the adsorbate molecule to the unoccupied orbitals of the cation.This suggests that chemisorption is more likely to occur in these systems.Comparing the EDA analysis of both systems, it can be observed that the ΔE CT term is higher for H 2 S adsorption on Co-BTC, although non-bonding interactions decrease the adsorption energy.In the case of H 2 O adsorption on Co-BTC, there is a tendency towards chemisorption with a low contribution of non-bonded energies.On the other hand, for H 2 O adsorption on Zn-BTC, there is a signi cant contribution from the ΔE FRZ + ΔE DISP term, accounting for approximately 59% of the adsorption energy.This indicates that electron transfer and intermolecular interactions play a crucial role in H 2 O adsorption.For COS adsorption in both M-BTC MOF clusters, the ΔE CT and ΔE POL terms contribute to increasing the adsorption energy, while the ΔE FRZ + ΔE DISP term decreases it.Conversely, for CO 2 adsorption, the nonbonded terms contribute to an increase in the adsorption energy.The small values of the geometric distortion terms indicate that there is minimal distortion of the equilibrium geometries of the M-BTC MOF clusters and adsorbates.In all systems, a contribution from the ΔE CT and ΔE POL terms is observed, indicating the occurrence of electron transfer between the adsorbate molecules and the metal cation, regardless of the strength of the interaction.The adsorption of these gases on M-BTC MOF clusters is less in uenced by long-range van der Waals interactions, except for CO 2 adsorption on Co-BTC.ΔE CT and ΔE POL terms favor adsorption in all systems, while the impact of (ΔE FRZ + ΔE DISP ) and ΔE GD terms on the adsorption energy can vary depending on the speci c system.Based on the results of this theoretical study, it can be inferred that Zn-BTC MOF is a promising candidate for selective H 2 S removal as an initial step in natural gas desulfurization.LanL2DZ level to preliminarily select M-BTC MOF as a potential candidate for selectively removing H 2 S from natural gas streams.The analysis involved evaluating adsorption energies, thermodynamic properties, and determining the nature of adsorption energies through NBO and EDA analyses.DFT calculations were conducted to investigate the adsorption of natural gas compounds (H 2 O, H 2 S, COS, CO 2 , and CH 4 ) on Co-BTC, Ni-BTC, Cu-BTC, and Zn-BTC MOF clusters.These clusters represented the coordinatively unsaturated sites of the M-BTC MOF structure.Among the studied adsorption systems, H 2 S adsorption on Zn-BTC and Co-BTC MOF clusters exhibited higher energies of -79.36 and 55.76 kJ mol − 1 , respectively, suggesting potential selectivity desulfurization compared to other clusters.Importantly, the adsorption energy of H 2 S on these clusters was at least 80% higher than that of COS, CO 2 , and CH 4 .However, it should be noted that Zn-BTC MOF demonstrated a propensity for H 2 O adsorption despite its strong interaction with H2S molecules.NBO and EDA analyses revealed that the transfer of d electrons from the H 2 S molecule to unoccupied orbitals of the cation played a signi cant role in determining the adsorption energy.Furthermore, the adsorption of H 2 S and COS on Co-BTC and Zn-BTC MOF clusters was found to be primarily governed by charge transfer and polarization energy, indicating the presence of chemisorption.
The NBO analysis results, as shown in Table2, demonstrate that M-BTC MOF induces polarization in all adsorbates, resulting in an increase in magnitude of their atomic partial charges.Similar ndings have been reported in previous studies for H 2 S adsorption on transition metal-exchanged Y zeolite clusters (Braga et al. 2022).Furthermore, signi cant electron transfer is observed between adsorbate, MOF cluster, and adjacent metal cation, as indicated by the partial charge values.Most adsorbates exhibit a de cit of electrons (positive partial charges), while the partial charge of the metal cation decreases compared to systems without adsorbate molecules, indicating the migration of electron density from adsorbate to metal atom.H