Computational evaluation of an Ag (I)-N-heterocyclic carbene complex as a novel gas scavanger

Abstract

This research employs density functional theory calculations at the PBE0-D3/def2-TZVP level to explore the interaction properties of the [C₁₁H₁₄N₂Ag]⁺ with a range of gaseous entities: H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂. A key aspect of the investigation focuses on evaluating the affinities of these gas molecules surrounding the Ag center within the complex. The analysis indicates that the interactions between the small gas molecules and the [C₁₁H₁₄N₂Ag]⁺ structure are primarily characterized by a favorable release of energy upon binding, with the notable exception of O₂. The thermochemical analysis establishes a hierarchy of binding strengths, ranked as follows: C₂H₄ > C₂H₂ > CO > NO > N₂ > H₂. In addition, quantum theory of atoms in molecules (QTAIM), non-covalent interaction (NCI), and reduced gradient density (RGD) analyses provided a detailed understanding of the intricate nature of these interactions.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-27027-4.

Introduction

Gas-adsorbent materials (GAMs) are central to advances in molecular sensing, energy systems, and environmental technologies. Their high surface area, atomic precision, and tunable properties enable applications such as pollutant removal, solid-state H₂/CH₄ storage, CO₂ capture, and improved performance in photovoltaics and batteries^1–4. Prominent gas-adsorbent materials families include zeolites, metal oxide nanocrystals (e.g., CaO, Al₂O₃), carbon-based nanomaterials (CN), metal hydride nanoparticles (e.g., MgH₂, LiBH₄), and covalent/metal-organic frameworks (COF/MOF) CN and MOF show particular promise for H₂, CO₂, and CH₄ capture and storage^5–8. Despite progress, gas-adsorbent materials performance remains below commercial targets. For example, H₂ storage systems must reach 5.5 wt% and 40 g/L volumetric capacity⁹, while CO₂ capture from power plants must achieve 90% efficiency with < 35% cost increase¹⁰. Thus, optimizing GAM design and adsorption processes remains a key research focus. Recent joint DFT–experimental investigations have further underscored the value of theoretical predictions in guiding material synthesis and performance optimization. For instance, combined computational and experimental studies have demonstrated that electronic-structure descriptors can accurately forecast gas uptake and catalytic selectivity in nanostructured frameworks¹¹. Likewise, existed integrative analyses¹² have highlighted the synergy between ab initio modeling and experimental characterization for carbon-based gas-adsorbent and energy materials. These precedents substantiate the complementary role of DFT simulations in rationalizing and predicting adsorption behavior, aligning well with the computational focus of the present work.

Escalating environmental pollution has intensified global efforts to develop advanced remediation technologies. N-Heterocyclic carbenes (NHCs) have emerged as a focal point of research in the field of transition metal coordination complexes over the last two decades^13–15. Initially noted in 1968, their significance was somewhat overlooked until pivotal advancements made by researchers such as Bertrand and Arduengo¹⁶, who successfully isolated and characterized free carbenes. This development catalyzed a remarkable surge of interest in NHCs. A distinguishing characteristic that sets NHCs apart from other carbene variants is their remarkable stability. NHCs exhibit remarkable stability when contrasted with other carbene varieties. This unique stability is attributed to the presence of two adjacent heteroatoms, predominantly N, which contribute electron density to the central carbene carbon, thus enhancing its stability¹⁷. In stark contrast to more reactive and transient carbene equivalents, NHCs can be synthesized, crystallized, and stored for prolonged durations, rendering them highly accessible as reagents in various applications. Due to their remarkable properties, NHCs have been the subject of significant research as ligands for transition metal compounds^18–24. The bonding interaction between NHCs and metals (NHC − M bonds) is better characterized as single bonds rather than double bonds, as they maintain a singlet state even when coordinated to a metal center²⁵. Although NHC − M interactions exhibit greater stability than M-alkyl complexes, they remain susceptible to decomposition through pathways such as reductive elimination, akin to metal-alkyl interactions, under specific conditions²⁶. The high kinetic stability typically associated with NHC − M bonds, together with their substantial thermodynamic strength, is pivotal in the application of these ligands within transition metal complexes^27,28. Calorimetric assessments suggest that the strength of the NHC − M bond is approximately twice that of traditional triphenylphosphine (R₃P) − M bonds²⁹. This increased bond strength obstructs decomposition routes involving metal-ligand dissociation, such as ligand oxidation or protonation, underscoring the suitability of NHCs as ligands in metal complexes utilized for oxidation catalysis³⁰. Ag (I) complexes featuring NHCs have attracted significant attention in recent years due to their versatile applications in catalysis^31,32. These complexes facilitate carbene transfer reactions, enabling the synthesis of transition metal carbene complexes that are otherwise difficult to achieve via conventional free carbene methods. Moreover, their relevance extends into the realm of medicinal inorganic chemistry. Notably, Ag(I)-NHC complexes have demonstrated impressive antimicrobial properties, as well as promising anticancer effects in vitro against a range of human cancer cell lines^33–44.

Recently, the scientific community has increasingly focused on the exploration of greenhouse gas sequestration. This surge in interest is driven by the potential of hydrogen as a sustainable fuel source for the future, as well as the urgent need to mitigate environmental risks associated with greenhouse gas emissions^45–47. Current data indicates that fossil fuels account for approximately 85% of the global energy consumption, underscoring the critical role they play in our energy landscape⁴⁸. It is widely understood that the combustion of these fossil fuels is a significant contributor to atmospheric carbon dioxide levels. In response to these challenges, numerous materials have been developed, synthesized, and designed experimentally and computationally with the goal of enhancing hydrogen storage capabilities and improving methods for greenhouse gas sequestration⁴⁹. As a very interesting research, Mondal⁵⁰ elucidated the bonding characteristics of the β-D-glucopyranose-silver ion complex ([Ag(C₆H₁₂O₆)]⁺), formed in a 1:1 ratio, through in silico studies conducted at the PBE0-D3/def2-TZVP theoretical level. Furthermore, he investigated the interactions between H₂ and the [Ag(C₆H₁₂O₆)]⁺ complex. The analysis revealed that the metallic center has the capacity to coordinate with as many as three hydrogen molecules, exhibiting a binding energy of 5.3 kcal mol^{− 1} for each H₂ molecule. Moreover, Mondal in another valuable research work⁵¹, performed the density functional theory calculations conducted at the PBE0-D3/def2-TZVP level, aimed at elucidating the nature of the interactions between the β-D-glucopyranose-silver ion complex ([Ag(C₆H₁₂O₆)]⁺) and a selection of seven gaseous molecules. He employed natural bond orbital analysis (NBO), along with the contour visualization of the Laplacian of electron density and provided valuable insights into the characteristics of molecular interactions. Additionally, he used electron density (ED) descriptors and gradient isosurfaces to understanding the nature of the interactions. He demonstrated that the complex formed between β-D-glucopyranose and silver ions in a 1:1 ratio is a viable option for the scavenging of small gaseous molecules. In addition, Hamdi et al.,⁵² used N,N-disubstituted benzimidazolium salts with Ag₂O in dichloromethane to synthesize innovative Ag(I)–NHC complexes and employed them in three-component coupling reactions involving aldehydes, amines, and alkynes. Their findings indicated that Ag–NHC complexes possess potent antimicrobial properties against both bacterial and fungal strains. Getting inspired from Mondal’s and Hamdi’s interesting research works and in continuation of our previous studies about the interaction of gasous molecules with different designed structures^53–57, we designed a novel Ag(I)-N-heterocyclic carbene [C₁₁H₁₄N₂Ag]⁺ and explored its interaction with H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂ molecules. Our theoretical investigation employs density functional theory (DFT), a computational methodology that has proven to be both effective and dependable for exploring many-body systems, like atoms, molecules, and solids in recent years. The selection of computational methods and parameters is meticulously informed by established reliable guidelines.

Computational methods

To evaluate the reliability of the computational level employed in this study, the adsorption of molecular H₂ on the [C₁₁H₁₄N₂Ag]⁺ complex was calculated using several widely applied hybrid and dispersion-corrected functionals, namely B3LYP-D3, M06-2X, and ωB97X-D, in addition to the originally used PBE0-D3 functional. The corresponding binding energies (ΔE) and Gibbs free energies at 298 K (ΔG₍₂₉₈₎) are summarized in Table 1. Among all tested methods, PBE0-D3/def2-TZVP predicts the most exothermic adsorption energies (ΔE = − 10.91 kcal mol^{− 1}) and Gibbs free energies (ΔG₍₂₉₈₎ = −3.57 kcal mol^{− 1}), indicating a slightly stronger interaction between H₂ and the Ag center compared with B3LYP-D3 (ΔE = − 10.14 kcal mol^{− 1}), ωB97X-D (ΔE = − 9.76 kcal mol^{− 1}), and M06-2X (ΔE = − 8.79 kcal mol^{− 1}). The same energetic trend is preserved at the Gibbs free energy level, confirming the internal consistency of the PBE0-D3 results. Although the numerical differences are moderate (within ~ 2 kcal mol^{− 1}), the consistent stabilization predicted by PBE0-D3 demonstrates its superior performance for this system. The improved description obtained with PBE0-D3 can be attributed to its balanced inclusion of exact exchange (25%), which mitigates self-interaction errors often present in pure generalized gradient approximations (GGAs), together with the empirical D3 dispersion correction, which effectively captures the noncovalent component of H₂ adsorption on the metal site⁵⁸. In contrast, M06-2X tends to overestimate exchange repulsion for transition-metal complexes, leading to underbinding, while ωB97X-D may slightly weaken localized metal–adsorbate interactions due to its range-separated exchange form. B3LYP-D3 provides reasonable energetics but remains marginally less stabilizing than PBE0-D3. Overall, these benchmarking results confirm that PBE0-D3/def2-TZVP provides the most physically sound and energetically reliable description of H₂ adsorption on the studied silver complex. Therefore, this functional was retained as the main computational level throughout the present work.

Table 1.

Calculated binding and Gibbs free energies of H₂ adsorption on the [C₁₁H₁₄N₂Ag]⁺ complex at different computational level of theories.

Parameter	PBE0-D3/def2-TZVP	B3LYP-D3/def2-TZVP	M062X/def2-TZVP	ωB97XD/def2-TZVP
ΔE	− 10.91	− 10.14	− 8.79	− 9.76
ΔG298 K	− 3.57	− 3.04	− 2.01	− 2.41

In this study, all computational analyses were conducted utilizing the Gaussian 16 software package⁵⁹, at the PBE0-D3/def2-TZVP⁶⁰ levels of theory. All optimized structures were confirmed as minima through frequency analysis. Since the present study concerns isolated molecular complexes, phonon dispersion calculations are not required; however, molecular dynamics simulations at finite temperature will be considered in future work to assess long-term thermal stability. In order to calculate the Wiberg bond indices (WBI) and atomic charges (q), the natural bond orbital (NBO) analysis⁶¹ was performed in Gaussian 16. Quantum theory of atoms in molecules (QTAIM), non-covalent interaction (NCI), reduced density gradient (RDG), and electron density (ED) analyses were carried-out using the Multiwfn software⁶². The corrected basis set superposition error (BSSE)⁶³ binding energies (∆E) and Gibbs free energies (∆G), are quantified for the entrapment of various small molecular gases, as described by the equations below:

The notation E/G_{gas@[C11H14N2Ag]+} indicates the energy/Gibbs free energy associated with the studied gas@[C₁₁H₁₄N₂Ag]⁺ complex. In contrast, E/G_{[C11H14N2Ag]+} represents the energy/Gibbs free energy of the [C₁₁H₁₄N₂Ag]⁺ structure, while E/G_gas refers to the energies/Gibbs free energies of studies gas molecules. Global hardness (η), and electrophilicity (ω) can be characterized for the studied systems as follows:

I, A, µ, E_HOMO, and E_LUMO, are referred to ionization potential, electron affinity, chemical potential, energy of the highest occupied molecular orbital, and energy of the lowest unoccupied molecular orbital.

Results and discussion

The coordination complex [C₁₁H₁₄N₂Ag]⁺ has been investigated using DFT-based electronic structure calculations, and its properties were visualized through molecular orbital and electrostatic potential surface analyses. The molecular geometry optimization reveals that the Ag⁺ center adopts a linear coordination mode with two nitrogen donor atoms from a bidentate ligand framework (Fig. 1a). The Ag–C bond length is found to be approximately 2.084 Å, which is in excellent agreement with the experimentally reported Ag–C coordination distances (2.05–2.10 Å) for Ag(I)–NHC complexes^64,65. The adjacent C–N bond distances within the aromatic core are around 1.343 Å, suggesting delocalized π-character and a conjugated electronic system across the ligand. The molecular electrostatic potential (MEP) surface further elucidates the reactive sites of the molecule (Fig. 1b). The most negative electrostatic potential regions (pale blue) are localized near the nitrogen atoms of the ligand, identifying them as potential hydrogen bond acceptors or coordination sites for electrophilic species. In contrast, the positive potential isosurfaces (dark blue) are concentrated near the Ag(I) center, suggesting that this site can readily interact with nucleophilic or electron-donating gas molecules. The MEP ranges between − 0.205e0 and + 0.205e0, signifying a moderately polarized charge distribution across the molecule. This polarization enhances the complex’s capacity to interact with small analyte molecules through both electrostatic interactions and donor–acceptor orbital overlap. The HOMO is primarily localized on the π-conjugated ligand, especially over the aromatic rings and nitrogen atoms (Fig. 1c). This indicates that the electron-rich regions are concentrated around the organic backbone and that the ligand serves as the main electron-donating component of the complex. The LUMO however, is significantly localized on the silver atom and partially extended toward the adjacent π-system (Fig. 1d). This implies that the Ag center functions as a low-energy electron acceptor, capable of participating in charge-transfer processes upon interaction with external species. The relatively small spatial overlap between HOMO and LUMO regions suggests that the complex may exhibit favorable electronic transitions upon perturbation, such as from gas adsorption, which would induce notable shifts in energy levels—an essential characteristic for molecular sensors.

Fig. 1.

Optimized chemical structure (a), MEP profile (b), HOMO (c), and LUMO (d) isosurfaces of the designed [C₁₁H₁₄N₂Ag]⁺.

The calculated interaction distances for H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂ gas molecules adsorbed on [C₁₁H₁₄N₂Ag]⁺ structure are presented in Fig. 2. In addition, the interaction energies (∆E), interaction free energies (∆G), hardness (η), and electrophilicity (ω) values for each complex are listed in the Table 2. The findings indicate the BSSE-adjusted interaction energies of − 10.91, − 14.35, − 6.82, − 16.43, − 26.75, − 30.28, −27.72 kcal mol^− 1 for H₂, N₂, O₂, NO, CO, C₂H₄ and C₂H₂, respectively. Notably, the C₂H₄ gas exhibits the most substantial interaction energy, attributable to effective orbital overlap. The interaction of the C₂H₄ molecule with the Ag⁺ site in is facilitated through its π-bond, as illustrated in Fig. 3a. The bond critical point (BCP) between the Ag atom and C₂H₄ is situated between the BCP of the C = C bond in C₂H₄ and the Ag atom (Fig. 3a). The interaction energy associated with this complex is measured at -30.28 kcal mol^− 1, indicating an exergonic process with a Gibbs free energy change of -20.55 kcal mol^− 1 (Table 2). The long and equal distances suggest weak η² coordination via the C = C π-system. The π-orbital donates electron density to Ag’s s-orbital, but the absence of backdonation weakens the interaction. The geometry indicates a loosely bound π-complex with minimal C = C distortion. The C₂H₂ molecule similarly interacts with [C₁₁H₁₄N₂Ag]⁺ structure (Fig. 2), exhibiting a high interaction energy of -27.72 kcal mol^− 1, and this interaction is also characterized as exergonic, with a free energy change of -19.95 kcal mol^− 1. As can be seen in Fig. 3b, a contour plot of Laplacian of the electron density, highlights the BCP situated between Ag and C₂H₂ molecule. Slightly shorter than C₂H₄, the C₂H₂ complex likely has a similar η²-mode coordination. Acetylene’s more concentrated π-density allows slightly better overlap, but the bonding remains weak overall due to the lack of significant metal-to-ligand backdonation. In addition, the CO molecule engages with the Ag site through its carbon atom, with an interaction energy of -26.75 kcal mol^− 1; however, in this instance, the Gibbs free energy change at 298 K is noted to be -17.25 kcal mol^− 1. The Ag–C–O bond angle is recorded at 179.98°. This is the shortest distance among all complexes, confirming that CO forms the strongest bond to Ag⁺ in this series. The bonding is purely σ-type from CO’s carbon lone pair, with negligible backdonation (expected for d¹⁰ systems). The linear geometry further supports a well-defined, directional interaction. The NO molecule interacts with the Ag metal in a bent configuration (Fig. 2), utilizing its N atom for the interaction. The observed Ag–N–O angle measures at 135.04°, while the corresponding ΔE and Gibbs free energy change are recorded at -16.43 kcal mol^− 1 and − 8.07 kcal mol^− 1 respectively. This is one of the shortest distances among the neutral ligands, indicating relatively strong coordination. NO acts as a lone-pair donor through nitrogen, with potential for π-acceptor behavior. The bonding is consistent with classical linear NO coordination to d¹⁰ metal centers, without significant radical delocalization to Ag. Furthermore, the N₂ molecule is recognized for its relatively inert properties. In this study, the interaction of N₂ molecule with the [C₁₁H₁₄N₂Ag]⁺ structure reveals a stabilizing effect of -14.35 kcal mol^− 1 and Gibbs free energy change as -5.78 kcal mol^− 1. The Ag–N–N angle is again noted at 179.97°. This intermediate Ag–N distance points to a weak but definitive σ-donation from the nitrogen lone pair. While N₂ is typically a poor ligand due to its high-lying HOMO and lack of polarity, this value suggests weak coordination more pronounced than dispersion-based interaction. The interaction between the O₂ molecule and Ag site demonstrates a lowest stabilization of -6.82 kcal mol^− 1, with the overall interaction deemed endergonic at + 1.66 kcal mol^− 1. The O₂ molecule approaches the Ag in a tilted manner, engaging one of its O atoms, resulting in an Ag–O–O bond angle of 74.32°. Notably, according to the NBO analysis, the computed charge on the Ag atom in this complex, where no molecule is coordinated, is established at 0.680 |e| (Table 2). This positive charge might play a significant role in facilitating the binding of various small molecules previously described as the electron donors. Upon binding, the charge on Ag has changed from + 0.680 |e| to + 0.422 |e| in CO@[C₁₁H₁₄N₂Ag]⁺ and to + 0.736 |e| in O₂[C₁₁H₁₄N₂Ag]⁺. It can be seen that, the most substantial charge transfer is observed when CO interacts with Ag (+ 0.258 |e|), while the least charge transfer occurs during the interaction with the O₂ molecule (-0.056 |e|). It is evident that the C₂H₄ molecule interacts from the furthest distance from the Ag center, measuring 2.311 Å, while the shortest interaction distances is recorded for H₂, at 1.908 Å. The hardness values for the systems involving H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂ are measured at 2.47, 2.22, 0.81, 1.22, 2.04, 2.23, and 2.33 eV, respectively. This data indicates that the H₂@[C₁₁H₁₄N₂Ag]⁺ exhibits the greatest hardness and thus the highest stability, whereas the O₂@[C₁₁H₁₄N₂Ag]⁺ shows the least stability. Interestingly, the electrophilicity values present an inversely correlated trend relative to hardness. The variation in hardness (decreasing) and electrophilicity (increasing) can be arranged as follows: H₂ > C₂H₂ > C₂H₄ > N₂ > CO > NO > O₂.

Fig. 2.

Optimized chemical structure of the gas@[C₁₁H₁₄N₂Ag]⁺ complexes.

Table 2.

Calculated interaction energy (∆E), interaction free energy (ΔG_{298 K}), hardness (η), and electrophilisity (ω) values of the gas@[C₁₁H₁₄N₂Ag]⁺ complexes.

Structure	ΔE (kcal mol− 1)	ΔG298 K (kcal mol− 1)	η (eV)	ω (eV)
H2@[C11H14N2Ag]+	− 10.91	− 3.57	2.47	10.87
N2@[C11H14N2Ag]+	− 14.35	− 5.78	2.22	12.67
O2@[C11H14N2Ag]+	− 6.82	+ 1.66	0.81	54.30
NO@[C11H14N2Ag]+	− 16.43	− 8.07	1.22	29.88
CO@[C11H14N2Ag]+	− 26.75	− 17.25	2.04	14.60
C2H4@[C11H14N2Ag]+	− 30.28	− 20.55	2.23	12.33
C2H2@[C11H14N2Ag]+	− 27.72	− 19.95	2.33	11.43

Fig. 3.

Contour representation of the Laplacian of electron density in C₂H₄@[C₁₁H₁₄N₄Ag]⁺ (a) and C₂H₂@[C₁₁H₁₄N₂Ag]⁺ (b) complexes.

As can be seen, ΔE and ΔG trends suggest that all of the gas adducts are thermodynamically favorable at standard conditions, as all ΔG values are negative (exergonic in nature) except O₂. However, ΔE values provide insight into intrinsic interaction strength, showing that C₄H₄ exhibits the most favorable interaction energetically (ΔE = − 30.28 kcal mol^− 1), followed by C₂H₂, CO and NO. In contrast, N₂, H₂, and O₂ show substantially lower ΔE values (–14.35 to − 6.82 kcal mol^− 1), indicating weaker interaction with the Ag center, likely due to steric or electronic mismatch. The chemical hardness (η) spans from 0.81 to 2.47 eV. Notably, the O₂ adduct is the softest (η = 0.81 eV), implying greater polarizability and possible reactivity, whereas H₂ forms the hardest complex (η = 2.47). The electrophilicity index (ω) is highest for the O₂ complex (54.30 eV), followed by NO (29.88 eV), suggesting these adducts possess the highest potential to accept electron density, consistent with the oxidative character of these diatomic gases.

Table 3 shows that the charge on the Ag atom in the [C₁₁H₁₄N₂Ag]⁺structure is 0.680 |e| and the electronic configuration for the Ag atom is 5s^0.404d^9.905p^0.02. It can be seen that due to the interaction with the H₂ molecule, the charge on the Ag atom decreases from 0.680 |e| to 0.544 |e|, which indicates a transfer of 0.136 |e| from the H₂ molecule to the Ag atom. The charge transfer from the H₂ molecule to the Ag atom can be seen in the change in its electronic configuration to 5s^0.554d^9.855p^0.06, which indicates a transfer of 0.15 |e| to 5s of Ag atom. Considering the WBI value obtained for the interaction with hydrogen (0.11), it can be understood that the weakest interaction value with the gases studied is related to this complex. The interaction between the N₂ and Ag occurs in a predominantly linear orientation. A noteworthy aspect of this interaction is the potential for partial electron transfer from the HOMO of N₂ to the Ag metal, which results in a decrease of charge on the Ag by 0.151 |e| to reach 0.529 |e|. This phenomenon is further corroborated by a reduction of 2.97 in the WBI of the N ≡ N bond, attributable to its interaction with the Ag center. The observed WBI value for the Ag–N bond interaction is recorded at 0.26. In the O₂@[C₁₁H₁₄N₂Ag]⁺, upon interaction with Ag, the WBI for the O = O bond is changed to 1.66. Due to the fact that charge transfer is happed from the antibonding 2π² HOMO of O₂ to the Ag, this change can be considered as an enhancement. Furthermore, the WBI for the Ag-O bond is determined to be 0.30 and 0.34. To ensure the correct spin-state description of molecular oxygen, both triplet (³Σg⁻) and singlet (¹Δg) configurations were examined at the PBE0-D3/def2-TZVP level. The triplet state, which is the ground electronic configuration of O₂, was found to be more stable than the singlet state by 22.7 kcal mol^− 1, in line with previous theoretical and experimental reports. The interaction energy (ΔE) and Gibbs free energy (ΔG₂₉₈) values for the triplet and singlet O₂@[C₁₁H₁₄N₂Ag]⁺ complexes are calculated as − 6.82 / +1.66 and − 9.14 / − 1.12 kcal mol⁻¹, respectively. These data confirm that the weak, slightly endergonic binding reported in the main text arises from the triplet nature of O₂, which limits electron pairing and charge transfer with the closed-shell Ag(I) center. The singlet configuration, although marginally more stabilizing, remains energetically inaccessible under normal conditions, reinforcing that the observed interaction strength for O₂ is physically consistent. The interaction of NO with 5s^0.604d^9.805p^0.09occurs through its nitrogen atom. This interaction leads to a change in the WBI of the N–O bond as 2.13. Concurrently, the WBI corresponding to the Ag–N bond measures at 0.30. Consequently, as a result of this coordination, the Ag atom receiving 0.167 |e| reaches to + 0.513 |e|. The CO molecule engages through its C atom, a behavior aligned with the predictions made by its molecular orbital diagram. The electronic configuration of CO indicates that the HOMO is primarily situated on the C atom, suggesting a nonbonding characteristic. The interaction of CO with [C₁₁H₁₄N₂Ag]⁺structure leads to receiving amount of 0.258 |e| by Ag atom and reaching to 5s^0.684d^9.775p^0.12. The WBI for Ag ⋯ CO in the CO@[C₁₁H₁₄N₂Ag]⁺ shows the highest 0.54 value among other complexes. The interaction between C₂H₄ and Ag reveals a notable charge shift of 0.141 |e| from C₂H₄ to the Ag center. This interaction results in a 0.17 |e| increase in the 5s electron occupancy of Ag. It is important to highlight that the Ag center does not engage with the BCP of the C-C bond in C₂H₄, as illustrated in Fig. 3. This observation is further corroborated by the distinct charge distributions found on the C₂H₄ carbon atoms, which exhibit values of -0.42 |e|. Following the complexation with the Ag center, the WBI for the C-C bond decreases from 2.00 to 1.82, suggesting a potential transfer of electron density from the π bonding molecular orbital. The alteration in the WBI for C₂H₂ shifts from 3.00 to 2.79, demonstrating a significant transformation. This variation corresponds to a change in the NBO partial charge of the Ag center, which decreases from + 0.680 |e| to + 0.530 |e|. Furthermore, the occupancy of the 5s orbital is altered due to this interaction, showing a decrease of 0.19 |e|. It is important to note that the descriptors of binding strength, namely ΔE, charge transfer, and WBI, emphasize different physical aspects of the binding process. The binding energy (ΔE) captures the total thermodynamic stabilization, integrating both electrostatic and dispersion forces, whereas charge transfer and WBI quantify the degree of orbital overlap and covalent character in the localized Ag–gas bond. Consequently, while C₂H₄ exhibits the most negative ΔE (–30.28 kcal mol^− 1) due to significant dispersion and polarization contributions, CO shows the largest WBI (0.54) and charge transfer (+ 0.258 |e|), reflecting its stronger localized σ-type coordination. This distinction reconciles the observed trends and underscores the multifaceted nature of bonding in the [C₁₁H₁₄N₂Ag]⁺–gas systems.

Table 3.

Calculated Ag⋯gas distance (d_Ag⋯gas), ag atomic charge (q_Ag), Wiberg index (WBI), and electronic configuration of ag in the studied structures.

Structure	dAg⋯gas (Å)	qAg (|e|)	WBI		ECAg
[C11H14N2Ag]+	–	0.680	–	–	5s0.404d9.905p0.02
H2@[C11H14N2Ag]+	1.908	0.544	Ag ⋯ H29	0.11	5s0.554d9.855p0.06
			Ag ⋯ H30	0.11
N2@[C11H14N2Ag]+	2.144	0.529	Ag ⋯ N29	0.26	5s0.584d9.815p0.08
O2@[C11H14N2Ag]+	2.116	0.736	Ag ⋯ O29	0.30	5s0.484d9.675p0.11
			Ag ⋯ O30	0.34
NO@[C11H14N2Ag]+	2.140	0.513	Ag ⋯ N30	0.30	5s0.604d9.805p0.09
CO@[C11H14N2Ag]+	2.053	0.422	Ag ⋯ C29	0.54	5s0.684d9.775p0.12
C2H4@[C11H14N2Ag]+	2.311	0.539	Ag ⋯ C29	0.19	5s0.574d9.805p0.09
			Ag ⋯ C31	0.19
C2H2@[C11H14N2Ag]+	2.288	0.530	Ag ⋯ C29	0.21	5s0.594d9.805p0.08
			Ag ⋯ C32	0.21

The adsorption mechanism of H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂ on the [C₁₁H₁₄N₂Ag]⁺ complex can be rationalized in terms of donor–acceptor orbital interactions and charge transfer processes. The NHC ligand, being a strong σ-donor, enhances the electron density on the Ag(I) center, facilitating weak σ–acceptor interactions with incoming gas molecules. For H₂ and N₂, the interaction mainly arises from dispersion and minor σ-donation from their occupied σ orbitals to the Ag 5s/5p orbitals, with negligible back-donation due to the d¹⁰ configuration of Ag. The π-bonded gases (C₂H₄ and C₂H₂) interact through η²-coordination via their π orbitals, leading to stronger binding (ΔE = − 30.28 and − 27.72 kcal mol^− 1, respectively). CO and NO exhibit mixed σ–donation/π* back-donation character, consistent with their known metal–ligand chemistry, resulting in notable charge transfer (0.167–0.258 |e|) to the Ag center. The O₂ molecule, however, shows a weak and endergonic adsorption (ΔG = + 1.66 kcal mol^− 1), primarily limited to van der Waals contact due to unfavorable orbital alignment. This trend confirms that the adsorption strength correlates with the extent of π-orbital availability and charge transfer capability of the gas molecules.

To deepen the understanding of the interactions between the selected gas molecules and [C₁₁H₁₄N₂Ag]⁺ structure, a Quantum Theory of Atoms in Molecules (QTAIM) analysis was performed. QTAIM parameters, including electron density at the bond critical point ρ(r), its Laplacian ∇²ρ(r), kinetic G(r) and potential V(r) energy densities, and total energy density H(r), were evaluated at the Ag ⋯ gas interaction sites. The Laplacian of electron density, denoted as ∇²ρ(r), serves as a valuable tool for evaluating the nature of chemical bonding. A bond may be classified as either covalent or noncovalent. The presence of a covalent bond is typically indicated by an enhancement in electron density, which is reflected in a negative value of ∇²ρ(r) at the BCP. Conversely, a positive value at the BCP suggests a reduction in electron density, indicative of noncovalent interactions. However, this rule is not universally applicable across all molecular systems. In addition to the Laplacian, other descriptors of electron density, particularly total energy density H(r), are instrumental in further elucidating the bond characteristics. When H(r) is negative at the BCP, it points to the presence of a partial covalent bond⁶⁶. Specifically, if ∇²ρ(r) > 0 and H(r) ˂ 0, this indicates a partially covalent interaction. The total energy density H(r) combines local kinetic energy density G(r) with local potential energy density V(r). A ratio of -G(r)/V(r) > 1 signifies a purely noncovalent interaction, whereas a ratio falling between 0.5 ˂ -G(r)/V(r) ˂ 1 suggests the presence of partial covalent interactions. Furthermore, the G(r)/ρ(r) provides additional insight, with values exceeding 1 signifying predominantly noncovalent characteristics. The analysis reveals that the ρ(r) values observed at the designated bond critical points for the gas molecule complexed systems exhibit relatively low magnitudes. In contrast, the concomitant positive values of the Laplacian of electron density suggest the likelihood of noncovalent interactions. The presence of negative total energy density values at these critical BCPs indicates some degree of partial covalency in these interactions. Conversely, the ratio -G(r)/V(r), which falls within the range of 0.5 to 1, suggests the existence of partial covalent interactions. Consequently, it can be concluded that the interactions across all investigated systems exhibit a hybrid nature, comprising both covalent and noncovalent characteristics with predominantly noncovalent aspect. Electron density ρ(r) values range from 0.067 to 0.1070. The strongest interaction appears in the CO adduct (ρ(r) = 0.107), while weaker values are observed for C₂H₂ (0.067) and C₂H₄ (0.069) and. The Laplacian of electron density [∇²ρ(r)] is positive for all systems, consistent with closed-shell (electrostatic or dative) interactions rather than pure covalent bonding (Table 4).

Table 4.

Key topological parameters at the BCP: electron density (ρ(r), laplacian of electron density (∇²ρ(r), electron kinetic energy density (G(r)), electron potential energy density (V(r)), and total electron energy density (H(r)) at BCP.

Structure	BCP	ρ(r)	∇2ρ(r)	G(r)	V(r)	H(r)	-G(r)/V(r)	G(r)/ρ(r)
H2@[C11H14N2Ag]+	Ag ⋯ H	0.069	0.275	0.078	-0.087	-0.009	0.896	1.130
N2@[C11H14N2Ag]+	Ag ⋯ N	0.076	0.377	0.105	-0.116	-0.011	0.905	1.381
O2@[C11H14N2Ag]+	Ag ⋯ O	0.076	0.364	0.100	-0.110	-0.009	0.909	1.315
		0.071	0.363	0.097	-0.104	-0.007	0.932	1.366
NO@[C11H14N2Ag]+	Ag ⋯ N	0.080	0.357	0.102	-0.115	-0.013	0.886	1.275
CO@[C11H14N2Ag]+	Ag ⋯ C	0.107	0.372	0.128	-0.163	-0.035	0.785	1.196
C2H4@[C11H14N2Ag]+	Ag ⋯ C	0.069	0.246	0.071	-0.081	-0.009	0.876	1.028
C2H2@[C11H14N2Ag]+	Ag ⋯ C	0.067	0.204	0.062	-0.073	-0.011	0.849	0.925

The analysis conducted through Noncovalent Interaction (NCI) methodology yields vital insights into the non-covalent interactions of molecules. Developed by Johnson and colleagues, the NCI method evaluates areas of molecular bonding and nonbonding interactions through the reduced density gradient (s), mathematically represented as follows^67,68:

The NCI analysis was applied to visually represent the interactions in real space. The plotted Reduced Gradient Density (RGD) against electron density, multiplied by the sign of the second eigenvalue (sign(λ₂)ρ), is illustrated in Fig. 4 (right), while the accompanying NCI plot is shown on the left. The isosurfaces are color-coded to elucidate the various types of non-covalent interactions observed. Strong attraction, like hydrogen bonding, is represented by blue, while weak interactions, such as van der Waals forces, are depicted in green. The strong steric repulsion is indicated by red. Additionally, the red isosurface illustrates the steric effects present in the molecular rings, characterized by significant repulsion in all complexes. In H₂@[C₁₁H₁₄N₂Ag]⁺ the RDG plot shows faint, diffuse green isosurfaces in the proximity of the H₂ molecule and the Ag center, indicative of weak van der Waals (vdW) interactions. The absence of intense blue or red regions confirms the nonpolar nature of H₂ and the lack of strong electrostatic or hydrogen-bonding contributions. Similar to H₂, the interaction of N₂ is dominated by weak dispersion forces, as shown by green isosurfaces near the coordination sphere. The linearity and low polarizability of N₂ limit stronger donor–acceptor interactions, although a slightly more extended green region compared to H₂ suggests marginally higher interaction strength. In the case of O₂@[C₁₁H₁₄N₂Ag]⁺, the RDG plot reveals both green vdW regions and small patches of blue isosurface, the latter suggesting weak attractive electrostatic or charge-transfer interactions between O₂ and the Ag center. This may be attributed to the π* antibonding orbital of O₂ participating in a minor back-donation process. NO exhibits distinct blue isosurfaces in close contact with the Ag coordination site, indicative of stronger attractive interactions, potentially involving partial covalent character or significant charge transfer. The asymmetric distribution of the isosurfaces reflects the polar nature of NO and its open-shell electronic structure, enabling enhanced binding. In the CO@[C₁₁H₁₄N₂Ag]⁺, pronounced blue regions near the OC⋯Ag interface confirm strong attractive interactions, consistent with the classical σ-donation from CO’s lone pair to Ag and possible π-backbonding from Ag to CO’s π* orbital. In the C₂H₄@[C₁₁H₁₄N₂Ag]⁺ complex, the RDG isosurface shows green vdW regions combined with subtle blue areas above the C = C bond, suggesting weak π–metal interactions. This agrees with the η²-coordination often observed between olefins and transition metals. Similarly, in C₂H₂@[C₁₁H₁₄N₂Ag]⁺, a combination of green dispersion regions and blue patches along the C ≡ C axis indicates π–metal interactions which are considerable due to the high polarizability and linear geometry of acetylene that facilitates orbital overlap.

Fig. 4.

Non-covalent interaction (NCI) plots and corresponding RDG scatter plots (left) of the studied complexes.

It should be emphasized that the apparent difference between QTAIM and NCI interpretations does not indicate a contradiction but rather reflects the complementary nature of these analyses. In QTAIM, the positive Laplacian of electron density (∇²ρ > 0) and moderate ρ(r) values signify a closed-shell topology dominated by electrostatic or donor–acceptor components. However, when the total energy density H(r) is negative and the –G(r)/V(r) ratio lies between 0.5 and 1, a degree of covalent character is implied even within this closed-shell classification. Consistently, the NCI plots for the CO and NO complexes display distinct blue regions and substantial charge transfer, confirming that these interactions possess mixed character—predominantly electrostatic but accompanied by partial covalency arising from σ-donation and limited π-backbonding. This interpretation reconciles all descriptors and provides a unified picture of the bonding nature in the studied Ag(I)–gas systems.

One critical factor determining the practical applicability of the Ag–NHC scaffold is its chemical stability under oxidative and humid environments. To evaluate this, we analyzed the interaction of the [C₁₁H₁₄N₂Ag]⁺ complex with molecular oxygen (O₂) and water (H₂O) at the same PBE0-D3/def2-TZVP level of theory employed throughout this study. The O₂ adsorption results reveal an interaction energy (ΔE) of − 6.82 kcal mol⁻¹ and a slightly positive Gibbs free energy of + 1.66 kcal mol⁻¹ at 298 K, indicating that the adsorption process is endergonic and therefore thermodynamically disfavored. As mentioned earlier, the optimized O₂@[C₁₁H₁₄N₂Ag]⁺ structure shows a tilted approach of the O₂ molecule toward the Ag center, with an Ag–O–O bond angle of 74.3°, characteristic of weak, non-classical coordination. The NBO and QTAIM analyses confirm minimal charge transfer (− 0.056 |e|) from O₂ to Ag and a positive Laplacian of electron density at the Ag···O bond critical point. Together, these descriptors strongly support that the O₂ interaction is purely noncovalent in nature, dominated by weak electrostatic attraction and van der Waals forces. Importantly, the positive ΔG value implies that the Ag–NHC scaffold resists oxidative coordination and is unlikely to undergo spontaneous oxidation under ambient air exposure. This theoretical prediction is consistent with experimental reports on the exceptional air stability of Ag(I)–NHC complexes^31,35,41, where the closed-shell d¹⁰ configuration of Ag⁺ and the σ-donating/π-accepting characteristics of the carbene ligand collectively suppress oxidative degradation. Thus, the computed thermodynamic behavior of O₂ corroborates the experimentally observed inertness of Ag–NHC complexes toward oxygen. To further investigate environmental durability, an additional single-point calculation was carried out for H₂O adsorption at the PBE0-D3/def2-TZVP level, followed by BSSE correction and thermochemical analysis at 298 K. The predicted binding energy (ΔE) for the H₂O adduct is approximately − 9.0 kcal mol⁻¹, while the corresponding Gibbs free energy (ΔG₂₉₈) is estimated to be slightly positive, around + 1.0 kcal mol⁻¹. These results suggest a weak, non-spontaneous physisorption process, driven primarily by electrostatic attraction between the Ag center and the lone pairs on the oxygen atom of H₂O. The absence of significant charge transfer (Δq ≈ − 0.08 |e|) and the small Wiberg bond index (WBI ≈ 0.12) further confirm the noncovalent and reversible nature of this interaction. The combined O₂ and H₂O analyses clearly indicate that the [C₁₁H₁₄N₂Ag]⁺ complex possesses high intrinsic stability under both oxidative and humid conditions. The slightly endergonic adsorption free energies (ΔG > 0) for these environmental molecules demonstrate that neither oxidation nor hydrolysis pathways are thermodynamically favorable. Consequently, the Ag–NHC framework can be considered chemically robust, retaining its structural and electronic integrity even in the presence of air and moisture — a property that greatly enhances its practical viability for gas scavenging and sensing applications.

The adsorption energies calculated in this work (ΔE = − 6.82 to − 30.28 kcal mol⁻¹) are consistent with previously reported ranges for Ag–NHC and Ag-based complexes interacting with small molecules. Mondal^50,51 reported binding energies of − 5.3 to − 28 kcal·mol⁻¹ for the [Ag(C₆H₁₂O₆)]⁺ complex with similar gases, while Lin and Vasam³¹ and Mnasri et al.³⁵ observed comparable trends for Ag–NHC complexes. The slightly stronger adsorption of π-bonded gases (C₂H₄, C₂H₂, CO) in our study reflects the enhanced electron density and polarizability of the Ag–NHC fragment, which promotes weak π–metal coordination. These similarities validate the reliability of the PBE0-D3 level and demonstrate that the designed [C₁₁H₁₄N₂Ag]⁺ complex behaves analogously to known Ag–NHC systems, while offering improved stabilization toward unsaturated adsorbates.

Conclusions

An DFT investigation has been conducted to assess the comparative binding affinities of seven distinct small molecules-namely H₂, N₂, O₂, NO, CO, C₂H₄, and C₂H₂, with the [C₁₁H₁₄N₂Ag]⁺ structure. The orientation of the molecular axes for H₂, C₂H₄, and C₂H₂ exhibits a perpendicular alignment with the silver metal, while CO and N₂ interact in a linear configuration, and both NO and O₂ display a tilted binding posture. Notably, the interactions involving all examined small molecules are characterized as exergonic, with the exception of O₂. The binding preference towards the [C₁₁H₁₄N₂Ag]⁺, as determined by binding energy and free energy of association, is ranked as follows: C₂H₄ > C₂H₂ > CO > NO > N₂ > H₂ > O₂. Among these, the CO molecule demonstrates the strongest affinity for the silver center of the complex, indicated by its maximum WBI = 0.54. Additionally, the binding of CO is marked by the most significant electron transfer from CO to Ag as 0.258 |e|. The presence of noncovalent interactions in all binding scenarios is underscored by the emergence of noncovalent interaction surfaces. This research indicates that the [C₁₁H₁₄N₂Ag]⁺ complex exhibits stronger theoretical affinity toward unsaturated and π-acceptor molecules such as C₂H₄, C₂H₂, CO, and NO. These results suggest potential gas-capture capability at the theoretical level; however, further studies addressing kinetic and thermodynamic stability would be necessary to confirm its experimental applicability. It should be noted that all calculations in this study were carried out in the gas phase, without explicit or implicit solvation effects. While this approach provides a reliable measure of the intrinsic interaction strength between [C₁₁H₁₄N₂Ag]⁺ and the examined gaseous species, environmental factors in condensed phases—such as dielectric screening, solvent coordination, or crystal-packing effects—may modify the quantitative binding energetics. Future work will address these aspects by incorporating continuum solvation models and periodic boundary simulations to extend the current findings toward more realistic conditions.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Shiva Mousavi: Formal analysis, Data curation, Investigation, Methodology, Software.Morteza Rouhani: Conceptualization, Data curation, Formal analysis, Investigation, Project administration, Software, Supervision, Validation, Visualization, Writing – review & editing.Shahin Ahmadi: Investigation, Methodology, Data curation, Formal analysis.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.