Exploring N2 activation using novel Lewis acid/base pairs: computational insight into frustrated Lewis pairs reactivity

Dalton Transactions PAPER Cite this: Dalton Trans., 2025, 54, 4338 Received 10th December 2024, Accepted 6th February 2025 DOI: 10.1039/d4dt03425b rsc.li/dalton Exploring N 2 activation using novel Lewis acid/ base pairs: computational insight into frustrated Lewis pair reactivity† Xuban Gastearena, a Jon M. Matxain * a and Fernando Ruipérez * b The activation of dinitrogen (N 2 ) is a crucial step in synthesizing nitrogen-based compounds and remains a significant challenge due to its strong triple bond. Currently, industrial N 2 conversion relies on the Haber–Bosch process, a highly energy-intensive method that utilizes transition metal-based catalysts. Frustrated Lewis pairs (FLPs) have emerged as a promising alternative for N 2 activation without the need for transition metals. In this work, we employ density functional theory (DFT) to investigate the activation of N 2 by transition metal-free Lewis acids (LAs) and bases (LBs). Our study demonstrates that LAs play a crucial role in capturing N 2 and determining the thermodynamics of activation, while LBs play a complementary role by reducing the bond order of the N 2 molecule, thereby promoting activation. The efficiency of N 2 capture is directly linked to the electroaccepting characteristics of the LAs. A principal component analysis (PCA) reveals that the key factors influencing the electroaccepting power of LAs are the degree of pyramidalization and orbital occupation at the acidic site, as well as the local electrophilicity index. The LA-N 2 interaction is found to be electrostatic with partially covalent character. Among the 21 LAs analyzed, triptycene-based systems exhibit the highest stability in forming LA-N 2 complexes, highlighting their potential as effective N 2 -capturing agents. However, the N 2 triple bond remains largely intact, necessitating the involvement of LBs in LA-N 2 -LB complexes for full activation, in a “push–pull” mechanism. Six LBs are analyzed in complexes with the most promising LAs. Bonding analysis indicates that the LB-N 2 interaction can be regarded as a covalent bond, which may explain the main role of the LB in the reduction of the N 2 bond order. Furthermore, the bond activation is significantly enhanced by increasing the nucleophilicity of the LB. Among all the LA–LB pair combinations, only three exhibit the defining characteristics of frustrated Lewis pairs (FLPs), with moderate interaction energies and substantial LA–LB distances. Our findings suggest that FLPs composed of triptycene-based LAs and tris-tert-butylphosphine represent the most promising candidates for N 2 activation. 1 Introduction Nitrogen is a vital element for all life forms and serves as a precursor to essential nitrogen-containing compounds such as amino acids, DNA, and fertilizers. 1 It is the most abundant element in Earth’s atmosphere, comprising 78% of the air in its diatomic form, N 2 . However, most organisms are unable to directly utilize nitrogen in its gaseous form; it must first be converted or “fixed”into a more accessible form. This process occurs naturally through two primary mechanisms. Lightning can convert atmospheric nitrogen into nitrogen oxides (NO x ), 2 while nitrogenase enzymes, found in certain bacteria, play a more critical role. These enzymes facilitate the multi-electron reduction of N 2 to NH 3 , a reaction catalyzed by the iron-molybdenum cofactor (FeMoco). 3,4 The nitrogen fixation process requires the hydrolysis of at least 16 equivalents of adenosine triphosphate (ATP) and achieves up to 65% selectivity. However, biological N 2 fixation remains kinetically slow due to its dependence on electron tunneling, making it inadequate to support the demands of modern intensive agriculture. 5 Over the past century, nitrogen activation has predominantly been achieved through the Haber–Bosch process, in which atmospheric N 2 is reduced by hydrogen gas to produce ammonia, which is then converted into various fertilizers. Despite its industrial success, the initial step of nitrogen reduction is †Electronic supplementary information (ESI) available. See DOI: https://doi.org/ 10.1039/d4dt03425b a Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU and Donostia International Physics Center (DIPC), Paseo Manuel Lardizábal 4, 20018 Donostia, Euskadi, Spain b POLYMAT and Physical Chemistry Department, Faculty of Pharmacy, University of the Basque Country UPV/EHU, 01006 Vitoria –Gasteiz, Euskadi, Spain. E-mail: [email protected] 4338 |Dalton Trans.,2025,54,4338–4352 This journal is © The Royal Society of Chemistry 2025 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online View Journal | View Issue inherently challenging due to the extreme stability of the N 2 triple bond. This necessitates harsh reaction conditions (elevated temperature and pressure) and the use of a metal catalyst, often powered by fossil fuels, leading to the emission of fossilderived CO 2 as a by-product. 6–9 Consequently, the activation of N 2 has become a focal point of scientific research, with efforts focused on developing environmentally sustainable alternatives that operate under mild conditions and utilize maingroup elements rather than transition metals. The widespread use of transition metals in dinitrogen activation is due to their ability to provide both unoccupied and occupied d orbitals that are energetically and symmetrically suited for accepting electron density from N 2 and back-donating it into the molecule’s antibonding orbitals, thereby weakening its triple bond. 10–13 Recently, the “push–pull”hypothesis has been introduced, suggesting that electron depletion caused by Lewis acid complexation (the pull effect) enhances the delocalization of d electrons from the metal center into N 2 antibonding orbitals (the push effect), further promoting bond weakening. A representative example involves boron, which acts as a Lewis acid through sp 3 hybridization with its 2s 2 2p 1 electronic configuration. When combined with low-valent iron (Fe), molybdenum (Mo), and tungsten (W) centers, tris(pentafluorophenyl)borane (B(C 6 F 5 ) 3 ) significantly enhances the activation of N 2 in M–N–N–B(C 6 F 5 ) 3 complexes. 14 Conceptually, the push–pull reactivity observed in frustrated Lewis pairs (FLPs) can be compared to that of transition metal systems, where a Lewis acid (LA) and Lewis base (LB) cooperate to activate small molecules. In both cases, the reactivity is driven by the synergistic action of a strong LA pulling electron density and a bulky LB pushing its electron pair into the antibonding orbitals of a substrate, facilitating activation. 15 In this context, the combination of free LA and LB, which are prevented from interacting due to steric hindrance from bulky substituents, exhibits intriguing catalytic properties that mimic the role of metallic catalysts (Fig. 1). The LA mimics the empty d orbitals of a metal by interacting with nitrogen lone pairs via σ-bonding, while the LB performs the π-backdonation into the π* antibonding orbitals of the nitrogen molecule. In recent years, FLPs and other main group systems have demonstrated the ability to replicate the reactivity of various transition metal complexes, enabling both stoichiometric and catalytic reactions that were once thought to be exclusive to transition metals. 16 This realization has led to the hypothesis that main group compounds could serve as viable alternatives to transition metal complexes for N 2 fixation. 17 Examples include experimental studies on borylene-based FLPs, such as cyclic alkyl(amino)carbene (CAAC)-supported borylene complexes [(Dur)B(CAAC)]. 18–20 Additionally, computational investigations of N-heterocyclic carbenes (NHC) emphasize the role of aromaticity in the activation process. 21–23 The activation potential of borylenes lies in the ambiphilic character of boron, which possesses a sp hybridization with one empty 2p orbital and one filled, allowing them to function as both LA and LB, similar to transition metals. However, most FLP systems studied so far are based on intramolecular FLPs, where both acidic and basic sites are incorporated into the same molecule. Moreover, these FLPs typically involve carbenes as the basic sites and borylenes as the acidic sites. 24,25 The highly reactive nature of borylenes necessitates stabilization as Lewis base adducts, usually with NHC or CAAC. The electronic characteristics of borylenes limit the selection of LA and LB for N 2 activation, making it challenging to develop alternative systems with the same activation capacity but with greater stability and flexibility. In the realm of metal-free N 2 activation, the use of common tricoordinate borane species presents a promising alternative, potentially broadening the range of LAs and LBs that can be utilized. Despite this potential, attempts to develop such systems are limited and still in the early stages. One of the pioneering efforts involved exploring the reactivity of diphenyldiazomethane (Ph 2 CNN) with B(C 6 F 5 ) 3 , 26 where the adduct formed can be viewed as a system where N 2 is effectively trapped between a borane LA and a carbene LB. However, this adduct was found to be unstable, often releasing N 2 rather than maintaining it in a trapped state. Other approaches have sought to capture and activate N 2 through LA-N 2 adducts. For instance, the (N 2 )BF 3 species has been transiently generated, albeit under specific conditions of 170 K and 600 Torr, 27 suggesting that metal-free N 2 activation with tricoordinate boranes may be feasible. Consequently, the binding of N 2 to Lewis acids has been a focus of several computational studies. Given the low Lewis basicity of N 2 , it is necessary to use strong LAs or superacids. Computational studies have shown examples such as the use of carboranes, 28 which have demonstrated successful N 2 activation, although the initial LA-N 2 adducts were not found to be thermodynamically stable. Additionally, computational studies on B(SiMe 3 ) 3 and B(CF 3 ) 3 have shown that these species can form stable adducts with N 2 , with stabilization energies around −15 kcal mol −1 . 29 The pyramidalization of the acidic center has been shown to significantly enhance Lewis acidity by lowering the reorganization energy and reducing the structural changes required during complex formation. 30 This decrease in reorganization energy increases the effectiveness of the Lewis acid in accepting electron pairs from Lewis bases. 31–35 Additionally, this characteristic contributes to the stability of Lewis acid–Lewis base (LA–LB) complexes, often resulting in higher dissociation energies for complexes involving pyramidal Lewis acids. 36 Computational studies indicate that pyramidal boron-containing Lewis acids, such as 9-boratriptyFig. 1 Transition metal (M-N 2 )vs. frustrated Lewis pairs (LA-N 2 -LB) complexes (left) and N 2 valence molecular orbital diagram (right). Dalton Transactions Paper This journal is © The Royal Society of Chemistry 2025 Dalton Trans.,2025,54,4338–4352 | 4339 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online cene, exhibit significantly greater Lewis acidity compared to their planar analogs. 37 For instance, pyramidal compounds like boraadamantane and alaadamantane are capable of forming donor–acceptor complexes with noble gases. 38 Furthermore, Lewis acidity can be enhanced through fluorination, due to the electron-withdrawing properties of fluorine atoms, 37,39 or via cationic effects. 32–34 Despite these advances, finding common tricoordinate borane species that can form stable adducts with N 2 remains a significant challenge. Based on all this previous experience and challenges, the main goal of this work is to determine which are the key factors that determine and improve the dinitrogen capture and activation by LAs and LBs, respectively. In order to do so, different complexes of dinitrogen and various tricoordinate boron-based LAs and LBs from different families with diverse electronic and structural characteristics have been studied. Then, the nature of the interactions between LAs, LBs and dinitrogen was thoroughly analyzed by means of computational tools to understand and predict the binding patterns. These results will allow in the design of improved LA/LB and FLP combinations for further dinitrogen reduction to ammonia. 2 Computational details All geometry optimizations and vibrational frequency calculations were carried out within density functional theory (DFT) 40,41 using the Gaussian 16 program package. 42 Specifically, geometries were optimized using the ωB97XD functional, 43 combined with the 6-31+G(d) basis set. 44 Harmonic vibrational frequencies were obtained by analytical differentiation of gradients, at the same level of theory, to identify if the characterized structures were minima in the potential energy surface. Such frequencies were then used to evaluate the zeropoint vibrational energy (ZPVE) and the thermal (T= 298 K) vibrational corrections to the enthalpy (H) and the Gibbs free energy (G). These corrections are calculated in gas phase, while experiments would be carried out in solution. The simplification of our reaction model introduces entropy overestimation errors associated to the overestimation of the entrophy due to the neglect of temperature-dependent solvation effects. To partially overcome this overestimation, the Gibbs free energy correction proposed by Finkelstein and Janin is applied: 45 Gcorr ¼HT½Svib þ1=2ðStrans þSrotÞ ð1Þ This correction mitigates the overestimation of entropy changes, thus providing more accurate results for comparison with experimental values. The non-corrected Gibbs free energy values are available in the ESI.† To refine the electronic energies single-point calculations with the 6-311++G(2df,2p) basis set 46 were carried out in the optimized structures. The natural charges were computed by the natural bonding orbital (NBO) methodology. 47–49 The computational approach used in this work has been validated against higher-level theoretical data from the literature 29,32,50 (see Tables S1, S2, S3 and S4 in the ESI†). 2.1 Calculation of acidity and basicity The electrophilicity of the Lewis acids has been estimated by several paramters: hydride ion affinity (HIA), 51 global electrophilicity index (ω) 52 and local electrophilicity index (ω B ). 53 The HIA is defined as the enthalpy change (ΔH) in the reaction between and acid (LA) and a hydride anion (H − ) in gas phase: LA þH!½LA Hð2Þ The HIA values have been calculated using the following isodesmic reaction: 50 LA þMe3Si H!½LA HþMe3Siþð3Þ after substracting the reaction: Me3Si H!Me3SiþþHð4Þ The larger the enthalpy (more negative or highest absolute value) the larger the acidity of the LA. The global electrophilicity index (ω) is a measure of the overall ability of a molecule to accept electrons from any electron-rich species (nucleophile), and is defined as: ω¼χ2 2ηð5Þ where χ≈− 1 2(ε H +ε L ) is Mulliken’s electronegativity, ε H and ε L are the energy of HOMO and LUMO orbitals, and η≈ε H −ε L is the chemical hardness. The local electrophilicity index (ω B ) describes the electrophilic nature of specific atoms or regions within a molecule and can be defined as the product of the global electrophilicity with a local Fukui function ( f B+ ) on the boron atom (or the acidic atom): ωB¼ωfBþð6Þ where the Fukui function can be conveniently expressed from the electron population of boron (Q B ) in the system of Nand N + 1 electrons: 32 fBþ¼QBðNþ1ÞQBðNÞ¼ΔQBð7Þ The ωand ω B indexes are quantitative and base-independent metrics of Lewis acidity and provide the electroaccepting capacity of the LA, globally and locally (referred to the 2p orbital of B). Larger absolute values of these parameters should indicate a higher affinity towards binding the N 2 . The basicity is estimated with the empirical global nucleophilicity index (N), a relative scale based on the HOMO energy of the base (LB) referred to tetracyanoethylene (TCE). This compound shows the lowest HOMO in a large set of previously studied molecules 54 and allows a positive scale of basicities: N¼εHðLBÞεHðTCEÞð8Þ 2.2 Analysis of bonding interactions The nature of the interaction was analyzed using the Quantum Theory of Atoms in Molecules (QTAIM) 55–58 and Electron Decomposition Analysis (EDA) 59,60 methodologies. In QTAIM, Paper Dalton Transactions 4340 |Dalton Trans.,2025,54,4338–4352 This journal is © The Royal Society of Chemistry 2025 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online the bond critical point (BCP) of a particular bond is characterized by the electron density (ρ), its Laplacian ( ∇ 2 ρ) and the kinetic (V), potential (G) and total (H) electron energy density. A negative value of ∇ 2 ρdenotes electron density concentration in the interatomic region, corresponding to covalent bonds. The condition |V|≥2Galso denotes a covalent interaction. A positive Laplacian indicates depletion of electron density, which is usually attributed to non-covalent interactions. If the Laplacian is positive but His negative, the interaction can be classified as partially covalent. Lastly, if the density value is large enough (more than 0.03 a.u.) and His negative, the interaction is partially covalent. The EDA method is based on Morokuma’s energy partitioning scheme, 61 and examines the instantaneous interaction energy (ΔE int ) between two fragments (A and B) within a bond (A–B). This analysis is performed in the specific electronic reference state and with the frozen geometry of the AB complex. The interaction energy is typically divided into two main components, ΔE elstat and ΔE orb , along with an additional dispersion term (ΔE disp ). The term ΔE elstat represents the quasi-classical electrostatic interaction between the unperturbed charge distributions of the prepared atoms, which is generally attractive. Lastly, ΔE orb accounts for charge transfer and polarization effects within the system. 3 Results and discussion The activation of N 2 was studied through a two-step process: capturing nitrogen followed by its activation. Initially, the capture mechanism was investigated by examining interactions with individual Lewis acids (LAs) or Lewis bases (LBs). This was followed by an analysis of the activation process via the formation of LX-N 2 -LX complexes, where LX denotes either a LA or a LB. This study provides an in-depth analysis of the electroaccepting and electrodonating capacities of LAs and LBs, the molecular geometries of the formed complexes, their interaction energies, and the nature of the interactions involved. 3.1 N 2 capture by Lewis acids The capture of a small molecule like N 2 can occur through interactions with either a Lewis acid or a Lewis base. When interacting with a Lewis acid, the process typically involves a σtype interaction between the nitrogen lone pair and the empty orbital of the acid. In contrast, interaction with a Lewis base often involves πdonation of electron density into the π* antibonding orbitals of N 2 . In this work, we have employed a set of 21 Lewis acids (see Fig. 2) and 6 Lewis bases (see Fig. 3) to explore their potential for capturing N 2 . Attempts to capture free N 2 using Lewis bases have been unsuccessful, as none of the tested bases were able to form a stable LB-N 2 complex. This outcome was anticipated because a Lewis base is unlikely to interact favorably with another Lewis base, such as N 2 . As a result, the proposed mechanism involving πdonation from the Lewis base to the antibonding orbitals of N 2 is inefficient for capturing N 2 . Therefore, the analysis of the N 2 capture is performed only with Lewis acids. N 2 is a very weak Lewis base due to its unique electronic structure. The lone pairs in N 2 are located in sp hybrid orbitals, which are more localized and less available for interaction compared to sp 3 hybrids or pure atomic p orbitals. Additionally, the high electronegativity of nitrogen further reduces the availability of these lone pairs for bonding with other molecules. The linear structure of N 2 can also hinder effective overlap with the orbitals of other molecules approaching from different angles. Therefore, the acidity and electrophilicity of Lewis acids are crucial factors in achieving effective capture of N 2 . The acidity of the LAs represented in Fig. 2 is studied using the following parameters: hydride ion affinity (HIA), global (ω) and local (ω B ) electrophilicity indexes and occupation number of the 2p empty orbital of boron atom (η(2p)). Note that, with the exception of two, all the acids under consideration are boron-based. The interaction of LAs with N 2 is evaluated using the interaction (ΔH int ,ΔG int ) and Fig. 2 Lewis acids studied in this work: boraadamantane (1), 1-borabarrelene (2), B-cubane (3a, X = CH), B,N,N,N-cubane (3b, X = N), BN 3 (4), boratriptycene (5a, Y = B; X = CH; R = H), Al-triptycene (5b: Y = Al; X = CH; R = H), Ga-triptycene (5c: Y = Ga; X = CH; R = H), cationic S-boratriptycene (5d: Y = B; X = S; R = H), F-boratriptycene (5e:Y=B;X = CH; R = F), cationic F-S-boratriptycene (5f: Y = B; X = S; R = F), Cl-boratriptycene (5g: Y = B; X = CH; R = Cl), cage-shaped borate ester (6), subporphyrin borenium cation (7) and the BX 3 derivatives (8a:X=H,8b: X=F;8c: X = Cl; 8d: X = Br; 8e:X=CH 3 ;8f:X=CF 3 and 8g:X=C 6 F 5 ). Fig. 3 Lewis bases studied in this work: guanidine (1), triphenylphosphine (2), tris-t-butylphosphine (3), phosphazene (4), Verkade base (5) and cyclic bent allene (CBA) (6). Dalton Transactions Paper This journal is © The Royal Society of Chemistry 2025 Dalton Trans.,2025,54, 4338–4352 | 4341 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online deformation (E def ) energies, as well as the pyramidalization angle (α). The interaction energy is estimated as both the enthalpy (ΔH) and the Gibbs free energy (ΔG) change in the reaction between an acid and N 2 , while the deformation energy corresponds to the enthalpy change associated to the geometry rearrangement of the acid following the formation of the LA-N 2 complex. The αangle reflects the initial geometrical configuration of the LA before interacting with N 2 (see Fig. 4). The degree of pyramidalization can influence E def , with higher values expected for planar LAs. Additionally, planar LAs may facilitate π-backbonding from substituents to the empty orbital at the acidic site (boron), thereby increasing orbital occupation (η(2p)) and reducing the capacity to accept electron density from N 2 . 3.1.1 Electroaccepting power of the Lewis acids. In this subsection, the acidity and electroaccepting capacity of the 21 LAs from Fig. 2 are evaluated via the HIA, ω,ω B and η(2p), and the results summarized in Table 1. General trends can be observed for the HIA across all studied LAs. Typically, the highest HIA absolute values are associated with compounds that feature a pyramidal geometry around the boron atom and electron-withdrawing substituents (EWGs), particularly in compounds 5a–g, with HIA values ranging from −103.87 kcal mol −1 to −225.77 kcal mol −1 , in agreement with previous results. 32,33,62 In contrast, lower HIA values are observed for planar LAs with electron-donating substituents (EDGs), such as 6(−76.31 kcal mol −1 ) and 8e (−50.92 kcal mol −1 ). EWG groups enhance the acidity of LAs by withdrawing electron density from the boron atom through inductive effects. 37 This trend is evident when comparing compounds such as 8a (R = H, −70.62 kcal mol −1 ), 8e (R = CH 3 , −50.92 kcal mol −1 ), and 8f (R = CF 3 ,−138.38 kcal mol −1 ). The electronic nature of the substituents also impacts the occupation of the boron 2p orbital, with EDGs leading to higher values. For example, η(2p) is larger in 8e (0.15) compared to 8f (0.09). In general, η(2p) is influenced by the retrodonation ability of the ligands, which depends on both their electronic nature (EWG or EDG) and the geometry of the acids. For 8a, η(2p) is 0.00 due to hydrogen’s inability to participate in retrodonation. Substituents with nitrogen, oxygen or halogens can exhibit dual characteristics, acting as EWGs via inductive effects (due to high electronegativity) and as EDGs through lone-pair conjugation. Nitrogen atoms directly bonded to boron increase both HIA and η(2p), as seen in compounds 3a and 3b. Notably, η(2p) values for BCl 3 and BBr 3 are not reported due to substantial retrodonation from halogen atoms, which leads to the formation of partial double bonds. The importance of the local geometry at the acidic site lies in reducing the energy penalty associated with the geometric rearrangement during hydride ion binding. 31,37,63 Specifically, non-planar geometries minimize this penalty while also hinFig. 4 Definition of the pyramidalization angle, α. Table 1 Interaction (ΔH int ,ΔG int ) and deformation (E def ) energy, in kcal mol −1 , hydride ion affinity (HIA, in absolute value), in kcal mol −1 , global (ω) and local (ω B ) electrophilicity indexes, in eV, occupancy of empty 2p orbital of boron (η(2p)), pyramidalization angle (α), in degrees, B–N and N–N bond distances (R BN and R NN ), in Å, and Wiberg bond index of the B–N (WBI 1 ) and N–N (WBI 2 ) bonds LA ΔH int ΔG int E def HIA ωω B η(2p) αR BN R NN WBI 1 WBI 2 12.98 6.46 8.21 70.17 0.85 −0.48 0.15 11.0 1.616 1.103 0.656 2.874 2−7.00 −3.02 7.71 91.92 0.83 −1.02 0.09 15.3 1.569 1.102 0.723 2.866 3a −0.47 3.37 9.73 79.49 0.84 −0.90 0.25 30.0 1.492 1.110 0.806 2.738 3b ———88.25 0.87 −0.03 0.33 24.4 ———— 4−51.90 −47.79 9.71 169.62 3.20 −3.91 0.28 49.4 1.426 1.111 0.860 2.687 5a −10.71 −6.99 7.33 110.40 0.93 −1.25 0.08 15.4 1.565 1.101 0.727 2.876 5b −8.55 −6.98 0.63 108.56 1.18 −0.89 0.04 a 21.8 2.190 b 1.099 0.312 c 2.991 5c −5.46 −3.64 −0.01 109.24 1.20 −0.88 0.04 d 21.9 2.276 e 1.099 0.292 f 2.999 5d g −15.36 −11.48 7.23 200.70 3.71 −5.22 0.07 13.8 1.589 1.099 0.706 2.908 5e −17.78 −13.52 7.93 146.12 1.76 −2.45 0.08 16.6 1.589 1.098 0.714 2.906 5f g −22.60 −18.17 8.43 230.47 5.05 −7.18 0.07 14.8 1.596 1.097 0.704 2.912 5g −0.42 4.78 15.86 138.68 1.60 −1.32 0.12 15.8 1.590 1.097 0.707 2.904 6———81.00 0.78 0.00 0.42 0.0 ———— 7———153.23 4.42 0.03 0.45 0.0 ———— 8a −5.19 −0.89 9.33 75.32 1.51 −1.82 0.00 0.0 1.579 1.102 0.860 2.687 8b ———72.14 1.35 −1.19 0.32 0.0 ———— 8c ———96.42 1.38 −1.22 —0.0 ———— 8d ———104.59 1.40 −0.96 —0.0 ———— 8e ———55.61 0.95 −0.57 0.15 0.0 ———— 8f −12.39 −10.99 10.88 143.07 2.72 −3.22 0.09 0.0 1.619 1.098 0.669 2.915 8g ———114.62 2.07 −1.05 0.21 0.0 ———— a Al 3p orbital. b Al–N bond distance. c Al–N bond index. d Ga 4p orbital. e Ga–N bond distance. f Ga–N bond index. g Cationic. Paper Dalton Transactions 4342 |Dalton Trans.,2025,54,4338–4352 This journal is © The Royal Society of Chemistry 2025 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online dering potential retrodonation from substituents to the boron 2p orbital, which would otherwise reduce acidity. This effect is evident when comparing the calculated HIA values for 8g (−109.93 kcal mol −1 ) and 5e (−141.42 kcal mol −1 ), where 5e can be considered a pyramidal analogue of 8g. The non-planar geometry of 5e leads to a higher HIA, as well as a lower η(2p) value (0.08 vs. 0.21), due to the orthogonal arrangement between the triptycene aryl p-orbitals and the boron 2p orbital, which prevents π-conjugation that would otherwise increase η(2p) (see Fig. S1 in the ESI†). The highest HIA values are observed for the cationic species 5f (−225.77 kcal mol −1 ) and 5d (−196.00 kcal mol −1 ), where the combined effects of EWGs, non-planar geometry and a cationic sulfur atom, which strongly enhances acidity through its electron-withdrawing character, are evident. Notably, this strong acidity occurs without affecting η(2p). Finally, compounds 3b,6,7,8b–eand 8g were found to not bind to N 2 . When examining the electrophilicity parameters, ω(global) and ω B (local), a trend similar to that observed for HIA is apparent. The highest ωvalues are found in pyramidal LAs with EWGs, specifically 5a–g, where ωranges from 0.93 eV to 5.05 eV. Conversely, planar LAs with EDGs display the lowest ω values, such as 6(0.78 eV) and 8e (1.51 eV). The largest ωis observed in cationic 5f (5.05 eV), while the smallest corresponds to 6(0.78 eV), mirroring the HIA trends. Significant discrepancies between global (ω) and local (ω B ) electrophilicity indexes are evident in compounds like 1(ω= 0.85 eV, ω B = −0.48 eV), 3b (ω= 0.87 eV, ω B =−0.03 eV), 6(ω= 0.78 eV, ω B = 0.00 eV) and 7(ω= 4.42 eV, ω B = 0.03 eV). This difference arises because the global index reflects the overall electronaccepting capability of the entire molecule, while the local index specifically measures electrophilicity at the boron site. For example, compound 7has a high global electrophilicity (ω = 4.42 eV), likely due to its cationic nature, but shows low boron-site electrophilicity (ω B = 0.03 eV), illustrating the nonuniform distribution of electrophilic character across the molecule. 3.1.2 Geometrical and electronic characteristics of the LA-N 2 complexes. In this subsection, the interaction between the N 2 lone pair and the empty orbital of the LAs will be analyzed using interaction (E int ) and deformation (E def ) energies, and geometric parameters of the LA-N 2 complex, such as bond lengths (R BN ,R NN ) and Wiberg bond indexes (WBI 1 , WBI 2 ), see Table 1. Firstly, it is important to note that several acids (3b,6,7, 8b–eand 8g) form weakly bonded van der Waals complexes and will therefore not be considered in the discussion. These acids exhibit shared features, such as planarity, increased occupation of the boron 2p orbital and diminished electrophilicity, which contribute to their limited interaction with N 2 . The remaining LAs form thermodynamically favorable LA-N 2 complexes through B–N interactions in almost all cases, with interaction energies (ΔG int ) ranging from −0.89 kcal mol −1 for 8a to −47.79 kcal mol −1 for 4, except for compounds 1,3a and 5g which show positive values. Compounds 5b and 5c exhibit unusually low deformation energies (0.63 kcal mol −1 and −0.01 kcal mol −1 , respectively), which can be attributed to the highly electrostatic nature of the interaction, as will be discussed later. Compound 5g shows a relatively high positive deformation energy (15.86 kcal mol −1 ), likely due to steric hindrance between the nitrogen and the lone pairs of chlorine atoms, which hinders effective B–N coordination. Regarding the geometries of the LA-N 2 complexes, the B–N bond lengths range from 1.426 Å to 1.619 Å, with Wiberg bond indices (WBI 1 ) between 0.706 and 0.860, indicating a weak single bond in most cases. However, 5b and 5c exhibit significantly longer B–N bond distances (2.190–2.276 Å) and lower WBI 1 values (0.292–0.312), consistent with the electrostatic nature of the interaction. The N–N bond lengths range from 1.097 Å to 1.111 Å, closely matching the experimental bond distance of 1.0977 Å, 64 suggesting that interaction with the LA causes only a slight weakening of the N 2 bond. This minimal weakening is further reflected in the Wiberg bond indices for N 2 (WBI 2 ), which range from 2.687 (indicating a slightly weakened triple bond) to 2.999. 3.1.3 Principal component analysis of the LA-N 2 interactions. Given the complexity of the interactions between the LAs and N 2 , identifying the primary factors influencing this interaction is challenging. To address this, Principal Component Analysis (PCA) was employed to reduce the dimensionality of the dataset and highlight the most significant parameters governing the interaction. PCA simplifies the analysis by transforming the large set of variables into a smaller subset, which retains the essential patterns and trends of the interaction while reducing the overall number of variables. Principal components are newly constructed, uncorrelated variables formed as linear combinations of the original ones, capturing the directions with the highest variance in the dataset. The greater the variance within a principal component, the more information it retains, indicating that the component reflects a substantial amount of the underlying structure of the interaction. Fig. 5 illustrates the results of the PCA analysis and the corresponding correlation matrix for the acidity and electrophilicity parameters. In the PCA analysis (left panel), the five original parameters have been reduced to two principal components (PC1 and PC2). The orange dots represent LA-N 2 complexes (labeled as 1), while the blue dots indicate LAs that do not bind to N 2 (labeled as 0). The PCA results reveal that η(2p) and αare the most influential parameters. Specifically, a higher η(2p) value is associated with a reduced tendency to bind to N 2 , whereas a higher αvalue corresponds to an increased tendency to bind. HIA, ωand ω B exhibit lower vector magnitudes in the PCA, indicating their lesser relevance in the interaction with N 2 . Additionally it seems to be a connection between the size of the lone pair and the interaction with N 2 in the boratriptycenes (5a–g) and compound 2(see Fig. S2 and S3 in the ESI†). These findings are corroborated by the correlation matrix (right panel), which shows that the parameters most strongly correlated with interaction energy are η(2p) (−0.68) and α(0.54). ω B also shows a moderate correlation (−0.46), while ωand HIA have the weakest correlations (−0.36 Dalton Transactions Paper This journal is © The Royal Society of Chemistry 2025 Dalton Trans.,2025,54,4338–4352 | 4343 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online and 0.12, respectively). Therefore, HIA and global electrophilicity indices alone are insufficient to fully explain the binding patterns with N 2 . Instead, the trends in LA-N 2 interactions can be more accurately rationalized by focusing on α,ω B , and η(2p). Generally, non-planar compounds tend to have lower deformation energy (E def ) values (7.23–9.73 kcal mol −1 ) compared to planar compounds (9.33–10.88 kcal mol −1 ), and these non-planar compounds also prevent back-donation to the 2p orbital, resulting in lower η(2p) values. Additionally, higher ω B values are indicative of greater electroaccepting power. Acoording to this results, the LAs can be classified into three groups based on these three parameters. In Fig. 6, each circle represents LAs that meet the following criteria: α>0°,ω B >0.9 eV and η(2p) < 0.09. This classification highlights how different combinations of these parameters influence the exothermic nature of the LA-N 2 binding. The group of LAs with the largest interaction energies is found at the intersection of the three circles. This intersection represents LAs that meet all the specified parameter thresholds. Notably, this group includes members of the 2and 5families, with the exception of 5g. The next group of LAs includes those with α= 0°, but meeting the conditions for the other two parameters (intersection of the red and green circles): 8a and 8f. These LAs are planar, but their substituents attached to boron (H for 8a and CF 3 for 8f) do not participate in back-donation of electron density, resulting in low η(2p) values. The third group comprises LAs that satisfy the criteria for αand ω B but not for η(2p) (intersection of the green and blue circles): 3a,4, and 5g. Notably, 4demonstrates a very high ω B value (−3.91 eV), which is likely due to its unusual geometry and sp 2 hybridization of the boron atom, facilitating a strong interaction with N 2 (ΔG int =−47.79 kcal mol −1 ). In contrast, 3a and 5g exhibit significantly lower ω B values (−0.90 eV and −1.32 eV, respectively). Additionally, 5g shows an unusually high deformation energy (15.86 kcal mol −1 ), probably due to steric hindrance between the Cl atoms and N 2 , resulting in a positive interaction energy (ΔG int = 4.78 kcal mol −1 ). The remaining LAs either meet only one of the specified parameters or none at all, leading them to either not bind with N 2 or form complexes with positive ΔG int . 3.1.4 Nature of the bonding in LA-N 2 complexes. The analysis of the interaction with N 2 using the Quantum Theory of Atoms in Molecules (QTAIM) methodology reveals the following (see Table 2): for all complexes, the Laplacian of the electron density is positive (∇ 2 ρ> 0), indicating that the LA-N 2 interaction is predominantly electrostatic. Despite this, the large values of electron density (ρ> 0.03) and the negative values of the energy density (H) suggest that the interaction also exhibits a significant covalent character. This partial covalency arises from the donor–acceptor interaction between the lone pair of the nitrogen atom and the empty 2p orbital of the boron atom. The results of the EDA analysis are also summarized in Table 2, providing additional complementary insights. Notably, LAs such as 5b and 5c, which are characterized by predominantly electrostatic interactions, exhibit lower ρvalues, longer LA-N 2 distances, and weaker interaction energies. In contrast, LAs with greater orbital contributions show higher ρvalues, leading to stronger interaction energies and shorter LA-N 2 distances, especially in the case of compound 4. Furthermore, considering that EDA and QTAIM analyses are Fig. 5 Left: results of the Principal Component Analysis (PCA). Right: correlation matrix of the acidity/electrophilicity parameters. Fig. 6 Classification of the LAs in terms of the most important parameters in the formation of the LA-N 2 complexes: α,ω B and η(2p). Paper Dalton Transactions 4344 |Dalton Trans.,2025,54,4338–4352 This journal is © The Royal Society of Chemistry 2025 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online complementary, as supported by the literature, 65 the following discussion of bonding nature will be based solely on the QTAIM results. 3.2 Activation of N 2 with Lewis acids and bases In the previous section, it was observed that several LAs can capture N 2 through a donor–acceptor interaction between the nitrogen lone pair and the empty orbital of the acid. However, this interaction does not activate the strong N 2 triple bond. To facilitate this activation, a second active species is required. For example, a Lewis base can interact with the LA-N 2 complex to form a LA-N 2 -LB “push–pull”complex (see Fig. 7). In this system, the acid withdraws electron density from the N 2 bond (“pull”), while the base donates electron density to the antibonding π* orbitals of N 2 (“push”). This combined effect weakens the N 2 triple bond in a manner similar to that observed with transition metals. 15,66,67 To explore the role of the bases in activating the N 2 bond, the interaction of several LA-N 2 complexes with the LBs shown in Fig. 3 was investigated. Initially, the basicity of these LBs was assessed using the global nucleophilicity index (N), as this property is expected to be critical for the activation process. The most basic LBs identified are LB-5 and LB-6, with nucleophilicity values of 4.80 eV and 4.79 eV, respectively (see Table 3). Compound LB-6 is a cyclic bent allene (CBA), a type of pyrazolin-4-ylidene with two nitrogens in the ring. This structure transmits a strong σ-donation capacity to the central carbon atom. 68–70 LB-5 is Verkade’s base, a triaminophosphine known for its exceptionally high basicity, which surpasses many traditional bases. 71 LB-4 is a phosphazene (R 2 PvN type compound), whose basicity is significantly attributed to the resonance stabilization and the electronic characteristics of the PvN bond, which increases electron density over the nitrogen. 72 Additionally, the well-known guanidine (LB-1), triphenylphosphine (LB-2), and tris-tert-butylphosphine (LB-3) were also included in the study for comparison. 3.2.1 Geometrical and electronic characteristics of the LA-N 2 -LB complexes. In order to investigate the effect of the Lewis bases, only the complexes that showed the strongest LA-N 2 interactions have been selected, namely, LA-4,LA-5a, LA-5b, cationic LA-(5d–f) and LA-8f. In Table 3 are collected the LA-N 2 -LB interaction energies, defined as the enthalpy (ΔH) and Gibbs free energy (ΔG) change in the following reaction: LA þLB þN2!LA N2LB ð9Þ LA-4, as well as the cationic acids LA-5d and LA-5f, form stable LA-N 2 -LB complexes with all bases, except for LA-5d with LB-1, which exhibits a slightly positive interaction energy (ΔG int = 2.22 kcal mol −1 ). Similarly, LA-5e and LA-8f form stable complexes with all LBs, except LB-1 and LB-2.Onthe other hand, LA-5a and LA-5b only form stable complexes with the exceptionally nucleophilic LB-6. The results show a correlation between the capacity of the LAs to capture N 2 (ΔG int , Table 1) and the stability of the LA-N 2 -LB complexes (ΔG int , Table 3), with the most favorable LA-N 2 -LB interactions following this order (except for the exchange between LA-5e and cationic LA-5d): LA-4 >LA-5f >LA-5d >LA-5e >LA-8f >LA-5a > LA-5b. For the triptycenes (LA-5 family), these trends can be attributed to the ω B parameter, due to their identical geometric structure. Besides, for the same acid, the interaction energy appears to correlate with the nucleophilicity index (N), reflecting the influence of the base. Stronger bases yield more negative interaction energies. LB-6 shows significantly more negative interaction energies, notable greater than LB-5, despite having similar strength, even for LA-5a, which shows Table 2 EDA and QTAIM analyses for selected LA-N 2 complexes. Electrostatic interaction (ΔE elstat ), orbital attraction (ΔE orb ) and dispersion energy (ΔE disp ), in kcal mol −1 . Values in brackets are the percentage contributions to the total attractive interactions: ΔE elstat +ΔE orb +ΔE disp . Electron density (ρ), its Laplacian ( ∇ 2 ρ), total electron energy density (H), potential electron energy density (G) and kinetic electron energy density (V) LA ΔE elstat ΔE orb ΔE disp ρ∇ 2 ρVGH 1−220.65 (43.6) −271.35 (53.7) −13.51 (2.7) 0.093 0.611 −0.243 0.198 −0.045 2−212.60 (40.3) −304.34 (57.7) −10.33 (2.0) 0.107 0.674 −0.283 0.226 −0.057 3a −343.31 (42.6) −451.46 (56.1) −10.49 (1.3) 0.135 0.775 −0.369 0.281 −0.088 4−214.42 (30.0) −495.90 (69.3) −5.45 (0.8) 0.169 0.867 −0.479 0.348 −0.131 5a −214.61 (39.7) −308.14 (57.0) −17.76 (3.3) 0.109 0.680 −0.288 0.229 −0.059 5b −71.78 (46.8) −72.47 (47.3) −8.99 (5.9) 0.030 0.152 −0.337 0.358 0.021 5c −69.21 (50.1) −59.95 (43.4) −9.09 (6.6) 0.041 0.144 −0.507 0.433 −0.073 5d a −700.39 (34.0) −1341.12 (65.1) −19.01 (0.9) 0.104 0.615 −0.267 0.210 −0.057 5e −197.69 (37.2) −311.95 (58.7) −22.03 (4.1) 0.106 0.592 −0.269 0.208 −0.060 5f a −637.70 (32.3) −1315.59 (66.6) −22.55 (1.1) 0.107 0.553 −0.264 0.201 −0.063 5g −239.46 (40.8) −323.09 (55.1) −24.26 (4.1) 0.107 0.583 −0.269 0.207 −0.061 8a −191.55 (38.8) −297.98 (60.4) −3.95 (0.8) 0.103 0.688 −0.279 0.225 −0.053 8f −191.02 (37.6) −300.02 (59.1) −16.89 (3.3) 0.099 0.570 −0.249 0.196 −0.053 a Cationic. Fig. 7 Representative molecular geometries of the LA-N 2 (left) and LA-N 2 -LB (right) complexes. Dalton Transactions Paper This journal is © The Royal Society of Chemistry 2025 Dalton Trans.,2025,54,4338–4352 | 4345 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online unfavorable interactions with the rest of the LBs and a stable complex is found with LB-6. This suggests that the remarkable stability provided by LB-6 is also linked to the nature of the interaction, as will be explained later. Thus, both the electronic characteristics of the LA and LB determine the feasibility and strength of the interaction. The degree of activation of the N 2 molecule can also be deduced from the geometry of the complexes, especially from the N 2 bond length. Upon reaction with a Lewis base, the LA-N 2 complex undergoes a significant geometry rearrangement (see Fig. 7). Specifically, while the LA-NuN bond angles in LA-N 2 complexes are nearly linear (close to 180°), the LA-NvN and NvN-LB bond angles in the resulting LA-N 2 -LB complexes shift to around 120°, and can also be represented as the zwitterionic form LA − -N 2 -LB + . This structural transformation reflects the formation of a covalent bond between the Lewis base and N 2 . In Table 4 are collected selected bond distances and bond orders. The N–N bond length oscillates between 1.208–1.281 Å, notably longer than the bond length in the isolated molecule (1.10 Å). This feature is reflected in the reduction of the bond order from triple to double (WBI 3 , around 2.000), clearly indicating an effective bond activation. Furthermore, in some cases a weakened double bond is observed, as in the complexes formed by the acid LA-4 and bases LB-2,LB-3,LB-5 and LB-6 (WBI 3 less than 1.800). The LA-N 2 bond distances range between 1.415–1.563 Å and WBI 1 values of 0.756–1.002, indicating a bonding interaction. For LA-5b, notably longer distances and lower WBI 1 values are calculated, suggesting a weaker interaction with this acid. LB-N 2 bond distances between 1.370–1.786 Å and WBI 2 values between 0.790–1.111 are calculated, therefore, a bonding interaction is also expected. 3.2.2 Nature of the bonding in LA-N 2 -LB complexes. QTAIM methodology has been employed to understand the interactions in LA-N 2 -LB complexes. The results for the LA-N 2 and LB-N 2 bond critical points are collected in the ESI (see Table S4†). Regarding the LA-N 2 interaction, the same pattern observed in the LA-N 2 complexes is reproduced here in all cases (∇ 2 ρ>0,|V|≤2G and ρ> 0.03) and, therefore, the interaction can be regarged as electrostatic with partially covalent character. On the other hand, all the LB-N 2 interactions can be considered as covalent (∇ 2 ρ> 0 and |V|≥2G), which may explain the main role of the base in the reduction of the bond order of N 2 . The remarkable σ-donation ability of LB-6 is reflected in larger ρvalues and bond orders, and shorter bond lengths. In summary, the results support the proposed model of N 2 activation, where the Lewis acid plays a key role in capturing N 2 and is primarily responsible of the thermodynamics of the process, stabilizing the complex and influencing the overall energy profile of the reaction. On the other hand, the Lewis base is primarily responsible for the kinetics of the activation, since the weakening of the bond directly impacts the rate at which the N 2 molecule is activated. To investigate the kinetics of the Lewis base attack on the LA-N 2 complex, we computed Table 3 Nucleophilicity index (N), in eV, of the Lewis bases (LB) and LA-N 2 -LB interaction energy (ΔH int and ΔG int ), in kcal mol −1 LB LA-4 LA-5a LA-5b LA-5d a LA-5e LA-5f a LA-8f NΔH int ΔG int ΔH int ΔG int ΔH int ΔG int ΔH int ΔG int ΔH int ΔG int ΔH int ΔG int ΔH int ΔG int LB-1 2.64 −29.04 −21.97 26.32 32.33 —— −3.83 2.22 6.83 13.85 −21.10 −14.15 7.09 10.87 LB-2 3.48 −40.25 −34.05 16.81 22.50 ——−15.02 −9.35 −2.70 3.11 −32.57 −25.93 −2.29 1.15 LB-3 3.74 −50.06 −43.35 6.78 13.93 ——−22.40 −15.37 −11.73 −4.02 −38.17 −29.91 −13.51 −8.36 LB-4 4.00 −41.75 −33.29 ————−23.30 −14.76 −10.57 −13.9 −39.31 −32.99 −13.66 −6.24 LB-5 4.80 −57.65 −50.52 0.15 6.11 9.65 16.81 −32.68 −25.24 −20.05 −13.06 −44.45 −35.65 −13.66 −9.33 LB-6 4.79 −80.50 −72.71 −25.52 −17.71 −18.94 −12.39 −62.46 −54.64 −49.27 −40.97 −83.77 −75.04 −49.23 −42.80 a Cationic. Paper Dalton Transactions 4346 |Dalton Trans.,2025,54, 4338–4352 This journal is © The Royal Society of Chemistry 2025 Open Access Article. Published on 07 February 2025. Downloaded on 3/4/2025 11:13:53 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online