A theoretical study on borenium ion affinities toward ammonia, formaldehyde and chloride anions

Center for Chemistry ICTM, University of Be Belgrade, Serbia Faculty of Chemistry, University of Belgra 11000 Belgrade, Serbia. E-mail: mbaranac@ † Electronic supplementary information employed in the study, additional calcula and MP2/6-311++G(d,p) levels, inuence calculated B–R/R0 and B–L bond length electron occupancies of boron's p-orbit decomposition analysis of binding inte optimized structures of borenium cation and Cl , absolute energies and x, y, z co See DOI: 10.1039/c5ra13825f Cite this: RSC Adv., 2015, 5, 75895


Introduction
The chemistry of the three-coordinate boron cations, known as borenium ion 1, 1 is characterized by their exceptional Lewis acidity arising from the intrinsic electron deciency of boron, enhanced by an overall positive charge (Fig. 1). 2 These species can be viewed as Lewis adducts of even more electrophilic di-coordinate borinium ion 2 with a Lewis base L. If another neutral ligand L 0 binds to borenium ion 1, a four-coordinate boronium ion 3 is formed. While the majority of older reports were focused on the synthesis, characterization and gas-phase reactivity of boron cations, 1,2a their condensed-phase reactions have attracted considerable interest in recent years. Borenium ions 1 are increasingly exploited as (chiral) Lewis acid catalysts in organic synthesis 2b,3 and as electrophilic borylation agents. 2b,4 Although the borenium ion chemistry is based on their Lewis acidity, quantitative data that would allow one to rank a broader range of borenium species according to Lewis acidity are rather scarce. Prokoevs 2b,5 calculated gas-phase ammonia affinities of a series of borenium ions, the majority of which comprised structures of synthetic interest. The results showed a wide range of DH values (>50 kcal mol À1 ), 2b,5 compared to the narrower one for neutral borane derivatives (>30 kcal mol À1 ). 6 Solomon et al. 4c ranked [CatBNR 3 ] + [AlCl 4 ] À and [(CatS 2 )BNR 3 ] + [AlCl 4 ] À with respect to their ability for electrophilic arene borylation and found the reactivity of [(CatS 2 )BNR 3 ] + [AlCl 4 ] À to lie between that of dichloro-and catecholato-boron electrophiles. The related N,N 0 -(2,6-diisopropylphenyl)-2-bromo-1,3,2-diazaborole was resistant to halide abstraction, obviously due to steric and MP2/6-311++G(d,p) 15 levels for NH 3 -complexes of 4-8, see Table S2 in the ESI † and the associated discussion). All geometries were fully optimized using the Gaussian 09 program package, 16 followed by frequency calculations to nd whether they correspond to energy minima (no imaginary frequencies). The G09 default geometry convergence criteria were used, that is max force 4.5 Â 10 À4 , RMS force 3 Â 10 À4 , max disp 1.8 Â 10 À3 and RMS disp 1.2 Â 10 À3 , and ne integration grid. At the theory level employed, structure 4, with shallow potential energy surface, could not be optimized as a true minima, that is, it contained an imaginary frequency: 140.23i cm À1 .
Binding enthalpies (DH) and binding energies (DE) were calculated as shown in eqn (1). Gas-phase values are corrected for the basis set superposition error (BSSE) by using the counterpoise (CP) method of Boys and Bernardi 17 (for the effect of BSSE corrections on molecular geometries and thus obtained DHs/DEs, see Table S2 in the ESI † and the associated discussion).
The binding energy DE consists of two parts, deformation energy (DE def ) and interaction energy (DE int ), as shown in eqn (2): When two species (cation and ligand L 0 ) associate, their geometries change. An energy required for this change is described as deformation energy (DE def ), and represents energy of isolated cation and ligand L 0 at adduct geometry minus energy of isolated cation and ligand L 0 at their optimal geometry, eqn (3).
In the analysis, structural changes due to (partial) rehybridization of boron atom, following the complex formation, are involved in this energy term. The interaction energy (DE int ) reects the energy of adduct formation from two deformed fragments, cation and L 0 .
To gain an insight into the nature of borenium cation-ligand interactions, the DE int was partitioned into ve energy terms (eqn (4)), by using the localized molecular orbital energy decomposition analysis (LMOEDA), developed by Su and Li 18 and implemented into the Gamess programe package. 19 The electrostatic energy (DE elstat ) comprises attractive (nucleus-electron) and repulsive (nucleus-nucleus, electronelectron) forces between the two deformed fragments that adopt their position in the adduct. This energy is usually stabilizing, since attractive interactions outweigh the repulsive ones. The exchange energy (DE ex ) refers to the quantum mechanical exchange between the same-spin electrons and is simultaneously counteracted by the repulsion energy (DE rep ). Taken together, they form the exchange repulsion 20 or Pauli repulsion 21 of other EDA schemes. Herein, we use the sum of DE ex and DE rep to represent the Pauli repulsion. The polarization energy (DE pol ) is an orbital relaxation energy accounting for charge transfer (donor-acceptor interactions between occupied orbitals on one fragment with empty orbitals on the other) and polarization (empty-occupied orbital mixing within one fragment due to the presence of another fragment). Although, this energy component is denoted as DE pol in the original reference, 18 herein we will label it as DE oi , to account for all orbital interactions, and refer to it as the orbital interaction energy. The dispersion energy (DE disp ) comes from mutual correlation of electrons. All interaction energy terms are also counterpoise-corrected. The EDA was done for the gas-phase conditions, as was the natural bond orbital (NBO) analysis, performed at the same theory level by using the NBO version 6.0 (ref. 22) linked to Gaussian 09.
The gas-phase optimized geometries were used for the liquid-phase calculations of DEs. Solvent effects were taken into account by using the integral equation formalism polarizable continuum model (IEFPCM, solvent ¼ CH 2 Cl 2 ). 23

Geometries of borenium ions 4-29
Optimized geometries of borenium ions 4-29 are presented in Fig. S1 in the ESI. † The [H 2 BNH 3 ] + cation 4 possesses a quite shallow potential energy surface (PES) with respect to the B-N bond rotation. The energy difference between the eclipsed (4 HBNH ¼ 0 ) and orthogonal (4 HBNH ¼ 90 ) structures, both of C s symmetry, was less than 5 cal mol À1 . The lowest energy structure (by 0.9 cal mol À1 more stable than the orthogonal one) had the HBNH torsional angle of 97 and it was taken as a reference for estimation of adduct formation energies. Halosubstituted borenium cations 5 and 6 feature the C s symmetry structure with one of the N-H bonds lying perpendicularly to the Hal 2 B plane. Dimethyl-substituted cation 7 has almost eclipsed N-H/B-C bonds with 4 HNBC ¼ À1.5 . Two of the C-H bonds are also nearly eclipsed with the B-N and B-C bonds (4 HCBN ¼ 12.7 and 4 HCBC ¼ À8.8 ). All they point into the same direction. Optimization of Me,Ph-substituted cation 9 resulted in a structure in which one of the C-H bonds of Me part and one of the N-H bonds of NH 3 moiety are found almost in plane with the phenyl ring, and they point into the same direction, the C-H bond being oriented toward the Ph ring. In diphenylsubstituted borenium ion 10 one of N-H bonds forms a small diedral angle with one of the B-C bonds (4 HNBC ¼ 11.4 , while both phenyl rings are tilted from the CBN plane by $30 and $20 . Five-membered heterocyclic ring in borenium ions 8 (P,P), 14 (S,S), 16 (O,S), 17 (N,S) and 20 (N,N) adopts a half-chair conformation, which is signicantly attened in 20. One of the N-H bonds in the NH 3 moiety is nearly perpendicular to the RBR 0 plane in 8 (4 ¼ 89.4 ), 14 (4 ¼ 86.7 ) and 20 (4 ¼ 89.8 ). When heteroatoms connected to boron atom differ, one of the N-H bonds in the NH 3 part is almost eclipsed with the B-O ring bond in 16 (4 HNBO ¼ À4 ) and B-N ring bond in 17 (4 HNBN ¼ À5.1 ). The N-H bond in the heterocycle is mostly in the NBN(S) plane in 17 (N,S) and 20 (N,N), which is not the case for the P-H bond. This is consistent with stronger electron-donating ability of N atom compared to P atom. The ve-membered ring in cations 12, (P,S), 13 (P,O) and 19 (P,N) exists in envelope-like conformation with the C(4) atom, bound to phosphorus, being out of plane of the other four atoms. The conformation around the exocyclic B-N bond is such that one of the N-H bonds is found nearly eclipsed with the B-S ring bond in 12, (4 HNBS ¼ À10.4 ), B-O ring bond in 13 (4 HNBO ¼ À6.4 ) and B-N ring bond in 19 (4 HNBN ¼ À5.4 ). The heterocyclic part in cations 15 (O,O) and 18 (N,O) is nearly planar, while one of the N-H bonds in the NH 3 group is oriented almost perpendicularly with respect to the OBO(N) plane (4 ¼ 83.9 in 15, 4 ¼ 86.2 in 18). The structure of [CatBNH 3 ] + 11 possesses the C s symmetry with one of the N-H bonds being perpendicular to the aromatic ring.
The B-R bond lengths in symmetrically substituted heterocyclic structures decrease in the following order: 1.865Å in 8 (P,P) > 1.766Å in 14 (S,S) > 1.389Å in 20 (N,N) > 1.328Å in 15 (O,O). If we order the heteroatoms as N, O, S, P it can be said that the replacement of any of these atoms in any of the heterocyclic structure (symmetrically or unsymmetrically substituted) by the one which is le to it will lengthen the remaining B-heteroatom bond, whereas substitution of any atom by the one which is right to it will shorten the remaining B-heteroatom bond. 24 The strength of the effect follows the above atomic order, that is nitrogen/phosphorus most increases/decreases the other B-heteroatom bond. For example, the B-P/B-N bond is the longest/shortest in 19, 1.913/1.369Å. The B-L bond lengths range from 1.535Å in 11 to 1.592Å in 9. The B-R/R 0 and B-L bond lengths for all studied borenium ions are given in Table S3 in the ESI. † The 1,3,2-oxazaborolidine ring in all cations 21-29 adopts a signicantly attened half-chair conformation. One of the C-N, C-P and H-P bonds in L part of structures 23-25 is almost eclipsed with the B-N ring bond (4 CNBN ¼ À3.5 in 23, 4 CPBN ¼ À7.8 in 24 and 4 HPBN ¼ À3 in 25). In 22, both C-O bonds form small diedral angles with the B-N ring and B-O ring bonds (4 COBN ¼ 5.8 and 4 COBO ¼ À14.3 ), which is the result of a strong O to B electron-donation making the oxygen atom mostly sp 2 hybridized. By contrast, ion 21, stabilized by Me 2 S, is most stable in conformation in which the B-O ring bond bisects the MeSMe angle. The two rings in carbene-stabilized structures 26 and 27 are just slightly twisted (by less than 11 ). In the case of 26, the cis-ON conformation is by 1.5 kcal mol À1 more stable than the cis-OS one, and it was used as a reference for the complex formation energies. The carbene part in 28 is tilted by 31 from the NBO plane of 1,3,2-oxazaborolidine moiety, while the two rings in 29 adopt a perpendicular conformation. Cartesian coordinates of all optimized structures are given in the ESI. † Geometries of borenium ion complexes with NH 3 , HCHO and Cl À Optimized geometries of all complexes are presented in Fig. S2-S4 in the ESI. † In the case of NH 3 -complexes with 4-9, 11-20 and 23-29, one binding geometry was obtained. For those formed from 10, 21 and 22, some conformational variations may be possible, particularly around the C Ar -B bond in 10. In these cases one geometry was optimized. One binding geometry was obtained for HCHO-complexes derived from cations having the same R/R 0 . When R s R 0 , two geometries, having HCHO oriented toward either substituent, were optimized. The more stable ones are discussed in this section and shown in the ESI. † Upon complex formation, the trigonal planar geometry around boron atom changes to, more or less, tetrahedral. The hydrogen-, halo-, methyl-and Cat-substituted ammonia adducts formed from 4-7 and 11 feature the C 2v symmetry structures, while the adduct formed from Me,Ph-borenium ion 9 possesses the C s symmetry with the B-Me bond lying in the plane of the phenyl ring. In ammonia adducts with ions having a heterocyclic ring, this ring adopts (attened) half-chair conformation. Just one exception is complex formed from 12 (P,S), in which the heterocyclic part exists in the envelope conformation having the C(4) atom out of plane of the other four atoms. The structures with the same heteroatoms have the C 2 symmetry. While Me 2 S-, Me 2 O-, Me 3 N-and Me 3 P-stabilized borenium cations 21-24 form Lewis complexes with ammonia, reaction of phosphine-stabilized ion 25 ends up with PH 3 substitution. All carbene-and lut-stabilized ions 26-29 bind ammonia. Upon complex formation, the most drastic geometry change in a cation occurs in the case of 26 and 29. In the former, near-to-planar geometry changes to the orthogonal one having NH 3 at the sulfur side of thiazole ring. The opposite happens with 29, the structure of which changes from orthogonal to wing-shaped, in order to make a place for the NH 3 ligand. Otherwise, ligand approach to boron is blocked by the two ortho-methyl groups. These geometry changes are reected in high DE def values, as will be discussed. Geometries of 27 and 28 in an adduct are wing-shaped, due to the change in hybridization of the boron atom.
The lowest energy structures of Lewis adducts formed from hydrogen-, halo-and methyl-substituted cations 4-7 with formaldehyde (slightly) deviate from the fully symmetric ones (C s    + , and other in which HCHO binds to boron atom. Hydrogen bonded complexes are by 4.8 kcal mol À1 and 5.5 kcal mol À1 , respectively, lower in energy. In both boron-bound adducts, ring conformation is envelope with C(4) bound to N in   + and bound to P in [19-HCHO] + pointing out of plane. In [18-HCHO] + , formaldehyde hydrogen atom lies above the ring oxygen atom (4 COBN ¼ 137 ). The COBN diedral angle is larger in [19-HCHO] + (4 COBN ¼ À172 ), the HCHO just slightly pointing toward the ring nitrogen atom. Cation 20 (N,N) forms only hydrogen bonded complex in which carbonyl oxygen atom orients towards the two N-H bonds, one belonging to the heterocycle, the other to the NH 3 part. The heterocyclic ring in [21-HCHO] + adduct adopts an envelope conformation with C(4) atom bound to N pointing out of plane of the other four atoms. One of the formaldehyde hydrogen atoms is placed above the ring oxygen and 4 COBS amounts 132.9 . In complexes formed from 22-25, the heterocyclic part is in the half-chair conformation, which is appreciably attened in [24-HCHO] + . In In the case of HCHO binding, the geometry of cation 26 does not change to the orthogonal one, as it does upon NH 3 binding. This could be ascribed to the long B-OCH 2 distances in adducts derived from 26-28 (together with [24-HCHO] + , they are the longest among all complexes studied), so that HCHO does not interfere much with the original cation structure. Borenium cation 29 does not bind HCHO at boron atom, but forms hydrogen-bonded complex involving carbonyl oxygen and NH ring group.
Reactions of hydrogen-, uoro-, methyl-and Cat-substituted borenium cations 4, 5, 7 and 11 with chloride anion result in structures with the C s symmetry. The structure formed from chloro-substituted cation 6 has the C 3v symmetry. In the case of product obtained from Me,Ph-substituted ion 9, the Me-B bond forms small diedral angle with the phenyl ring, 4 CBCC ¼ À15.5 .

Binding enthalpies and energy decomposition analysis
We rst checked if there exists any correlation between the gasphase binding enthalpies (DH)/energies (DE) and the following parameters: (1) B-L 0 distance in a complex (given in Tables 1-4), (2) calculated NBO charge at boron atom of a borenium cation and (3) calculated electron occupancy of boron's p-orbital in a borenium cation. Values for the latter two are shown in Table S3 in the ESI. † The results show that DHs/DEs are moderately correlated with the B-L 0 bond length having correlation coefficients of R 2 ¼ 0.74/0.74 for NH 3 complexes with cations 4-20, R 2 ¼ 0.88/0.88 for NH 3 complexes with cations 21-29, R 2 ¼ 0.56/0.57 for HCHO complexes with 4-20, R 2 ¼ 0.37/0.35 for Cl À adducts with 4-20 and R 2 ¼ 0.77/0.78 for Cl À adducts with 21-29. As expected, better accommodation of a ligand (shorter B-L 0 bond) leads to stronger attractive interactions (nucleus-electron electrostatic attraction, orbital and dispersion interactions), but also to larger repulsive interactions (nucleus-nucleus, electron-electron electrostatic repulsion and Pauli repulsion). It is their relative magnitude (substituent-dependent) that determines the strength of cation-ligand interaction, along with energy spent for fragment deformations. There was no correlation between DHs/DEs and B-O distance in the case of HCHO-complexes with cations 21-29.
The DHs/DEs did not show any correlation with the positive charge located at boron atom in borenium cations. Likewise, charges at boron do not correlate with the net electrostatic attractive energies between cation and ligand L 0 . This lack of correlation can be rationalized by taking into account the two effects: (1) distance-sensitivity of this type of interactions and (2) electrostatic forces could better be explained as an all-charge phenomenon, not as partial interactions between individual atoms or group of atoms. Therefore, these results show that electrostatic interactions between boron and ligand do not play an important role in overall binding affinity and are even not dominant electrostatic forces.
As the electron occupancy of boron's p-orbital increases, binding enthalpies/energies should decrease (become less negative), due to diminished availability of boron to accept electron density. This trend was found for complex formation between 4-20 and all examined ligands, though correlation coefficients were low: R 2 ¼ 0.44/0.45 for NH 3 complexes, R 2 ¼ 0.47/0.49 for HCHO complexes and R 2 ¼ 0.27/0.29 for adducts with Cl À . Variations of boron's p-orbital electron occupancies due to change of L bound to boron in cations 21-29 did not show the correct correlation with DHs/DEs. The same stands for the orbital interaction energy DE oi of complexes and boron's p-orbital occupancies. This can be explained by taking into account the following: (1) distance-dependence of orbital interactions and (2) in addition to coordinate covalent bonding, other cation-ligand charge transfer (hyperconjugative) interactions and polarization have important contribution to total orbital interactions.
Thus, the overall strength of cation-ligand interactions will be considered as an interplay of various interactions involving all atoms contained in cation and ligand L 0 , and a distance at which cation and L 0 approach each other.

Ammonia affinity of cations 4-20
Calculated binding enthalpies (DH), energies (DE) and LMOEDA analysis of binding interactions between borenium ions 4-20 and NH 3 are presented in Table 1, along with the calculated B-NH 3 distances. The gas-phase results will be discussed rst, followed by discussion of solvent effects on DEs, which are presented in the last paragraph of this section.
The DHs range from À54.4 kcal mol À1 for the strongest acceptor 4 (H,H) 25 to À12.9 kcal mol À1 for the weakest acceptor 20 (N,N). The DEs show almost the same trend as DHs (there are two exceptions, cations 13 and 14, and 15 and 16, for which the trend in DEs is the reverse to that in DHs, though energy differences are quite small and correlation between DHs and DEs is high, R 2 ¼ 0.999). Calculated B-NH 3 distances range from 1.608Å in 6 (Cl,Cl) to 1.667Å in 20. As a comparison, the experimentally determined B-N bond length in BH 3 -NH 3 complex amounts 1.6576(16)Å. 26 Deformation energy (DE def ) is the smallest for 4 (18.6 kcal mol À1 ), which is expected due to the small steric hindrance from hydrogen atoms, and the largest for 15 (O,O) (33 kcal mol À1 ). The net stabilizing energy of a complex is determined by the relative magnitudes of deformation and interaction energies, so that DE int do not follow exactly the same trend as DHs/DEs.
The LMOEDA shows that the nature of binding interactions is pretty much the same in complexes formed from all cations 4-20: major contributions to complex stabilization come from The strongest ammonia acceptor 4 (H,H), DH/DE ¼ À54.4/ À58.9 kcal mol À1 owes its large binding affinity to the small deformation energy and large interaction energy (DE int is larger only in adduct formed from 5). As a comparison, the counterpoise-corrected interaction energy in BH 3 -NH 3 ranges from À39.8 kcal mol À1 to À44.2 kcal mol À1 , at various theory levels employed. 18 In the case of [4-NH 3 ] + , the magnitudes of electrostatic and dispersion energies are the smallest among all complexes studied, while orbital interactions exceed those in only four ammonia adducts (formed from 7, 15, 18 and 20). This means that the large DE int originates from the small Pauli repulsion, not from strong attractive interactions, again related to the small steric hindrance in the case of hydrogen atoms as substituents.
The NH 3 affinity of 4 is followed by that of 5 (F,F), DH/DE ¼ À49.8/À52.4 kcal mol À1 , and then by that of 6 (Cl,Cl), DH/DE ¼ À44.8/À48.2 kcal mol À1 . Interestingly, whereas BCl 3 binds ammonia more strongly than BF 3 by DH/DE ¼ 3.2/3.8 kcal mol À1 at the employed theory level (see Tables S1 and S4 in the ESI † and ref. 6), the order of NH 3 affinities of 5 and 6 is reversed: cation 5 binds NH 3 more strongly than 6 by DH/DE ¼ 5/4.2 kcal mol À1 . The reason for this opposite trend lies in the interaction energy term, since deformation energies are almost the same in the case of the two neutral boranes (Table S4 †), and slightly larger for the adduct formation from 5. As LMOEDA reveals, in both borane and borenium ion adducts with NH 3 the Pauli repulsion is larger in the case of chloro derivatives and more so for neutral boranes. Thus, the reversed order of interaction energy (DE int ¼ À48.3/À52.1 kcal mol À1 for BF 3 -NH 3 /BCl 3 -NH 3 , DE int ¼ À81.2/À75.3 kcal mol À1 for [5-NH 3 ] + /[6-NH 3 ] + ) stems from a signicant increase in DE elstat (by 13.1 kcal mol À1 ) and DE oi (by 25.2 kcal mol À1 ) when one uorine in BF 3 is replaced with NH 3 . In the case of chloro-compounds, the increase in electrostatic and orbital stabilization in complexes upon one chlorine substitution in BCl 3 with NH 3 is much smaller, by 0.9 kcal mol À1 and 7 kcal mol À1 , respectively. Dispersion interactions practically do not change in the case of uoro derivatives, but decrease by 1.2 kcal mol À1 when more polarizable chlorine is exchanged with the ammonia. It should also be noted that 5 deserves its higher affinity toward ammonia than 6 to smaller Pauli repulsion, while all attractive energy components are larger in [6-NH 3 ] + . Thus, in the case of complex formation with borenium cations, larger atoms, from the second octal row of periodic table, provide more electrostatic, orbital and dispersion stabilization and larger Pauli destabilization. This holds for other heteroatoms, too, as will be seen in further discussion. When halogen substituents in borenium ion are substituted with two methyl groups to form 7, the affinity toward NH 3 drops by DH/DE ¼ 8.1/7.8 kcal mol À1 , compared to 6, and by DH/DE ¼ 13.1/11.9 kcal mol À1 , compared to 5. This drop is related exclusively to less favourable DE int , because DE def decreases, too. The Pauli repulsion in [7-NH 3 ] + is almost the same as in  ] + and smaller than in [6-NH 3 ] + (Table 1). Thus, the decrease in the interaction energy by 13.5 kcal mol À1 compared to [6-NH 3 ] + and by 19.4 kcal mol À1 compared to  ] + is connected with a decrease in electrostatic and orbital interactions. As mentioned before, electrostatic stabilization is not simply related to the charge at boron atom, which amounts 1.412, 0.566 and 1.087 for 5, 6 and 7, respectively, but to all charge interactions (attractive and repulsive) and B-NH 3 distance, which is longer in [7-NH 3 ] + , 1.640Å, compared to 1.618Å and 1.608Å in  ] + and [6-NH 3 ] + , respectively, and diminishes DE elsatat . The NBO analysis shows that the electron occupancy of boron's p-orbital decreases in the order: 6 (0.460e) > 5 (0.289e) > 7 (0.167e). Thus, the drop in the orbital interactions should be related to a decrease in covalency due to the larger B-NH 3 bond, smaller polarization and other cationligand hyperconjugative interactions.
Replacement of one or both methyl groups in 7 with phenyl ring to form 9 and 10 further decreases affinity of borenium cations toward ammonia by DH/DE ¼ 3.8/4.2 kcal mol À1 and DH/DE ¼ 5.8/6.8 kcal mol À1 , respectively. In the case of [9-NH 3 ] + , this is related both to the increase in deformation energy (by 1.8 kcal mol À1 with respect to [7-NH 3 ] + ) and decrease in the interaction energy (by 2.4 kcal mol À1 compared to [7-NH 3 ] + ). Major factor responsible for smaller binding affinity of 10 is increase in deformation energy (5.9 kcal mol À1 with respect to [7-NH 3 ] + and 4.2 kcal mol À1 with respect to [9-NH 3 ] + ), while interaction energy drops by only 0.9 kcal mol À1 compared to  ] + , and is by 1.5 kcal mol À1 more stabilizing compared to [9-NH 3 ] + . For both [9-NH 3 ] + and [10-NH 3 ] + , DE int reduces solely due to the increased Pauli repulsion, while all attractive energy components become more favourable than in [7-NH 3 ] + . The increase in DE oi and DE disp partly relates to the presence of more polarizable p-electrons enhancing dispersion interactions and affecting polarization part of DE oi more than the charge transfer interactions associated with the B-N bond formation. For the latter, presence of one or two phenyl rings is not favourable because it decreases availability of boron's p-orbital to accept nitrogen lone pair, due to the p Ph / p B electron donation (calculated boron's p-orbital occupancies are 0.249e in 9 and 0.285e in 10 compared to 0.167e in 7). The B-N bond lengths in [9-NH 3 ] + and [10-NH 3 ] + are almost equal/slightly smaller than in [7-NH 3 ] + , suggesting the presence of strong attractive forces.
In the rest of borenium cations to be discussed, boron atom is included in a heterocycle, structures 8 and 12-20, or is connected to catechol, structure 11. The strongest affinity toward NH 3 is found for 8 (P,P), DH/DE ¼ À33.8/À37.1 kcal mol À1 , and it is even higher than that observed for Me,Ph-and Ph,Phsubstituted cations 9 and 10. Binding affinity of 11, DH/DE ¼ À29.4/À31.7 kcal mol À1 , is somewhat weaker than that of 10. Among the complexes formed from 8 and 11-20, the [8-NH 3 ] + possesses the shortest B-NH 3 bond length, d BN ¼ 1.621Å, and its formation is accompanied by the smallest deformation energy, DE def ¼ 25.1 kcal mol À1 , and the largest interaction energy, DE int ¼ À62.2 kcal mol À1 . These observations could be ascribed to the long B-P bonds in 8, which sterically least impedes with the NH 3 approach. Once the complex is formed, the Pauli repulsion becomes strong, DE ex+rep ¼ 187.8 kcal mol À1 , but is signicantly exceeded by very favourable DE elstat ¼ À115.1 kcal mol À1 , DE oi ¼ À110.7 kcal mol À1 and DE disp ¼ À24.2 kcal mol À1 . All interaction energy components are similar or larger only in adducts derived from 6 (Cl,Cl), 12 (P,S) and 14 (S,S), which have similar or shorter B-NH 3 bonds and both heteroatoms come from the second octal row of the periodic table. Dispersion interactions are also more prominent in [9-NH 3 ] + (Me,Ph) and [10-NH 3 ] + (Ph,Ph), having polarizable p-electrons, than in [8-NH 3 ] + . In addition,  ] + shows similar Pauli repulsion as [8-NH 3 ] + , slightly stronger electrostatic stabilization, but somewhat weaker orbital and dispersion interactions. This results in 1.2 kcal mol À1 smaller DE int compared to that in [8-NH 3 ] + . Deformation energy accompanying the formation of  ] + is by 4.2 kcal mol À1 higher than that needed for the formation of [8-NH 3 ] + , so that both energy terms lead to lower association energy in the case of [CatBNH 3 ] + . As the major part of deformation energy relates to geometry change of a cation, bending of the exocyclic B-N bond in the aromatic 11 is energetically more costly than the same change in 8, which is the main structural change in these two cations. Even more energy is spent to deform cation 15, having two oxygen atoms connected to boron, like 11. In fact, DE def ¼ 33 kcal mol À1 needed for the formation of  ] + is the highest one in Table 1 and has to be ascribed to a signicant ring puckering occurring during the cation-NH 3 association, along with the B-N bond bending. The reason why 15 is weaker NH 3 acceptor than 11 is solely its high DE def , while DE int are almost equal in the formation of both complexes. This somewhat contrasts with our intuitive prediction that 11 would be a weaker lone pair acceptor, because boron's p-orbital in it is part of the aromatic 10p-electron system. Even so, orbital interaction energy is more stabilizing in  ] + than in  ] + , resulting from slightly shorter B-N distance and polarization part of orbital interactions. In addition, electrostatic energy is by the similar magnitude more stabilizing in  ] + , but Pauli repulsion is smaller in In fact, cations 13-16 have very similar NH 3 affinities, DH ¼ À26.4 AE 0.2 kcal mol À1 , and are followed by the group of three cations, 17-19, the affinities of which amount DH ¼ À18.5 AE 0.3 kcal mol À1 . The weakest ammonia acceptor is 20 (N,N), DH ¼ À12.9 kcal mol À1 . All these enthalpies are exceeded by that of 12 (P,S), DH ¼ À28.6 kcal mol À1 . The strongest affinity of 12, among 12-20, owes to the relatively low DE def and high DE int , the latter exceeded by only  ] + just because of smaller Pauli repulsion. Therefore, the P,S heteroatom combination in 12 lowers association enthalpy compared to the P,P heteroatom combination in 8, but leads to somewhat larger ammonia affinity with respect to all other combinations involving P, S and O. This is the result of relative magnitudes of DE def and DE int , and could not be ascribed to any particular interaction. Weak ammonia affinities of nitrogen-containing heterocyclic cations 17-20 certainly come from a decrease in the interaction energy, which does not exceed À54 kcal mol À1 , while deformation energy values compare with those of other heterocycle-containing cations. Small magnitudes of DE int are a consequence of long B-NH 3 distances (the longest among all NH 3 -complexes studied) and a change in individual energy components affected by the type of atoms involved in a heterocycle. The reason why 17-20 keep the NH 3 ligand at the longest distance could be a combination of good electron-donating ability of nitrogen which increases boron's p-orbital electron occupancy and steric hindrance due to the short B-N ring bonds. Although, it should be noted that electrostatic and orbital interaction energies in some of adducts formed from 17-20 are larger than in those obtained from nitrogen-lacking heterocyclic structures and boron's p-orbital occupancy is not the highest. Here, again, elements from the second octal row (S and P) provide more electrostatic and orbital stabilization, and larger Pauli repulsion, more pronounced for S than for P. This is evident when comparing interaction energy components in adducts derived from 17-19, which all have (almost) the same B-N distances.
When comparison between related heterocycles is made, the following can be said.  N), affects mainly the Pauli repulsion upon complex formation which increases by 3.1-5.7 kcal mol À1 and orbital interaction energy which decreases by 1.5-2.3 kcal mol À1 . In addition to a slight increase in the B-NH 3 distance by 0.012-0.015Å, which inherently decreases interaction energy components, the drop in DE oi is consistent with nitrogen's better electron-donating ability with respect to oxygen (also see electron occupancy values in Table S3 † Inclusion of solvent into calculations either decrease or increase binding energies. For majority of cations, the effect does not exceed 3.3 kcal mol À1 . The largest decrease in DE is observed for 4, 5.3 kcal mol À1 . The above mentioned three cationic groups with similar DEs can still be discerned: 20 as the poorest NH 3 acceptor (DE ¼ 13.6 kcal mol À1 ), 17-19 having larger acceptor abilities (DE $20 kcal mol À1 ) and the third group now involves cations 11-16, the DEs of which are around 30 kcal mol À1 . In solvent conditions, 8 (P,P) binds NH 3 somewhat stronger than 7 (Me,Me) by 1.5 kcal mol À1 , and 5 (F,F) appears to be a poorer acceptor than 6 (Cl,Cl), though the difference in binding energies is small (0.6 kcal mol À1 ).

Formaldehyde affinity of cations 4-20
Calculated binding enthalpies (DH), energies (DE) and LMOEDA analysis of binding interactions between borenium ions 4-20 and HCHO are given in Table 2, along with the calculated B-OCH 2 distances. Discussion of the gas-phase results is followed by discussion of solvent effects, which is given in the last paragraph of this section.
In this case, DHs/DEs span a somewhat narrower range from À40.5/À44.6 kcal mol À1 for 4 (H,H) to À9.2/À10.7 kcal mol À1 for 17 (N,S). Magnitudes of all HCHO association enthalpies are smaller than the corresponding NH 3 binding enthalpies by 7.8-14 kcal mol À1 , which should be ascribed to the sp 2hybridized oxygen lone pair being poorer electron donor than ammonia lone pair. DHs and DEs follow the same trend (R 2 ¼ 0.998) which, with few exceptions, match that for NH 3 affinity. Differences in affinities toward NH 3 and HCHO are the following: (1) cation 14 is slightly weaker HCHO acceptor than cations 15 and 16 by 1.4 and 0.5 kcal mol À1 , respectively; (2) cation 17 is slightly weaker HCHO acceptor compared to 18 and 19 by 1.8 and 0.05 kcal mol À1 , respectively. Calculated distances between boron and carbonyl oxygen atom of HCHO range from 1.563Å in 8 (P,P) to 1.754Å in 18 (N,O). Deformation energy (DE def ) is the smallest for complex formation from 4 (15.1 kcal mol À1 ) and the largest for complex formation from 16 (24.1 kcal mol À1 ). All DE def and DE int values are smaller than those in the corresponding ammonia complexes. Like in NH 3 -adducts, DE int do not follow the same trend as DHs and DEs, since the latter two are inuenced by deformation energies, as well.
The LMOEDA shows that in the case of adducts formed from 4-6 and 8 the percentage contribution of the orbital interaction energy (DE oi : 44.6-46%) slightly prevails over the electrostatic interaction energy (DE elstat : 42.5-43.8%), while for all other complexes contribution of electrostatic stabilization (DE elstat : 43.5-46.5%) is slightly more pronounced than that of orbital interaction energy (DE oi : 38.3-43.8%). The role of dispersion interactions in complex stabilization is slightly increased (11.4-15.2%) compared to cation-NH 3 complexes (9.2-11.6%), which is possibly due to the presence of more polarizable p-electrons in the ligand (HCHO).
Cation 4, again, exhibits the strongest tendency to bind the ligand (HCHO), DH/DE ¼ À40.5/À44.6 kcal mol À1 , which stems from small DE def ¼ 15.1 kcal mol À1 and large DE int ¼ À59.7 kcal mol À1 (DE int is larger only in adduct formed from 5, which is similar to NH 3 -complexes). The The HCHO affinity of 5 (F,F), DH/DE ¼ À37.2/À39.4 kcal mol À1 , is larger than that of 6 (Cl,Cl), DH/DE ¼ À30.9/À33.3 kcal mol À1 , because of the more favourable DE int (by 5.9 kcal mol À1 ), while DE def is smaller by only 0.2 kcal mol À1 . Like in NH 3complexes, it is the lower Pauli repulsion which is responsible for the larger DE int in [5-HCHO] + compared to [6-HCHO] + , while all attractive energy terms are more stabilizing in the latter.
The effect of methyl and phenyl substituents on HCHO affinity of cations 7 (Me,Me), 9 (Me,Ph) and 10 (Ph,Ph) is the same as their inuence on NH 3 affinity and can be rationalized in a similar way as already discussed in the preceding section, where it was compared to halo-substituted cations. If compared with 4 (H,H), the replacement of hydrogen atoms by two methyl groups decreases affinity toward HCHO mainly due to the interaction energy, which decreases by 15.4 kcal mol À1 (DE def rises by only 1.1 kcal mol À1 ). The drop in the DE int has to be attributed to the increased Pauli repulsion and much more to the decreased orbital interactions, which together reduce DE int by 16.7 kcal mol À1 (the net effect of DE elstat and DE disp is stabilization by 1.2 kcal mol À1 , the former/latter becoming less/ more stabilizing). A decrease in DE oi can be ascribed to s CH / p B hyperconjugation which enhances boron's p-orbital occupancy to 0.167e compared to only 0.023e in 4, resulting in smaller coordinate covalent bond strength and longer boronligand distance (also affected by steric hindrance from methyl groups). The latter, in turn, reduces polarization, which should actually increase upon hydrogens substitution with methyl groups. Further substitution of one methyl group in 7 with phenyl group to form 9 decreases binding affinity by DH/DE ¼ 3.1/3 kcal mol À1 due to somewhat larger deformation of interacting fragments and less stabilizing DE int . The latter is made less favourable solely due to the increase in the Pauli repulsion. Replacement of another methyl by phenyl group to give 10 decreases HCHO affinity exclusively due to increase in the DE def , while enhancement of all attractive energy components makes the DE int slightly more favourable with respect to that in [7-HCHO] + and [9-HCHO] + . Among the heterocycle-containing cations 8 and 11-19, high binding affinity of 8 (P,P), DH/DE ¼ À22.8/À25.1 kcal mol À1 , owes to the favourable interaction energy which partly results from the very short B-O bond. This is the shortest B-O bond among all HCHO-complexes studied and can be explained in the same way as for NH 3 -complexes. Thus, due to the long B-P bonds in 8, ligand approach is sterically least impeded. In the complex, all interaction energy terms, attractive (DE elstat , DE oi and DE disp ) and repulsive (DE ex+rep ), are the strongest, compared to all other complexes. Their net result is very favourable DE int , being stronger in just three other complexes obtained from 4-6.
While [CatBNH 3 ] + 11 showed the highest affinity toward NH 3 among heterocyclic cations 11-20 mostly due to the favourable interaction energy (Table 1)   ] + is also longer than in [11-NH 3 ] + , but the difference is smaller, 0.011Å). The reason why interaction energies are almost the same in adducts formed from 11 and 15 is not larger attraction in the case of 15, but smaller Pauli repulsion.
Unlike the case of NH 3 as ligand, cations 12-16, containing P, O and S as heteroatoms, are poorer HCHO acceptors than 11 due to the larger geometry changes associated with the complex formation, while the interaction energy is similar or higher than that in The trend in HCHO affinities of 12-19 differs somewhat from that found for NH 3 affinities. Whereas in the case of the latter, two cation groups, having very similar affinities within each, could be identied, the HCHO accepting ability continually decreases in the order: balance between DE def and DE int . Compared to 8 (P,P), cation 12 (P,S) shows weaker HCHO affinity by 4.3 kcal mol À1 mostly because of smaller attractive energy components making DE int less favourable. This is mainly related to the longer B-O bond in [12-HCHO] + compared to that in [8-HCHO] + , by 0.038Å. The B-N distances in the corresponding NH 3 -complexes vary by less than 0.01Å resulting in quite similar attractive interaction energy components, but larger Pauli repulsion in [12-NH 3 ] + (Table 1).
Sulfur substitution in 12 with oxygen to give 13 (P,O) decreases all interaction energy components and net DE int , but also DE def . The resulting HCHO affinity drops slightly by DH/DE ¼ 0.5/0.8 kcal mol À1 . A change in DE int partially comes from the change in the type of atoms, as already discussed, and partially from the increase in the B-OCH 2 distance by 0.025Å. When two oxygen atoms are connected to boron, such as in 15, formaldehyde approach is even more impeded leading to the long boron-ligand distance of 1.682Å (by 0.056Å longer than in [13-HCHO] + and by 0.081Å longer than in [12-HCHO] + ). This further decreases all interaction energy components. As decrease in attractive part is larger than decrease in the repulsive part, overall interaction energy becomes less favourable, which is the cause for the drop in HCHO affinities along the series: 12 > 13 > 15 (DE def decreases, as well). This contrasts with the behaviour of NH 3 -complexes in which the B-N distance in  ] + is comparable to that in  ] + and attractive interactions are just slightly reduced due to P / O exchange. In that case, the overall DE int is increased in  ] + , compared to [13-NH 3 ] + (Table 1)  In HCHO-adduct obtained from 16 (S,O), the B-OCH 2 distance is marginally increased relative to that obtained from 13 (P,O) and its lower HCHO affinity by DH/DE ¼ 2.9/3 kcal mol À1 mainly stems from the large DE def ¼ 24.1 kcal mol À1 , which is the largest value among all studied HCHO-adducts (DE int decreases by only 0.8 kcal mol À1 ). While all 13-16 have very similar affinities toward NH 3 (Table 1), 14 (S,S) shows the weakest affinity for HCHO. This is the result of high DE def ¼ 24 kcal mol À1 and high Pauli repulsion, whereas two sulfur atoms provide favourable electrostatic, orbital and dispersion interactions.
The remaining three cations 17-19, possessing one N ring atom, form complexes with the longest B-OCH 2 distances (1.704-1.754Å). Cation 20 forms only hydrogen-bonded complex with HCHO. The long B-ligand bond should be ascribed to a combination of electronic (increase of boron's p-orbital occupancy) and steric effects, both more pronounced in complexes with the less nucleophilic formaldehyde. Although    P,N)).

Chloride affinity of cations 4-20
The chloride anion binding enthalpies (DH), energies (DE), LMOEDA results and boron-chlorine bond lengths are listed in Table 3. Gas-phase results are analyzed rst and solvent effects are included in the last paragraph of this section.
Since the formation of chloride-adducts involve oppositely charged species, all binding energies are signicantly larger than the previous ones. Binding enthalpies/energies span a range from DH/DE ¼ À119.4/119 kcal mol À1 for the weakest acceptor 20 (N,N) to DH/DE ¼ À165.3/165.3 kcal mol À1 for the strongest acceptor 5 (F,F). DHs and DEs are more similar in this case (R 2 ¼ 0.999) and do not differ by more than 1.7 kcal mol À1 (the majority of values differ by less than 1 kcal mol À1 ). Deformation energies are larger with respect to the corresponding values calculated for NH 3 -and HCHO-complexes, which could be ascribed to larger nucleophilicity of Cl À . They range from 22.2 kcal mol À1 for 4 (H,H) to 50.2 kcal mol À1 for 17 (N,S). In this case, these energies correspond solely to deformation of borenium ion upon its reaction with Cl À . Boron-chlorine bond lengths vary from 1.833Å in 6-Cl to 1.913Å in 20-Cl. The LMOEDA shows that the nature of chloride-borenium cation interactions is primarily electrostatic. Percentage contribution of DE elstat to all attractive interactions amounts 54.7-59.5%. Next come orbital interactions, contribution of which ranges from 33.2-38.5%, and the smallest stabilization is provided by dispersion forces, 6.8-8.6%. Contribution of the latter is also smaller than in NH 3 -and HCHO-complexes, which is expected for charged species.
The order of Cl À affinities differ from the order of NH 3 and HCHO affinities. This could be related to Cl À increased nucleophilicity and stronger attractive forces with a cation, while Pauli repulsive energies compare with those observed for NH 3adducts. Thus, cation 5 (F,F) binds chloride more strongly than cation 4 (H,H) (by DH ¼ 2.8 kcal mol À1 ), which originates from somewhat altered balance between interaction and deformation energies: DE int overcomes DE def to the extent that the total binding energy in 5-Cl exceeds the value in 4-Cl. Next comes the affinity of cation 6 (Cl,Cl), which is quite similar to that of 4. In the case of NH 3 and HCHO as ligands, the binding enthalpies of 4 and 6 differ by $9.5 kcal mol À1 . This can also be explained by the altered balance between DE int and DE def . In the adduct 6-Cl, DE elstat and DE oi are very favourable, and are the strongest compared to all other chloride-adducts. Dispersion interactions in 6-Cl are exceeded only by those in 9-Cl and 10-Cl, obviously due to the presence of polarizable p-electrons in the latter two. These strong attractive forces in 6-Cl are also attenuated by the large Pauli repulsion and deformation energy, which are both higher than those in 4-Cl. In fact, the two chlorine substituents in 6 also provide the strongest DE elstat and DE oi in  ] + compared to all other ammonia-complexes, and very strong electrostatic and orbital interactions in [6-HCHO] + , exceeded by only those in [8-HCHO] + . The existence of strong attractive interactions in the case of 6 is also evident in very short B-L 0 bonds. The chloride affinity of 8 (P,P) (DH/DE ¼ À144.4/À144.8 kcal mol À1 ) is slightly stronger than that of 7 (Me,Me) (DH/DE ¼ À143.3/À144.3 kcal mol À1 ) which differs from the order of NH 3 and HCHO affinities. This again comes from a somewhat altered balance between DE int and DE def , because all interaction energy components, as well as DE def , are larger in the case of 8 and this concurs with NH 3 -and HCHO-adducts. [CatBNH 3 ] + 11 binds Cl À slightly stronger (DH/DE ¼ À139.8/À139.5 kcal mol À1 ) than 9 (Me,Ph) (DH/DE ¼ À138.3/À139.3 kcal mol À1 ) and stronger than 10 (Ph,Ph) (DH/DE ¼ À136.2/À136.2 kcal mol À1 ). Since DE int in 9-Cl and 10-Cl is very similar to DE int in 7-Cl, weaker Cl À affinity of 9 and 10 compared to 7 is associated with larger deformation energies. The reversed order of Cl À affinities, 11 being stronger acceptor than 9 and 10, comes from the short B-Cl bond in 11-Cl, which is by $0.05Å shorter than in 9-Cl and 10-Cl. This leads to favourable DE int , which now overcomes DE def to the larger extent.
Among the heterocycle-containing borenium cations 8 and 12-20, the affinity of 8 (P,P) toward Cl À is the largest (DH/DE ¼ À144.4/À144.8 kcal mol À1 ), next coming that of 12 (P,S) (DH/DE ¼ À137.4/À137.5 kcal mol À1 ). This concurs with NH 3 and HCHO affinities. Chloride affinities then follow the trend:  (N,N), which partly reects chloride steric demand. Thus, in the case of 8 and 12-16, the affinity drops as the sum of the two B-R/ R 0 bonds become smaller, though it is clear that DHs/DEs are determined by the nal B-Cl distances, which do not follow the same trend. In fact, the worst correlation between DHs/DEs and B-L 0 distances was found for Cl À as a ligand, suggesting that Cl À interactions with other atoms are least dependent on its proximity to boron. The regularity between Cl À affinity and the sum of the two B-R/R 0 bonds does not hold for nitrogen-containing heterocyclic ions 17-20. Here, a decrease in interaction energy fully follows the trend in binding enthalpies/energies (not found for NH 3 and HCHO ligands). This trend of decreasing DE int is mostly determined by the magnitudes of orbital interactions, the drop of which is the most prominent. However, this should not be attributed only to electron-donating properties of heteroatoms connected to boron, since boron's p-orbital electron occupancy does not follow the same trend: it is the highest for 17 (N,S) having the largest Cl À affinity and highest DE oi among the four cations, 17-20, and the shortest B-Cl bond in the adduct. Obviously, other charge transfer interactions, polarization and electrostatic stabilization play an important role in determining the magnitude of total binding interactions.

Ammonia affinities of cations 21-29
Ammonia affinities of cations 21-24 and 26-29 range from DH/ DE ¼ À21/À23.8 kcal mol À1 for 21 (L ¼ Me 2 S) to DH/DE ¼ À4.2/ À6.6 kcal mol À1 for 29 (L ¼ 2,6-lutidine). As mentioned before, interaction of 25 (L ¼ PH 3 ) with NH 3 results in PH 3 substitution. Except for 29, DHs and DEs show the same trend, with R 2 ¼ 0.997. Deformation energies range from 26.1 kcal mol À1 for the complex formation from 27 (L ¼ 1,3-dimethylimidazol-2ylidene) to 39.6 kcal mol À1 for the association of ammonia with 22 (L ¼ Me 2 O). Apart from   Replacement of ammonia ligand L in 18 with weaker nucleophiles (better leaving groups) such as Me 2 S in 21 and Me 2 O in 22 increases NH 3 affinity by 2.3 kcal mol À1 and 1.6 kcal mol À1 , respectively. The B-NH 3 distance in a complex reduces by $0.028Å. In fact, nitrogen from the incoming NH 3 ligand forms stronger bond with boron than sulfur and oxygen from dimethyl(thio)ether, resulting in a signicant increase in the B-SMe 2 and B-OMe 2 bond lengths by 0.201Å and 0.214Å, respectively. The presence of L ¼ NMe 3 in 23 and L ¼ PMe 3 in 24 decrease complex formation enthalpies by 4.2 kcal mol À1 and 5.4 kcal mol À1 , respectively, compared to 18. Since DE def are smaller than in the case of 18, weaker NH 3 affinity of 23 and 24 is associated with a decrease in the DE int . Thus, substitution of L ¼ NH 3 in 18 with the larger ligand NMe 3 increases the B-NH 3 distance by 0.016Å. This, in turn, weakens orbital and electrostatic stabilization by 4.6 kcal mol À1 and 2 kcal mol À1 , respectively. Otherwise, charge transfer interactions corresponding to the B-NH 3 bond formation should be increased due to the somewhat lower boron's p-orbital occupancy in 23 (0.438e) than in 18 (0.457e). The NMe 3 stabilizing ligand brings about larger Pauli repulsion in the complex, though larger by only 2.8 kcal mol À1 with respect to that in  ] + . The complex geometry is obviously adjusted to escape strong repulsive interactions, for example by somewhat increased cation-ligand distance. As data in Table 4 show, even in this case the dispersion interactions are larger in  ] + than in [18-NH 3 ] + . The presence of phosphorus in 24 instead of nitrogen in 23 leads to the shorter B-NH 3 bond, quite similar to that in  ] + , and larger electrostatic and orbital stabilization. The ammonia approach is here less hindered due to the longer B-PMe 3 bond (1.939Å) with respect to B-NMe 3 bond (1.535Å). What makes 24 to be weaker NH 3 acceptor than both 18 and 23 is complex destabilization by larger Pauli repulsion.
All carbene-stabilized cations 26-28 form more labile adducts with ammonia than all the previously discussed ones. The DHs/ DEs decrease in the order: 26 (DH/DE ¼ À8.8/À10.8 kcal mol À1 ) > 27 (DH/DE ¼ À6.3/À8.2 kcal mol À1 ) > 28 (DH/DE ¼ À4.8/À6.3 kcal mol À1 ). These cations keep ammonia at relatively long distance, 1.694-1.715Å, resulting in smaller Pauli repulsion, but also in weaker attractive energies (DE elstat and DE oi ). Calculated boron's p-orbital occupancy amounts 0.441e in 26, 0.436e in 27 and 0.430e in 28, which are all smaller than in 18 (0.457e) and majority of cations 21-24 (Table S3 †). This means that the lower NH 3 affinities of 26-28 do not originate from smaller capability of boron's p-orbital to accept an electron pair. Rather, it seems as if steric factors interfere with ligand approach, keeping it somewhat farther from boron and thus decreasing the cation-L 0 interaction energy. This is the cause of smaller binding energy of these cations, since DE def is also smaller than in the case of 18 and 21-24. Among the three carbene-stabilized cations, 26 (L ¼ 3-methylthiazole-2-ylidene) shows the highest affinity and 28 (L ¼ 1,3-dimethybenzimidazole-2-ylidene) is the weakest NH 3 acceptor. Higher affinity of 26 comes from more favourable DE int , related to the smaller steric hindrance to ligand approach and shorter B-N bond. Only in [26-NH 3 ] + the 1,3,2-oxazaborolidine The weaker NH 3 affinity of 29 relative to affinities of 26-28 stems from an increased deformation energy needed to accommodate NH 3 . The most favourable geometry of cation 29, having the two rings in an orthogonal position, must change to a wing-shaped one to allow NH 3 to approach boron atom. When the complex is formed, the interaction energy becomes more stabilizing than in adducts formed from 26-28.

Formaldehyde affinities of cations 21-29
Formaldehyde affinities of cations 21-28 span a narrow range from DH/DE ¼ À10.2/À11.5 kcal mol À1 for 24 (L ¼ PMe 3 ) to DH/ DE ¼ À6.5/À8.2 kcal mol À1 for 23 (L ¼ NMe 3 ), and are all smaller than the affinity of 18 (L ¼ NH 3 ). As mentioned before, 29 (L ¼ lut) forms only hydrogen-bonded complex with HCHO. The trend in DHs and DEs is the same, having R 2 ¼ 0.929. Interaction and deformation energies vary greatly (Table 4)  The LMOEDA shows that in all adducts having long boronligand distances the percentage contributions of electrostatic and dispersion forces (42.5-46.7% and 38.1-43.5%, respectively) to all attractive interactions is much greater than the contribution of orbital interactions (3.3-16.5%). Therefore, they should be considered as electrostatic-dispersion adducts rather than coordinate covalent ones. In other complexes, the percentage contributions of the three attractive interactions are more similar to those found for adducts derived from 4-20.
It is not clear why 24 forms an adduct with such a long B-OCH 2 . Steric factors may be involved, and they are more prominent in the case of the less nucleophilic HCHO than for NH 3 and Cl À . Nevertheless, the weak DE int in [24-HCHO] + is counteracted by the very small energy required to deform fragments at such large distances, and is strong enough to place 24 at the beginning of the affinity scale of 21-28. By contrast, its nitrogen counterpart 23 binds HCHO at shorter distance increasing both DE int and DE def , though they are still smaller than in the case of 18, due to longer B-OCH 2 distance. The latter could be induced by steric repulsion with NMe 3 in 23. The relative magnitudes of DE int and DE def determined the lowest HCHO affinity of 23 amongst 18, 21, 22 and 24-28. Due to longer B-ligand distance, the role of dispersion attraction in complex stabilization is increased in  + , at the expense of DE oi , compared to adducts derived from 4-20 and 21, 22, 24 and 25.
Cations 21, 22 and 25, containing better leaving groups L ¼ SMe 2 , OMe 2 and PH 3 , respectively, form complexes with short B-OCH 2 bonds which inherently increases interaction and deformation energies, compared to those corresponding for the complex formation from 18, 23 and 24. The 21, 22 and 25 are weaker HCHO acceptors than 18 and 24 just because of larger deformations, but stronger acceptors than 23 due to the increased interaction energy. The trend of decreasing HCHO affinities along the series 21 > 25 > 22 is determined by their DE def which increase in the same order, while DE int become more stabilizing. As in the case of NH 3 -complexes, the B-ligand distances in [21-HCHO] + and [22-HCHO] + are almost the same and the more favourable DE int for the latter results from smaller Pauli repulsion, whereas sulfur in 21 provides more electrostatic and orbital stabilization. The latter possibly comes from polarization part, since boron's p-orbital occupancy in 21 (0.474e) is higher than in 22 (0.447e).
The three carbene-stabilized cations 26-28 show quite similar affinities toward formaldehyde, which also compare with that of 22. The highest and the lowest enthalpy differ by only 0.6 kcal mol À1 , while ammonia affinities of cations 26 and 28 differ by $4 kcal mol À1 , which should be related to NH 3 closer approach to boron thus more inuencing interaction and deformation energy parts. In fact, 27 and 28 show smaller tendency to bind ammonia than to bind formaldehyde, while NH 3 and HCHO affinities of 26 are comparable.
The LMOEDA results show that the nature of the cationchloride interactions in adducts derived from 22-24 and 26-29 is the same as in adducts formed from 4-20: the main percentage contribution to all attractive interactions comes from DE elstat (55-58%), next come orbital interactions (33.1-37.4%), and dispersion forces provide the smallest contribution (7.6-9%).
As in the case of L 0 ¼ NH 3 and HCHO, substitution of L ¼ NH 3 in 18 for better leaving group OMe 2 in 22, decreases the B-L 0 distance. In the case of Cl À , the exocyclic B-O bond in 22 is signicantly elongated upon adduct formation, by 0.294Å, while the newly formed B-Cl bond is by 0.086Å longer than it would be if a full OMe 2 substitution occurred. Large geometry changes in the cation leading to high DE def are responsible for weaker Cl À affinity of 22 compared to 18, even though interaction energy increases by as much as 12.5 kcal mol À1 . When better nucleophiles than NH 3 are bound to boron, such as NMe 3 and PMe 3 in cations 23 and 24, respectively, the Cl À affinity drops by more than 10 kcal mol À1 . The presence of NMe 3 in 23 instead of NH 3 in 18 results in just a slight B-Cl bond elongation (<0.01Å), which is smaller than in the case of L 0 ¼ NH 3 and HCHO and can be attributed to the larger nucleophilicity of Cl À . The reason why 23 behaves as weaker Cl À acceptor than 18 lies in the smaller interaction energy, made such mostly by increase/decrease in the Pauli/electrostatic interactions, while orbital and dispersion interactions are more favourable in the case of 23. The B-Cl bond in 24-Cl is the same as in 23-Cl and smaller Cl À affinity of 24 relates to larger repulsive energy (by 8.2 kcal mol À1 ), but curiously to a drop in DE elstat by $3 kcal mol À1 and DE disp by 1.9 kcal mol À1 . This could be explained by the longer distances between Cl and atoms contained in the ligand L, due to longer B-P bond relative to B-N bond. The reason why 23 and 24 are weaker Cl À acceptors than 22 is a drop in DE int , related to longer B-Cl bonds, which outweighs the drop in DE def .
The Cl À affinities of carbene-stabilized cations 26-28 and lutstabilized cation 29 are all within 1.5 kcal mol À1 , the highest affinity found for 26 (L ¼ 3-methylthiazole-2-ylidene) and the lowest for 27 (L ¼ 1,3-dimethylimidazole-2-ylidene). Cation 26 binds Cl À at shorter distance than the related cations 27 and 28, resulting in signicantly higher interaction energy, but also more energy costly geometry changes (near-to-planar geometry in 26 becomes orthogonal in the adduct, with Cl being positioned at the sulfur side of thiazole ring). Their relative magnitudes are such that 26 shows slightly higher affinity toward Cl À than 27 and 28, whose affinities are the same. Although, 29-Cl formation results in a (signicantly) more favourable interaction energy than the adduct formation from the carbene-stablized ions 26-28, the high deformation energy places the Cl À affinity of 29 close to those of 26-28. In this case, too, high DE def mostly originates from cation geometry change from orthogonal to the wing-shaped, which is necessary in order to make a space for the incoming ligand.
Generally, borenium cations 21-25 having L with sp 3hybridized heteroatom possess higher affinities toward a new ligand L 0 than carbene-stabilized cations 26-28 and lutstabilized cation 29. In the case of 29, its weak affinity is determined by high DE def and smaller DE int , the latter partly related to the longer B-L 0 distance compared to that in adducts derived from 21-25. The smaller binding energies of 26-28 have to be attributed to lower interaction energies, which is primarily due to the long B-L 0 distances, particularly in the case of HCHOadducts. The relative order of L 0 affinities compares when L 0 ¼ NH 3 and Cl À , but differs signicantly when L 0 ¼ HCHO.

Conclusions
In this paper, we have theoretically studied borenium ion affinities toward the three ligands: L 0 ¼ NH 3 , HCHO and Cl À . General trend in both gas-and liquid-phase is such that R/R 0 ¼ H, F, Cl provide the strongest L 0 binding. Then come cations with R/R 0 ¼ Me and P, the latter contained in the ve-membered heterocycle. Substitution of Me groups with one or two Ph decreases affinity toward the L 0 (in solvent conditions the inuence on Cl À affinity is opposite). Cat-containing cation shows higher affinity than other studied heterocycle-containing cations, in which R/R 0 ¼ O, S, N and P, except the cation 8 (P,P) in the gas-phase, and 8 and 12 (P,S) in the solvent, when L 0 ¼ NH 3 and HCHO. The high calculated affinity of 8 has been attributed to the long B-P bonds, which sterically least impedes with ligand approach. Among the heterocyclic cations, those that possess O, S and P as heteroatoms show stronger tendency to bind new ligand than nitrogen-containing ones. The variations of L showed that, with two exceptions, Me 2 S-, Me 2 O-, H 3 N-, Me 3 N-and Me 3 P-stabilized borenium cations bind L 0 more strongly than carbene-and 2,6-lutidine-stabilized cations.
When L ¼ constant, the observed trend is determined by the cation-ligand distances and type of substituents R/R 0 . It was found that heteroatoms from the second octal row of the periodic table (P, S, Cl) provide larger electrostatic and orbital stabilization than heteroatoms from the rst row (N, O, F) and it appears that the stabilizing effect increases when going from le to the right in the period. However, the repulsive Pauli energy is also stronger for larger heteroatoms. Phenyl substituents show larger electrostatic, orbital and dispersion stabilization than methyl groups, but also larger repulsion. It is the relative magnitude of attractive and repulsive interactions, along with the B-L 0 distance that determines the overall interaction energy. When L 0 ¼ NH 3 and HCHO, the B-L 0 distance is determined by the three factors: (1) steric effects, in the case of 4-20 mostly related to the B-R/R 0 bond lengths (as they are longer, approach to the boron atom is easier), (2) substituent electronic effects inuencing boron's p-orbital occupancy and (3) net attractive forces. Thus, the B-L 0 distance is longer when one or both heteroatoms are nitrogen, and shorter for R/R 0 ¼ H, F, Cl and P. No such regularity was found for the more nucleophilic Cl À . When R/R 0 ¼ constant, the B-L 0 distances are generally longer when L ¼ carbene and shorter when L ¼ S(O)Me 2 .
We have to keep in mind that the total binding enthalpies/ energies are not determined only by the magnitude of cationligand interaction energy. There is another factor that inuences DHs/DEs: the energy that has to be spent to deform the two interacting molecules from their equilibrium geometry to that they have in a complex. Therefore, predictions and rationalizations of DHs/DEs must consider both DE int and DE def . For example, 29 (L ¼ 2,6-lutidine) interacts more strongly with NH 3 than any of the carbene-stabilized cations 26-28, but its NH 3 affinity is the weakest because this cation has to undergo a signicant conformational change in order to bind the L 0 .