On the multiple B–N bonding in boron compounds using the topological analysis of electron localization function (ELF)

Abstract

Topological analysis of the Electron Localization Function (ELF) within the framework of Quantum Chemical Topology (QCT) has been applied to study the nature of the boron–nitrogen bonds. A series of 10 compounds have been chosen, with the B–N bond length ranging between 1.698 Å (B–N) and 1.258 Å (B≡N). According to the Lewis formula three types of bonds have been recognized. These are: the single B–N bond with a basin population of 1.91 ÷ 2.09e, the double B=N bond with a population of 3.78 ÷ 4.28e, and the triple B≡N bond with a basin population of 5.72 ÷ 5.74e. In the case of partial double bonds (B[horiz bar, triple dot above]N), where formally two or more resonance hybrids have to be considered, our calculations strongly support the concept of double boron–nitrogen bonding (B=N).

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1. Introduction

After Quantum Chemical Topology† (QCT) method¹ based on the topological analysis of the electron localization function (ELF)^8,9 was introduced for modern bond analysis,^10–12 the majority of chemists wanted to find a correlation between the mathematical definition of bonding through the ELF-localization basin associated with its attractor,⁹ and the classical Lewis representation.¹³ Although the Lewis formula¹³ was introduced before the quantum chemistry era, a representation of the multiple covalent bond (A–A, A=A, A≡A) with shared electron pairs was confirmed through the concept of σ and π-orbitals in molecular orbital (MO) and valence-bond (VB) theories.^14–16 It is worth mentioning that another QCT method, based on topological analysis of the electron density, AIM^17–19 relates the multiple character of the chemical bond through the ellipticity parameter, calculated for the bond critical point.

In general, there is no direct correspondence between the number of valence disynaptic attractors V_i(A,A) representing the multiple bond in topological analysis of ELF and the Lewis structure. For example, in molecules of cylindrical symmetry with a formal triple bond such as acetylene (HC≡CH) or dinitrogen (N≡N), only single bonding attractors (the ring V(C,C)^9,11,20–22 and the point type V(N,N)^9,11,20,23) are observed. Similarly, in formaldehyde (H₂C=O), a molecule of planar symmetry, only a single V(C,O) attractor is found.^11,24,25 On the contrary, in ethylene (H₂C=CH₂) two disynaptic attractors V_i=1,2(C,C) are localized.^11,21 As pointed out by Silvi et al.,¹¹ “the disynaptic basins multiplicity can be explained by symmetry considerations rather than by chemical arguments”.

The general rule of thumb, which applies to almost all circumstances, is that for a given pair of atoms longer bonds will be weaker, and shorter ones stronger. This can be explained by the fact that more electrons shared by two atoms leads to better attraction between the two nuclei. Since the number of electrons in the chemical bond can easily be obtained from topological analysis of ELF,^21,26 it is interesting to study the correlation between the formal bond order or bond length, and the basin population (N̄).

Savin et al.²¹ showed for the first time that such a correlation exists for the ethylene, propene, and trans-butadiene molecules, where formal double C=C bonds were characterised by larger basis populations (3.6 ÷ 3.7e) than the single C–C bonds (1.9 ÷ 2.2e). A comparative study on single, double and triple bonds for the first and second row hydrides, in context of the formal bond order and delocalization, has been undertaken by Chesnut.²⁵ He observed that molecules with increasing bond order displayed higher basin populations.

In a search for a correlation between formal multiple bonding (represented by Lewis structures) and its ELF-topological characterisation, we focus on the very interesting case of boron–nitrogen bonds, important in the area of nanotubes.²⁷ The boron atom contains empty p-orbitals interacting with occupied p-orbitals of nitrogen, so π-bonding (the so called dative pπ–pπ bonding) is responsible for multiple boron–nitrogen bonds. A set of boron compounds (Fig. 1) with the bond length ranging from 1.258 to 1.698 Å has been chosen. As previously reported by Straub,²⁸ they can be characterized as the B≡N, B=N, B[horiz bar, triple dot above]N and B–N bonds.

Fig. 1 Optimized structures of the molecules with multiple boron–nitrogen bonds.

In this paper we propose to answer the following questions:

1. Is it possible to confirm the concept of multiple boron–nitrogen bond on the grounds of QCT using topological analysis of the ELF function?

2. Can we observe the nitrogen lone pair participating in the donor–acceptor bonds (pπ–pπ bonding) with boronvia the non-bonding, monosynaptic basin V(N)?

3. Is there a correlation between the population of the V(B,N) basin representing the B–N bond and the bond length?

2. Computational details

Full optimization of geometrical structures with the Becke3LYP electron density functional^29–31 has been performed using the Gaussian 03 program.³² The pure 5d and 7f atomic orbitals are used. The minima on the potential energy surface have been confirmed by non-imaginary vibrational frequencies. In the case of B(NH₂)₃ the optimization was carried out with the D_3h symmetry, but it converged to a minimum on the PES only for the aug-cc-pVTZ^33,34 basis set.

Topological analysis of the ELF function has been carried out using the DGrid and DBasin-4.2 programs.³⁵ Graphical representations of molecules have been constructed using the ChemCraft and 3D-representations of ELF and 2D-maps using the VMD³⁶ program.

Comparative analysis of the basin populations has been performed using basis sets from 6-311++G(2d,2p)^37,38 upwards and no unexpected attractors have been found.

ELF analysis of the formally triple B≡N bond displays a number of localization basins, which have subsequently been merged into a single V(B,N) basin.

3. Results and discussion

For the single type B–N bond, three amine-boranes (X₃B–NR₃): (CH₃)₃B–N(CH₃)_3,(CH₃)₃B–NH₃ and H₃B–NH₃ (a well known prototype of the dative bond) were chosen. The respective experimental bond lengths (r_exp) are: 1.698 Å,³⁹ 1.629⁴⁰ and 1.672 Å.⁴¹ Geometry optimizations have been carried out using the 6-311++G(2d,2p), 6-311++G(2df,2pd), 6-311++G(3d,3p), 6-311++G(3df,3pd), aug-cc-pVTZ basis sets, and the calculated B–N bond lengths (r_opt) are presented in Table 1. The mean values of r_opt are: 1.784, 1.703, and 1.657 Å, differing from the experimental ones by 0.086, -0.074, and -0.015 Å respectively. These results confirm previously observed difficulties in modelling of the dative BN bond.⁴² This problem increases with the addition of methyl groups. In our opinion such discrepancies do not influence the results of bond analysis using ELF.

Table 1 The optimized and experimental lengths of the boron–nitrogen bond. The B3LYP method has been used

Compound	Formal bond order	Bond length (exp)/Å	Bond length (ropt) (calc)/Å
			6-311++G(2d,2p)	6-311++G(2df,2pd)	6-311++G(3d,3p)	6-311++G(3df,3pd)	aug-cc-pVTZ	Mean value
a The geometrical structure has been optimized under D3h symmetry point group. b The experimental B=N bond length determined in solid state for the Cl2BN(C6H5)2 molecule.^44
tBuBNtBu	B≡N	1.258	1.241	1.241	1.240	1.240	1.241	1.241
(CH3)3C6H2BNtBu	B≡N	1.232	1.242	1.242	1.236	1.241	—	1.240
H2BNH2	B=N	1.391	1.388	1.389	1.389	1.388	1.390	1.389
Cl2BN(H)C6H5	B=N	1.379^b	1.397	1.399	1.398	1.399	1.400	1.399
HB(NH2)2	B[horiz bar, triple dot above]N	1.418	1.413	1.413	1.413	1.412	1.414	1.413
B(NH2)3^a	B[horiz bar, triple dot above]N	—	1.430	1.430	1.430	1.429	1.431	1.430
B(N(CH3)2)3	B[horiz bar, triple dot above]N	1.439	1.442	1.443	1.442	1.442	1.443	1.442
H3BNH3	B–N	1.672	1.658	1.657	1.657	1.657	1.658	1.657
(CH3)3BNH3	B–N	1.629	1.703	1.702	1.704	1.702	1.706	1.703
(CH3)3BN(CH3)3	B–N	1.698	1.780	1.787	1.783	1.785	1.786	1.784

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A detailed study of the donor–acceptor bond in the H₃B–NH₃ molecule has been previously reported by Krokidis et al.,⁴³ who adopted catastrophe theory for a systematic description of the B–N bond evolution during dissociation. It has been shown that dissociation into H₃B and NH₃ fragments results in change of the disynaptic V(B,N) basin into the monosynaptic V(N) in ammonia. Such behaviour is considered a proof of existence of the dative bond. In the case of “normal” covalent bonds A–B (for example in C₂H₆), a dissociation process yields two non-bonding basins V(A), V(B) on the separated fragments A, B.

For (CH₃)₃B–N(CH₃)_3,(CH₃)₃B–NH₃ and H₃B–NH₃ molecules, topological analysis of the ELF function reveals the bonding disynaptic basin V(B,N), and an associated single point attractor situated at the interatomic B–N axis. From a topological point of view such attractors and basins characterize the boron–nitrogen bonding as covalent,⁹ displaying a one-to-one correspondence with the Lewis formula. The V(B,N) localization basin is observed close to the atomic C(N) core, and resembles the distorted lone electron pair V(N) in isolated NH₃ or N(CH₃)₃ molecules.

The basin populations calculated with different basis sets are presented in Table 2. The amount of electron density “concentrated” in the V(B,N) basin does not deviate significantly from 2.0e. It is important to stress that these values are in a good agreement with the classical concept of a single shared electron pair. The largest population is obtained for the (CH₃)₃B–N(CH₃)₃ molecule (2.07 ÷ 2.11e), and its value slightly diminishes along with a decrease in the number of methyl groups. The mean values of the basin populations of V(B,N) are as follows: 2.09, 1.94 and 1.92e for (CH₃)₃B–N(CH₃)_3,(CH₃)₃B–NH₃ and H₃B–NH₃, respectively. Therefore, as the number of CH₃ groups in the system increases, there is an increase in the population on the B–N bond, thus confirming the electron-releasing character of the CH₃ group.

Table 2 The basin population of the boron–nitrogen bonds of different multiplicity calculated by means of topological analysis of the electron localization function (ELF)

Compound	Formal bond order	V(B,N) N̄[e]
		6-311++G(2d,2p)	6-311++G(2df,2pd)	6-311++G(3d,3p)	6-311++G(3df,3pd)	aug-cc-pVTZ	Mean value
a The total basin population of two bonding disynaptic basins Vi=1,2(B,N) is presented. b The geometrical structure of the B(NH2)3 molecule has been optimized under D3h symmetry point group tBu-tert-butyl.
tBuBNtBu	B≡N	5.77	5.75	5.75	5.72	5.73	5.74
(CH3)3C6H2BNtBu	B≡N	5.73	5.72	5.72	5.69	—	5.72
H2BNH2^a	B=N	3.86	3.74	3.78	3.74	3.80	3.78
Cl2BN(H)C6H5	B=N	3.98	3.93^a	3.89	3.85^a	3.91^a	3.91
HB(NH2)2	B[horiz bar, triple dot above]N	4.04	3.99	3.97	3.93	3.99	3.98
B(NH2)3^b	B[horiz bar, triple dot above]N	4.13	4.09	4.07	4.03	4.09	4.08
B(N(CH3)2)3	B[horiz bar, triple dot above]N	4.31	4.28	4.26	4.24	4.29	4.28
H3BNH3	B–N	1.93	1.91	1.90	1.89	1.92	1.91
(CH3)3BNH3	B–N	1.97	1.94	1.93	1.91	1.94	1.94
(CH3)3BN(CH3)3	B–N	2.11	2.08	2.08	2.07	2.09	2.09

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It is worth stressing that analysis of the correlation between the B–N bond lengths, decreasing from (CH₃)₃B–N(CH₃)₃ to H₃B–NH₃ (see Table 1), and the basin population of V(B,N), does not show the evidence to support the rule of “concentrating” a larger amount of electron density on the shorter bond. The B–N bond lengths (mean value) of 1.784, 1.703, 1.657 Å correspond to populations of 2.09, 1.94, 1.91e respectively, a completely opposite effect.

According to Paetzold,⁴⁴ a boron–nitrogen separation of 1.41 Å may be considered as indicative of the double B=N bond (in noncyclic aminoboranes), and 1.26 Å as a typical B≡N triple bond. For that reason, the B(N(CH₃)₂)₃, B(NH₂)₃, HB(NH₂)₂, H₂B=NH₂, and Cl₂B=N(H)C₆H₅ molecules (see Fig. 1) will be discussed together, even if B(N(CH₃)₂)₃ and HB(NH₂)₂ have been considered by Straub²⁸ as molecules with partially double B[horiz bar, triple dot above]N bonds. The mean values of the optimized B[horiz bar, triple dot above]N bond lengths in B(N(CH₃)₂)₃, B(NH₂)₃, HB(NH₂)₂ are 1.442, 1.430 and 1.413 Å, respectively (see Table 1). These values are in good agreement with the experimental data reported for B(N(CH₃)₂)₃⁴⁴ and HB(NH₂)₂^45,46 at 1.439 Å and 1.418 Å, respectively. The mean value of B=N optimized bond lengths in aminoborane H₂B=NH₂ (an analogue of ethane) is 1.389 Å, and is in very good agreement with the experimental value obtained from microwave spectra (1.391 Å).^47–49 In the case of the Cl₂B=N(H)C₆H₅ molecule, the average B=N bond length is 1.399 Å.

The boranediamine (HB(NH₂)₂) is molecule with formally partial double B[horiz bar, triple dot above]N bond therefore the nature of its bonding will be discussed in detail. Two nitrogen atoms with occupied non-bonding orbitals tend to share one vacant boron p-orbital, so two resonance hybrids with alternating B–N and B=N bonds can be introduced in accordance with the octet rule (see Scheme 1, hybrids I, II). Such an approach predicts the existence of the non-bonding electron density on the nitrogens, which is reflected in topological analysis of ELF by the non-bonding basins V(N). However, another resonance hybrid with two double B=N bonds can be proposed, violating the octet rule (see Scheme 1, hybrid III). In this case, the non-bonding basins V(N) are not present. The link between the Lewis representation of the chemical bonds and the topological partitions of the electron distributions, based on the gradient field analysis of local functions was proposed by Silvi.⁵⁰ The basin population operators are correlated, therefore the covariance matrix of the basin populations was chosen to be a tool for the description of the electron density delocalisation, in terms of resonant Lewis structures. On the other hand if direct correspondence to the Lewis-style representation can be applied, topological analysis of ELF should reveal two pairs of the Vi _=1,2(B,N) attractors, situated both above and below the symmetry plane. If such a correspondence cannot be applied, only two single V(B,N) attractors, located on the interatomic axis should be found. It is worth stressing that regardless of the number of the V(B,N) attractors, unique evidence of the existence of the double B=N bond can be obtained by analysing the number of valence electrons “contained” in the V(B,N) or Vi _=1,2(B,N) basins. In this case, the basin population value (N̄) will be close to the formal value of 4e.

Scheme 1 Three resonance hybrids for HB(NH₂)₂ molecule.

Analysis of the results for HB(NH₂)₂ shows all attractors localized in the molecular plane, and the vicinity of the boron–nitrogen bond is described by a single V(B,N) attractor. All localised attractors and 3D representation of ELF for HB(NH₂)₂ are presented in Fig. 2. According to the classification of chemical bonds proposed by Silvi and Savin,⁹ the boron–nitrogen bonds are covalent. It is remarkable that the non-bonding V(N) attractors are not observed. Thus the resonance hybrids I, II (see Scheme 1) with the lone pairs on nitrogen do not correctly describe the electronic structure of HB(NH₂)₂. Calculated mean value of the basin population equal to 3.98e is in good correspondence to the expected value of 4e (the B=N bond). It is evident that the boron–nitrogen bonds have a real double bond character. The hybrid III, one of the three resonance hybrids shown in Scheme 1, is the most dominant. Because the basin population of the H–N bond varies between 1.87 and 1.97e, and the B–H bond population is within the range of 2.05 ÷ 2.09e, the resonance hybrids with H⁺ N⁻, H–N bonds and a small negative polarization of the B–H bond must also be taken into consideration.

Fig. 2 The valence and core attractors localized in the gradient field of ELF for HB(NH₂)₂ molecule. The Lewis structure with double B=N bonds is shown. The 2D plot of the ELF function in molecular plane. The basin populations are calculated at the B3LYP/aug-cc-pVTZ level. Positions of protonated attractors V(H,B), V(H,N) and V(H1,N) are displayed (black dots) in a schematic way.

The results of topological analysis for HB(NH₂)₂ are in a good agreement with an infrared and Raman spectroscopy study on the boron–nitrogen bond in boranediamine, which confirms that the BN bond is predominantly of a double bond character.⁴⁶ Microwave studies also support its partial double bond nature.⁴⁵

Topological analysis of ELF for B(N(CH₃)₂)₃ and B(NH₂)₃ reveals single bonding disynaptic basins V(B,N) in the boron–nitrogen bond area. All attractors localized in the B(N(CH₃)₂)₃ molecule are shown in Fig. 3. 2D and 3D representations of ELF for B(NH₂)₃ are presented in Fig. 4. According to the classification of chemical bonds proposed by Silvi and Savin,⁹ the boron–nitrogen bonds characterised as formally containing partial double character are covalent. Analysis of ELF-isosurfaces reveals that the bonding basin V(B,N) is contained in a large localization domain surrounding the core nitrogen C(N) basin and the protonated basins V(H,N). However, such a topological feature cannot be considered an indication of dative character.

Fig. 3 The valence and core attractors localized in the gradient field of ELF for B(N(CH₃)₂)₃ molecule. The Lewis structure with double B=N bonds is shown.

Fig. 4 The valence and core attractors localized in the gradient field of ELF for B(NH₂)₃ molecule. The Lewis structure with double B=N bonds is shown. The 2D plot of the ELF function in molecular plane. The basin populations are calculated at the B3LYP/aug-cc-pVTZ level. The positions of the protonated attractors V(H,N) are presented (black dots) in a schematic way.

Because each of the lone pairs associated with the three nitrogen atoms of the N(CH₃)₂ and NH₂ groups in B(N(CH₃)₂)₃ and B(NH₂)₃ interacts with a single vacant orbital on boron, three resonance hybrids (I–III) are proposed (see Scheme 2) to satisfy the octet rule. The resulting covalent-dative B[horiz bar, triple dot above]N bonds model assumes the presence of the non-bonding electron density on each nitrogen with population less than 2e. Thus the monosynaptic non-bonding basins V(N) should be observed in the ELF picture. On the other hand, another resonance hybrid (IV), with three covalent-dative B=N bonds and without non-bonding electron density on the N atom can be proposed (see Scheme 2). These two different models of the bonding, verified by topological analysis of ELF and showing no non-bonding attractors V(N), are presented in Fig. 3 and Fig. 4. It is apparent that topologically the BN bonding in B(N(CH₃)₂)₃ and B(NH₂)₃ displays properties of the double B=N bond.

Scheme 2 Four resonance hybrids for B(NH₂)₃ molecule.

Mean values of the basin populations calculated for V(B,N) using five basis sets (Table 2) range between 4.28e for B(N(CH₃)₂)₃ and 4.08e for B(NH₂)₃. It is evident that the boron–nitrogen bonds in B(N(CH₃)₂)₃ and B(NH₂)₃ have double bond character, represented by the B=N formula when the number of electrons “concentrated” in the bond (the disynaptic V(B,N) basin) is considered. Furthermore, this result supports the conclusion drawn on the basis of missing non-bonding basins V(N) in the ELF picture. The large basin population of V(B,N) in B(N(CH₃)₂)₃ (4.28e) can be connected to the polarisation of the C–N bonds, which “contain” only 1.62 ÷ 1.67e (V(C,N) basins), with the remaining electron density presumably transferred to the three B=N bonds.

A comparison between B(NH₂)₃ and HB(NH₂)₂ molecules reveals that one of the NH₂ groups in B(NH₂)₃ is replaced by the hydrogen atom. As a result, a smaller basin population of 3.98e for V(B,N) is obtained in comparison to the population of 4.08e for B(NH₂)₃. This can be associated with the smaller inductive effect of the H atom. It is worth noting that the V(B,N) basin populations around 4e computed for B(NH₂)₃ and HB(NH₂)_2, are also an effect of a depopulation of the N–H bonds (1.86 ÷ 1.89e). The “missing” electron density (in respect to the formal value of 2e) is distributed to the B=N bonds. The difference in basin population of V(B,N) in B(N(CH₃)₂)₃ and B(NH₂)₃ (4.28evs. 4.08e) can be considered as an illustration of the inductive effect of the methyl and amine groups. The smaller basin population (4.08e) of V(B,N) in B(NH₂)₃ can be explained by smaller electron-donating effect of the NH₂ group compared to N(CH₃)₂. Fourré et al.⁵¹ studied the electron withdrawing group (−I) and electron donating group (+I) effects using topological analysis of ELF function. They found that a very short ranged inductive effect was essentially localized on the valence basins related to the carbon-X bonding.

The H₂B=NH₂ and Cl₂B=N(H)C₆H₅ molecules formally contain a B=N double bond. 2D and 3D plots of the ELF function are presented in Fig. 5 and Fig. 6. Interestingly, the largest basis set aug-cc-pVTZ^33,34 yields B=N bonds described by two bonding disynaptic attractors Vi _=1,2(B,N), localized above and below the symmetry plane. This result is in accordance with the Lewis formula. Such topology of ELF is obtained for H₂B=NH₂, regardless of the basis set used. On the contrary, the results for the Cl₂B=N(H)C₆H₅ molecule display dependence on the basis set used. Calculations performed with the 6-311++G(3d,3p) and 6-311++G(2d,2p) basis sets yield only a single V(B,N) attractor. It is worth stressing that the monosynaptic non-bonding basins V(N) are not observed (see Fig. 5 and Fig. 6). Moreover, topological description of B(N(CH₃)₂)₃, B(NH₂)₃, HB(NH₂)₂, as well as H₂B=NH₂ and Cl₂B=N(H)C₆H₅ molecules, does not show any evidence for B[horiz bar, triple dot above]N partial double bonds.

Fig. 5 The valence and core attractors localized in the gradient field of ELF for H₂B=NH₂ molecule. The Lewis structure with double B=N bonds is shown. The 2D plot of the ELF function in plane perpendicular to molecular plane. The basin populations presented are calculated at the B3LYP/aug-cc-pVTZ level. Positions of protonated attractors V(H,B), V(H,N) are presented (black dots) in a schematic way.

Fig. 6 The ELF-localization basins and valence and core attractors localized in the gradient field of ELF for Cl₂B=N(H)C₆H₅ molecule. The 2D plot of the ELF function in molecular plane. The basin populations presented are calculated at the B3LYP/aug-cc-pVTZ level.

The sum of basin populations for the B=N bond [V₁(B,N)+V₂(B,N)] is 3.74 ÷ 3.86e for H₂B=NH₂ and 3.85 ÷ 3.98e for Cl₂B=N(H)C₆H₅. These values confirm that formal characterization of the B=N bond as a double bond is correct. However, a resonance of equilibrium forms has to be invoked in order to correctly describe basin population values of less than 4.0e.

In the case of single B–N bonds, we have noticed that a shorter bond length does not correspond to a larger amount of electron density in the V(B,N) basin. The same effect is observed for molecules with formal B[horiz bar, triple dot above]N and B=N bonds. Along with decreasing B[horiz bar, triple dot above]N bond lengths (mean value) of 1.442, 1.430 and 1.413 Å for B(N(CH₃)₂)₃, B(NH₂)₃ and HB(NH₂)₂, respectively, the basin populations of V(B,N) decrease from 4.28, 4.08 to 3.98e. Similarly, for B=N bonds in H₂B=NH₂ and Cl₂B=N(H)C₆H₅ (mean bond lengths 1.399 and 1.389 Å, respectively), the basin populations of V(B,N) are 3.91 and 3.78e.

The formal triple B≡N bond has been investigated using two exemplar iminoborane molecules, (CH₃)₃C₆H₂B≡NtBu and tBuB≡NtBu (see Fig. 1), where the experimental (solid state) B≡N bond lengths are 1.232 Å for (tBu)₃C₆H₂B≡NtBu⁵² and 1.258 Å⁵³ for tBuB≡NtBu. The mean optimized values (see Table 1) are 1.240 and 1.241 Å.

Topological analysis of the ELF function shows a torus-like V(B,N) disynaptic basin situated between the C(B) and C(N) cores (see Fig. 7), with basin populations in the range 5.69 ÷ 5.73e for (CH₃)₃C₆H₂B≡NtBu, and 5.72 ÷ 5.77e for tBu-B≡NtBu (Table 2). There is no direct correspondence with the Lewis description since only one bonding basin V(B,N) is observed. Calculated values of the basin population (5.72e, 5.74e) are smaller than the value of 6e formally expected for the triple bond, but the topological bond orders 2.86 and 2.87 obtained from the mean values of N̄ strongly support the triple bond character.

Fig. 7 The ELF-localization basins in the (CH₃)₃C₆H₂–B≡N–tBu molecule. The basin populations presented are calculated at the B3LYP/6-311++G(2d,2p) computational level.

4. Conclusions

Topological analysis of the ELF within the QCT framework confirms that the ELF is a powerful tool for investigation of the multiple boron–nitrogen bonding character.

1. All studied molecules show covalent boron–nitrogen bonds described by the bonding basin V(B,N). Topological analysis of the ELF functions confirms the existence of the multiple boron–nitrogen bonds. Three different types can be distinguished, notably single B–N, double B=N and triple B≡N bonds with the disynaptic valence basins V(B,N), corresponding to chemical bonds containing 1.91 ÷ 2.09e, 3.78 ÷ 4.28e and 5.72 ÷ 5.74e, respectively. However, from a topological point of view there is no difference between the B=N double bonds in H₂B=NH₂, Cl₂B=N(H)C₆H₅ and B[horiz bar, triple dot above]N partial double bonds in B(N(CH₃)₂)₃, B(NH₂)₃, HB(NH₂)₂ distinguished by Straub.²⁸

2. The lone pair of nitrogen participating in the donor–acceptor bonds (pπ–pπ bonding) is not confirmed within the topological analysis of ELF framework. Even for the molecules with a single, empty p-orbital, shared by two or three lone pairs, for example HB(NH₂)₂, B(N(CH₃)₂)₃ or B(NH₂)₃, the non-bonding basins V(N), expected on a basis of the resonance hybrids, are not observed. Only single bonding basins V(B,N), are localized in the vicinity of the boron–nitrogen bonds

3. The results obtained in this study clearly show the correlation between the basin population, V(B,N), and the bond length. For different B–N bond types (e.g. single, double, triple), the shorter bond lengths usually correspond to a larger number of electrons in the V(B,N) basin. The opposite effect applies for the same type bonds (e.g. B=N), where the shorter bond length is related to the smaller number of electrons in the basin.

4. In general, there is no direct correspondence between the multiplicity of the BN bond and the number of localisation basins V_i(B,N). The exceptions are H₂B=NH₂ and Cl₂B=N(H)C₆H₅, where the formally double B=N bond is described by two Vi _=1,2(B,N) basins. The presence of the Vi _=1,2(B,N) basins depends on molecular symmetry and computational level.

Acknowledgements

The authors would like to thank the The Wroclaw Networking and Supercomputing Centre for generous allocation of computer time. Dr Charles M. Gordon is thanked for editing and proofreading the manuscript.

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Footnote

† The beginning of Quantum Chemical Topology (QCT) is associated with studies on topological properties of the electron density by R. Bader, who in the years 1979–1981 published a series of papers in which he used the term “quantum topology”.^2–6 However, the term “quantum topology” is also a branch of mathematical physics, exploring topological knot theory, quantum groups and quantum field theory.⁷

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