ORIGINAL PAPER

Borazine: to be or not to be aromatic

Rafael Islas Æ Eduardo Chamorro Æ Juvencio Robles Æ Thomas Heine ÆJuan C. Santos Æ Gabriel Merino

Received: 23 April 2007 / Accepted: 16 May 2007 / Published online: 31 August 2007

� Springer Science+Business Media, LLC 2007

Abstract Aromaticity of borazine, which has been sub-

ject of controversial discussions, is addressed. Beside a

short review on aromaticity of borazine we report a

detailed analysis of two molecular fields, the induced

magnetic field (Bind) and the electron localization function

(ELF). The induced magnetic field of borazine shows a

long-range shielding cone perpendicular to the molecular

plane, as in benzene, but lower in magnitude. Contrary to

benzene, borazine shows two weakly paratropic regions,

one of them inside the ring, and the second one enveloping

the boron atoms. It is necessary to separate r and p con-

tributions to identify whether borazine exhibits p-aromatic

character comparable to benzene. Nucleus-independent

chemical shift (NICS) isolines show that the r electrons are

much stronger localized than p electrons, their local para-

magnetic contributions generate a short-range response and

a paratropic (deshielding) region in the ring center (similar

to an anti-aromatic response). Three regions can be iden-

tified as chemically meaningful domains exhibiting an

internally strong electron delocalization (ELF = 0.823).

Borazine may be described as a p aromatic compound, but

it is not a globally aromatic species, as the electronic

system is not as delocalized as in benzene.

Keywords Aromaticity � Borazine � ELF � NICS �Induced Magnetic Field

Introduction

The study of aromaticity in borazine has a long history. In

1926, Stock and Pohland synthesized this molecule by a

reaction of diborane and ammonia [1]. In 1940, Wiberg

proposed the alias of ‘‘inorganic benzol’’ for borazine

based on the fact that all the B–N bond lengths are

equivalent [2], which is the landmark of aromaticity for

hydrocarbons, and because the number of p electrons is the

same as in benzene [3]. However, due to the electronega-

tivity difference between boron and nitrogen, aromaticity

may be expected to be lower in borazine than in benzene.

Chemically, borazine has a preference for addition

reactions. It seems than even if borazine may be endowed

with some aromatic character, its reactivity behavior is not

driven toward reassembling the p-ring system. However,

Dedicated to the 70th birthday of Prof. Tadeusz Marek Krygowski.

R. Islas � J. Robles � G. Merino (&)

Facultad de Quımica, Universidad de Guanajuato,

Noria Alta s/n, Guanajuato, GTO CP 36050, Mexico

e-mail: gmerino@quijote.ugto.mx

E. Chamorro � J. C. Santos

Departamento de Ciencias Quımicas, Facultad de Ecologıa y

Recursos Naturales, Universidad Andres Bello, Republica 217,

Santiago, Chile

T. Heine

Institut fur Physikalische Chemie und Elektrochemie,

TU Dresden, 1062 Dresden, Germany

123

Struct Chem (2007) 18:833–839

DOI 10.1007/s11224-007-9229-z Electron delocalization and aromaticity

the group of Fornarini reported the first example of elec-

trophilic substitution on the borazine ring [4]. Based on

ab initio calculations, they showed that the most basic sites

of borazine are the nitrogen atoms, and its conjugate acid,

H3B3N3H4+, is similar in structure to the benzenium ion [5].

Kiran et al. calculated the protonation and methylation

energies of benzene, cyclobutadiene, and borazine [6].

Having in mind that substitution rather than addition is a

characteristic of benzene, the energetics of these reactions

could be an indicator of aromaticity. On this basis they

concluded that borazine should be considered as an aro-

matic molecule, though its aromaticity is about half of that

in benzene. Recently, Timoshkin and Frenking considered

dimerization enthalpies as a principle for evaluating aro-

maticity [7]. Based on this criterion, they summarized that

borazine is aromatic, with a degree of aromaticity of about

half of that of benzene.

Several energetic criteria of aromaticity have been

proposed [8]. They are based on assessments of energies

relative to reference systems. One of them is the aromatic

stabilization energies (ASE) [9]. Nevertheless, ASE

calculations depend strongly on the equations used

(isodesmic, homodesmotic, hyperhomodesmotic), the

adopted reference molecules, and the computational levels

and basis sets. For instance, while Fink and Richards used

the ASE via homodesmotic reactions with trans configu-

rations of the reference molecules for benzene

(22.1 kcal mol–1) and borazine (11.1 kcal mol–1) [10]

Schleyer et al. obtained different values of the ASE using

homodesmotic reactions for benzene (34.1 kcal mol–1) and

borazine (10.0 kcal mol–1) [11] with cis configurations of

the reference molecules.

Benker et al. performed a series of valence bond cal-

culations for borazine and for benzene in order to

determine the relative weights of individual standard Lewis

structures [12] In the delocalized resonance scheme of

borazine, the structure without double bonds and with three

lone electron pairs at the three nitrogen atoms is the major

contributor with a structural weight of 0.17, followed by

six equivalent Lewis structures with one double bond and

two lone pairs at two nitrogen atoms with weights of 0.08

each. They estimated the values of 54.1 and 45.8 kcal mol–1

for the delocalization energies of borazine and benzene,

respectively. Based on the resonance energies they con-

cluded that borazine has substantial aromatic character of

the same magnitude as benzene.

Recently, using the energy decomposition analysis

(EDA), Fernandez and Frenking found that the calculated

value for the total p bonding energy in borazine (–131.1

kcal mol–1) is significantly smaller than that for benzene

(–217.7 kcal mol–1) [13]. The EDA value for the p conjuga-

tion between three B-N p bonds, which gives the vertical

resonance energy of borazine, is also less (–70.4 kcal mol–1)

than in benzene (–107.7 kcal mol–1). According to the EDA

results, borazine is less stabilized by aromaticity than benzene.

Magnetically, borazine shows a singular behavior.

Fowler and Steiner computed the p and the total current

density induced by a magnetic field perpendicular to the

molecular plane of borazine [14]. They found that the pcurrents are localized in three islands of circulation on the

nitrogen atoms and concluded that borazine is moderately

aromatic. On the contrary, nucleus-independent chemical

shift (NICS) values suggest little or no evidence of ring

currents [11, 15], and Schleyer et al. suggested that bor-

azine is not aromatic due to the polar B–N bond [11]. In the

same line, magnetic susceptibility exaltation data, based on

group increment values, indicate no aromaticity for bor-

azine (–1.7 compared to benzene –13.7) [16]. Using the

spectral decomposition of the current, Steiner et al. sug-

gested that borazine is a non-aromatic system and supports

neither a diatropic nor a paratropic global ring current [17].

Soncini et al. probed that for aromatic, anti-aromatic, and

non-aromatic p-systems (benzene, cyclooctatetraene, bor-

azine), the characteristic pattern of current density leads to

a distinctive map for the p-contribution to the perpendic-

ular components of 1H shielding-density [18].

Other criteria have been employed to evaluate aroma-

ticity in borazine. Using the calculated charge densities and

Mulliken population analysis, Boyd et al. showed the

substantial decrease of the p-electron delocalization rela-

tive to benzene and the increase in ring bond polarities of

borazine [19]. Using the ring current index, Jug suggested

that borazine is moderately aromatic [20]. Using the Har-

monic Oscillator Model of Aromaticity (HOMA) model

and the Bird model, Madura et al. concluded that borazine

exhibits less aromatic character than benzene [21]. Pukhan

et al. compared a series of annelated acenes and their BN

analogs. NICS values in acenes suggest that aromaticity of

the inner rings is more pronounced than that of benzene,

whereas in the BN analogs of acenes there is no substantial

change in aromaticity of the individual rings. In contrast,

the topological analysis of molecular electrostatic potential

shows that acenes and their BN analogs are substantially

different, with BN-acenes showing more localized p-elec-

tron features compared to those of acenes [22].

According to the 1999 definition provided by IUPAC

(http://www.iupac.org/goldbook/AT06991.pdf), aromatic-

ity is the concept of spatial and electronic structure of

cyclic molecular systems displaying the effects of cyclic

electron delocalization which provide for their enhanced

thermodynamic stability (relative to acyclic structural

analogs) and tendency to retain the structural type in the

course of chemical transformations. The special case of

borazine shows that this definition is still not free of

controversy. Is borazine aromatic or not? In this article

we report a detailed analysis of two molecular fields, the

834 Struct Chem (2007) 18:833–839

123

induced magnetic field (Bind) [23] and the electron

localization function (ELF) [24], in order to improve our

knowledge about electron delocalization in borazine. The

first one is a vector field and the second is a scalar field.

Both molecular fields, and their orbitals contributions

[25, 26], reveal important information on electron delo-

calization [27, 28].

Computational details

Structures were optimized using Becke’s exchange (B)

[29], Lee, Yang, and Parr (LYP) correlation [30], and

within the hybrid functional (B3LYP) approach, as

implemented in Gaussian [31]. All geometry optimizations

and wave functions were obtained using the 6-311++G(d,p)

basis set [32]. The NMR calculations were performed using

the PW91 functional and IGLO-III basis set [33]. Cartesian

shielding tensors were computed using the IGLO method

[34]. The deMon program [35] was used to compute the

molecular orbitals and the deMon-NMR package [36]

for the shielding tensors. Induced magnetic fields were

computed by

BindðRÞ ¼ �rabðRÞBext: ð1Þ

from Cartesian shielding tensors, and are in ppm of the

units of the external field. Assuming an external magnetic

field of |Bext| = 1.0 T, the unit of the induced field is

1.0 lT, which is equivalent to 1.0 ppm of the shielding

tensor. The r and p contributions to the induced magnetic

field have been separated using the IGLO method, where

localized molecular orbitals (LMOs) have been created

using the procedure suggested by Pipek and Mezey [37].

We have chosen a LMO representation [38] in favor over a

canonical MO representation [39, 40]. The VU program

was employed for visualization of the induced field vectors

[41], their contour lines and isosurfaces. The ELF topo-

logical analysis and its graphical representation were made

using the TopMod [42] and Molekel [43] programs,

respectively.

The induced magnetic field (Bind) is directly accessible

through the shielding function. By the simple linear rela-

tion of Eq. 1, it is computed as the negative product of the

shielding tensor with the external (or applied) magnetic

field. Hence, the knowledge of the shielding function can

be immediately transferred to the induced field. Using this

methodology, we have studied aromatic, non-aromatic, and

anti-aromatic hydrocarbons [23]. We showed that Bind

reveals important information on electron delocalization

and, furthermore, of its kind: If organic cycles are studied

and p-delocalization, or a ring current, is assumed, the

external field is pointing perpendicular to the ring. In this

case, non-conjugated systems, such as cyclobutane or

cyclohexane, only show a short-range response to the

magnetic field. In all areas of the molecule except for the

immediate vicinity of atoms and bonds, the induced field is

small. This is different for conjugated rings: Both cyclo-

butadiene and benzene show induced magnetic fields far

away from the molecule and significant contributions in the

ring centers. The induced fields are either in line with the

applied field, hence increasing it (paratropic) for anti-aro-

matic compounds, or against the field, shielding it

(diatropic) for aromatic compounds. The induced magnetic

field analysis has been applied recently to understand the

electronic properties of compounds containing a planar

tetracoordinate carbon [44, 45], aluminum clusters [46],

and studies of other systems, including conjugated double

rings, are in progress.

The electron localization function (ELF) [24]

g rð Þ ¼ 1þ t rð Þth rð Þ

� �2" #�1

; ð2Þ

is a useful tool which provides deeper insight into the nature of

the chemical bonding in a variety of stationary and reacting

systems [47–50] g(r) can be conveniently written (and inter-

preted) for monodeterminantal wavefunctions in terms of the

excess of local kinetic energy density due to the Pauli repul-

sion, t(r), where the Thomas–Fermi kinetic energy density,

th(r), is chosen as a reference for comparison. Hence,

g(r) ? 0 in those regions where the relative probability of

finding electrons with parallel spin close together is high (i.e.,

where the local Pauli repulsion is strong), whereas g(r) ? 1

in regions with a high probability of finding a single electron or

a pair of opposite spin electrons. The analysis of the gradient

field rg(r) provides a division of the molecular space in

basins of attractors (i.e., maxima) that can be associated to

units of chemical meaning (i.e., core, valence, bonding, and

non-bonding regions), and whose density-integrated proper-

ties can be associated to chemical properties which are

connected with electron localization and delocalization con-

cepts. A hierarchy of the electron localization domains can be

established by using the concept of synaptic order. The basins

become ordered with respect to the ELF values at the critical

points which determine the separation of the different locali-

zation domains. The higher the separation value, the higher is

the expected degree of localization of electron pairing

between these domains [47–49]. Such a bifurcation analysis is

a useful tool to rationalize the nature of chemical bonding of

aromatic substitution and reactive sites [51, 52], pericyclic

reactions [53–55], radical systems (e.g., through the analysis

of the a-b spin components) [56], and the definition of an

aromaticity scale for organic molecules and clusters via the

analysis of r and p contributions to density [26, 57].

Struct Chem (2007) 18:833–839 Electron delocalization and aromaticity 835

123

Results and discussion

The induced magnetic field

Figure 1 shows the induced magnetic field of an external

field applied perpendicular to the molecular plane of bor-

azine. A magnetic field in this direction can induce a ring

current in and parallel to the molecular plane. Similar to

benzene [23], the induced magnetic field for borazine

shows a long-range shielding cone perpendicular to the

molecular plane. Note that all atoms and bonds lie in the

shielding area of the induced field (Fig. 1). However,

contrary to benzene, borazine shows two weakly paratropic

regions, one of them inside the ring, and the second one

envelopes the boron atoms. As our method allows the

separation into core, r and p orbitals, we can discuss the

role of each contribution [25]. The core electrons do not

contribute to Bind except in very close vicinity of nuclei.

The r orbital contributions to Bind have a shape which is

quite similar to the total Bind of nonaromatic molecules,

such as cyclobutane or cyclohexane [23]. The local para-

magnetic contributions of the r electrons generate a short-

range response and a paratropic (deshielding) region in the

center of the ring.

In contrast, the p orbital contribution to Bind shows the

typical response of an aromatic system. The field lines

parallel to the molecular plane lose the shape of the

molecular framework and become circles. No paratropic

contributions are found inside the ring. Outside of the

molecule the field lines form longrange cones (shielding

cones). The p contributions are, however, smaller in

magnitude than those of benzene, which results in the

different topology of the total induced magnetic field, in

particular in the paratropic area in the ring center. The

long-range response dominates at larger distances and has

similar impact on borazine’s properties as the p system for

benzene, for example for intermolecular shielding contri-

butions [58] or for its polarizability and H2 physisorption

[59]. Nevertheless, close to the molecular plane, the rcontribution is dominating the total response.

Isolines of the z-component of the induced magnetic

field, Bindz , and isolines of NICS are given in Fig. 2. Note

that Bindz for an external field perpendicular to the ring is

equivalent to the NICSzz [60]. The shielding cones of

borazine on top and bottom, induced by the p-electrons, are

comparable in shape to those of benzene, but they are

smaller in magnitude and extension. As r electrons are

much stronger localized than p electrons, their local para-

magnetic contributions generate a short-range response and

a paratropic (deshielding) region in the center of the ring

(similar to an anti-aromatic response). The NICSp does not

account for r contributions, but still includes the effects of

the currents induced by magnetic fields parallel to the ring

[25, 61, 62], which are not negligible and have an impact to

the shape of the shielding cones. The r-component is

responsible for the local stationary point observed in both

scalar fields above the ring center.

The electron localization function

The topological analysis of ELF provides a clear picture of

bonding that can be rationalized through the analysis of

basins bifurcations. As shown in Fig. 3, the first separation

occurs at the ELF critical value 0.403 for the domains

associated to the three B–H bonds. These populations

appear more localized than those associated with the three

N–H bonds, which bifurcate at a higher ELF critical value

of 0.765. The localization pattern leaves three separated

localization domains associated to B–N–B regions (i.e.,

B1–N1–B2, B3–N2–B2, and B3–N3–B1), which become

finally separated at the ELF value 0.823. These three

regions can be identified as chemically meaningful

domains exhibiting an internally strong although asym-

metric electron delocalization. The co-variance matrix

elements associated to adjacent B–N bond regions are 0.49

(N common atom) and 0.12 (B common atom), while the

covariance between the B–N bond basin populations

with those associated to B–H and N–H bond regions are

0.13, and 0.31, respectively. This pattern shows clearly

that delocalization is smaller around B atoms than around

N ones.

The analysis of separated r and p ELF functions shows

a weak sigma interaction. The same three B–N–B regions

described above were obtained, which posses a bifurcation

value of 0.432. This value is low compared to the typical

Fig. 1 The induced magnetic

field of borazine. Blue and red

areas denote diatropic

(shielding) and paratropic

(deshielding) regions,

respectively, with indicated

directions of the Bind vectors

836 Struct Chem (2007) 18:833–839

123

ones (about 0.75) obtained in the analysis of classical

organic compounds. It is clear from such a picture that the

difference in electronegativity between B and N, produces

a weak B–N bond interaction.

The borazine p system bifurcates at the ELF value

0.682, a value lower than benzene (0.91). The p density is

highly localized over the nitrogen p-orbital, while in con-

trast, such at the boron center it has a lower population.

Based on the resulting bifurcation values and within the

context of the scale proposed recently, borazine could be

described as a p aromatic compound (See Fig. 4). We

must, however, emphasize that it is not a globally aromatic

species because the r-p average bifurcation value (0.56)

belong to the range of the anti-aromatic species like

cyclooctatetraene, cyclobutene, and bicycle(2,2,0)-hex-

atriene, with values of 0.54, 0.45, and 0.47, respectively.

Conclusions

The electronic system of borazine is not as homogeneous

as that of benzene. The different electronegativity of B and

N has an impact to the chemical bonding pattern and on

electron delocalization. It is necessary to separate r and pcontributions to understand if borazine exhibits or not a

similar aromatic character than benzene. Our combined

Bind and ELF analysis shows that the p system of borazine

is indeed aromatic. Due to the stronger varying potential,

Fig. 2 (A) The z-component of

Bind, shielding (diatropic, blue)

or enforcing (paratropic, red)

the external field, shown in the

molecular plane and

perpendicular to it. (B) Contour

lines of NICS(r) (equivalent to

the negative shielding density

and to isochemical shielding

surface) are shown in the same

planes as the field lines

Fig. 3 Snapshots of selected

ELF isosurfaces

Struct Chem (2007) 18:833–839 Electron delocalization and aromaticity 837

123

the electronic system is not as equally delocalized as in

benzene. Therefore, also the induced magnetic field is

weaker than that of benzene, but nevertheless pronounced

and long-ranged. This long-range response dominates at

larger distances and has similar impact on borazine’s

properties as the p system for benzene, for example for

intermolecular shielding contributions or for its polariz-

ability and H2 physisorption. The picture of bonding

arising from the topological analysis of ELF reveals in fact

three well-defined and weakly interacting fragments cor-

responding to the HB–NH–BH moieties. These constitute

strongly correlated subunits of chemical interest. Indeed,

bifurcation schemes of the total ELF and the analysis of

r-p separation reveals that borazine has not a global aro-

matic character despite its p aromaticity in agreement with

the Bind analysis. It should be remarked that in such a case,

the high accumulation of electron density at the nitrogen

atoms precludes an effective cyclic electron delocalization

through boron.

Acknowledgments This work was funded in part by grants from

DINPO-UGTO, and the Deutsche Forschungsgemeinschaft (DFG). RI

gratefully acknowledges a Conacyt Ph.D. fellowship. JCS and EC

thank Fondecyt (Chile), grants 11060197 and 1070378, and the

Millennium Nucleus for Applied Quantum Mechanics and Compu-

tational Chemistry (Mideplan-Conicyt, Chile), grant P02-004-F for

continuous support. JCS and EC also thank to UNAB by support

through the DI 22-05/R and 21-06/R research grants.

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