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Inorganica Chimica Acta 360 (2007) 619–624

Theoretical study of borazine and its derivatives

Wei Shen a, Ming Li b,*, Ying Li b, Silei Wang b

a Faculty of Chemistry, Sichuan University, Chengdu 610064, People’s Republic of Chinab Department of Chemistry, Southwest-China University, Chongqing 400715, People’s Republic of China

Received 3 July 2006; received in revised form 4 August 2006; accepted 4 August 2006Available online 30 August 2006

Abstract

The density functional theory is used to study the geometries, electronic structures, and aromaticity of borazine and its fused ringderivatives. Some new evidences for the ionic nature of B–N bond are found. Geometry studies show that the B–N bond lengths areequal. The lone pair VSCCs of the N atoms are found. As shown, the B–N bonds are of ionic nature based on their positive Laplacian.Magnatic shielding constants also are computed. The shielding and deshielding contributions are divided into Lewis and non-Lewis partsby the NCS-NBO method. It is demonstrated in the NICS studies that there are the ring current effects on borazine and its derivatives arevery weak. The aromaticity of borazine is weakened with the fused ring number increasing.� 2006 Elsevier B.V. All rights reserved.

Keywords: Borazine; DFT; Topological properties; Aromaticity

1. Introduction

The ring borazine, B3N3H6, which involves a six-mem-bered ring with six p-electrons, has attracted much atten-tion theoretically and experimentally [1–5]. The ringborazine (–BH–NH–) compounds are important classesof boron–nitrogen compounds. Its derivatives, borazinecyclacenes and borazine nanotube, are also studied bymany scientists [6–9]. Due to the same number of valenceelectrons and the sum electronegativities as well as atomicradii in the BN and CC units, the parent compound, bor-azine, is often compared to inorganic benzene. Addition-ally, the B–N bond lengths in borazine are equal witheach other, which resemble the situation in benzene. Itssimilarity to benzene is also visible in some physical (e.g.density, surface tension) and chemical (e.g. hexahaptoligands in organometallic complexes [10,11]) properties.Furthermore, it is shown in the experiments of Chiavarinoand co-workers [12,13] that borazine undergoes electro-

0020-1693/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.ica.2006.08.028

* Corresponding author.E-mail address: Liming@swu.edu.cn (M. Li).

philic aromatic substitution in the gas phase much like itsorganic counterpart.

Nevertheless, because of the considerable differencebetween the electronegativity of boron and nitrogen, thering delocalization of electrons in the borazine ring isweakened greatly. The properties of borazine have beendiscussed in many theoretical and experimental studies,and its aromaticity is focused by many scientists [4–9,14–16]. Almost all the theoretical computations for aromatic-ity (magnetic, energies, etc.) show that borazine is less aro-matic or non-aromatic.

It is a primary purpose of this work to demonstrate theproperties of ring borazine and its fused ring derivatives,and to present the relationship between the aromaticityand the electronic structure by some new theoretical meth-ods. To obtain more information about the electronicstructure, the compounds, BNH4, B2NH5, and B3NH5,are also discussed.

2. Computational details

In the present computations, the density functional the-ory (DFT) [17] is employed to optimize all the structures.

620 W. Shen et al. / Inorganica Chimica Acta 360 (2007) 619–624

The Becke’s three-parameter nonlocal exchange functionalong with the Lee–Yang–Parr nonlocal correlation func-tion (B3LYP) [18,19] and the dunning’s aug-cc-pVDZ(5d) basis set [20] are used throughout. There are no imag-inary frequencies for all the optimized structures at thepresent theoretical level, which implies that all the opti-mized structures are the local minima on the potentialenergy surface.

The magnetic shielding constants are calculated bymeans of the GIAO method [21] at the B3LYP/aug-cc-pVDZ level. Since the GIAO approach is gauge-invariant,it can be used to calculate the nucleus-independent chemi-cal shift (NICS) [22]. NICS is defined as the negative of themagnetic shielding at a ring critical point (RCP), which isattained from atom in molecule (AIM) analysis [23]. In thispaper, NICS(0) and NICS(1) are denoted as the NICS atRCP and 1 A above RCP, respectively. The NBO 5.0 pro-gram [24–26] is linked to the GAUSSIAN 98 [27] calculationprogram. The natural chemical shielding (NCS)-NBO anal-ysis partition quantitatively the magnetic shielding of a cer-tain nucleus into magnetic contributions from chemicalbonds, core and lone pairs. The shielding and deshieldingcontributions are divided into Lewis and non-Lewis parts[28].

The topological properties of the electronic charge den-sities are characterized by use of the atoms in molecules(AIM) method of Bader with the AIM 2000 programpackage.

Fig. 1. Optimized molecular structures and symmetry for BNH4, B2NH5, B3NH

3. Results and discussion

The geometries of borazine and its derivatives are opti-mized at the B3LYP/aug-cc-pVDZ level. The molecularstructures, along with their geometrical parameters, areillustrated in Fig. 1. As shown in Fig. 1, those moleculeshave a rigid planar and high symmetrical structure.

In those molecules, the N atoms have three differentchemical situations due to the different connection num-ber with the B atoms. It can be seen in Fig. 1 that theB–N bonds are lengthened with the connection numberof the N atom with the B atom increasing. The B–N bondin BNH4 is 1.393 A, whereas the bonds in B2NH5 andB3NH6 are 1.424 and 1.449 A, respectively. There is sim-ilar situation for the ring compounds. The N atoms in theperiphery of the system connect with two B atoms, andthe corresponding B–N bonds are shorter than those inthe center region. For the compound 1, the B–N bondlengths (1.432 A) are equal and it is longer than the C–C bond lengths (0.033 A) in its organic counterpart, ben-zene. The structural characters of the ring borazine implythe existence of the ring delocalization. By comparison ofB2NH5 with 1, it can be easily found that the B–N bondlengths in the ring compounds are longer than those inthe acyclic compounds. This result is due to the tensilityof the B–N–B angles in the ring compounds. It is identi-fied by the NBO analysis that the B–N bonds in the ringcompounds deviate slightly from the nuclear axes. Simi-

6 and compounds 1, 2, 3, along with bond lengths (in A) and angles (in �).

Fig. 2. (a–d) Selected isosurface maps of �r2qðrÞ: (a) for BNH4, (b) for

B2NH5, (c) for 2 and (d) for 3. (e–f) contour plot of Laplacian of selectedatoms for BNH4 and 2 (black for �r2

qðrÞ and green for r2qðrÞ).

(For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

W. Shen et al. / Inorganica Chimica Acta 360 (2007) 619–624 621

larly, there is the bond bending in the compounds 2 and3.

3.1. Topological analysis and Laplacian distributions for

B–N bonds

To obtain more insight on the bonding character, thecompletely topological analysis is performed for all thecompounds. Bond critical points (BCPs), denote as(3,�1), representing saddle points in the electron densitiesbetween two atoms are examined for all the bonds. In thetopological definition, a chemical bond is represented bythe bond path. The gradient path links two neighboringnuclei along with maximal qr in any neighboring line.The values of the charge densities, qr, the negative Lapla-cian, �r2

qðrÞ, the ellipticities, �BCP, and the eigenvalues ofHessian matrix, ki, at the BCPs are presented in Table 1.According to the atoms in molecules theory of Bader, theseproperties can be used to distinguish various interactiontypes. The negative values of the Lapacian accompaniedby high electron densities at the BCPs are commonly asso-ciated with a distinct covalent bonding character (shareinteractions), whereas high positive values of the Laplacianaccompanied by the relatively small electronic densities atthe BCPs are attributed to an ionic bonding character(closed shell interaction).

All the VSCCs (VSCC presenting valence shell chargeconcentration) appearing as (3,�3) critical points in thenegative Laplacian are found for theoretical models. TheseVSCCs are used to identify the lone pairs of the valenceshell electron pair repulsion model. Selected isosurface of�r2

qðrÞ and the contour plot of r2qðrÞ for the N atoms

are illustrated in Fig. 2.It can be seen from Table 1 that, for all the examined

compounds, the position of BCPs for all the B–N bondsis located extremely close to boron atoms, which indicatesthat the electrons are concentrated around nitrogen atoms.As shown in Table 2, there is a large charge differencebetween B and N atoms, both of NBO charge and AIMcharge. The Laplacian of BCPs for all the B–N bonds are

Table 1BCP properties and Wiberg bond index of selected B–N bonds in compounds

Bond d dBCP qr

BNH4 B–N 1.393 0.939 0.2034NB2H5 B–N 1.424 0.964 0.1966NB3H6 B–N 1.449 0.9830 0.18961 B1–N2 1.432 0.969 0.1948

2 B1–N2 1.429 0.964 0.1963N2–B3 1.441 0.975 0.1905B3–N8 1.459 0.989 0.1892

3c N1–B2 1.429 0.966 0.1959N3–B3a 1.442 0.976 0.1935B3a–N9b 1.453 0.984 0.1908

a The value are calculated by B3LYP/aug-cc-pvdz, d is the bond path lengt(i = 1,2,3) are the eigenvalues of the Hessian matrix, �BCP is the ellipticity, qp

positive ðr2qðrÞ > 0Þ. These results imply that the B–N

bonds are of ionic nature.BNH4, shown in Fig. 1, is a typical electron donor–

acceptor compound. The B–N bond in BNH4 is the short-est bond length of all the examined B–N bonds with thelargest density and the small ellipticity at the BCP. In thetheoretical density distribution of BNH4, the nitrogen atomreveals one single lone-pair VSCC which oriented to the Batom (shown in Fig. 2 and r2

qðrÞ ¼ �2:489 a:u:). The lone

a

�k1/�k2/k3 r2qðrÞ �BCP Wiberg index

0.51/0.47/1.89 0.9074 0.0811 1.230.51/0.43/1.67 0.7213 0.1880 1.010.49/0.39/1.48 0.5928 0.2623 0.890.47/0.44/1.58 0.6656 0.0838 0.97

0.48/0.44/1.60 0.6726 0.0913 0.980.46/0.41/1.46 0.5803 0.1258 0.920.44/0.41/1.35 0.5008 0.0659 0.83

0.47/0.44/1.59 0.6752 0.0789 0.980.46/0.44/1.49 0.5868 0.0433 0.910.45/0.42/1.40 0.5282 0.5832 0.84

h, and dBCP denotes the distances of the BCP from the nitrogen atom. ki

tr is the charge density, and r2qðrÞ is the Laplacian at the BCP.

Table 2NBO charge and AIM charge of selected atoms for borazine and itsderivatives

Atom NBO charge AIM charge

BNH4 B 0.460 2.023N �1.080 �1.549

B2NH5 B 0.563 2.034N �1.152 �1.864

B3NH6 B 0.619 2.035N �1.278 �2.188

1 B1 0.820 2.109N2 �1.150 �2.448

2 B1 0.826 2.111N2 �1.166 �1.888B3 1.196 2.214N8 �1.243 �3.302

3 N1 �1.159 �1.891B2 0.822 2.109B3a 1.197 2.217N9b �1.258 �2.746

Fig. 3. Selected stabilization interaction energies E(2) for cyclic borazines.

622 W. Shen et al. / Inorganica Chimica Acta 360 (2007) 619–624

pair of the nitrogen atom is inclined to the electropositiveboron atom. This fact should be interpreted as lone-pairback bonding, and this ‘‘covalent’’ bond is in fact predom-inantly ionic [29,30].

For B2NH5 and the compound 1, the chemical situa-tions of the N atoms are similar and each N atom connectswith two B atoms. Analyzed by AIM, the lone pairs of Natoms are redistributed to two directions, which connectto B atoms. Fig. 2 illustrates the lone pair VSCC of theN atoms for the compound 1. Since it is similar to the com-pound 1, the figure of VSCC for B2NH4 is not shown. TheLaplacian r2

qðrÞ of the N atoms are �2.503 a.u. for B2NH4

and �2.372 a.u. for the compound 1, respectively.For the compound 2, the N8 atom connects with three B

atoms and its lone pair is redistributed to three directions.Three lone pair VSCCs of the N8 atom are found (shownin Fig. 2), and it can be easily found that the VSCC of lonepair in the direction to the B3 atom is much smaller thanthat in other directions. Correspondingly, the Laplacianr2

qðrÞ of VSCC in the N8! B3 direction, �2.189 a.u., issmaller than that in others directions, �2.297 a.u.. Withthe B–N connection number for N atoms increasing, theB–N bonds are lengthened and the electron densities ofBCPs and the Laplacian of the N atoms are decreased.

The central N atoms in both B3NH6 and the compound3 are bonded with three B atoms and their chemical situa-tions are similar. The lone pair VSCC of the N9a atom isshown in Fig. 2. The Laplacian r2

qðrÞ of VSCCs are�2.195 a.u. for N9a in the compound 3 and �2.403 a.u.for the N atom in B3NH6. It is clear in Fig. 2 that the lonepair of the N9a atom is redistributed and is averagely dis-tributed to three directions.

For all the examined compounds, the symmetry allowsthe formation of the p-system perpendicular to the molec-ular plane. The delocalizational p-orbital is shown inFig. 4. The delocalizational orbital shape implies that there

may be p-electronic conjugated systems in those molecules.Nevertheless, those m-center-n-electron p-bonds are ofapparent polarization. Because of the great electronegativedifference between the N and B atoms, the p-electron delo-calization is incomplete. This result can also be verified bystabilization interaction energies E(2) which obtained fromNBO analysis. In Fig. 3, all of interaction energies (value>5 kcal/mol) are presented. As illustrated, all of the E(2)values are either between p bonding orbital and p* bondingorbital or between lone pair and p* bonding orbital. It canbe seen in Fig. 3 that the p–p* interaction in benzene is bi-directional, whereas the interactions in borazine and itsderivatives are single direction, which implies that the p-electron delocalization are limited between B atom and Natom, not in whole ring, and that there are not electroncurrents above ring borazine planes.

3.2. Aromaticity of ring borazines

Because ring borazine has the same p-electron numberas its organic counterpart, benzene, the aromaticities ofborazine and its derivatives have attracted much attentiontheoretically and experimentally. Almost all of those stud-ies indicate that borazine is a few aromaticity or non-aro-maticity. However, for those ring borazines, the numbersof p-electrons obey the 4n + 2 rule and their B–N bondlengths are equal. Based on this consideration, those bor-azine compounds maybe be aromatic.

By employing the natural chemical shielding (NCS)analysis based on the NBO method, the theoretical NMRshielding tensors at RCPs and at 1 A above RCPs, whichobtained by GIAO calculations of borazines, are parti-tioned into magnetic contributions from the r-bond, p-bond and lone pair. Both the localized contributions fromchemical bonds and the delocalized contributions (fromhyperconjugation) to NICS(0) and NICS(1) are collectedin Table 3.

The shielding and deshielding contributions are dividedinto Lewis and non-Lewis, and non-Lewis parts assign

Fig. 4. Shape of delocalized p occupied orbitals in borazines.

Table 3Magnetic shielding contributions for ringed borazines at points 1 A aboveand at RCPsa,b,c

Bond Contribution(L)

Contribution(NL)

Contribution(L + NL)

1 N–B(p) 9.99 (1.38) 3.27 (2.22) 13.26 (3.60)N–B(r) �16.08 (�3.54) 9.96 (4.44) �6.12 (0.90)B–H(r) �1.44 (�0.99) �0.24 (0.78) �1.68 (�0.21)N–H(r) �1.26 (�0.62) �0.36 (0.36) �1.62 (�0.26)B(cr) �2.76 (�1.53) 0.15 (0.09) �2.61 (�1.44)N(cr) 0.06 (0.03) 0.00 (�0.03) 0.06 (0.00)

Total �11.49 (�5.27) 12.78 (7.86) 1.29 (2.59)

2 N–B(p) 11.13 (1.38) 3.3 (2.37) 14.43 (3.75)N–B(r) �12.33 (0.09) 2.64 (�0.17) �9.69 (�0.08)B–H(r) �0.59 (�1.06) �0.11 (0.99) �0.70 (�0.07)N–H(r) �1.08 (�0.62) �0.18 (0.29) �1.26 (�0.33)B(cr) �3.21 (�1.93) 0.26 (0.18) �2.95 (�1.75)N(cr) 0.88 (0.58) 0.01 (�0.01) 0.89 (0.57)

Total �5.20 (�1.56) 5.92 (3.65) 0.72 (2.09)

3 N–B(p) 8.20 (1.12) 3.61 (2.62) 11.81 (3.74)N–B(r) �15.00 (�1.29) 4.77 (0.92) �8.46 (�0.37)B–H(r) �0.45 (�0.59) �0.42 (0.19) �0.87 (�0.40)N–H(r) �1.72 (�0.89) �0.14 (0.30) �1.86 (�0.59)B(cr) �3.52 (�2.22) 0.31 (0.19) �3.21 (�2.03)N(cr) 0.62 (0.50) �0.05 (�0.06) 0.57 (0.44)N(LP) 3.68 (0.25) 0.73 (0.22) 4.41 (0.47)

Total �8.19 (�3.12) 8.81 (4.38) 0.62 (1.26)

a The values in parenthesis are at 1 A above the RCPs and it muchsmaller than the values at RCPs due to the decrease of local contributionsrelative to the ring current effects.

b L means Lewis, NL means non-Lewis, LP means lone pair, cr means core.c For 2 and 3, the contribution of only one cycle is listed.

W. Shen et al. / Inorganica Chimica Acta 360 (2007) 619–624 623

hyperconjugation [28,31]. For those studied compounds,the magnetic shielding contributions of Lewis and non-Lewis are much more different. Especially, the sigma N–B

bond contributions involve deshielding in Lewis whereasshielding in non-Lewis. But the sum of sigma N–B bondcontributions, Lewis and non-Lewis (L + NL), presentsdeshielding. Other two kind r-bonds (N–H and B–H),both Lewis and non-Lewis, present deshielding, but theyare very weak. The core contribution of B and N atomsare very small. For the compound 3, the contribution ofN9a lone pair shielding is larger due to the lone pair partic-ipating in p bond.

As shown in Table 3, it is apparent that the shieldingcome mainly from the B–N p bond contributions(13.26 ppm for 1, 14.43 ppm for 2, and 11.81 ppm for 3),which implies the existence of the electron delocalizationbetween B and N atoms. But those shieldings are counter-acted by deshieldings of sigma B–N bonds. Considering thesingle-direction p–p* interaction shown by NBO, the elec-tron delocalization is limited between B and N atoms,and thus the electron ring current above whole ring cannotbe formed.

In 1996, Schleyer et al. proposed a novel magnetic probefor local aromaticity, a nucleus-independent chemical shift(NICS), which is defined as the negative of the magneticshielding at some selected points in space. In general, thenegative and positive NICS at ring center are associatedwith local aromaticity and antiaromaticity, respectively.In Table 3, the sum of L + NL contributions is the negativeNICS. For all the compounds, NICS are very small(�1.29 ppm for 1, �0.72 ppm for 2 and �0.62 ppm for3).It can be concluded that those ring borazines have aroma-ticity, but they are very weak.

With the number of fused ring increasing, the aromatic-ities are decreased due to decreasing NICS. For the threestudied compounds, because of the obvious electronegativ-ities difference between N and B atoms, the electron delo-calization is restricted and the ring current effect isweakened.

624 W. Shen et al. / Inorganica Chimica Acta 360 (2007) 619–624

4. Conclusion

In summary, the present results show that borazine andits derivatives have rigid planes and high symmetries andthe similar B–N lengths. For all the examined compounds,the lone pair VSCCs of the N atoms are found. The Lapla-cian of BCPs at the B–N bonds are positive, which implythat the B–N bonds are of ionic nature. The interactionenergies of p–p* and LP–p* are single direction in ring com-pounds. The electron delocalizations of borazine and itsfused ring derivatives are limited in B–N bond, and thereare few electron currents above molecular planes. For allthe examined ring borazines, the aromaticities are very weakdue to a small NICS. Furthermore, the aromaticity of bor-azines is weakened with the fused ring number increasing.

Acknowledgment

We thank Prof. Anmin Tian of SiChuan University tosupport AIM calculation and to advise for this work.

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