Jules Tshishimbi Muya

Ring currents in boron and carbon buckyballs, B80 and C60

The ipsocentric method at the coupled Hartree-Fock level is used for the calculation of magnetically induced ring currents in the boron buckyball B(80), for both I(h) and distorted T(h) geometries. A close similarity between the current patterns in boron and carbon buckyballs is noted, but with a higher current density in B(80). Paratropic currents on the pentagons are predominant in the boron buckyball, and the central NICS value is positive. These observations support the conclusion that B(80) should be considered (weakly) anti-aromatic. The largest orbital contributions to the ring currents in both molecules are identified and related to specific excitations in the frontier orbital region.

Encapsulation of small base molecules and tetrahedral/cubane-like clusters of group V atoms in the boron buckyball: a density functional theory study.

A density functional theory study of small base molecules and tetrahedral and cubane-like group V clusters encapsulated in B(80) shows that the boron buckyball is a hard acid and prefers hard bases like NH(3) or N(2)H(4) to form stable off-centered complexes. In contrast, tetrahedral and cubane-like clusters of this family are metastable in the cage. The most favorable clusters are the mixed tetrahedral and cubane clusters formed by nitrogen and phosphorus atoms such as P(2)N(2)@B(80), P(3)N@B(80), and P(4)N(4)@B(80). The boron cap atoms are electrophilic centers, and prefer mainly to react with electron rich nucleophilic sites. The stability of the complexes will be governed by the size and electron donating character of the encapsulated clusters. B(80) forms stable complexes with hard materials where a bidentate interaction of the encapsulated molecule with two boron cap atoms is preferred over a single direct complex toward a single endohedral boron.

Theoretical Study on the Regioselectivity of the B80 Buckyball in Electrophilic and Nucleophilic Reactions Using DFT-Based Reactivity Indices

Density functional theory calculations at the B3LYP/SVP and B3LYP/6-311G(d) levels were carried out for a series of XH(3)B(80) complexes with X = {N, P, As, B, Al}. To probe the regioselectivity of B(80), the electronic Fukui function, the molecular electrostatic potential (MEP), and the natural bond orbital (NBO) were determined. These indices were shown to provide reliable guides to predict the relative reactivities of the boron buckyball sites. Thermodynamic stabilities of the complexes formed by the reaction of B(80) with nucleophiles (NH(3), PH(3), AsH(3)) and electrophiles (BH(3), AlH(3)) are in good agreement with the prediction of regioselectivity indicated on the basis of Fukui and MEP indices. The qualitative results suggest the boron buckyball to be an amphoteric and hard molecule. It has two distinct reactive sites localized on caps and frame, which act as acids and bases, respectively. Most of the complexes are stable with formation energies comparable to that of the analogous complexes of the borane molecule, BH(3)BH(3), BH(3)NH(3), and BH(3)AlH(3). The B-H-B bond characteristics of diborane are recovered in B(80)BH(3). Exohedral complexes are more stable than endohedral complexes. The most stable complexes are those with NH(3) on the caps and BH(3) on the pentagonal ring of B(80).

The Boron Conundrum: Which Principles Underlie the Formation of Large Hollow Boron Cages?

Extensive optimisation calculations are performed for the B(80) isomers in order to find out which principles underlie the formation of large hollow boron cages. Our analysis shows that the most stable isomers contain triangular B(10) or rhombohedral B(16) building blocks. The lowest-energy isomer has C(3v) symmetry and is characterised by a belt of three interconnected B(16) units and two separate B(10) units. At the B3LYP/6-31G(d) level of theory, this newly discovered isomer is 2.29, 1.48, and 0.54 eV below the leapfrog B(80) of Szwacki et al., the T(h) -B(80) of Wang, and the D(3d) -B(80) of Pochet et al., respectively. Our C(3v) isomer is therefore identified as the most stable hollow cage isomer of B(80) presently known. Its HOMO-LUMO gap of 1.6 eV approaches that of the leapfrog B(80). The leapfrog principle still remains a reliable scheme for producing boron cages with larger HOMO-LUMO gaps, whereas the thermodynamically most stable B(80) cages are formed when all pentagonal faces are capped. We show that large hollow cages of boron retain a preference for fullerene frames. The additional capping is in accordance with the following rules: preference for capping of pentagonal faces, formation of B(10) and/or B(16) units, homogeneous distribution of the hexagonal caps, and hole density approaching 1/9. Although our most stable B(80) isomer still remains higher in energy than the B(80) core-shell structure, we show that by applying the bonding principles to larger structures it is possible to construct boron cages with higher stabilisation energy per boron atom than the core-shell structure; a prototypical example is B(160). This clearly shows the continuous competition between the two suggested construction schemes, namely, the formation of multiple-shell structures and hollow cages.

Theoretical Study of the Regioselectivity of the Interaction of 3-Methyl-4-pyrimidone and 1-Methyl-2-pyrimidone with Lewis Acids

A density functional theory (DFT) study is performed to determine the stability of the complexes formed between either the N or O site of 3-methyl-4-pyrimidone and 1-methyl-2-pyrimidone molecules and different ligands. The studied ligands are boron and alkali Lewis acids, namely, B(CH(3))(3), HB(CH(3))(2), H(2)B(CH(3)), BH(3), H(2)BF, HBF(2), BF(3), Li(+), Na(+), and K(+). The acids are divided into two groups according to their hardness. The reactivity predictions, according to the molecular electrostatic potential (MEP) map and the natural bond orbital (NBO) analysis, are in agreement with the calculated relative stabilities. Our findings reveal a strong regioselectivity with borane and its derivatives preferring the nitrogen site in both pyrimidone isomers, while a preference for oxygen is observed for the alkali acids in the 3-methyl-4-pyrimidone molecule. The complexation of 1-methyl-2-pyrimidone with these hard alkali acids does not show any discrimination between the two sites due to the presence of a continuous delocalized density region between the nitrogen and the oxygen atoms. The preference of boron Lewis acids toward the N site is due to the stronger B-N bond as compared to the B-O bond. The influence of fluorine or methyl substitution on the boron atom is discussed through natural orbital analysis (NBO) concentrating on the overlap of the boron empty p-orbital with the F lone pairs and methyl hyperconjugation, respectively. The electrophilicity of the boron acids gives a good overall picture of the interaction capabilities with the Lewis base.

C60+ and B80+: A Comparative Study of the Jahn-Teller Effect

The ground state wave function of the neutral icosahedral C60 and B80 belong to the totally symmetric representation, where the HOMOs are fivefold degenerate and form the basis of the Hu representation of the Ih point group. Hence both C60+, and B80+ are prone to a molecular distortion of the Jahn-Teller type. Density Functional Theory calculation is applied and revealed that a minimum energy configuration in D5d point group is obtained for C60+; whereas a slight S6 distortion of a D3d nuclear configuration is obtained for B80+. Thus the vibronic coupling between the 2Hu electronic states of both systems with the degenerate normal modes in the Ih point group are analysed and presented here in a comparative point of view. Moreover, a simple and efficient procedure, which is fully non-empirical, based on the harmonic approximation, is presented in order to calculate the Jahn-Teller parameters and the first order vibronic coupling coefficient.

Investigations of the Boron Buckyball B80: Bonding Analysis and Chemical Reactivity

The boron fullerene B80 is a spherical network of 80 boron atoms, which has a shape similar to the celebrated C60. The 80 Bs span two orbits: while the first contains 60 atoms localised on the vertices of a truncated icosahedron like C60, the second includes 20 extra B atoms capping the hexagons of the frame. Quantum chemical calculations showed that B80 is unusually stable and has interesting physical and chemical properties. Its geometry is slightly distorted from I h to T h symmetry. However, the boron buckyball is only observed in silico, so far the synthesis of this molecule is only a remote possibility. Using DFT at the B3LYP/SVP level, we have analyzed the chemical bonding in B80, the possibility of methyne substitution and the stability of endohedral boron buckyball complexes. A symmetry analysis revealed a perfect match between the occupied molecular orbitals in B80 and C60. The cap atoms transfer their electrons to the truncated icosahedral frame, and they contribute essentially to the formation of σ bonds. The frontier MOs have π character and are localised on the B60 truncated icosahedral frame. The boron cap atoms can be replaced by other chemical groups, such as methyne (CH), which are also able to introduce three electrons in the cage. Symmetrical substitutions of the boron cap atoms by methyne groups in T and T h symmetries revealed two stable endo methyne boron buckyballs, endo-\({\mathrm{B}}_{80-\mathrm{x}}\mathrm{{(CH)}_{x}}\), with x = 4, 8. The stability of these compounds seems to be due to the formation of six boron 4-centre bonding motifs in between the substituted hexagons. These localized bonding motifs are at the basis of the observed symmetry lowering, via a pseudo-Jahn-Teller effect. The methyne hydrogen atoms in the two endohedral fullerenes can be replaced by other atoms, which can lead to cubane or tetrahedral endohedral boron fullerenes. Theoretical study on encapsulated small bases molecules, tetrahedral and cubane like clusters of Group V atoms, showed that the boron buckyball is a hard acid and prefers hard bases like NH3 or N2H4, to form stables off-centred complexes with B80. Tetrahedral and cubane like clusters of this family are usually metastable in the encapsulated state, due to steric strain. The most favorable clusters are mixed tetrahedral and cubane clusters formed by nitrogen and phosphorus atoms such as \(\mathrm{{P}_{2}{N}_{2}@{B}_{80},\ {P}_{3}N@{B}_{80}}\) and P4N4@B80. The boron cap atoms act as electrophilic centres, which react with nucleophilic sites rich in electrons.