Theoretical Investigation On The Multi-Center Bonding System In Carbon/Boron Based Clusters

Carbon and boron based clusters are the significant parts of nanochemistry.It is well known that there are delocalized multi-center π bondings in the classical carbon based systems,such as benzene,ferrocene and fullerene.Boron atoms could also form multi-center σ/π bondings by sharing electron pairs in boron based clusters due to the electronic deficiency character.Therefore multi-center bonding is the key part in the electronic structure of carbon/boron based clusters.Diversity of multi-center bonding patterns makes the geometry structures of these clusters flexible,which is also the cause of their aromaticity.In order to study the structure and stability connected with the various multi-center bonding patterns of carbon/boron based clusters,we choose three representatives-C₆₀-ferrocene hybrid component Ih-C₆₀（FeCp）₁₂,B-H binary system BxHy（x+y = 20）and transition metal centered double-ring boron clusters M@B2n（M＝Ti,Cr,Fe,Ni,Zn;n = 6,7,8）as the objects of this study,and discuss their geometry structure,bonding pattern and aromaticity using density functional theory method.This paper includes the following six chapters:In Chapter 1,the research developments of carbon/boron based clusters are briefly introduced,which include fullerene-ferrocene hybrid clusters,all boron clusters,borane clusters and metal doped boron clusters.The experimental and theoretical developments in these fields are reviewed comprehensively,mainly include structures,bonding patterns and the similarity of the electronic structure between carbon and boron based clusters.Moreover,the multi-center bonding system in these two kinds of clusters is discussed.In Chapter 2,the theories of quantum chemistry and computational methods related to this study are reviewed.The density functional theory is the fundamental of this paper.Started from Schrodinger equation,the Kohn-Sham equation,developments of exchange and correlation functional and the key points of pseudo potential method are introduced.Three classical chemical bonding theories and computational methods-molecular orbital theory,natural bond orbital theory and adaptive natural density partitioning method used for the analysis of multi-center bonding are introduced for the chemical bonding study in this work.Moreover,the theory of aromaticity and some criterions are reviewed in the last part of this chapter.In Chapter 3,the structure and chemical bonding of C₆₀-ferrocene hybrid cluster icosahedral C₆₀（FeCp）₁₂ are investigated theoretically.A perfect hybrid complex C₆₀（FeCp）₁₂ is studied in this chapter and its geometry and electronic structure are discussed using density functional theory method.This fullerene derivative could be view as a C₆₀ cage of which each C5 ring coordinates a（FeCp）ligand.Theoretical calculation reveals that it keeps the Ih symmetry of G60 after optimization and has a large highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap（2.53 eV）.However,the C-C bond length of its inner C₆₀ cage trends to be uniform,which is quite different from the bonding character of C₆₀ fullerene.Further investigation reveals that the C₆₀（FeCp）₁₂ cluster has the similar multi-center bonding system,total density of states and aromaticity as ferrocene molecule,which indicates the similarity of their electronic properties.Therefore,this compound could be viewed as the combination of ferrocene molecules.Thus its unconventional formation process from 12 Fe（Cp）2 molecules is proposed and the reaction energy is calculated.As the C₆₀（FeCp）₁₂ cluster has the geometry framework as C₆₀ and the electronic characters as ferrocene,it would inherit the outstanding properties from both two molecules and have wild potential applications in nanochemistry.In Chapter 4,the energy landscape of B-H binary systems from the structural phase diagram and the bonding pattern of BxHy（x +y = 20）are investigated theoretically.The bonding pattern and structure of B-H binary clusters are flexible due to their diversity multi-bonding systems.Although lots of experimental and theoretical researches have been reported about the B-H binary systems,the evolutional rules of their structures connected with energy landscapes still remain unclear.Therefore,theoretical study on the energy landscape of BxHy（x+y=20）systems is carried on in this chapter and their structural phase diagram is plotted.The shape of the energy landscape indicates the relative energy of these systems goes down firstly and then rises up with B10H10 as the turning point which shows the highest reliability.What’s more,the relative energies of B₁₂H₀₈,Bi₆H₀₄and B₂₀H₀₀ exhibit the significant fluctuations,which indicates they are magic numbers of these systems with higher reliability.The overall evolutional rules of the BxMy（x+y＝20）systems are summarized as 3D open cage（x=3-9）-3D close cage（x= 10-16）-irregular 3D（x= 17,18）-2D planar/quasi-planar（x= 19,20）.Further analysis of AdNDP chemical bonding reveals that multi-center bonding is the key part of the electronic structures in these clusters.When x ≤ 9,there are B-H bonds,B-H-B hydrogen bridge bonds and n center-2 electrons Bn bonds in the clusters.The hydrogen bridge bonds disappear whenx = 10,and when x=14,B-B single bonds appear,which are the signals for their bonding pattern transformation.This study reveals the evolutional rules of structure,energy and bonding pattern for B-H binary systems,which makes sense for the further theoretical and experimental study of borane clusters.In Chapter 5,the transition metal centered double-ring boron clusters M@B_2n（M=Ti,Cr,Fe,Ni,Zn;n=6,7,8）are investigated theoretically.It is well known that double-ring boron clusters have delocalized orbitals in both tangential and radial directions,which are potential ligands centered by a transition metal.In this chapter,the transition metal centered double-ring boron clusters M@B2n（M = Ti,Cr,Fe,Ni,Zn;n = 6,7,8）are investigated using density functional theory method.Theoretical calculation results indicate that Ni@B₁₂,Cr@B₁₄,Ni@B₁₄,Cr@B₁₆ and Fe@B₁₆ in this series of clusters keep high stability,which have double aromaticity in both tangential and radial directions.Interestingly,the tangential delocalized π orbitals of their boron ligands following the Huckle’s（4n + 2）rule do not interact with the central metal,while the radial π orbitals of boron ligands are bonded with the central metal to form spd-πmulti-center endohedral bondings.The spd-π endohedral bondings follow the 18e-principle in Ni@B₁₄ and Fe@Bi6 which makes these clusters stable.However,due to the flat shape of the compounds,14e(Cr@B₁₄)and 16e(Ni@B₁₂/Cr@B i6)can also be electronically very stable where the energy levels of the.spd-n orbitals delocalized in z-direction rise up.The intriguing bonding model revealed by this chapter enriches the bonding system of boron based clusters and makes sense in further experimental and theoretical study of boron chemistry.In Chapter 6,the work in this paper is summarized and the future plans are proposed.