Quantum-chemical calculation of stability of graphite nanoclusters

1. Quantum-chemical calculation of stability of graphite nanoclusters Olga Ananina, Pavel Butrimov and Alexandr Yanovsky Zaporozhye National University, Zaporozhye, Ukraine Outline Interlayer distance in graphite nanoclusters Interlayer interaction energy in graphite nanoclusters Influence of edge hydrogen saturation on interlayer interaction energy in graphite nanoclusters Influence of edge form on interlayer interaction energy in graphite nanoclusters

2. A.M.Ziatdinov, Nanographenes and nanographites: synthesis, structure and electronic properties. Vestnik DVO RAN 2006. № 5 graphite nanographite overlap integral γ=390 meV γ=5 meV B. T. Kelly, Physics of Graphite, Applied Science, London 1981 R. R. Hearing, P. R. Wallace, J. Phys. Chem. Solids 1957, 3, 253. the value of interlayer interactionis 52±5 meV per atom R. Zacharia, H. Ulbricht, T. Hertel, Phys. Rev. B: Condens. Matter 2004, 69, 155 406

3. Forms of the layers and edges One layer of С200H80cluster С50H20 One layer of С126H54cluster С42Н18 mixed edge zigzag edge

4. Calculation methods Simulation of nanographites was carried out by a group of methods: semi-empirical MNDO, MINDO/3, AM1 and PM3 methods of МОРАС software, and also ab-initio Hartree-Fock methods of GAMESS program Secular Equation Approximations used in MNDO The general Fock Matrix elements

5. Interlayer distance depending on number of atoms in cluster with combined (mixed) edge Geometry optimization result for C60H36 cluster (MNDO method) * - the distance between the nearest carbon atoms in two adjacent graphene layers turned from each other in graphite nano-cluster is specified.

6. Geometric and electronic characteristics of graphite nano-clusters One of С126Н54 graphite nano-cluster layers С126Н54 graphite nano-cluster after geometry optimization red C-C bond lengths is 1,46 Å ÷ 1,49 Å green C-C bond lengths is 1,42 Å ÷ 1,44 Å blue C-C bond lengths is 1,40 Å ÷ 1,43 Å

7. Estimation of interlayer interactionenergy.Semi-empirical calculations graphene sheets with the mixed (combined) edge and about 40 atoms in a layer, with dangling bonds saturated by hydrogen atoms interact with energy 6,35 ÷ 8,57 meV/atom; the distance between layers is about 3,73 ÷ 3,85 Å.

8. Estimation of interlayer interactionenergy for nanocluster with mixed edge. Ab initio calculations C126H54 cluster Interlayer interaction energy in C126cluster is 0,529 eV (6.3 eV per atom) dmin=3,94 Å C126H54 cluster is 0,009 eV dmin=4,1 Å The obtained result somewhat contradicts results of simulation obtained by semi-empirical methods which fix a minimum on “interlayer interaction energy - interlayer distance” curve for similar nanoclusters.

9. Estimation of interlayer interactionenergyfor nanocluster with zigzag edge. Ab initio calculations С200Н80 and C200 graphite nano-clusters with zigzag edges before and after geometry optimization d0=3,35 Å d=3,86 Å ÷ 4, 16Å d0=3,35 Å d=3,88 Å ÷ 4, 21Å

10. Simulation of vacancy defect in С126Н54 cluster d0=3,86 Å d=3,88 Å ÷ 4, 16Å Interlayer interaction energy in defect cluster is on 0,14 eV more, than in cluster without defect. Energy gap between HOMO and LUMO in defect cluster is on 0,74 eV less, than in cluster without defect. a) Optimized С126Н54 cluster; b) Cluster С125Н54 with vacancy in the middle of second layer after geometry optimization; с) DOS of С126Н54 system; d) DOS of С125Н54 system

11. Simulation of vacancy defect in C200H80 cluster Cluster С199Н80 with vacancy in the middle of second layer after geometry optimization • Results of calculation: • The value of interlayer distance in C199H80 defect cluster increases in comparison with optimized C200H80 on 0,08 Å ÷ 0, 22 Å • Interlayer interaction energy in defect cluster is on 0,11 eV more, than in cluster without defect. • Energy gap between HOMO and LUMO in defect cluster is on 0,46 eV less, than in cluster without defect.

12. Summary • Nanographite clusters without point defects and with small number of atoms in the layer (up to 40) are set of weakly interacting nanographenes. In our opinion, existence of such graphite nanoclusters as single system is not observed, and it is impossible. • The tendency to decrease of interlayer distance in nanographite with increase of number of atoms in a layer is observed. And although the calculated interlayer interaction energy per one atom does not increase with increase of number of atoms in a layer, the increase in interlayer interaction energy as a whole is observed, which leads to formation of more stable graphite nanoclusters. • The form of nanocluster edges influences the value of interlayer interaction energy and value of interlayer distance. Interlayer interaction energy and interlayer distance in nanoclusters with zigzag edge is larger, than in nanoclusters with the mixed edge. • Saturation of nanoclusters edges (with the mixed and zigzag edges) by hydrogen atoms results in decrease of interlayer interaction energy in comparison with nano-clusters with σ-dangling bonds at edges. • Results of simulation can essentially depend on the chosen calculation procedure. Edge type more strongly influences the calculated parameters of small-size systems.