Clusters Of Indium-doped Sodium Indium Clusters Structure And Electronic Properties Of The Theory

In this dissertation,using density functional theory B3LYP functional and high accuracy CCSD(T) methods,the geometries,stability and spectroscopic properties of In.and In_n^-(n=2-10),as well as In_nNa_m and In_nNa_m+(n=2-9,m=1-2) clusters are investigated.The dissertation includes the following three parts:1.In_n and In_n(n=2-10) clustersThe geometries of In_n and In_n(n=2-10) clusters are optimized at the B3LYP/DGDZVP level and the vibrational frequencies are calculated at the same level of theory.The geometries and vibrational frequencies of In_n and In_n^-(n=2-4) clusters are further performed at B3LYP/CEP-121G+spd and the CCSD(T)/CEP-121G+spd and CCSD(T)/DGDZVP high level of theory.The binding energies, second-order difference of energy and electron affinities of the most stable In_n and In_n^-(n=2-10) clusters were calculated.The results show that the symmetries and electron states of the most stable structures of In_n(n=2-10) clusters are D_∞h(3П_u),C_2v(⁴A₂),D_4h(³A_2u),C_s(²A′),D_3h(³A1′),C_s(²A′), D_2h(¹A_g),C₁(²A) and C_s(¹A′),respectively.Also the symmetries and electron states of the most stable structures of In_n^-(n=2-10) clusters are D_∞h(Σ_g^-),D_3h(¹A1′),D_4h(²A_2u),C_s(¹A′),C_2v(²A₁),C_s (¹A′),C_2v(²B₁),C₁(¹A) and C_s(²A′),respectively.The geometrical parameters of In_n and In_n^-(n=2-4) at the ground state obtained from CCSD(T) are consistent with those from B3LYP,again,the optimized geometries,the order of energies and vibrational frequencies of the In_n and In_n^- cluster are little influenced by the basis sets.The electron affinities of In_n(n=2-10) cluster calculated by B3LYP method are in good agreement with the experiment.The binding energies and second-order difference of energy of In_n and In_n^-(n=2-10) indicate that the In₄,In₈,In₄^- and In₉^- clusters are more stable than the other size clusters.2.In_nNa and In_nNa⁺(n=2-9) clustersStrcutures of In_nNa and In_nNa⁺(n=2-9) clusters were optimized by the B3LYP,and their vibrational frequencies are calculated to evaluate their stability.The results show that the most stable structures of In_nNa(n=2,3,4 and 6) have C_2v,C_3v,C_4v and C_2v symmetry,respectively,while the symmetry of the In_nNa(n=5,7,8 and 9) clusters are C₁ point group.The structures of In_nNa(n=4-9) clusters have a same character,which the Na atom locates on the plane formed by four indium atoms. The most stable structure of In_nNa⁺(n=2-9) clusters are similar to their neutral structure except for In₂Na⁺,In_nNa⁺,In₇Na⁺ and In₉Na⁺.Furthermore,the average binding energy,second-order difference of energy,and adiabatic ionization potentials of In_nNa(n=2-9) clusters were calculated at the same level of theory.We find that the local peaks appear at n=4 and 6,indicating In₄Na and In₆Na are more stable than others.Moreover,the calculated adiabatic ionization potentials are in good agreement with the experiment values.3.In_nNa₂ and In_nNa₂⁺(n=2-9) clustersThe strcutures of In_nNa₂ and In_nNa₂⁺(n=2-9) clusters were optimized using B3LYP level,and their vibrational frequencies are calculated to evaluate their stability.The most stable structures of In_nNa₂(n=2,4,6 and 7) have C_2v,C_s,C_2v and C_2v symmetry,respectively,while the symmetry of the In_nNa₂(n=3,5,8 and 9) clusters are C₁ point group.The structures of In_nNa₂(n=4-9) clusters have a same character,i.e.the two Na atoms locates on the plane formed by four indium atoms.The most stable structure of In_nNa₂⁺(n=2-9) clusters are similar to their neutral structure except for In₂Na₂⁺,In₃Na₂⁺ and In₇Na₂⁺.Furthermore,the average binding energy,second-order difference of energy,and adiabatic ionization potentials of In_nNa₂(n=2-9) clusters were calculated at the same theoretical level,we find that the there is odd-even alternative character between second-order difference of energy and the size of the cluster.Also,the In₄Na₂ and In₆Na₂ are more stable than others.Moreover,the calculated adiabatic ionization potentials of In_nNa₂(n=4-9) consist with the experiment values.