Application Of Relativistic Density Functional Theory On The Molecules And Clusters Of Heavy Elements

The four-component Dirac equation is the basis of the relativistic electronic structure theory.Due to its computational complexity,however,the two-component or scalar quasi-relativistic methods are often used instead,which may also be classified into all-electron quasi-relativistic methods and relativistic pseudo-potential?PP?according to whether the core electrons being calculated variationally.Among these methods,the recently developed exact two-component?X2C?method has attracted much attention since it makes the analytic derivative calculations much faster and more efficient.As the most representative quasi-relativistic methods,X2C and PP are selected in this dissertation to combine with the density functional theory?DFT?,and are used to study some heavy element-containing molecules and clusters.The molecular system of heavy element to be studied is Hg?CN?₄,which is the first case of the fast derivative algorism of X2C used in vibrational frequencies and chemical reactions.Using the PBE0 functional with either X2C or PP,its structure,properties,and chemical decomposition reaction have been calculated,and its stability has been predicted.It is found that the Hg?CN?₄ molecule has a planar structure with the D_4h symmetry,where Hg and C are bonded by a polar covalent single bond along with a covalent triple bond between C and N,and the oxidation state of Hg is+4.The computational results show that Hg?CN?₄ is kinetically stable and may exist under low temperature conditions below 180 K.These results provide a great potential for searching mercury compounds with high oxidation states.In the case of clusters with many heavy atoms,PP is more efficient than X2C.We use PP to study a uranium atom embedded into lead clusters of different sizes,in which the often overlooked spin-orbit coupling effects have been especially evaluated.The structures of ground and metastable configurations of UPb_n?n=6-16?clusters have been obtained after configuration searching,and the stability of ground configurations and the effects of spin-orbit coupling on the clusters have been analyzed.It is found that with the increasing of n,the U atom tends to transfer from surface to interior of the clusters,and the evolution process of structure transformation takes place roughly within the range of n between 8 and 11.After spin-orbit coupling being taken into account,the UPb_n clusters become more stable,and the magnetic moments of both the clusters and the U atom are significantly affected.The results also show that the UPb₁₀ and UPb₁₂ clusters are more stable than their neighbor ones.In future studies,we want to change the properties of the UPb_n clusters by adjusting the clusters to get better performance for a specific goal.