改进的相对论量子化学计算ZORA方法

An Improved ZORA Method for Relativistic Quantum Chemical Calculations

提出一种改进的ZORA(Zeroth-Order Regular Approximation to the Dirac Equation)方法,其单电子方程为:[σ·p(c^2/(2c^2-V_0))σ·p+V(r)]Ψ=εΨ式中VO为空间限域的势能函数:V_0(r=sum from A to(V_0~A(r_A)),r_A=|r-R_A|,V_0~A(r_A)=V^A(r_A{1+exp[α(r_A-r_0~A)]}^(-1)其中A表示分子的某个组成原子,R_A为A原子的位置矢量,V^A(r_A)为自由A原子的势函数,α和r_0~A为参数.改进的ZORA方法具有原来方法的所有优点,避免了原有ZORA方法因不满足标度变换不变性带来的缺陷,而且计算过程简单.具体计算表明,通过适当选择参数α和r_0~A,用本研究提出来的方法,在计算分子几何结构和键合能时,基本上消除了ZORA方法由于标度变换依赖性产生的误差.

An improved ZORA (Zeroth - Order Regular Approximation to the Dirac Equation) method is presented. The related eigen equation reads where V0 is a proper space - limited potential function: where A denotes any one of the constitutional atoms of a molecule, VA( rA) is the potential of atom A in its free state. rA = |r - RA| , RA is the position vector of atom A. α and r0A are parameters to be fixed. The improved ZORA method possesses all the advantages of the ZORA method, while the error due to gauge dependence is reduced considerably. The calculations by use of the improved ZORA method on several molecules containing heavy elements show that with suitably selected parameters a and r0A the gauge dependence errors in the calculation of bond lengths and bonding energies are reduced to be comparable with those of the ESA or Scaled method presented by Lenthe et al. whereas the related computation is simpler.