An improved ZORA 9Zeroth-Order Regular Approximation to the Dirac Equation) method is presented. The related eigen equation reads [σ· p(c^2/2c^2-V~0)σ·p+V(r)]ψ=εψ. Where V~0 is a proper space-limited potential function; V~0(r=~A∑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. Where A denotes any one of the constitutional atoms of a molecule, V^A(r~A) is the potential of atom A in its free state. r~A=|r-R~A|, R~A is the position vector of atom A. α and r~0^A 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 α and r~0^A 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.

Key words: QUANTUM CHEMISTRY, BINDING ENERGY, RELATIVISTIC EFFECTS, BINDING ENERGY