Abstract: The formulae of two-electron integrals are optimized by using complex Slater orbitals. Analysing both the formula structure and the instability of auxiliary functions, we obtain some approximate conditions of realizing the best balance between the required accuracy and the computational speed.

Key words: two-center two-electron integrals, the best balance between required accuracy and speed, complex Slater orbital, high accuracy calculation, auxiliary functions, optimization of algrithm, analysis of error