Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude.