Accurate Wichmann-Kroll vacuum polarization calculations with Gaussian basis set

We apply a large Gaussian basis set of size up to N = 500 to calculate the all-order Wichmann-Kroll vacuum polarization correction in highly-charged ion. For a hydrogen-like system, this allows us to obtain an accurate correction value with a level of precision comparable to that of traditional methods. We demonstrate that values of effects that can be calculated as the difference between two quantities, such as the nuclear model correction, converge faster than the absolute value of the correction. We discuss the basis extrapolation methods and show their use in estimating the error due to incomplete convergence. Finally, we show an application of the Gaussian basis set to calculation of the vacuum polarization screening correction in lithium-like ions.