To calculate the nuclear spectroscopic properties and solve the structure of element f oxides and other strongly correlated powders, it is necessary to use more accurate quantum chemical methods. For the actual modeling of nuclear-electron spectroscopy, it is necessary to consider the Britt interaction, so it is necessary to use the Gantt expression, which shows the rotation of the spin of an electron on its axis and is responsible for creating a vector potential that is equal to the vector potentials produced by all other electrons. will interact in the system and the gauge term that describes the retardation effects caused by the mutual interaction between the spin vector fields of the two electrons will be added to the Hamiltonian. In this paper, the full implementation of the four-component Dirac-Coulen-Britt Hamiltonian according to multi-resolution analysis with multi-wavelength basis has been done. The accuracy of the work is checked by comparing the ground state energies of charged helium-like ions in the increase of Z,X^((Z - 2)+) which is done with Python code (VAMPyR) and numerical radial interference in GRASP and Gaussian basis set calculations in DIRAC program. It was observed that the obtained results are independent of the selected nuclear charge model and depend on the tolerance and polynomial order of the selected multiwavelength legend. Moreover, the results confirmed that in the two-electron species, the magnetic and gauge contributions of the s orbitals are the same in value.