A reason why to use the Gaussian-type-orbital is not suitable for the relativistic calculation of the nuclear-magnetic-resonance spectra with using the restricted magnetic balance

[Display omitted] •There is the physical quantity σ→·(p→+A→)Vσ→·(p→+A→) in the Hamiltonian of the matrix Dirac equation.•The precision of the STO-30G is less than one significant figure for the quantity given by iσ→·(p→×VA→+VA→×p→) in the Gauss-type charge density distribution model.•As seen in Table 3, the precision calculated even with the STO-30G is less than one significant figure for the quantity given by iσ→·(p→×VA→+VA→×p→) in the homogenous charge density distribution model, although it is 13 significant figures for the overlap integral as seen in Table 2.•With the present numerical results, we can conclude that to use the GTO is not suitable for the calculation of the physical quantity given by iσ→·(p→×VA→+VA→×p→). Numerical calculations are performed for a physical quantity which is appearing in the Hamiltonian of the matrix Dirac equation with containing the vector potential of the magnetic field due to the nuclear spin and with considering the restricted magnetic balance. This quantity is necessary for the relativistic calculation of the nuclear-magnetic-resonance spectra. It is shown that to use Gaussian-type orbital is not suitable for the calculation of this quantity.