We examined numerically the equivalence between the expectation values calculated by the four-component wave function and those calculated by the two-component wave functions generated by the infinite-order Douglas-Kroll (IODK) transformation. We showed the expectation values and in several closed-shell atoms using the so-called picture-changed 2x2 operators at some levels of approximation. The effect of the two-electron Coulomb term was also discussed. The numerical results indicated that the accuracy of mainly depends on the level of the wave functions, while that of is affected by the accuracy of both the wave functions and the picture-changed operators. As expected, the picture-changed operators and the IODK wave functions generate essentially equivalent expectation values in comparison with those calculated by the four-component Dirac-type method.

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