We perform calculations of the core properties using various relativistic Hamiltonians to explore their impact on the properties. Firstly, we have performed a couple of calculations with the four-component (4c) Hamiltonians: Dirac-Coulomb (4c-DC) and Dirac-Coulomb-Gaunt (4c-DCG) Hamiltonian to see the effects of relativity. Then, we replace the 4c-Hamiltonian with exact twocomponent (2c) Hamiltonian, X2C . It is noteworthy that in the X2C Hamiltonian scheme of DIRAC10 program package, the two-electron spinsame-orbit (SSO) coupling contribution is treated in mean-field fashion using the AMFI code , and the X2C Hamiltonian that includes the two-electron spin-other-orbit (SOO) coupling along with the SSO interaction in the same way is termed as the X2C-G Hamiltonian in this article. The calculated results are presented in Table and it is clear from this table that the 2c-Hamiltonian results are in excellent agreement with those obtained using the 4c-DC Hamiltonian within an uncertainty of 3.5%. Thus, the use of computationally less expensive X2C Hamiltonian in lieu of the 4c-Hamiltonian in the molecular calculation of the core properties of SrF could be reliable. However, the use of the 4c-DCG Hamiltonian (i.e., the mean-field Gaunt correction) slightly lowers the numerical values of the core properties compared to the corresponding 4c-DC results whereas the S-PS interaction constant is almost unaffected. So, we can comment from our study that the missing of the higher-order relativistic effects would not affect the molecular calculations of current interest significantly.