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The potential utilization and development of the Ba isotope tool depend on an accurate δ137/134Ba determination of the samples. During the chemical purification, whether the adsorption process on the surface of the ion-exchange resin could lead to the Ba isotopic fractionation and the degree of fractionation directly influence the accurate δ137/134Ba determination. In the present work, first-principles calculations based on the density functional theory were used to quantify the Ba isotopic equilibrium fractionation factor between the aqueous solution and the resin in the acid leaching process. By constructing and optimizing the geometric configurations of Ba-containing species, (Ba(H2O)n2+, Ba(H2O)nCl2, Ba(H2O)n(NO3)2, and the adsorbed Ba2+ on the surface of the resin, extracting the harmonic vibrational frequencies, we finally at 298 K obtained the fractionations, Δ137/134Basoln-ads = 0.07‰, Δ137/134BaBa(H2O)nCl2-ads = 0.05‰, and Δ137/134BaBa(H2O)n(NO3)2-ads = 0.02‰. Overall, there were almost no Ba isotope fractionations during leaching. Although the Ba isotope fractionation can be magnified by the Rayleigh fractionation process in purification, the difference in δ137/134Ba between the initial and final stages did not exceed 0.060‰ (or 0.045‰) when leaching the standard sample with HCl or HNO3, which is equal to or less than the accuracy of Ba isotopic analysis. At a common yield of 89.75%, Ba isotopic fractionation induced by incomplete recovery was 0.015‰ for HCl (or 0.011‰ for HNO3). Finally, if the influence of an incomplete recovery on the δ137/134Ba determination needs to be ignored, the recovery is suggested to be not less than 67% for HCl (or 46% for HNO3). [ABSTRACT FROM AUTHOR]