Hitherto known formulas for the translation of Slater-type orbitals (STOs) from one center to another encounter serious difficulties in practical applications. In contrast, those derived by the use of arbitrary complete orthonormal sets of exponential-type functions (ETFs) expansion formulas appear to be free of these difficulties. We have examined in this paper the applicability of translation formulas for STOs obtained from the two kinds of ETFs, namely, from the Lambda (A) and Coulomb Sturmian (CS) functions (Int. J. Quant. Chem. 81 (2001) 126) to the quantum-mechanical multicenter problems from the computational point of view and found it very useful. Test calculations on three-center nuclear attraction and four-center electron-repulsion integrals by single-center expansion method are reported. It is shown that these integrals in the case of Coulomb Sturmian ETFs exhibit a faster convergence rate. Therefore, it is recommended to use the expansion formulas for translation of STOs, obtained from the Coulomb Sturmian ETFs, in the calculation of multielectron multicenter molecular integrals. (C) 2001 Elsevier Science B.V. All rights reserved.