Using new complete orthonormal sets of exponential-type orbitals introduced by the author (I.I. Guseinov, Int J Quantum Chem, submitted), the different analytical expressions are derived for the expansion of one- and two-center electron charge density over Slater-type orbitals (STOs) in terms of STOs about a new center. The expansion coefficients in these formulas are expressed through the overlap integrals with the same screening parameters. The one-center expansion formulas in terms of STOs are also obtained for arbitrary central and noncentral potentials (CPs and NCPs). Using the expansion formulas obtained for the electron charge density and potentials, the general formulas are established for the multicenter molecular integrals of CPs and NCPs. In the formulas for the multicenter molecular integrals of CPs and NCPs, all the expansion coefficients and the overlap integrals are expressed through the binomial coefficients. The final results are especially useful for the calculation of these quantities for large quantum numbers. Using the derived expressions in terms of binomial coefficients, one-electron molecular integrals over STOs can be evaluated efficiently and accurately from the series expansion formulas. The relationships obtained are valid for the arbitrary location, quantum numbers, and screening constants of atomic orbitals. (C) 2002 Wiley Periodicals, Inc.