Abstract <p>This paper presents an analytical calculation by the operator method of complex multicenter integrals of quantum chemistry (three- and four-center) from the Coulomb and Yukawa potentials in the basis of Slater atomic orbitals that make up the elements of the Hamiltonian energy matrix in the numerical simulation of the electron shells of polyatomic molecules in the orbital representation. The obtained formulas of matrix elements are expressed in terms of elementary functions and can be used to develop new algorithms for the integral block of quantum chemical programs in the Slater basis of atomic orbitals.</p>