Abstract <p>An operator method for calculating the elements of the Hamiltonian matrix of quantum chemistry in the basis of Slater atomic orbitals is proposed and formulas for two-center integrals from the generalized particle interaction potential in the form of the Yukawa potential, both single-particle and two-particle, are obtained. The explicit dependencies of the expressions obtained on the interatomic distances make it possible to analyze matrix elements and develop simple algorithms for calculating matrix elements of quantum chemistry in the AO basis of the Slater type.</p>