A general expression for the nonrelativistic Hamiltonian for n-electron and N-mu-center molecules with S, P and higher angular momentum states is straightforward derived using the chain rule. The kinetic energy part is transformed into the interparticle distance coordinates r(i mu), r(ij), and internal polar angles theta(i mu), and rho(i mu) of the electrons with respect to every nucleus. This form of the Hamiltonian is appropriate to obtain the matrix elements in molecular calculations using wave functions as HF and CI with Slater orbitals, Hylleraas-CI, Hylleraas and explicitly correlated wave functions (ECG). (c) 2005 Elsevier B.V. All rights reserved.