A method to approximate ab initio shielding constants is presented, in which the ab initio density matrix is replaced in the gauge invariant atomic orbital formalism with the density matrix resulting from an effective fragment potential calculation. The resulting first-order density matrix is then iterated to self-consistency. The method is compared with fully ab initio gauge invariant atomic orbital restricted Hartree-Fock calculations on hydrogen chloride, water, and ammonia solutes with up to nine solvent water molecules using the 6-31G, 6-31G(d,p), and 6-31+G(d,p) basis sets. Using the 6-31G(d,p) basis sets, the average of the average absolute deviations for the three environments tested is 0.34 ppm. This is sufficiently accurate to allow for the identification of specific H-1 nuclei in a solvated molecule when the chemical shift between nuclei is not less than 1 ppm. The success of the method at this level of approximation is due to a cancellation of errors between the paramagnetic and diamagnetic terms of the shielding constant: the diamagnetic term is underestimated by roughly the same amount that the paramagnetic term is overestimated. (C) 2004 American Institute of Physics.