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A method to derive the atomic multipole moments cumulatively up to quadrupole mo-ments was developed.The multipole moments are obtained by least-square simulating the molecularelectrostatic potentials.Only the components of the term of highest order in the atomic multipoleexpansion are optimized while the lower terms remain fixed.The calculations on HF,H_2O and NH_2show that the cumulative method can give reasonable qualitative and fairly good quantitative results.