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The calculation of average properties of atoms in molecules and interatomic surfaces is a difficult problem that requires the evaluation of two- and three-dimensional integrals over regions with nontrivial borders. A mathematical formalism is presented that maps these regions onto the whole of ℝ2 and/or ℝ3 and allows the construction of efficient and reliable numerical methods for the calculation of these integrals. These methods, which will be part of a forthcoming program package, are described and examples are given. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1040–1048, 2000
Friedrich W. Biegler-K�nig (Sat,) studied this question.