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A method for calculating multiple long-range interaction potentials between an atom (C in this particular case), and closed-shell molecules is described. This method was recently utilized by Bettens and Collins [J. Chem. Phys. 114, 10342 (2001)] for determining capture rate coefficients for collisions of C ([sup 3]P[sub j]) and Ge ([sup 1]S[sub 0]) with unsaturated hydrocarbons. The method takes account of the physical size of the molecule and exactly treats the electrostatic interaction between the quadrupole of the atom and all electrostatic moments of the molecule. This method requires a molecular density matrix, which can be obtained from an ab initio calculation. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]