The Faraday B term of magnetic circular dichroism is expressed in terms of
single residues of quadratic response functions. These residues contain, ho
wever, singularities where the frequency parameter is equal to the excitati
on energy. The singularities are removed by solving the ill-defined linear
response equations in a space orthogonal to the excitation vector. The B te
rms are calculated for the N --> V pi --> pi* and Rydberg pi --> 3s transit
ions at the SCF and MCSCF levels for ethylene and for the lowest-lying X(1)
A(g) --> 1(1)B(1u) transition in p-benzoquinone at the SCF level. (C) 1999
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