Calculating zero-field splitting (ZFS) parameters, D and E, as a function of molecular geometry is one of the few methods available for elucidating the conformations of organic molecules having more than one unpaired electron.1,2 The ZFS parameter D gives an indication of the dipolar interaction of unpaired electrons in molecules in the absence of spin-orbit coupling and therefore is related to interelectronic distance.Rigorous theoretical determinations of D using highquality ab initio wavefunctions have been performed for the excited-triplet states of formaldehyde, 3 benzene and naphthalene 4 and ground-triplets states of methylene 5 and trimethylenemethane. 6 Although it is theoretically possible to determine D with ab initio basis sets and electron correlation, it may not be computationally practical-a fact which has led to the derivation of approximate methods to simplify the task of evaluating the large number of integrals involved for even moderatesized molecules.7 These various approximations used for the theoretical determination of D have been presented in the literature over the last several decades. 1,4,[8][9][10][11][12][13][14][15][16][17][18][19][20][21] An approximation which is frequently used by Mukai and co-workers 1,19,20 iswhere r ij is the distance between atoms i and j, m ij is the distance vector along the axis which gives rise to the largest dipole-dipole interaction and r i and r j are the spin densities on atoms i and j. This equation has been used to give reasonable D value approximations for biradicals with localized electron distributions that can be separated into monoradical halves with atoms i and j belonging to different halves (hereafter referred to as localized biradicals.) The spin densities used are those of each monoradical half. It has been noted that this equation provides only crude approximations for delocalized biradicals, 21 which initiated an investigation in our laboratory into finding a simple approximate method that would provide more reasonable D values for delocalized biradicals owing to our interest in moderate-sized nondisjoint organic molecules with S b 1/2. 22 The problem we encountered in trying to use Eqn (1) for delocalized radical systems was that the delocalized system could not be separated into monoradical halves due to shared spincontaining atoms (hereafter referred to as delocalized biradicals). Since the dipole-dipole interaction, and thus the D value, strongly depend on the average distance between the two unpaired electrons (varying as 1/r where atom i is a spin-containing atom (spin density !0.01) in one SOMO and atom j is a spin-containing atom (also with spin density !0.01) in the other SOMO, and r ij refers to the distance between spin-containing