Calculation of Quadrupole moments with Gaussian 90

[CHAKA%CWGK.DECNET(-(at)-)cwjcc.INS.CWRU.Edu]

    I am using Gaussian90 on the OSC Cray Y-MP to calculate molecular
 multipole moments.  For benzene, using a 6-31G** basis set, the nonzero
 diagonal elements of the quadrupole tensor are as follows:
                       Qxx   -31.2983  Debye-Ang.
                       Qyy   -31.2984
                       Qzz   -39.4673
 The molecule is in the standard position, i.e. in the  xy-plane, centered
 at the origin, with the C6 axis coincident with the z-axis.  I've run a
 few different basis sets, and the sign and relative magnitudes aren't
 affected very much.
    For a charge distribution with the symmetry of a benzene molecule,
 the  quadrupole tensor should be traceless and Qxx = Qyy = -0.5*Qzz.
     My question is this:  How are the quadrupole moments calculated in
 Guassian, and why are the diagonal elements all the same sign and
 nearly the same magnitude?
    I also have a question about the units.  Gaussian reports the quadrupole
 moment in units of Debye-Ang. ( Debye-Ang = 10E-18 esu-cm-Ang
 = 10E-26 esu-cm-cm.)  Experimental results, however,  give the benzene
 quadrupole moment (Qzz) as -33.3E-40 Coulomb-m-m, which is converted to
 -10.0E-26 esu-cm-cm, in a 1980 paper by J. Vrbancich & G.L.D. Ritchie,
 J.C.S. Faraday II, 76, 648-649.  The results I've been getting from
 Gaussian for the quadrupole moments are more consistent with C-m-m than
 Debye-Ang.  The dipole moments, on the other hand, agree fairly well
 (within an order fo magnitude) with experimental results in Debyes.
    Any light anyone can shed on this would be greatly appreciated. Thanks!
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 Anne Chaka                             (216)-368-3699
 Dept. of Chemistry
 Case Western Reserve University
 Cleveland, Ohio  44106
 chaka%cwgk.decnet(-(at)-)cwjcc.ins.cwru.edu
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