  We show that quasi-periodic fluctuations in the charging energy E_C of small,
chaotic quantum dots result from strongly scarred states which are the remnant
of periodic orbits in the classical confining potential. We perform
self-consistent, density functional and spin density functional calculations
for the dots used in the recent experimental studies of Sivan et al. [PRL 77,
1123 (1996)]. We directly compute the direct Coulomb matrix elements W_{pq},
screened by the gates, between self-consistent states. We show that diagonal
elements (denoted U_p) are uniformly larger than off diagonal elements,
resulting in spin polarization of the dot. We show that strongly scarred
states, which are quasi-one dimensional, have particularly large values of U_p
which causes them to remain, partially occupied, at the Fermi surface as gate
voltage V_g is swept and more homogeneous, ``chaotic'' states pass through. We
show that ultimate double-filling of these scars results in large upward
fluctuations of E_C. In addition, we show that V_g dependence of capacitances
and level energies substantially enhances fluctuations in the gate voltage
spacing dV_g of Coulomb oscillations, as compared to and distinct from
fluctuations in the ``inverse compressibility'' (i.e. E_C). Moreover, these
dependences modify the distribution of dV_g fluctuations so that purely upward
fluctuations of E_C produce symmetric fluctuations in dV_g. Consequently, gate
voltage fluctuations (normalized by the appropriate capacitance ratio) are
substantially greater than the single particle level spacing, Delta, but, as we
show by direct calculation, their temperature T scaling is consistent with
Delta/T and not E_C/T, in complete agreement with experiment.
