  We report on a first-principles investigation of the electronic structure and
of the magnetic properties of the quasi-two-dimensional Mott insulator
SrCu$_{2}$(BO$_{3}$)$_{2}$. Based on the hopping integrals and Coulomb
interactions calculated with LDA and LSDA+U, we provide a microscopic
explanation of the symmetric Heisenberg and antisymmetric Dzyaloshinskii-Moriya
exchange integrals of SrCu$_{2}$(BO$_{3}$)$_{2}$. The intra-atomic exchange
interaction of oxygen is shown to strongly contribute to the intra-dimer
isotropic exchange. The results are in good agreement with those derived from
experimental data, both regarding the orientation of the Dzyaloshinskii-Moriya
vectors and the magnitude of all exchange integrals. The microscopic analysis
is confirmed by the results of Green function's and total energies difference
methods.
