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A robust density fitting method for calculating Coulomb matrix elements overBloch functions based on calculation of two- and three-center matrix elementsof the Ewald potential is described and implemented in a Gaussian orbital basisin the Exciton code. The method is tested by comparing Coulomb and exchangeenergies from density fitting to corresponding energies from SCF HFcalculations for diamond, magnesium oxide and bulk Ne. Density fittingcoefficients from the robust method are compared to coefficients from avariational method applied to wave function orbital products in bulk Ne. Fourcenter Coulomb matrix elements from density fitting are applied to timedependent Hartree-Fock (TDHF) calculations in diamond, magnesium oxide andanatase and rutile polytypes of titanium dioxide. Shifting virtual statesdownwards uniformly relative to occupied states and scaling the electron-holeattraction term in the TDHF Hamiltonian by 0.4 yields good agreement witheither experiment and/or Bethe-Salpeter equation calculations. This approachmirrors similar 'scissors' adjustments of occupied and virtual states andintroduction of a scaled electron-hole attraction term in some time dependentDFT calculations.

Density fitting in periodic systems: application to TDHF in diamond and oxides