Molecular spectra are usually found from Casida's TDDFT based Hamiltonian. The TDDFT linear response equations of Gross, Petersilka and Gossman are difficult so solve (except for very small molecules) because they involve the free density-density reponse $\chi _{0}$ that lives in a space of too large dimensions. I use collinearity in the space of particle hole excitations to construct $\chi _{0}$ with a precision that is exponential in the number of degrees of freedom used. This simplifies the calculation of molecular spectra and might be useful elsewhere, for example in the GW method.