An atomic integral direct implementation of the second order polarization propagator approximation (SOPPA) for the calculation of electronic excitation energies and oscillator strengths is presented. The SOPPA equations are solved iteratively using an integral direct approach and, contrary to previous implementations, the new algorithm does not require two-electron integrals in the molecular orbital basis. The linear transformation of trial vectors are calculated directly from integrals in the atomic orbital basis. In addition, the eigenvalue solver is designed to work efficiently with only three trial vectors per eigenvalue. Both of these modifications dramatically reduce the amount of disk space required, thus, increasing the range of applicability of the SOPPA method. Calculations of the lowest singlet excitation energies and corresponding dipole oscillator strengths for naphthalene and anthracene employing basis sets of 238 and 329 atomic orbitals, respectively, are presented. The overall agreement of our results with experimental spectra is good. The differences between the vertical excitation energies calculated by SOPPA and the position of the maximum intensity peaks in the experimental spectra are within the range of +/- 0.35 eV with two exceptions, the 4 (1)A(g) state of naphthalene and anthracene where a 0.85 eV and 0.41 eV deviation is found, respectively. The relatively large discrepancy for this transition is due to large contributions from two-electron excitations which cannot accurately be described in SOPPA. For naphthalene we find additional excitations to Rydberg states of (1)A(u) and B-1(2u) symmetry as compared with previous calculations. (C) 2000 American Institute of Physics. [S0021-9606(00)30908-4].