We have computed physical parameters such as density, degree of ionization and temperature, constrained by a large observational data set on atomic and molecular species, for the line of sight toward the single cloud HD147889. Diffuse interstellar bands ( DIBs) produced along this line of sight are well documented and can be used to test the PAH hypothesis. To this effect, the charge state fractions of different polycyclic aromatic hydrocarbons (PAHs) are calculated in HD147889 as a function of depth for the derived density, electron abundance and temperature profile. As input for the construction of these charge state distributions, the microscopic properties of the PAHs, e. g., ionization potential and electron affinity, are determined for a series of symmetry groups. The combination of a physical model for the chemical and thermal balance of the gas toward HD147889 with a detailed treatment of the PAH charge state distribution, and laboratory and theoretical data on specific PAHs, allow us to compute electronic spectra of gas phase PAH molecules and to draw conclusions about the required properties of PAHs as DIB carriers. We find the following. 1) The variation of the total charge state distribution of each specific class ( series) of PAH in the translucent cloud toward HD147889 ( and also of course for any other diffuse/ translucent cloud) depends strongly on the molecular symmetry and size ( number of p electrons). This is due to the strong effects of these parameters on the ionization potential of a PAH. 2) Different wavelength regions in the DIB spectrum are populated preferentially by different PAH charge states depending on the underlying PAH size distribution. 3) The PAH size distribution for HD147889 is constrained by the observed DIB spectrum to be Gaussian with a mean of 50 carbon atoms. 4) For the given PAH size distribution it is possible to constrain the total small catacondensed PAH column density along the line of sight to HD147889 to 2.4 x 10(14) cm(-2) by comparing the total observed UV extinction to the strong UV absorptions of neutral PAHs in the 2000-3000 Angstrom region. 5) Catacondensed PAHs with sizes above some 40 C-atoms are expected to show strong DIBS longward of 10 000 Angstrom. Large condensed PAHs in the series, pyrene, coronene, ovalene,...., on the other hand, mainly absorb between 4000 and 10 000 Angstrom but extrapolation to even larger pericondensed PAHs in this series also shows strong absorptions longward of 10 000 Angstrom. 6) Only the weak DIBs in HD147889 could be reproduced by a mix of small catacondensed PAHs (< 50 C atoms) while for large pericondensed PAHs ( 50 < C atoms < 100) the intermediate DIBs are well reproduced. Small catacondensed PAHs cannot contribute more than 50% of the total observed equivalent width toward HD147889. Strong DIBs can only be reproduced by addition of very specific PAH molecules or homologue series to the sample set (i.e., a small number of PAHs with high oscillator strength or a large number of PAHs with a low oscillator strength). An outline is provided for a more general application of this method to other lines of sight, which can be used as a pipeline to compute the spectroscopic response of a PAH or group of PAHs in a physical environment constrained by independent (non-DIB) observations.