The self-consistent field theory of Scheutjens and Fleer is implemented on a grid with (lattice) sites that are smaller than the segment size. In this quasi lattice-free implementation we consider united atom-like molecular models and study bilayer self-assembly of phospholipids in a selective solvent (water). We find structural as well as mechanical parameters for these bilayers. The mean (κ) and Gaussian ([small kappa, Greek, macron]) bending moduli, as well as the spontaneous curvature of the monolayer (Jm0), are computed for the first time following a grand canonical ensemble route. Results are in line with previous estimates for mechanical parameters that at the time could not be made following this correct route. This proves that the mean bending modulus is only a very weak function of the membrane tension. We performed a systematic study on the effects of model parameter variations. The mean bending modulus generally grows with increasing bilayer thickness. As expected Jm0 and [small kappa, Greek, macron] behave oppositely with respect to each other and for classical phospholipids assumes values near zero. As an example, an increase in the lipophilic to hydrophilic ratio in the lipids, may cause the Gaussian bending rigidity to switch sign from negative to positive, while - not necessarily at the same point - the spontaneous curvature of the monolayer may switch sign from positive to negative. Together with other investigated trends, these results point to mechanisms of how topological phase transitions of the lipid bilayer membranes may be regulated in the biological context, which correlates with known lipid phase behaviour.