The effects of longitudinal quadrupole moments on the formation of liquid crystalline phases are studied by means of constant NPT Monte Carlo simulation methods. The popular Gay-Berne model mesogen is used as the reference fluid, which displays the phase sequences isotropic-smectic A-smectic B and isotropic-smectic B at high (T*=2.0) and low (T*=1.5) temperatures, respectively. With increasing quadrupole magnitude the smectic phases are observed to be stabilized with respect to the isotropic liquid, while the smectic B is destabilized with respect to the smectic A. At the lower temperature, a sufficiently large quadrupole magnitude results in the injection of the smectic A phase into the phase sequence and the replacement of the smectic B phase by the tilted smectic J phase. The nematic phase is also injected into the phase sequence at both temperatures considered, and ultimately for sufficiently large quadrupole magnitudes no coherent layered structures were observed. The stabilization of the smectic A phase supports the commonly held belief that, while the inclusion of polar groups is not a prerequisite for the formation of the smectic A phase, quadrupolar interactions help to increase the temperature and pressure range for which the smectic A phase is observed. The quality of the layered structure is worsened with increasing quadrupole magnitude. This behavior, along with the injection of the nematic phase into the phase sequence, indicate that the general tendency of the quadrupolar interactions is to destabilize the layered structure. A pressure dependence upon the smectic layer spacing is observed. This behavior is in much closer agreement with experimental findings than has been observed previously for nonpolar Gay-Berne and hard spherocylinder models. (C) 2003 American Institute of Physics.