We have previously used the molecular three-body distorted-wave model to examine electron-impact single ionization of molecules. One of the possible weaknesses of this approach lies in the fact that the continuum electron wave functions do not depend on the orientation of the molecule. Here we introduce a model called the multicenter molecular three-body distorted-wave (MCM3DW) approach, for which the continuum electron wave functions depend on the orientation of the molecule at the time of ionization. The MCM3DW results are compared with experimental data taken from work by Dorn and colleagues [Ren, Phys. Rev. A 91, 032707 (2015)10.1103/PhysRevA.91.032707; Phys. Rev. A 93, 062704 (2016)10.1103/PhysRevA.93.062704; Phys. Rev. A 95, 022701 (2017)10.1103/PhysRevA.95.022701; Phys. Rev. Lett. 109, 123202 (2012)10.1103/PhysRevLett.109.123202; Gong, Phys. Rev. A 98, 042710 (2018)10.1103/PhysRevA.98.042710] in which they measured triple differential cross sections for single ionization of molecular hydrogen while simultaneously determining the orientation of the H2+ ion at the time of ionization. Comparisons are also made with previous theoretical calculations. It is found that orientation effects are important for low incident energy electrons. Very nice agreement with experiment and the time-dependent close coupling results is found for an incident electron energy of 26 eV. Orientation effects become relatively unimportant by the time the incident electron energy is 54 eV
