We have performed quantumchemical investigations towards a further explanation of the reaction mechanism of the hydrogen evolution reaction on semiconductor electrodes (continuation of Z. Phys. Chem. 210 (1999) 95). Details of the two-step-mechanism via Had-intermediates on both GaAs(111)A- and GaAs(110)-surfaces were studied on two different theoretical foundations. On the one hand we have made molecular cluster calculations on ab initio Hartree-Fock-, MP2- or DFT(B3LYP)-level. On the other hand we have performed calculation on periodically repeated supercells in the density functional formalism at special topics of our systems. Effects of solvation and of an applied electrode potential on the energy potential profiles along restricted reaction paths were investigated. On the (110)-surface a reaction sequence via Had-intermediates both on the gallium and on the arsenic sites should be possible. For the Volmer step we find a return of the preferred adsorption position from the arsenic site to the gallium site if the applied electrode potential runs from zero to negative values. Against it, the Heyrovsky step is always slightly preferred on the arsenic site, independent on the applied electrode potential. The hydrogen evolution on local structure motifs with 3-fold-coordinated, sp3-hybridised Ga-surface atoms and no concurrence of As-surface atoms, like on an ideal GaAs(111)A-surface structure, is slightly preferred in comparison to the (110)-surface and a shift of the onset potential towards a less negative value is expected. For all the treated reaction sequences we have calculated charge injection coefficients, which agree very well with the data from experiments and from macroscopic charge transfer dynamics simulations.