The structure, harmonic frequencies, and infrared intensities of the fundamental transitions of potassium hydrogen/deuterium maleate crystals have been computed by the density functional theory with periodic boundary conditions. Different functionals with all-electron Gaussian-type orbital (GTO) basis set have been used. It was found that BLYP/GTO approximation provides the best results for the structural parameters of the KH maleate crystal. Within this approximation, the hydrogen-bonded potential in the KH maleate crystal is extremely shallow. Delocalization of the bridging protons complicates a strict definition of the space group of the crystal; the space groups Pbcm and Pbc2(1) represent an equivalent choice. The periodic BLYP/GTO study provides detailed information on the nature of the internal vibrations of the hydrogen maleate anion, which are located in the range 300-1800 cm(-1). Assignment of the vibrational bands in this frequency region has been performed. The two most intensive bands in the infrared spectrum (similar to 500 and similar to 1450 cm(-1)) are caused by the "pure" asymmetric O center dot center dot center dot H center dot center dot center dot O stretching vibrations and the stretching motion of the bridging proton heavily mixed with the C-C stretching and CH bending vibrations, respectively. A crystalline environment is found to play an important role in the low-frequency region and is negligible above 1000 cm(-1). The H/D substitution slightly changes the vibration frequencies, involving the stretching motion of the bridging proton because of the strong coupling between this motion and the various internal vibrations of the hydrogen maleate anion.