The purpose of the present work was to develop a method allowing one to extract the information needed for the construction of the internal chemical hardness tensor at the molecular orbital level from standard density functional calculations. This method is based on the Janak theorem and on the extension of the Slater transition-state concept. A detailed discussion of the current ideas about the validity of the Janak theorem is presented as well as of the established relations of this subject with the ensemble V-representability problem. The internal chemical hardness tensor has been obtained for water molecule as an example system. Its structure is consistent with the criteria for the internal molecular stability.