Classification ...

The periodicity is related to the electronic configuration. That is, all chemical and physical properties are a manifestation of the electronic configurations of the elements.
The atomic and ionic radii generally decrease in a period from left to right. As a consequence, the ionization enthalpies generally increase the electron gain enthalpies become more negative across a period. In other words, the ionization enthalpy of the extreme left element in a period is the least and the electron gain enthalpy of the element on the extreme right is the highest negative. This results into high chemical reactivity at the two extremes and the lowest in the center. Similarly down the group, the increase in atomic and ionic radii result in a gradual decrease in ionization enthalpies and a regular decrease (with an exception in some third-period elements) in electron gain enthalpies in the case of main group elements.
These properties can be related to the:
(i) Reducing and oxidizing behaviour of the elements.
(ii) The metallic and non-metallic character of an element.
(iii) The acidic, basic, amphoteric and neutral character of the oxides of the elements.