NOVELTY - Selection of substituted element of lithium-nickel-containing complex oxide active material (I), involves selecting substituted element in which difference (Ea) of most stable energy (E2a) of lithium-nickel-complex oxide of spinel structure and most stable energy (E1a) of lithium-nickel-complex oxide of layered halite structure, is smaller than the difference (Eb) of most stable energies (E2b) and most stable energy (E1b) of lithium-nickel oxide, and performing energy calculation by plane wave first principle calculation based on density functional theory.    USE - Selection of substituted element of active material used for battery (all claimed). Uses include but are not limited to personal computer, video camera, mobile telephone, communication apparatus, electric vehicle and hybrid vehicles.    ADVANTAGE - The method efficiently and correctly selects substituted element, with excellent thermal stability. The battery using the active material has excellent charging/discharging efficiency.    DETAILED DESCRIPTION - Selection method of substituted element of lithium-nickel-containing complex oxide active material of formula: LiNi1-x MxO2 (I), involves selecting substituted element in which difference (Ea) of most stable energy (E2a) of lithium-nickel-complex oxide (LiNi2-2xM2xO4) of spinel structure and most stable energy (E1a) of lithium-nickel-complex oxide (Li0.5Ni1-xMxO2) of layered halite structure, is smaller than the difference (Eb) of most stable energy (E2b) of lithium-nickel oxide (LiNi2O4) of spinel structure and most stable energy (E1b) of lithium-nickel oxide (Li0.5NiO2) of spinel structure, and performing energy calculation process calculated by plane wave first principle calculation based on density functional theory. The arrangement of trivalent nickel and tetravalent nickel becomes most stable on the condition which set the molar ratio of 1:1.    M=groups II-XIV metallic element;and    x=more than 0 to 0.1.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of active material, which involves selecting substituted element by selection method, and synthesizing the active material having substituted element;    (2) active material; and    (3) battery, which has positive electrode active material layer, negative electrode active material layer, an electrolyte layer formed between the positive electrode material layer and negative electrode active material layer. The positive electrode active material layer and negative electrode active material layer contains active material.