Based on the background described above, in this study, we conducted systematic first-principles calculations on various layered intercalation compounds with different intercalants to calculate their structures and energies, creating a database. While databases specialized for layered structures, such as 2D-materials exists, this study is the first to establish a database specifically for the layered intercalation compounds. Notably, our database is distinctive in its coverage of not only stable compounds with high synthesizability but also comprehensive calculation of less stable compounds. This approach allows for a thorough examination of the underlying physics, facilitating discussions on factors influencing both stability and instability. Next, we attempted to identify the factors contributing to the stability of layered intercalation compounds from the perspective of HSAB principle. As a result, we discovered that the intercalation energy required for intercalation of layered intercalation compounds, obtained through the first-principles calculations, can be linearly regressed from the following two physical properties: 1) the standard Gibbs free energy of formation of the intercalant ion and 2) the ionic radius of the intercalant. This relationship is captured by a simple regression equation derived from the HSAB principle. Through this study, we have successfully extracted fundamental principles that provide valuable guidance for the efficient design of layered intercalation compounds within the vast combinatorial space. Our findings suggest potential advancements in diverse applications, and we anticipate the possibility of synthesizing new layered intercalation compounds based on this model.