To analyse that compound theoretically, Kusunose applied the concept of multipoles, which are useful for describing arrangements of electric charge or magnetic poles in space. The simplest multipole is a monopole; a single electric charge, such as a proton or an electron, is an example of a monopole. A dipole describes two equal but opposite charges; the north and south poles of a magnet are an example of a dipole, where the electric charge is replaced with a magnetic charge. Going up the multipole hierarchy adds increasing complexity. Any arrangement of electric charges or magnetic poles can be approximated by using a certain combination of multipoles — known as a multipole expansion.

Kusunose then embarked on an ambitious project to develop a truly comprehensive analysis framework of solids based on multipoles. That required quantum-mechanical expressions of four types of multipoles: electric multipoles, magnetic multipoles, and their vortex-like pattern, or toroidal, equivalents.