) is a component of a modified interaction tensor, which is defined further below. The Cartesian component of the multipole and interaction tensor is indicated by a multiindex in square brackets. For example, M [0,0,0] is a charge, M is the x-component of a dipole, M is the xz-component of a quadrupole, and so on. Moreover, eq 3 introduces the multi-index norm, which is defined as the sum of the elements, i.e. |α| = α x + α y + α z , and the multi-index factorial, which is defined by the product of factorials of the elements, i.e. α! = α x ! • α y ! • α z !. The sum over multi-indices includes all multi-indices whose norm is less than or equal to the upper summation limit, so that for A i = 1 it includes (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1). The maximum order of the multipoles is thus defined by A i .