ABSTRACT
The scaling technique suggested by White and Head-Gordon significantly reduces the number of floating-point operations in the recurrence relations for associated Legendre functions. This improvement naturally extends to the recurrence relations for solid harmonics, and, in turn, simplifies the series expansion of the electrostatic potential. Scaling also simplifies the equations for the electrostatic force when they are defined in Cartesian coordinates. This chapter details the derivation of the recurrence relationships for regular and irregular solid harmonics, describes the application of scaling to the equations of force, and explains the program design for calculating the solid harmonics and electrostatic force. The chapter provides examples of the computer implementation of the regular and irregular multipole expansions, electrostatic potential, and force.
