One algorithm using these functions to compute four-body integrals is partly named for Warren Hehre, and another algorithm for computing integrals over them involves 20 different paths from shell-quartet parameters and is called PRISM.  Multicenter integrals over these functions are often calculated using the Boys function. Diffuse functions and polarization functions are often used to modify groups of them, and "primitive" ones are multiplied by contraction coefficients. These functions follow a namesake rule stating that a product of two of them is the sum of them centered along the line connecting the cores of the first two, which allows the reduction of four-center integrals to two-center integrals. These constructs, n of which make up one of Pople's STO-nG (*) basis sets, have a radial component that drops of
One algorithm using these functions to compute four-body integrals is partly named for Warren Hehre, and another algorithm for computing integrals over them involves 20 different paths from shell-quartet parameters and is called PRISM.  Multicenter integrals over these functions are often calculated using the Boys function. Diffuse functions and polarization functions are often used to modify groups of them, and "primitive" ones are multiplied by contraction coefficients. These functions follow a namesake rule stating that a product of two of them is the sum of them centered along the line connecting the cores of the first two, which allows the reduction of four-center integrals to two-center integrals. These constructs, n of which make up one of Pople's STO-nG (*) basis sets, have a radial component that drops off as e to the power negative r-squared, in contrast with their counterparts, which drop off as e to the negative r. These constructs can be linearly combined into Slater-type orbitals. For 10 points, name this type of orbitals commonly used in quantum chemistry, which look like normal distributions.
One algorithm using these functions to compute four-body integrals is partly named for Warren Hehre, and another algorithm for computing integrals over them involves 20 different paths from shell-quartet parameters and is called PRISM.  
Gaussian orbitals [or Gaussian basis sets; accept basis sets before mention since basically all basis sets consist of Gaussian orbitals, etc; prompt on “orbitals”]