AN ALGORITHM FOR 3D NUMERICAL-INTEGRATION THAT SCALES LINEARLY WITH THE SIZE OF THE MOLECULE

The cost of numerical integration in density-functional theory scales as the cube of the size of the molecule: it is proportional to the num ber of grid points and to the square of the number of basis functions. We describe a scheme that makes this cost independent of the number o f basis functions, thus yielding an algorithm that scales linearly wit h the size of the molecule. The error introduced by the present scheme can be made as small as desired by lowering a threshold tau. The meth od can be applied to any quadrature rule and local basis set.