Linear scaling density functional calculations via the continuous fast multipole method

We apply the linear scaling continuous fast multipole method (CFMM) to form the J matrix for molecular density functional calculations. Our implementation involves a new definition of charge distribution extent that bounds absolute errors. We efficiently treat short range interactions via a J matrix engine without fully uncontracting the basis. Calculations on 1-d, 2-d and 3-d carbon systems with the 3–21G basis establish crossover points versus the conventional approach, and yield linear scaling coefficients between 106 and 108 floating point operation, depending on dimensionalit. The CFMM plus J engine is a dramatic improvement for molecules over 50 to 100 atoms.