Efficient and accurate numerical integration of exchange-correlation density functionals

We present a method for efficient calculation of exchange correlation in a density-functional theory calculation with Gaussian basis functions. It seamlessly combines the treatments of smooth (low-energy cutoff) and nonsmooth parts of the electron density such that computational performance can be maximized without approximation. Benchmark calculations show that the scheme can speed up the calculation of the exchange-correlation by as much as ten times or more without error.