Higher-order gradient corrections for exchange-correlation functionals

We examine whether it is possible to improve exchange-correlation functional through the introduction of fourth-order terms in the gradient expansion. On the whole our results are negative, principally because of the extreme numerical sensitivity of the matrix elements when higher powers of the gradient of the density are involved. The calculations are also more costly to perform. Our conclusion is that it appears to be very difficult to proceed to optimise functionals in this way.