The potentially most time-consuming part is the evaluation of the gradient and the Laplacian of an \( N \)-particle Slater determinant.

We have to differentiate the determinant with respect to all spatial coordinates of all particles. A brute force differentiation would involve \( N\cdot d \) evaluations of the entire determinant which would even worsen the already undesirable time scaling, making it \( Nd\cdot O(N^3)\sim O(d\cdot N^4) \).

This poses serious hindrances to the overall efficiency of our code.