Loading [MathJax]/extensions/TeX/boldsymbol.js

 

 

 

Project 2, VMC for fermions: Efficient calculation of Slater determinants

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.