where are coordinates of spin up electrons and of spin down electrons. For polarized system is possible extend the definition of the geminal wave-function. This generalization was first proposed by Coleman (110). In practise if we can define a matrix in the following way:

for | (B.9) | ||

for | (B.10) |

When we move an electron to ratio between the old and the new determinant will be given for a spin down electron:

(B.11) |

and for spin up:

For updating the inverse matrix , used here, after a move we follow the simple formula used for the Slater determinant(38) with indices that depend from the spin of the electron.

- Gradients and Laplacian
- The logarithmic derivatives
- Second derivatives
- Derivatives of the Local Energy