The wave-function for high pressure hydrogen

In order to study the high pressure hydrogen we used the periodic generalization of the JAGP wave-function defined in the chapter 1. In the two-body 1.2.3 terms and one-body 1.2.2 terms the distances electron-electron and electron-ion are replaced with the periodic distance:

$$\left\vert \vec \xi_i - \vec \xi_j \right\vert = \frac{L}{ \pi } ... ...i_j^2 ) \right ] + \sin^2\left [ \frac{ \pi }{L } (\xi_i^3-\xi_j^3 ) \right ] }$$ (4.8)

where $\xi$ indicates electron and proton coordinates $r_i$ ,$R_i$ . Both in the pairing determinant 1.2.1 and in the three-body Jastrow 1.2.4 we used one orbital per atom as basis set. In the first one we used periodic Gaussian orbitals 4.6 while in the second $2s$ orbitals defined as:

$$\phi_{2s}(r) = r^2 e^{-zr}$$

where the distance between electrons is defined as 4.8. We found that this basis set was sufficient to describe accurately the systems studied.