METALLIC DIRECT MINIZATION

One needs to minimize Y,V, and F. One usually obtains V by minimizing H~ (i.e. diagonal) to make it commute with F (diagonal). The problem is that one is minimizing H~ and not Elda. Also the new H~ is not diagonal with V and hence does not commute. So inner product is incorrect with F in the wrong basis.  

With Marazari Vanderbilt eDFT, the line minization for faulters when:

(1) near the beginning (~7 iterations) on the 4^th inner loop. At this point the nonquadratic behavior of the xc energy on F starts to be significant.

(2) (~iteration 25) when search direction is barely along gradient there also problems. I know is barely along as it reaches the minmum in the direction between 1d-3 and 1d-2(very small movement)

Another problem is that (G.H) sometimes becomes negative due to the F contribution in the metric at the same time usually (G.G) also becomes negative. IF F is in the “right” basis will this be allieved? But too expensive.

For Ni bar it is important to randomize the wavefunctions, or just include more orbitals. Otherwise the code might converge to a higher energy. More orbitals will give better convergence for the this method.

Also important not to have smearing temperature to be too high. Otherwise there is a problem with the minization of the occupations near the end. Possibly due to not enough orbitals( just speculation).