Initializing random_density

[zerothi]

The random_density could be improved slightly

Here are some general thoughts that may be helpful for you when reconsidering what to do:

• It is a little annoying that the random_density prints to std-out. I would simply remove it, generally remove as many print-statements and provide a logger functionality if required (I plan on doing something with the mixer, but I haven't looked at it yet).
• It would be really nice if one could (optionally) add a random_density instead of overwriting it, imagine a converged system, just to give it a bump one could add a random density (with some weight), for instance HH.dm += np.random.rand((2, no)) * 0.1 - 0.05. The thing is that sometimes one is not fully sure the SCF convergence finds the global minimum, for some of your systems I found that switching between Pulay and Linear mixing could result in two different minima. I didn't check their configurations.

[tfrederiksen]

Good suggestions! Which system were you looking at?

[zerothi]

I think it was the kondo, let me check.

…

On Fri, 20 Mar 2020, 17:12 Thomas Frederiksen, ***@***.***> wrote: Good suggestions! Which system were you looking at? — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#55 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABERMII6I46D237WRH4YMODRIOIVPANCNFSM4LQPHCIQ> .

[zerothi]

Yes in the kondo, U=3.5

For a random seed of 149012049 I get:

weight = 1.0
  history = 2
    Etot = -730.4125846500745
    ADIIS Etot = -730.4603478123743
  history = 3
    Etot = -730.4125857856704
    ADIIS Etot = -730.4125852355509
  history = 4
    Etot = -730.4125855660297
    ADIIS Etot = -730.4125855357343
weight = 0.95
  history = 2
    Etot = -730.460353110062
    ADIIS Etot = -730.4603491491763
  history = 3
    Etot = -730.4125860348335
    ADIIS Etot = -730.4125857845148
  history = 4
    Etot = -730.4125853963085
    ADIIS Etot = -730.412585460135

[zerothi]

The script is this:

import Hubbard.hamiltonian as hh
import Hubbard.sp2 as sp2
import Hubbard.density as dm
import numpy as np

import sisl
AdaptivePulayMixer = sisl.mixing.AdaptivePulayMixer
PulayMixer = sisl.mixing.PulayMixer
LinearMixer = sisl.mixing.LinearMixer


# Build sisl Geometry object
mol = sisl.get_sile('junction-2-2.XV').read_geometry()
mol.sc.set_nsc([1, 1, 1])
mol = mol.move(-mol.center(what='xyz')).rotate(220, [0, 0, 1])
Hsp2 = sp2(mol, t1=2.7, t2=0.2, t3=.18)

# Create mixer
seed = 149012049

for w in np.linspace(1, 0., 20, endpoint=False):
    print(f"weight = {w}")
    np.random.seed(seed)
    if w < .8:
        H = hh.HubbardHamiltonian(Hsp2, U=3.5)
        H.random_density()
        H.converge(dm.dm_insulator, mixer=LinearMixer(w))
        print(f"  Linear Etot = {H.Etot}")
    for h in range(2, 12):
        print(f"  history = {h}")
        np.random.seed(seed)
        H = hh.HubbardHamiltonian(Hsp2, U=3.5)
        H.random_density()
        H.converge(dm.dm_insulator, mixer=PulayMixer(w, history=h))
        print(f"    Etot = {H.Etot}")

        np.random.seed(seed)
        H = hh.HubbardHamiltonian(Hsp2, U=3.5)
        H.random_density()
        H.converge(dm.dm_insulator, mixer=AdaptivePulayMixer((max(0.0001, w-0.1), min(1, w + 0.1)), history=h))
        print(f"    ADIIS Etot = {H.Etot}")

[sofiasanz]

I guess that probably the first iterations critically matter in the sense that they might guide the convergence towards one SCF solution, which is not necessarily the global minimum, but a local one...

Maybe keeping a large history for the DIIS mixing scheme when one starts the convergence with a random density gives problems like this... Maybe we should encourage to use either a linear mixing scheme or a DIIS mixing scheme with smaller history for the first iterations (dn>>) and use a larger history when dn achieved some first tolerance (similarly as we had with the premix).