Dependence of the total energy on the number of empty states

Dear all,
I am trying to perform some Elk-calculations on uranium intermetallics using spin-orbit coupling. During my convergence tests I have found a slow convergence of the total energy with respect to the number of empty states:
nempty magnetization etot
10 -3.450099327 -91882.9940335
15 -3.452826418 -91883.0299241
20 -3.445244008 -91883.0537770
25 -3.437406076 -91883.0698630
30 -3.432943450 -91883.0807233
35 -3.427958377 -91883.0912408
40 -3.424538224 -91883.0984670
45 -3.422264385 -91883.1034817
50 -3.420282721 -91883.1075924
55 -3.418558013 -91883.1111122
60 -3.417301572 -91883.1138507
65 -3.416243296 -91883.1159232
70 -3.415507506 -91883.1173915
75 -3.414913847 -91883.1186779
80 -3.414326429 -91883.1198236

At a first glance, I am a little bit surprised as I do not expect any influence of the empty states on the total energy. So is this behavior "normal" and may results from the second-variational scheme used for SOC? Attached, please find my input:

tasks
0

avec
3.8470000000 0.0000000000 0.0000000000
0.0000000000 4.0210000000 0.0000000000
-1.9238888783 0.0000000000 5.3909950458

scale
1.889726135

! this is the relative path to the species files
sppath
'/work/scratch/ms41tuki/IrU/mag-elk-test/cmcm/'

xctype
20

stype
1

swidth
0.005

rgkmax
10.0

gmaxvr
16

msmooth
4

lmaxapw
10

lmaxo
6

lradstp
4

nempty
80

autolinengy
.true.

mixtype
3

broydpm
0.6 0.15

!Magnetismus

cmagz
.true.

spinpol
.true.

spinorb
.true.

! small magnetic field in the z-direction
bfieldc
0.0 0.0 0.01

atoms
2 : nspecies
'U.in' : spfname
2 : natoms
0.135510000 0.250000000 0.271020000 0.0 0.0 0.8
0.864490000 0.750000000 0.728980000 0.0 0.0 0.8
'Ir.in'
2
0.397850000 0.250000000 0.795700000 0.0 0.0 -0.1
0.602150000 0.750000000 0.204300000 0.0 0.0 -0.1

ngridk
8 8 6

Thank you very much and best regards,
Malte Sachs

Markus - 2019-06-13

Dear Malte,
yes, this is confusing at a first glance. The point is, that the empty states are used to construct the basis for the second-variational step during which magnetism and SOC are included. Without magnetism and SOC, you should not see any influence of nempty. However, with magnetism and/or SOC, you should see exactly this kind of dependence, because with increasing nempty you increase the basis size. But remember that the total energy has no meaning, only energy differences are relevant. So when you compute e.g. the volume optimization, you'll find that a fairly small number of empty states is already sufficient to converge that quantity.
Happy computing,
Markus

Malte Sachs - 2019-07-18

Dear Markus,
thank you very much for this clarification!
Best regards,
Malte

Dear Malte,

similar issues have been dicussed before in this forum.

The answer is found in a fairly old paper:
Spin-Orbit Coupling of the Actinide Elements: A Critical Evaluation of Theoretical Equilibrium Volumes by Lars Nordström, John Wills, Per Andersson, Per Söderlind, and Olle Eriksson in
PRB, 63, 035103 (2001).

Best regards,
LARS

https://sourceforge.net/p/elk/discussion/897820/thread/c4da4617f0/