Cp2k convergence test: is it possible that cutoff of 250 Ry has fairly lower total energy than 350 Ry (with same rel_cutoff 60 Ry)?

[anyu... at gmail.com]

Dear CP2K developers and users,

I did the convergence tests with cp2k 3.0 for hBN system, following the 
instructions of https://www.cp2k.org/howto:converging_cutoff . The energy 
values and the NG on grids are as follows. I wonder why higher cutoff 
values give fairly higher energies, for example, the total energy for 
cutoff 350 ry is higher than 300 ry, I thought in principle, higher cutoff 
values could have more stable energy (lower value), at least not that 
higher than the number with lower cutoffs. But here in my case, it's not, 
can anybody help me to see why?  Is 250Ry and rel_cutoff of 70 Ry here a 
good choice? 

Also, when one starts a calculation,  should the convergence tests always 
be taken with different values of cut off and rel_cutoff? or it's safe to 
just use larger values such as (cutoff 400 ry, rel_cutoff 80ry)?  

Thanks a lot in advance for all your suggestions.

Best regards,
Yun

# Grid cutoff vs total energy
# Date: Fri Aug 24 13:38:48 CEST 2018
# PWD: /home/Convergence_test
# REL_CUTOFF = 60
# Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on 
grid 3 | NG on grid 4
     50.00  -833.3666229006     559488   81536       0       0
    100.00  -824.4110369450     457024  180160    3840       0
    150.00  -824.3925595993     424576  134912   81536       0
    200.00  -824.3899074807     345088  210560   81536    3840
    250.00  -824.3979520649     294272  162752  180160    3840
    300.00  -824.3920162797   294272  162752  180160    3840
    350.00  -824.3858376968    271744  185280  119488   64512
    400.00  -824.3841314539    271744  152832  134912   81536
    450.00  -824.3831328479     271744  152832  134912   81536
    500.00  -824.3833590835     236416  184320  138752   81536


# Rel Grid cutoff vs total energy
# Date: Fri Aug 24 14:54:23 CEST 2018
# PWD: /home/Convergence_test/Rel_cutoff
# CUTOFF = 250
# Rel Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on 
grid 3 | NG on grid 4
     10.00  -824.9353843726     24384  212032  184320  220288
     20.00  -824.4674485372     117312  176960  162752  184000
     30.00  -824.3980791451    236416  184320  138752   81536
     40.00  -824.3980825574     271744  152832  134912   81536
     50.00  -824.3979520649     294272  162752  180160    3840
     60.00  -824.3979520649     294272  162752  180160    3840
     70.00  -824.3979509738     345088  210560   81536    3840
     80.00  -824.3979509738     345088  210560   81536    3840
     90.00  -824.3979509738     420736  138752   79616    1920
    100.00  -824.3979509738    424576  134912   81536       0


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