Unexpected ionic states in a series of LiCoO systems after nupdown calculations

[hongriTianqi]

Describe the bug

The test report is presented here: https://app.bohrium.dp.tech/abacustest?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.97-46416f

In the report table, Co atoms, Co3+ ions, Co4+ ions, O atoms, Li atoms are the number of atoms/ions expected.

Co3+ ions cal., Co4+ ions cal., O2- ions cal. Li+ ions cal. are the number of ions actually obtained after nupdown calculation. They are obtained in the following way: Co3+ should have spin 0, and the actual absolute value of the magnetic moment should not be larger than 0.5 uB. Co4+ should have spin 1, and the actual absolute value of the magnetic moment should not deviate from 1 uB more than 0.5 uB. Li+ should have spin 0, and the actual absolute value of the magnetic moment should not be larger than 1e-2 uB. O2- should have spin 0, and the actual absolute value of the magnetic moment should not be larger than 0.2 uB.

'Co3+ compare' compares 'Co3+ ions' with 'Co3+ ions cal.', it is true if equal, otherwise false. The same for 'Co4+ compare' to compare 'Co4+ ions' and 'Co4+ ions cal.', 'O2- compare' to compare 'O atoms' and 'O2- ions cal.' 'Li+ compare' to compare 'Li atoms' and 'Li+ ions cal.'

For example, the system Li3Co12O24-000 has calculated wrong number of Co3+ and Co4+ ions, we can check the magnetic moments here: https://app.bohrium.dp.tech/abacustest?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.97-46416f

The firstly 12 data from 0 to 11 are magnetic moments of Co ions: we see that 4 numbers are close to zero, 7 numbers are close to one, with one data being 1.606, larger than 1.5. Which is unacceptable.

Expected behavior

1. The convergence should be achieved for all the systems.

2. The number of ions calculated from the results of magnetic moments should equal to the expected values.

To Reproduce

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Environment

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Additional Context

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[hongriTianqi]

@dyzheng To update, the new magnetic moments method as raised in the dftu_new branch has been tested on the same series of materials, the report is represented here: https://app.bohrium.dp.tech/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.97-cf6652

The input parameters for U were set as

dft_plus_u    1
orbital_corr  2 1 0
hubbard_u    5.14 0.0 0.0

for Co, O, Li, respectively.

By the way, the results from Mulliken population after the same calculation are presented here: https://app.bohrium.dp.tech/abacustest?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.97-7902e8