# Effect of +U on energy of free atom

Satish Kumar satis... at gmail.com
Thu Oct 13 16:19:35 UTC 2016

```Hello CP2K users

I wanted to understand what is the effect of adding +U correction to the
energies of calculations without any U. For example, I have a Cu atom for
which I am interested in finding the DFT and DFT+U energy. I have provided
the input file below.

In an attempt to see what U does, I looked at the Fermi energies of the two
calculations. When I do an energy run without any U, I get the Fermi energy
to be -0.163318 Ha while upon inclusion of U=5.0 eV, I get the Fermi energy
to be -0.16497 Ha. The difference (Energy with U - Energy without U) is
-0.05 eV. This means that adding U shifts the energy levels of the
electronic states to more negative values. I tried the same calculation
with VASP and I get the same difference in fermi energies to be +0.12 eV. I
was thinking that adding U would shift the fermi energy to more positive
values compared to when no U is applied. Is that correct?

Secondly, with respect to the DFT energy of a Cu atom, in CP2K, the effect
of U is negligible. Adding U =5.0 eV gives a "DFT+U energy:
0.00000001917427", which is almost zero. However, Using VASP,  when U=5.0
eV was turned on, the DFT energy of Cu atom becomes more positive by +1.2
eV compared to calculation without U. Could someone help me with what is
going on? or if there are some changes to the input file that may fix this
issue of almost zero DFT+U energy?

On a different note, I was thinking that since Cu atom has all the d
electrons filled and paired up, application of U to these d electrons would
not change the electronic occupations and hence would not change the DFT+U
energy. But from VASP it did look like the electronic occupations were not
changed much by inclusion of U but the energies did change considerable. I
was confused what is going on.

Finally, I used PLUS_U_METHOD LOWDIN since MULLIKEN/MULLIKEN_CHARGES gave
me the following warnings. Does this change the above things by any chance?
I don't think so. But if it does, please let me know any suggestions to get
rid of the warning.

*** 13:28:53 WARNING in dft_plus_u:mulliken_charges :: DFT+U energy
***

*** contibution is negative possibly due to unphysical Mulliken charges.
***

*** Check your input, if this warning persists or try a different method!
***

Input file:

&FORCE_EVAL

METHOD Quickstep

&DFT

PLUS_U_METHOD LOWDIN

UKS

BASIS_SET_FILE_NAME /home/siyemperumal/GTH_BASIS_SETS_5-12-10

POTENTIAL_FILE_NAME /home/siyemperumal/GTH_POTENTIALS_5-12-10

WFN_RESTART_FILE_NAME mol-RESTART.wfn

&MGRID

CUTOFF 300

&END MGRID

&QS

WF_INTERPOLATION ASPC

EXTRAPOLATION_ORDER 3

&END QS

&SCF

EPS_SCF 1.E-6

SCF_GUESS RESTART

MAX_SCF 500

&DIAGONALIZATION

ALGORITHM STANDARD

&END DIAGONALIZATION

ADDED_MOS 60

&SMEAR  ON

METHOD FERMI_DIRAC

ELECTRONIC_TEMPERATURE [K] 300

&END SMEAR

&MIXING

METHOD DIRECT_P_MIXING

&END MIXING

&END SCF

&XC

&XC_FUNCTIONAL PBE

&END XC_FUNCTIONAL

&VDW_POTENTIAL

DISPERSION_FUNCTIONAL PAIR_POTENTIAL

&PAIR_POTENTIAL

TYPE DFTD3(BJ)

PARAMETER_FILE_NAME
/home/siyemperumal/Research/cp2k/package/cp2k/data/dftd3.dat

REFERENCE_FUNCTIONAL PBE

&PRINT_DFTD MEDIUM

&END PRINT_DFTD

&END PAIR_POTENTIAL

&END VDW_POTENTIAL

&END XC

&PRINT

&MO

EIGENVALUES

OCCUPATION_NUMBERS

&EACH

QS_SCF 0

&END EACH

&END MO

&END PRINT

&END DFT

&SUBSYS

&CELL

ABC 12.00 13.00 14.00

PERIODIC NONE

&END CELL

&COORD

Cu         0.0000153980        0.0000010425        0.0006891492

&END COORD

&KIND Cu

BASIS_SET DZVP-MOLOPT-SR-GTH

POTENTIAL GTH-PBE-q11

#I remove the following DFT calculation. I also tried ramping and other
associated keywords but with no success.

&DFT_PLUS_U

L 2

U_MINUS_J [eV] 5.00

&END  DFT_PLUS_U

&END SUBSYS

&END FORCE_EVAL

&GLOBAL

PROJECT mol

RUN_TYPE ENERGY

PRINT_LEVEL LOW

&END GLOBAL

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