Effect of +U on energy of free atom

[Satish Kumar]

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

[Matthias Krack]

Hi

indeed the +U energy should be always positive. A negative value indicates that the applied population analysis returns unreasonable d orbital occupations which can happen e.g. for Cu when slightly more than 10 electrons are assigned to the 3d orbitals by the Mulliken analysis. That is a known shortcoming of the Mulliken analysis. Lowdin is more robust in that respect, but there are no forces implemented for Lowdin in CP2K. Furthermore, I do not recommend to use the MULLIKEN_CHARGES method. So the only reasonable choice for the PLUS_U_METHOD is currently MULLIKEN. Note that PW codes like VASP use different atomic basis sets.for the determination of the orbital occupations which results in different orbital occupations and thus the U values are not transferable to CP2K.

Matthias

[Satish Kumar]

Thank you for the response Matthias. I just wanted to clarify the following. 

1) DFT+U energy using MULLIKEN is -0.00145081061337 Ha and using LOWDIN is +0.00000001917427 Ha. Since forces are not implemented for LOWDIN and MULLIKEN is the preferred approach (which for the present case is wrong), is there a way to get MULLIKEN working?

2) Is the energy contribution of +0.00000001917427 Ha using LOWDIN reasonable? It doesn't look like U is doing anything to affect the total DFT energy here. 

Thank you so much again.