Effect of +U on energy of free atom

[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

On Thursday, 13 October 2016 18:19:36 UTC+2, Satish Kumar wrote:
>
> 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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