Effect of +U on energy of free atom

[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.


On Friday, October 14, 2016 at 6:23:31 AM UTC-4, Matthias Krack wrote:
>
> 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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