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Rutile titanium dioxide †

In this example, we use titanium dioxide (TiO2) to explain how to use the on-site Hubbard U correction.

Input file (nfinp_ldau) †

     0     0     0     0     0     0                : I_CTRL(1:6)
  5.00 15.00     2     6     6                      : GMAX GMAXP NTYP NATM NATM2
   136     0                                        : NUM_SPACE_GROUP BRAVIS_LATTICE
  8.6808  8.6808  5.5894  90.0000  90.0000  90.0000 : A B C ALPHA BETA GAMMA 
     6     6     8     2     2     2                : N1 N2 N3  M1 M2 M3        
     0     0                                        : NCORD NINV : IWEI IMDTYP ITYP
   0.0000000000    0.0000000000    0.0000000000    1    0    1
   0.5000000000    0.5000000000    0.5000000000    1    0    1
   0.3048297777    0.3048297777    0.0000000000    1    1    2
   0.8048297777    0.1951702223    0.5000000000    1    1    2
  -0.3048297777   -0.3048297777    0.0000000000    1    1    2
  -0.8048297777   -0.1951702223    0.5000000000    1    1    2
    22  0.20     47.9479     6     1   0.0  : IATOMN ALFA AMION ILOC IVAN
     8  0.20     15.9949     6     1   0.0  : IATOMN ALFA AMION ILOC IVAN
     0     0     0     0     0              : ICOND INIPOS INIVEL ININOS INIACC 
     0     1                                : IPRE IPRI
   200   600     0     36000.0     0        : NMD1 NMD2 ITER_LAST CPUMAX IFSTOP
     6     1                                : WAYMIX MIXWHAT
     0    10  0.10                          : ITER_START KBXMIX ALPHA  
   0.2   0.3  0.20  0.20  0.20              : DTIM1 DTIM2 DTIM3 DTIM4 DTIM_LAST
 300.0     2     1      1.D-10              : DTIO IMDALG IEXPL EDELTA
0.0002    0.05D+02     0                    : WIDTH
 ldapw91   1                                : XCTYPE NSPIN
   1.00                                     : DESTM
   102                                      : NBZTYP
     2     2     2                          : NKX  NKY  NKZ  (DUMMY)
     2     2     2                          : NKX2 NKY2 NKZ2 (DUMMY)
    30                                      : NEG
     1                                      : NEXTST
     0                                      : (DUMMY)
     2                                      : IMSD
     0                                      : EVALUATE_EKO_DIFF
     0                                      : NPDOSAO
     0  0.0                                 : SM_N
&HUBBARD
 NPROJ     2
 IPROJ     1    2
 HUBBARD_U 8.00 8.00
 RCUT      2.30 1.60
 RSMEAR    0.20 0.12 
 NLMU      5
 LMU       5    6    7    8    9
&END

In the conventional method, xctype "lda+u" and alike was used to activate the Hubbard U correction. In this example on the other hand, however, we use a simplified interface implemented in recent versions.

• xctype

   ldapw91   1                                : XCTYPE NSPIN

  Use LDA/GGA/vdW-DF functinal, NOT *+u, when the &HUBBARD...&END block is present.
• Hubbard U related parameters

  &HUBBARD
   NPROJ     2
   IPROJ     1    2
   HUBBARD_U 8.00 8.00
   RCUT      2.30 1.60
   RSMEAR    0.20 0.12 
   NLMU      5
   LMU       5    6    7    8    9
  &END

  • Number of projectors

     NPROJ     2

  • Atomic indicies, on which Hubbard U correction is applied

     IPROJ     1    2

  • Effective Hubbard U

     HUBBARD_U 8.00 8.00

  • Cutoff radius for the localized orbitals (should be set for all the atomic species)

     RCUT      2.30 1.60

  • Smearing width for the smearing function for the localized orbital (should be set for all the atomic species)

     RSMEAR    0.20 0.12 

  • Number of lm components

     NLMU      5

  • lm indices

     LMU       5    6    7    8    9

    When the Hubbard U correction is activated, the following is written in the output file:

     DFT+U PARAMETERS
       NUMBER OF PROJECTORS         :   2
       NUMBER OF LM COMPONENTS      :   5
       INDICES FOR LM               :   5  6  7  8  9
       ATOMIC INDICES OF PROJECTORS :   1  2
       HUBBARD U (001)              :   8.000 (EV)
       HUBBARD U (002)              :   8.000 (EV)