Oxygen molecule
This example discusses how to obtain the ground state of a spin polarized system by using oxygen molecule (O2) as an example. How to calculate the atomization energy of O2 molecule is also discussed. In addition, how to perform the fixed moment calculation is described.
SCF calculation and geometry optimization
We use the following input file for this tutorial:
WF_OPT DAV
NTYP 1
NATM 2
GMAX 6.0
GMAXP 20.0
MIX_ALPHA 0.3
WIDTH 0.0010
EDELTA 1.D-09
NSPIN 2
NEG 8
CELL 20.00000000 20.00000000 20.00000000 90.00000000 90.00000000 90.00000000
&ATOMIC_SPECIES
O 15.999 pot.O_pbe1
&END
&INITIAL_ZETA
0.20
&END
&ATOMIC_COORDINATES CARTESIAN
0.000000000000 0.000000000000 0.000000000000 1 1 1
2.300000000000 0.000000000000 0.000000000000 1 1 1
&END
We obtain the following at the convergence:
ALPHA SPIN DENSITY = 6.9999812
BETA SPIN DENSITY = 4.9999914
TOTAL CHARGE DENSITY = 12.0000274
TOTAL ENERGY AND ITS COMPONENTS
TOTAL ENERGY = -32.31618390 A.U.
KINETIC ENERGY = 12.98783295 A.U.
HARTREE ENERGY = 32.57143798 A.U.
XC ENERGY = -7.16496195 A.U.
LOCAL ENERGY = -86.51787900 A.U.
NONLOCAL ENERGY = 10.31864495 A.U.
EWALD ENERGY = 5.48874117 A.U.
PC ENERGY = 0.00000000 A.U.
ENTROPIC ENERGY = 0.00000000 A.U.
FERMI ENERGY = -0.23111258
NKP= 1 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-1.20406 -0.74971 -0.49279 -0.49279 -0.49041 -0.25128 -0.25128 -0.01077
OCCUPATION
1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.00000
NKP= 2 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-1.15786 -0.68167 -0.45602 -0.42074 -0.42074 -0.16178 -0.16178 -0.00659
OCCUPATION
1.00000 1.00000 1.00000 1.00000 1.00000 0.00000 0.00000 0.00000
We can see that we obtain the triplet groud state electronic structure. However, if we use the following initial magnetization:
&INITIAL_ZETA
0.00
&END
we obtain the following singlet electronic state:
ALPHA SPIN DENSITY = 5.9999863
BETA SPIN DENSITY = 5.9999863
TOTAL CHARGE DENSITY = 12.0000274
TOTAL ENERGY AND ITS COMPONENTS
TOTAL ENERGY = -32.30151992 A.U.
KINETIC ENERGY = 12.98445516 A.U.
HARTREE ENERGY = 32.55414598 A.U.
XC ENERGY = -7.14642514 A.U.
LOCAL ENERGY = -86.48538519 A.U.
NONLOCAL ENERGY = 10.30294811 A.U.
EWALD ENERGY = 5.48874117 A.U.
PC ENERGY = 0.00000000 A.U.
ENTROPIC ENERGY = 0.00000000 A.U.
FERMI ENERGY = -0.22902914
NKP= 1 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-1.18263 -0.71749 -0.48328 -0.47439 -0.43394 -0.23872 -0.17867 -0.00897
OCCUPATION
1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.00000 0.00000
NKP= 2 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-1.18263 -0.71749 -0.48328 -0.47439 -0.43394 -0.23872 -0.17867 -0.00897
OCCUPATION
1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.00000 0.00000
This demonstrates the importance of the initial magnetization to obtain the correct ground state electronic state and energy.
By performing structural optimization by adding:
GEO_OPT QMD
and:
DTIO 100
FMAX 0.5D-3
we obtain the following spin densities:
ALPHA SPIN DENSITY = 6.9999810
BETA SPIN DENSITY = 4.9999909
TOTAL CHARGE DENSITY = 12.0000281
and energy and forces:
CONVERGED ENERGY AND FORCES
NIT TotalEnergy f_max f_rms edel vdel fdel
9 -32.31646650 0.000451 0.000450 0.24D-10 0.27D-07 0.24D-10
ATOM COORDINATES FORCES
MD: 9
MD: 1 O -0.014011 0.000000 -0.000001 0.00045 -0.00000 0.00000
MD: 2 O 2.313997 0.000001 -0.000002 -0.00045 0.00000 0.00000
Atomization energy calculation
To calculate the atomization energy of an oxygen molecule, one needs reference energy of an spin-polarized oxygen atom. Here is an sample input file:
WF_OPT DAV
NTYP 1
NATM 1
GMAX 6.0
GMAXP 20.0
MIX_ALPHA 0.3
WIDTH 0.0010
EDELTA 1.D-09
NSPIN 2
NEG 8
CELL 20.00000000 20.00000000 20.00000000 90.00000000 90.00000000 90.00000000
&ATOMIC_SPECIES
O 1.007940 pot.O_pbe1
&END
&INITIAL_ZETA
0.20
&END
&ATOMIC_COORDINATES CARTESIAN
0.000000000000 0.000000000000 0.000000000000 1 1 1
&END
By using this input file, we may obtain the following energy and occupations:
TOTAL ENERGY AND ITS COMPONENTS
TOTAL ENERGY = -16.02368798 A.U.
KINETIC ENERGY = 6.24782298 A.U.
HARTREE ENERGY = 11.25951432 A.U.
XC ENERGY = -3.48995100 A.U.
LOCAL ENERGY = -32.69695888 A.U.
NONLOCAL ENERGY = 5.20945234 A.U.
EWALD ENERGY = -2.55356773 A.U.
PC ENERGY = 0.00000000 A.U.
ENTROPIC ENERGY = 0.00000000 A.U.
FERMI ENERGY = -0.29748643
NKP= 1 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-0.86033 -0.37940 -0.30175 -0.26187 -0.01086 0.03342 0.03861 0.04023
OCCUPATION
1.00000 1.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000
NKP= 2 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-0.86034 -0.37940 -0.30175 -0.26191 -0.01091 0.03341 0.03854 0.04003
OCCUPATION
1.00000 1.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000
We see that this oxygen atom does not satisfy the Hund’s rule, and we want to have the correct electronic configuration. In this case, we try a different initial magnetization, for instance:
&INITIAL_ZETA
0.50
&END
then we obtain:
TOTAL ENERGY AND ITS COMPONENTS
TOTAL ENERGY = -16.05133528 A.U.
KINETIC ENERGY = 6.25764852 A.U.
HARTREE ENERGY = 11.28819032 A.U.
XC ENERGY = -3.52381255 A.U.
LOCAL ENERGY = -32.75842180 A.U.
NONLOCAL ENERGY = 5.23862797 A.U.
EWALD ENERGY = -2.55356773 A.U.
PC ENERGY = 0.00000000 A.U.
ENTROPIC ENERGY = 0.00000000 A.U.
FERMI ENERGY = -0.25692040
NKP= 1 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-0.92215 -0.39914 -0.39914 -0.32203 -0.01373 0.02897 0.03767 0.03771
OCCUPATION
1.00000 1.00000 1.00000 1.00000 0.00000 0.00000 0.00000 0.00000
NKP= 2 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-0.78239 -0.27594 -0.22496 -0.22496 -0.00704 0.03658 0.04081 0.04546
OCCUPATION
1.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
In addition to the electronic configuration, we can see that the energy is lower than the former one. By using the total energies obtained as above (Oxygen molecule and atom), we obtain the binding energy of -5.81 eV, which is in good agreement with a literature value [1].
Fixed moment calculation
In a recent version of STATE, the fixed moment calculation is enabled, and the spin multiplicity can be also specified. In the following example, how to set the spin multiplicity by using the oxygen molecule as an example:
For the oxygen molecule in the spin triple state, following input file can be used:
WF_OPT DAV
NTYP 1
NATM 2
GMAX 6.0
GMAXP 20.0
MIX_ALPHA 0.3
WIDTH 0.0010
EDELTA 1.D-09
NSPIN 2
SPIN TRIPLET
NEG 8
CELL 20.00000000 20.00000000 20.00000000 90.00000000 90.00000000 90.00000000
&ATOMIC_SPECIES
O 1.007940 pot.O_pbe1
&END
&INITIAL_ZETA
0.20
&END
&ATOMIC_COORDINATES CARTESIAN
0.000000000000 0.000000000000 0.000000000000 1 1 1
2.300000000000 0.000000000000 0.000000000000 1 1 1
&END
The following line allows the spin triplet calculation:
SPIN TRIPLET
As for the spin multiplicity, SIGLET, DOUBLET, TRIPLET, … OCTET are allowed.
For other cases, the key word SPMULT followed by the integer value can be used (for e.g. SMULT 3 for spin triplet).
Likewise for the spin singlet, we may use the following input file:
WF_OPT DAV
NTYP 1
NATM 2
GMAX 6.0
GMAXP 20.0
MIX_ALPHA 0.3
WIDTH 0.0010
EDELTA 1.D-09
NSPIN 2
SPIN SINGLET
NEG 8
CELL 20.00000000 20.00000000 20.00000000 90.00000000 90.00000000 90.00000000
&ATOMIC_SPECIES
O 1.007940 pot.O_pbe1
&END
&INITIAL_ZETA
0.20
&END
&ATOMIC_COORDINATES CARTESIAN
0.000000000000 0.000000000000 0.000000000000 1 1 1
2.300000000000 0.000000000000 0.000000000000 1 1 1
&END
We get the total energy for the singlet state:
TOTAL ENERGY = -32.30152055 A.U.
and for the triplet state:
TOTAL ENERGY = -32.31618390 A.U.
We can see that the triplet state is more stable than the single state as it should.
In addition to the spin multiplicity, it is possible to specify the magnetic moment using the keyword MAGMOM, which is desribed elsewhere.