Nitric oxide
This example explains how to perform a calculation of a system by taking spin polarization into account (see also atomization energy calculation of a hydrogen molecule) and examin if the system has a spin polarization.
SCF calculation with spin polarization
Below is an input file for a nitric oxide (NO) molecule in a box:
WF_OPT DAV
NTYP 2
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
N 1.007940 pot.N_pbe1
O 1.007940 pot.O_pbe1
&END
&INITIAL_ZETA
0.20
0.20
&END
&ATOMIC_COORDINATES CARTESIAN
0.000000000000 0.000000000000 0.000000000000 1 1 1
2.100000000000 0.000000000000 0.000000000000 1 1 2
&END
Make sure to set non-zero initial spin polarization.
It is also noted that there are 2 atomic species and thus 2 initial spin polarizations (ZETA1
) should be set as:
&INITIAL_ZETA
0.20
0.20
&END
Upon convergence, one finds the following in the output file:
ALPHA SPIN DENSITY = 5.9999897
BETA SPIN DENSITY = 4.9999944
TOTAL CHARGE DENSITY = 11.0000159
TOTAL ENERGY AND ITS COMPONENTS
TOTAL ENERGY = -26.30821655 A.U.
KINETIC ENERGY = 11.41892451 A.U.
HARTREE ENERGY = 27.07315959 A.U.
XC ENERGY = -6.34381088 A.U.
LOCAL ENERGY = -72.12366866 A.U.
NONLOCAL ENERGY = 7.92908549 A.U.
EWALD ENERGY = 5.73809340 A.U.
PC ENERGY = 0.00000000 A.U.
ENTROPIC ENERGY = 0.00000000 A.U.
We can see that the alpha (up) and beta (down) spin are 6.0 and 5.0, respectively, meaning that the system is spin polarized:
ALPHA SPIN DENSITY = 5.9999897
BETA SPIN DENSITY = 4.9999944
TOTAL CHARGE DENSITY = 11.0000159
We can also find the eigenvalues and occupations below the total energy and Fermi level, which clearly indicate that 6 (5) electrons occupy alpha/up (beta/down) spin states as:
NKP= 1 NGP= 29039 K=( 0.00000 0.00000 0.00000) WKP= 0.5000
EIGEN VALUE
-1.19024 -0.60659 -0.48880 -0.48534 -0.42606 -0.14951 -0.13615 -0.01025
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
-1.17319 -0.57956 -0.47617 -0.43755 -0.40540 -0.12202 -0.07752 -0.00580
OCCUPATION
1.00000 1.00000 1.00000 1.00000 1.00000 0.00000 0.00000 0.00000
Furthermore, local atomic charges are printed as follows:
<<< Atomic Charge >>>
ia is rd d_rd Charge(1) Charge(2) Charge(3)
1 1 1.40 0.10 1.703104 1.929256 2.151185
1 2 1.40 0.10 1.329765 1.522052 1.713526
2 1 1.40 0.10 2.251678 2.475492 2.683927
2 2 1.40 0.10 2.001271 2.209236 2.403069
The first, second, third, and forth column indicate atomic index (ia), spin state (is, 1 and 2 are for spin-up and spin-down, respectively), radius for the integration (rd), and increment of the radius (d_rd), respectively, and the following columns are the integrated charges within the radii. In this example the charges within the 1.40, 1.50, and 1.60 Bohrs are printed. Likewise, the local magnetic moments are also printed:
<<< Magnetization >>>
ia rd d_rd magmom(1) magmom(2) magmom(3)
1 1.40 0.10 0.373340 0.407204 0.437658
2 1.40 0.10 0.250407 0.266256 0.280858