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Oxygen molecule †In this tutorial, how to perform calculation(s) of a molecule with the spin degree of freedom (or spin unrestricted calculation of a molecule) is discussed by taking an oxygen (O2) molecule as an example. Preliminary †In this tutorial, the O2 molecule is placed in a cubic box with the cell edges of 10 Angstroms. The GBRV ultrasoft pseudopotential, kinetic energy cutoffs of 40 Ry and 320 Ry for the wave functions and augmentation charge, respectively, and the Gamma-point are used. SCF calculation †Fixed moment calculation †We start with an SCF calculation using the following input file. The bond length is set to 1.2 Angstrom.
To submit the job execute $ qsub o2.sh In this example, we perform the fixed moment calculation to obtain the ground state triplet state of the O2 molecule (with the magnetic moment of 2.0 Bohr magneton) by setting tot_magnetization = 2.0 in the namelist &SYSTEM. Note that nonzero initial magnetization should be given to obtain spin polarized solution as starting_magnetization(1) = 0.5d0 When the convergence of the SCF calculation is achieved, we can confirm that the desired magnetization is obtained by assessing the output file (o2_scf.out) as: The total energy is the sum of the following terms:
one-electron contribution = -124.42909406 Ry
hartree contribution = 64.11909734 Ry
xc contribution = -14.24282541 Ry
ewald contribution = 10.24736697 Ry
total magnetization = 2.00 Bohr mag/cell
absolute magnetization = 2.05 Bohr mag/cell
and electron configuration as (by setting verbosity = 'high'): ------ SPIN UP ------------
k = 0.0000 0.0000 0.0000 ( 14336 PWs) bands (ev):
-32.8993 -20.2605 -13.4590 -13.4590 -13.4215 -6.5703 -6.5703 -0.4687
0.8418 0.9710 0.9732 0.9749
occupation numbers
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.0000
0.0000 0.0000 0.0000 0.0000
------ SPIN DOWN ----------
k = 0.0000 0.0000 0.0000 ( 14336 PWs) bands (ev):
-31.7149 -18.4058 -12.4328 -11.5313 -11.5313 -4.1646 -4.1646 -0.3714
1.0168 1.0686 1.0826 1.0826
occupation numbers
1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
highest occupied, lowest unoccupied level (ev): -6.5703 -4.1646
Fixed occupation calculation †Alternatively, we can also perform calculations with fixed (desired) occupation number by using input file like:
Structural relaxation †Structural optimization can be performed by setting the calculation='relax' as
Calculation of the atomization energy †Let us calculate the atomization energy, which is the energy gain to form the molecule from isolated atoms, defined as \[ E_{\rm{a}} = E_{\rm{tot}}(\rm{O}_2) - 2 \times E_{\rm{tot}}(\rm{O}) \]
where \( E_{\rm{tot}}(\rm{O}_2) \) and \( E_{\rm{tot}}(\rm{O}) \) are total energies of (optimized) O2 molecule and O atom, respectively, and the total energy of the O atom should be that of the spin-polarized ground state. To perform the calculation of the spin polarized O atom in the ground state, an input file like following may be used:
After the SCF convrgence, we can calculate the binding energy, and I obtained -5.93 eV. Compare with the values in the literature, for example, Hammer et al., Phys. Rev. B 59, 7413 (1999). Exercise †The atomization energy, in particular the oxygen atom, is sensitive to the computational setup. Try to use
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