How to calculate the Binding Energy of a diatomic molecule

 For diatomic molecules, the binding energy is equal to the dissociation energy of the molecule.

 The total energy of Cl2 at the equilibrium bond length can be used to calculate the dissociation energy of this molecule (How to calculate the Equilibrium Structure of a diatomic molecule).

The dissociation energy is defined as the difference Ediss = ECl2 − 2ECl, with ECl the total energy of an isolated Cl atom.

In order to evaluate this quantity we first calculate ECl2 using the equilibrium bond length determined in the previous section. For this we modify the input file cl2.in as follows:

...
ATOMIC_POSITIONS bohr
Cl 0.00 0.00 0.00
Cl 3.725 0.00 0.00
...

cl2.in

&control
calculation = 'scf'
prefix = 'Cl2',
pseudo_dir = './',
outdir = './'
/
&system
ibrav = 1,
celldm(1) = 20.0,
nat = 2,
ntyp = 1,
ecutwfc = 100,
/
&electrons
conv_thr = 1.0d-8
/
ATOMIC_SPECIES
Cl 1.0 Cl.pz-bhs.UPF
ATOMIC_POSITIONS bohr
Cl 0.00 0.00 0.00
Cl 3.725 0.00 0.00
K_POINTS gamma

The first step is to find a suitable pseudopotential for Cl. We go to http://www.quantum-espresso.org/pseudopotentials and look for Cl. We recognize LDA psedupotential by the label pz in the filename. Let us go for the following:

$ wget http://www.quantum-espresso.org/wp-content/uploads/upf_files/Cl.pz-bhs.UPF

$ mpirun -np 4 pw.x -i cl.in |tee cl.out

 A calculation with this modified input file yields the total energy:

grep "\!" cl2.out

!    total energy              =     -59.99059544 Ry 

 

 Now we consider the isolated Cl atom. The only complication in this case is that the outermost (3p) electronic shell of Cl has one unpaired electron: ↑↓ ↑↓ ↑ . In order to take this into account we can perform a spin-polarized calculation using the following modification of the previous input file:

 cl.in

&control
calculation = 'scf'
prefix = 'Cl2',
pseudo_dir = './',
outdir = './'
/
&system
ibrav = 1,
celldm(1) = 20.0,
nat = 1,
ntyp = 1,
ecutwfc = 100,
nspin = 2,
tot_magnetization = 1.0,
occupations = 'smearing',
degauss = 0.001,
/
&electrons
conv_thr = 1.0d-8
/
ATOMIC_SPECIES
Cl 1.0 Cl.pz-bhs.UPF
ATOMIC_POSITIONS
Cl 0.00 0.00 0.00
K_POINTS gamma

 

$ mpirun -np 4 pw.x -i cl.in |tee cl.out

 A calculation with this modified input file yields the total energy:

grep "\!" cl.out

!    total energy              =     -29.86386108 Ry 

 

 By combining the last two results we find

Ediss = 0.262873 Ry = 3.58 eV

 This result should be compared to the experimental value of 2.51 eV from https://en.wikipedia.org/wiki/Bond-dissociation_energy. We can see that DFT/LDA overestimates the dissociation energy of Cl2 by about 1 eV: interatomic bonding is slightly too strong in LDA.