The Hydrogenation of N Molecules on a Stepped Ru(0001 ... - hi

The Hydrogenation of N2 Moleculeson a Stepped Ru(0001) Surface

Conversion of DFT into Gibbs Free Energyvalues and Approximate Effects of

Electrodes Potential Difference

Egill SkulasonUniversity of Iceland

Department of [email protected]

14th of April 2004

Contents• Background

– The ammonia synthesis in nature vs. industrial– Theoretical resource of ammonia synthesis

• The Methodology– Conversion of DFT into Gibbs Free Energy values– Approximate Effects of Electrodes Potential Difference

• The hydrogenation of N2 molecules and N atoms on astepped Ru(0001) surface

• Conclusions

Background

• The conversion of atmospheric N2 into abiologically accessible form of nitrogen such asammonia (NH3), is termed nitrogen fixation.

• Since the element N is present in manybiomolecules, such as amino acids, nitrogenfixation is a prerequisite for life.

• In spite of the vast quantities of atmospheric N2,the sources of biologically accessible nitrogen arefew.

• Oxidation of N2 to nitrogenoxides by lightning andcombustion.

• The commercial Haber-Boschprocess where N2 reacts withhydrogen on a Fe or Ru basedcatalyst to form ammonia.

• The enzyme catalyzedammonia synthesis where N2reacts with electrons andprotons to form ammonia.

L. Stryer, Biochemistry, 4. Ed. (W.H. Freeman and Company, New York, 1995), p. 714.

The Ammonia Synthesis inNature vs. Industrial

Theoretical Resource ofAmmonia Synthesis

• Hydrogenation of N atoms on the– Ru(0001) surface– Stepped Ru(0001) surface

• Hydrogenation of N2 molecules on the– FeMoco Model– Ru(0001) surface– Stepped Ru(0001) surface

Stepped Surface

Surface

FeMoco Model

Hydrogenation ofN atoms on the

Ru(0001) Surfacewith and without a Step

T.H. Rod, A. Logadottir & J.K. Norskov, J.Chem.Phys.,Vol 112, No. 12, 2000, p. 5343

Calculational detailsDFT program: DACAPOPlane-wavesGGAPseudopotentialsRPBE functional

Hydrogenation ofN2 Molecules in

Gas Phase and onthe FeMoco Model



Hydrogenation ofN2 Molecules on

the Ru(0001)Surface and on the

FeMoco Model



The Methodology

• Conversion of DFT into Gibbs Free Energy values :ΔH = ΔEDFT + ZPEΔG = ΔH - TΔS

• Approximate Effects of Electrodes PotentialDifference:

Over all reaction: N2 + 3H2 ↔ 2NH3The anode reaction: H2 ↔ 2H+ + 2e-

The cathode reaction: N2 + 6H+ + 6e- ↔ 2NH3

The Methodology

• The Gibbs free energy is calculated from the DFTand Zero Point Energy values (which are at 0 V).

• Than the number of electrons (with the elementarycharge e), multiplied with the cell potential (U), isadded to ΔG(0):

ΔG(U) = ΔG(0) + eU• All states involving an electron in the electrode, will

simply be shifted in energy by eU.

2

3

4

5

6

7

8

1. Ru + N2 + 6(H+ + e-) shifted by 6U2. Ru-N2 + 6(H+ + e-) shifted by 6U3. Ru-N2H + 5(H+ + e-) shifted by 5U4. Ru-N2H2 + 4(H+ + e-) shifted by 4U5. Ru-N2H3 + 3(H+ + e-) shifted by 3U6. Ru-N2H4 + 2(H+ + e-) shifted by 2U7. Ru-NH2 +NH3 + (H+ + e-) shifted by 1U8. Ru-NH3 +NH3 not shifted9. Ru + 2NH3 not shifted

The Hydrogenation of theN2 Molecules and the

Shifted Steps in the Reaction

E. Skulason, T. Bligaard, H. Jonsson & J.K. Norskov, unpublished

The Hydrogenation of N2 Moleculeson a Stepped Ru(0001) Surface.

- ΔE values at 0 V -

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

]

DE at 0 V

1 Ru + N2 + 3H22 Ru-N2 + 3H23 Ru-N2H + 5/2 H24 Ru-N2H2 + 2 H25 Ru-N2H3 + 3/2 H26 Ru-N2H4 + H27 Ru-NH2 +NH3 + 1/2H28 Ru-NH3 +NH39 Ru + 2NH3




- ΔG values at 0 V -

0.71 0.68

1.72 1.70 1.712.01

-0.15 -0.05 0.00

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

]

DG at 0 VDE at 0 V





- ΔG values at -0.3 V -

0.71 0.68

1.72 1.70 1.712.01

-0.15 -0.05 0.00

2.51 2.48

3.22

2.902.61 2.61

0.15-0.05 0.00

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

]

DG at 0 V

DG at -0.3 VDE at 0 V






0.71 0.68

1.72 1.70 1.712.01

-0.15 -0.05 0.00

2.51 2.48

3.22

2.902.61 2.61

0.15-0.05 0.00

4.31 4.28

4.72

4.10

3.513.21

0.45

-0.05 0.00

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

]

DG at 0 V

DG at -0.3 VDG at -0.6 VDE at 0 V






0.71 0.68

1.72 1.70 1.712.01

-0.15 -0.05 0.00

2.51 2.48

3.22

2.902.61 2.61

0.15-0.05 0.00

4.31 4.28

4.72

4.10

3.513.21

0.45

-0.05 0.00

6.11 6.086.22

5.30

4.41

3.81

0.75

-0.05 0.00

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

] DG at 0 VDG at -0.3 V

DG at -0.6 VDG at -0.9 V

DE at 0 V






0.71 0.68

1.72 1.70 1.712.01

-0.15 -0.05 0.00

2.51 2.48

3.22

2.902.61 2.61

0.15-0.05 0.00

4.31 4.28

4.72

4.10

3.513.21

0.45

-0.05 0.00

6.11 6.086.22

5.30

4.41

3.81

0.75

-0.05 0.00

6.95 6.92 6.92

5.86

4.83

4.09

0.89

-0.05 0.00

1.85

1.23

1.90

1.37

1.02 0.95

-0.73-0.93

0.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10

En

erg

y [

eV

] DG at 0 VDG at -0.3 V

DG at -0.6 VDG at -0.9 VDG at -1.04 V

DE at 0 V




The Hydrogenation of Nitrogen Atomson a Stepped Ru(0001) Surface.


A. Logadottir & J.K. Norskov, unpublished


Conclusions• The second hydrogen atom adsorbs on the outer nitrogen

atom on the stepped Ru(0001) surface while it adsorbs onthe inner nitrogen atom on the Ru(0001) surface and theFeMoco Model.

• The hydrogenation of the N atoms is more feasible than ofthe N2 molecules on the stepped Ru(0001).

Table with the CalculationsSpecies Energy [eV] ZPE [eV] S [J/(K*mol)] - TS [eV] H [eV] G [eV]

Ru -13650.28 0 0 -13650.28 -13650.28

Ru-N2 -14193.85 0.2 -0.05 -14193.65 -14193.70

Ru-N2H -14209.19 0.5 -0.05 -14208.69 -14208.74

Ru-N2H2 -14225.73 0.94 -0.05 -14224.79 -14224.84

Ru-N2H3 -14242.09 1.23 -0.05 -14240.86 -14240.91

Ru-N2H4 -14258.17 1.53 -0.05 -14256.64 -14256.69

Ru-NH2 -13955.43 0.8320 -0.0367 -13954.60 -13954.64

Ru-NH3 -13971.64 1.1245 -0.0984 -13970.51 -13970.61

H2 g -32.02 0.2730 130.6840 -0.4064 -31.75 -32.16

N2 g -542.94 0.1460 191.6100 -0.5959 -542.79 -543.39

NH3 g -320.43 0.8900 238.9700 -0.7432 -319.54 -320.28

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The Hydrogenation of N Molecules on a Stepped Ru(0001 ... - hi