A Theoretical Evaluation of Possible Transition Metal Electro-catalysts for N-2 Reduction Page: 3 of 22
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carried out. For each surface, the reduction of both the adsorbed N2 molecule and
adsorbed N atoms were studied. The influence of an external potential was subsequently
taken into account using the computational standard hydrogen electrode  and the
lowest overpotential required to reduce nitrogen into ammonia was estimated. The free
energy of the various intermediates formed on the surfaces was calculated as a function
of voltage. The binding energies of the adsorbed species on a range of close-packed and
stepped transition metal surfaces were calculated and used to identify the most active
transition metal catalyst in forming ammonia instead of hydrogen.
2.1 DFT calculations
A close-packed hcp(0001) surface was used to model the flat surfaces of Sc, Y, Ti, Zr Re,
Os, Co, and Ru while a fcc(111) surface was used for Rh, Ir, Ni, Pd, Pt, Cu, Ag, and
Au and a bcc(110) surface was used for V, Nb, Ta, Cr, Mo, W, and Fe. The calculations
were carried out using DFT with the RPBE functional [31, 32] implemented in the
Dacapo code. Plane wave basis sets were used to simulate a periodically repeated (2x2)
three layer supercell. The stepped surfaces were modeled with (6x2) three layer cells,
where three rows of the metal atoms in the top layer were removed to create a strip
island three rows wide. Increasing the strip size to five rows was found to change the
adsorption energy in test cases by less than 0.1 eV. The calculated lattice constants were:
Sc 3.30 A (c/a ratio: 1.59), Ti 2.96 A (c/a ratio: 1.59), Re 2.76 (c/a ratio: 1.62), Os
2.76 (c/a ratio: 1.58), Co 2.48 A (c a ratio: 1.62), Ru 2.75 A (c/a ratio: 1.58), Y
3.68 (c a ratio: 1.57), Zr 3.26 A (c a ratio: 1.59), Rh 3.85 A, Ni 3.56 A, Ir 3.87 , Pt
4.02 A, Pd 4.02 A, Cu 3.71 A, Ag 4.21 A, Au 4.22 A, Ta 3.33 A, V 3.02 A, Nb 3.33 A,
W 3.20 A, Mo 3.20 A, Cr 2.87 , and Fe 2.91 A. The slabs were separated by 10-12 A of
vacuum. For the close-packed surfaces, the two bottom metal layers were fixed and the
top layer was allowed to relax as were the adsorbed species. For the stepped surfaces,
the two top close-packed layers were allowed to relax, whereas the bottom layer was
fixed. The structural optimizations were considered converged when maximum force in
any direction on any moveable atom was less than 0.01 eV/A.
All the DFT calculations were spin restricted except those for Ni, Fe, and Co, where
spin-polarized calculations were made. The self-consistent electron density is determined
by iterative diagonalization of the Kohn-Sham Hamiltonian, with the occupation of
the Kohn-Sham states being smeared according to a Fermi-Dirac distribution with a
smearing parameter of kBT 0.1 eV. All calculated values of the energy have been
extrapolated to kBT 0 eV. A 6 x 6 x 1 Monkhorst-Pack k-point sampling was used
for the flat Ru surfaces and maximum symmetry was applied to reduce the number of
k-points in the calculations. For all the other metals, a 4x4x 1 k-point sampling was
used since the difference between this and the denser k-point sampling was found to be
less than 0.01 eV in test calculations. A 2x6x1 k-point sampling was used for all the
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Skulason, Egill; Bligaard, Thomas; Gudmundsdottir, Sigridur; Felix Studt3, Jan a Felix Studt; Rossmeisl, Jan; Abild-Pedersen, Frank et al. A Theoretical Evaluation of Possible Transition Metal Electro-catalysts for N-2 Reduction, article, January 9, 2013; United States. (digital.library.unt.edu/ark:/67531/metadc845199/m1/3/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.