Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized-gradient approximation (GGA), nonlocal correlation, meta-GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised-RPBE, vdW-DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW-DF and meta-GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of -2.62 and -1.1% for the N-N stretching and Rh-H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh-H and N-N stretching modes from the bulk phonons and by solving one- and two-dimensional Schrödinger equation associated with the Rh-H, Rh-N, and N-N potential energy we calculated the anharmonic correction for N-N and Rh-H stretching modes as -31 cm(-1) and -77 cm(-1) at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments.