11 An Evaluation of Density Functional Theory for CO Adsorption on Pt(111)
197
including more exact HF exchange contribution, and thus may improve the results
for the site preference of CO adsorption. By adopting the slab model calculation
with hybrid B3LYP functional, Doll described better LUMO property and successfully predicted top-CO adsorption preference [7]. The adsorption energies are 1.44
and 1.40 eV for CO at top and fcc sites, respectively. However, the energy splitting
between top site and fcc site is still too small and hard to confirm the experimental
observation. Similar results are also reported by Stroppa et al. who apply hybrid
PBE0 [54] and HSE03 [55] methods in the CO/Pt(111) slab model calculation with
the plane wave basis set [35]. Although hybrid-GGA functionals can improve the
results of site preference, it still cannot reproduce experimental observation in most
case. Hence, the CO/Pt(111) puzzle is still a unsolved problem up to now.
Recently many new density functionals were developed for different purpose.
For instance, Truhlar et al. developed M-series hyper-GGA functionals which are
better than conventional hybrid functionals in thermodynamics and kinetics calculations [56–63]. Boese et al. developed the hyper BMK functional which includes
the kinetic energy term and a large percentage of Hartree-Fock (HF) exchange energy (42 %). Zhao et al. has also tested the performance of these DFT functionals,
the results show that BMK, M052X, M062X and M06HF owns the better performance in the calculation of excitation energies of CO [63].
Therefore, in this study, we would like to apply various density functional theory
including LDA, GGA, meta-GGA, hybrid-GGA and hyper-GGA to calculate CO
adsorption on Pt(111) cluster model. Through the chemical bonding analysis, the
effect of different functionals to CO adsorption behavior on Pt(111) cluster can be
clearly presented.
In Sect. 11.2, a brief description of the computational method and cluster construction are given. In Sect. 11.3, the results and discussion of the adsorption energies and chemical bonding analyses on CO/Pt(111) cluster for different DFT functionals are presented. Conclusions are drawn in the final section.
11.2 Computational Method
In this study, the density functional theory (DFT) and the wavefunction theory
(WFT) were performed with the program package Gaussian 09 [64]. Several density functionals, including LDA (SVWN) [50], GGAs (BLYP [65], PBE, PW91,
B97D [66] and BP86, meta-GGA (M06-L) [59] and hybrid-GGAs (HSE03, HSE06,
B3PW91 [53], PBE0, B3LYP, B1B95 [67], BHandHLYP [68], BHandH [68],
wB97 [69], wB97X [69], M052X [58], M062X [63], M06HF [61], BMK), were
adopted to check the effect of exchange-correlation functional on computed CO
adsorption energy on Pt(111). The wavefunction theory HF and MP2 were also
applied for the comparison. The LANL2DZ basis set as well as effective core potentials was used for Pt atom [70]. In our previous study, several different basis sets
including 6–31G, 6–31G ∗ , 6–31 + G, 6–31 + G ∗ , 6–311G, 6–311G ∗ , 6–311 + G
and 6–311 + G ∗ , were adopted to check the effect to CO properties. Among these
197
including more exact HF exchange contribution, and thus may improve the results
for the site preference of CO adsorption. By adopting the slab model calculation
with hybrid B3LYP functional, Doll described better LUMO property and successfully predicted top-CO adsorption preference [7]. The adsorption energies are 1.44
and 1.40 eV for CO at top and fcc sites, respectively. However, the energy splitting
between top site and fcc site is still too small and hard to confirm the experimental
observation. Similar results are also reported by Stroppa et al. who apply hybrid
PBE0 [54] and HSE03 [55] methods in the CO/Pt(111) slab model calculation with
the plane wave basis set [35]. Although hybrid-GGA functionals can improve the
results of site preference, it still cannot reproduce experimental observation in most
case. Hence, the CO/Pt(111) puzzle is still a unsolved problem up to now.
Recently many new density functionals were developed for different purpose.
For instance, Truhlar et al. developed M-series hyper-GGA functionals which are
better than conventional hybrid functionals in thermodynamics and kinetics calculations [56–63]. Boese et al. developed the hyper BMK functional which includes
the kinetic energy term and a large percentage of Hartree-Fock (HF) exchange energy (42 %). Zhao et al. has also tested the performance of these DFT functionals,
the results show that BMK, M052X, M062X and M06HF owns the better performance in the calculation of excitation energies of CO [63].
Therefore, in this study, we would like to apply various density functional theory
including LDA, GGA, meta-GGA, hybrid-GGA and hyper-GGA to calculate CO
adsorption on Pt(111) cluster model. Through the chemical bonding analysis, the
effect of different functionals to CO adsorption behavior on Pt(111) cluster can be
clearly presented.
In Sect. 11.2, a brief description of the computational method and cluster construction are given. In Sect. 11.3, the results and discussion of the adsorption energies and chemical bonding analyses on CO/Pt(111) cluster for different DFT functionals are presented. Conclusions are drawn in the final section.
11.2 Computational Method
In this study, the density functional theory (DFT) and the wavefunction theory
(WFT) were performed with the program package Gaussian 09 [64]. Several density functionals, including LDA (SVWN) [50], GGAs (BLYP [65], PBE, PW91,
B97D [66] and BP86, meta-GGA (M06-L) [59] and hybrid-GGAs (HSE03, HSE06,
B3PW91 [53], PBE0, B3LYP, B1B95 [67], BHandHLYP [68], BHandH [68],
wB97 [69], wB97X [69], M052X [58], M062X [63], M06HF [61], BMK), were
adopted to check the effect of exchange-correlation functional on computed CO
adsorption energy on Pt(111). The wavefunction theory HF and MP2 were also
applied for the comparison. The LANL2DZ basis set as well as effective core potentials was used for Pt atom [70]. In our previous study, several different basis sets
including 6–31G, 6–31G ∗ , 6–31 + G, 6–31 + G ∗ , 6–311G, 6–311G ∗ , 6–311 + G
and 6–311 + G ∗ , were adopted to check the effect to CO properties. Among these