Using sound physical principles we modify the DFT-D2 atom pairwise semiempirical dispersion correction to density functional theory to work for metallic systems and in particular self-assembled monolayers of thiols on gold surfaces. We test our approximation for two functionals PBE-D and revPBE-D for lattice parameters and cohesive energies for Ni, Pd, Pt, Cu, Ag, and Au, adsorption energies of CO on (111) surfaces of Pd, Pt, Cu, Ag, and Au, and adsorption energy of benzene on Ag(111) and Au(111). Agreement with experimental data is substantially improved. We apply the method to self-assembled monolayers of alkanethiols on Au(111) and find reasonable agreement for PBE-D and revPBE-D for both physisorption of n-alkanethiols as well as dissociative chemisorption of dimethyl disulfide as an Au-adatom-dithiolate complex. By modifying the coefficient for Au, we obtain quantitative agreement for physisorption and chemisorption for both PBE-D and revPBE-D using the same set of parameters. Our results confirm that inclusion of dispersion forces is crucial for any quantitative analysis of the thiol and thiolate bonds to the gold surface using quantum chemical calculations. 1. Introduction Density functional theory (DFT) is the method of choice for first-principles calculations in condensed matter systems and has contributed greatly to our understanding of metallic systems such as heterogeneous catalysis of ammonia synthesis [1]. However, conventional DFT functionals do not take into account van der Waals interactions, that is, London dispersion. These interactions are crucial for many systems such as interlayer bonding in graphite [2] and biological systems. Research in the last decade has led to dispersion being included in DFT in many ways [3]. Some methods that have the correct asymptotic behavior are nonlocal dispersion-density functional (vdW-DF) [4, 5] and semiempirical atom pairwise dispersion [6–9]. Some highly parameterized meta-GGA functionals also include short-range dispersion effects, like the M06 family of functionals [10], but do not have the correct long-range asymptotic behavior [3]. The vdW-DF functional takes into account electronic effects such as electron transfer from first-principles. Its accuracy for normal thermochemistry is however not well established yet. It is furthermore not well defined for spin-polarized systems, such as Fe, Ni, Co, and their alloys. Dispersion effects included via semiempirical atom pairwise interactions using the DFT-D2 or DFT-D3 methods by Grimme et al. have been shown to give quite accurate thermochemistry for
References
[1]
K. Honkala, A. Hellman, I. N. Remediakis et al., “Ammonia synthesis from first-principles calculations,” Science, vol. 307, no. 5709, pp. 555–558, 2005.
[2]
V. Barone, M. Casarin, D. Forrer, M. Pavone, M. Sambi, and A. Vittadini, “Role and effective treatment of dispersive forces in materials: polyethylene and graphite crystals as test cases,” Journal of Computational Chemistry, vol. 30, no. 6, pp. 934–939, 2009.
[3]
S. Grimme, “Density functional theory with London dispersion corrections,” Wiley Interdisciplinary Reviews, vol. 1, pp. 211–228, 2011.
[4]
M. Dion, H. Rydberg, E. Schr?der, D. C. Langreth, and B. I. Lundqvist, “Van der Waals density functional for general geometries,” Physical Review Letters, vol. 92, no. 24, Article ID 246401, 2004.
[5]
O. A. Vydrov and T. Van Voorhis, “Nonlocal van der Waals density functional made simple,” Physical Review Letters, vol. 103, no. 6, Article ID 063004, 2009.
[6]
S. Grimme, “Accurate description of van der Waals complexes by density functional theory including empirical corrections,” Journal of Computational Chemistry, vol. 25, no. 12, pp. 1463–1473, 2004.
[7]
S. Grimme, “Semiempirical GGA-type density functional constructed with a long-range dispersion correction,” Journal of Computational Chemistry, vol. 27, no. 15, pp. 1787–1799, 2006.
[8]
A. Tkatchenko and M. Scheffler, “Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data,” Physical Review Letters, vol. 102, no. 7, Article ID 073005, 2009.
[9]
S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu,” Journal of Chemical Physics, vol. 132, no. 15, Article ID 154104, 2010.
[10]
R. Valero, J. R. B. Gomes, D. G. Truhlar, and F. Illas, “Good performance of the M06 family of hybrid meta generalized gradient approximation density functionals on a difficult case: CO adsorption on MgO(001),” Journal of Chemical Physics, vol. 129, Article ID 124710, 2008.
[11]
T. S. Bu?ko, J. R. Hafner, S. B. Lebègue, and J. N. G. ángyán, “Improved description of the structure of molecular and layered crystals: Ab Initio DFT calculations with van der Waals corrections,” The Journal of Physical Chemistry A, vol. 114, pp. 11814–11824, 2010.
[12]
G.-X. Zhang, A. Tkatchenko, J. Paier, H. Appel, and M. Scheffler, “Van der Waals interactions in ionic and semiconductor solids,” Physical Review Letters, vol. 107, no. 24, Article ID 245501, 2011.
[13]
P. Tongying and Y. Tantirungrotechai, “A performance study of density functional theory with empirical dispersion corrections and spin-component scaled second-order M?ller-Plesset perturbation theory on adsorbate-zeolite interactions,” Journal of Molecular Structure, vol. 945, no. 1–3, pp. 85–88, 2010.
[14]
M. P. Andersson and S. L. S. Stipp, “Sensitivity analysis of cluster models for calculating adsorption energies for organic molecules on mineral surfaces,” Journal of Physical Chemistry C, vol. 115, no. 20, pp. 10044–10055, 2011.
[15]
S. Ehrlich, J. Moellmann, W. Reckien, T. Bredow, and S. Grimme, “System-dependent dispersion coefficients for the DFT-D3 treatment of adsorption processes on ionic surfaces,” ChemPhysChem, vol. 12, no. 17, pp. 3414–3420, 2011.
[16]
W. Reckien, F. Janetzko, M. F. Peintinger, and T. Bredow, “Implementation of empirical dispersion corrections to density functional theory for periodic systems,” Journal of Computational Chemistry, vol. 33, pp. 2023–2031, 2012.
[17]
P. V. C. Medeiros, G. K. Gueorguiev, and S. Stafstr?m, “Benzene, coronene, and circumcoronene adsorbed on gold, and a gold cluster adsorbed on graphene: structural and electronic properties,” Physical Review B, vol. 85, no. 20, Article ID 205423, 2012.
[18]
K. Tonigold and A. Gross, “Adsorption of small aromatic molecules on the (111) surfaces of noble metals: a density functional theory study with semiempirical corrections for dispersion effects,” Journal of Chemical Physics, vol. 132, no. 22, Article ID 224701, 2010.
[19]
V. G. Ruiz, W. Liu, E. Zojer, M. Scheffler, and A. Tkatchenko, “Density-functional theory with screened van der Waals interactions for the modeling of hybrid inorganic-organic systems,” Physical Review Letters, vol. 108, no. 14, Article ID 146103, 2012.
[20]
T. S. Chwee and M. B. Sullivan, “Adsorption studies of C6H6 on Cu (111), Ag (111), and Au (111) within dispersion corrected density functional theory,” The Journal of Chemical Physics, vol. 137, Article ID 134703, 2012.
[21]
K. Toyoda, I. Hamada, S. Yanagisawa, and Y. Morikawa, “Adsorption of benzene on noble metal surfaces studied by density functional theory with Van der Waals correction,” Journal of Nanoscience and Nanotechnology, vol. 11, no. 4, pp. 2836–2843, 2011.
[22]
A. K. Kelkkanen, B. I. Lundqvist, and J. K. N?rskov, “Van der Waals effect in weak adsorption affecting trends in adsorption, reactivity, and the view of substrate nobility,” Physical Review B, vol. 83, no. 11, Article ID 113401, 2011.
[23]
G. Li, I. Tamblyn, V. R. Cooper, H.-J. Gao, and J. B. Neaton, “Molecular adsorption on metal surfaces with van der Waals density functionals,” Physical Review B, vol. 85, no. 12, Article ID 121409, 2012.
[24]
P. Lazi?, M. Alaei, N. Atodiresei, V. Caciuc, R. Brako, and S. Blügel, “Density functional theory with nonlocal correlation: a key to the solution of the CO adsorption puzzle,” Physical Review B, vol. 81, no. 4, Article ID 045401, 2010.
[25]
H. H?kkinen, “The gold-sulfur interface at the nanoscale,” Nature Chemistry, vol. 4, pp. 443–455, 2012.
[26]
M. Yu, N. Bovet, C. J. Satterley et al., “True nature of an archetypal self-assembly system: mobile Au-thiolate species on Au(111),” Physical Review Letters, vol. 97, no. 16, Article ID 166102, 2006.
[27]
P. Maksymovych, D. C. Sorescu, and J. T. Yates, “Gold-adatom-mediated bonding in self-assembled short-chain alkanethiolate species on the Au(111) surface,” Physical Review Letters, vol. 97, no. 14, Article ID 146103, 2006.
[28]
R. Mazzarello, A. Cossaro, A. Verdini et al., “Structure of a CH3S monolayer on Au(111) solved by the interplay between molecular dynamics calculations and diffraction measurements,” Physical Review Letters, vol. 98, no. 1, Article ID 016102, 2007.
[29]
N. A. Kautz and S. A. Kandel, “Alkanethiol/Au(111) self-assembled monolayers contain gold adatoms: scanning tunneling microscopy before and after reaction with atomic hydrogen,” Journal of the American Chemical Society, vol. 130, no. 22, pp. 6908–6909, 2008.
[30]
O. Voznyy, J. J. Dubowski, J. T. Yates Jr., and P. Maksymovych, “The role of gold adatoms and stereochemistry in self-assembly of methylthiolate on Au(111),” Journal of the American Chemical Society, vol. 131, no. 36, pp. 12989–12993, 2009.
[31]
H. Gr?nbeck, H. H?kkinen, and R. L. Whetten, “Gold—thiolate complexes form a unique c(4 × 2) structure on Au(111),” Journal of Physical Chemistry C, vol. 112, no. 41, pp. 15940–15942, 2008.
[32]
J. Gottschalck and B. Hammer, “A density functional theory study of the adsorption of sulfur, mercapto, and methylthiolate on Au(111),” Journal of Chemical Physics, vol. 116, no. 2, pp. 784–790, 2002.
[33]
F. Abild-Pedersen and M. P. Andersson, “CO adsorption energies on metals with correction for high coordination adsorption sites—A Density Functional Study,” Surface Science, vol. 601, no. 7, pp. 1747–1753, 2007.
[34]
K. J. Gaffney, C. M. Wong, S. H. Liu, A. D. Miller, J. D. McNeill, and C. B. Harris, “Femtosecond electron dynamics at the benzene/Ag(111) interface,” Chemical Physics, vol. 251, no. 1–3, pp. 99–110, 2000.
[35]
R. Caputo, B. P. Prascher, V. Staemmler, P. S. Bagus, and C. W?ll, “Adsorption of benzene on coinage metals: a theoretical analysis using wavefunction-based methods,” Journal of Physical Chemistry A, vol. 111, no. 49, pp. 12778–12784, 2007.
[36]
D. Syomin, J. Kim, B. E. Koel, and G. B. Elison, “Identification of adsorbed phenyl (C6H5) groups on metal surfaces: electron-induced dissociation of benzene on Au(111),” Journal of Physical Chemistry B, vol. 105, no. 35, pp. 8387–8394, 2001.
[37]
H. Ihm, H. M. Ajo, J. M. Gottfried, P. Bera, and C. T. Campbell, “Calorimetric measurement of the heat of adsorption of benzene on Pt(111),” Journal of Physical Chemistry B, vol. 108, no. 38, pp. 14627–14633, 2004.
[38]
J. N. Israelachvili, Intermolecular and Surface Forces, Academic Press, 3rd edition, 2010.
[39]
M. A. Ordal, R. J. Bell, J. R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Applied Optics, vol. 24, pp. 4493–4499, 1985.
[40]
D. J. Lavrich, S. M. Wetterer, S. L. Bernasek, and G. Scoles, “Physisorption and chemisorption of alkanethiols and alkyl sulfides on Au(111),” Journal of Physical Chemistry B, vol. 102, no. 18, pp. 3456–3465, 1998.
[41]
P. Giannozzi, S. Baroni, N. Bonini et al., “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials,” Journal of Physics Condensed Matter, vol. 21, no. 39, Article ID 395502, 2009.
[42]
P. Gianozzi, 2012, http://www.quantum-espresso.org/?page_id=190.
[43]
J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, no. 18, pp. 3865–3868, 1996.
[44]
Y. Zhang and W. Yang, “Comment on ‘Generalized Gradient Approximation Made Simple’,” Physical Review Letters, vol. 80, pp. 890–890, 1998.
[45]
S. Grimme, DFT-D3, http://www.thch.uni-bonn.de/tc/index.php?section=downloads&subsection=DFT-D3&lang=english.
[46]
H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Physical Review B, vol. 13, no. 12, pp. 5188–5192, 1976.
[47]
S. E. Mason, I. Grinberg, and A. M. Rappe, “First-principles extrapolation method for accurate CO adsorption energies on metal surfaces,” Physical Review B, vol. 69, no. 16, Article ID 161401, 2004.