Adsorption of Na and Hg on the Ice (Ih) Surface: A Density-Functional

Jan 28, 2010 - The adsorption of Na and Hg atoms on the ice(Ih) surface has been studied using ... Earth and Planetary Science Letters 2014 408, 355-3...
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J. Phys. Chem. C 2010, 114, 2941–2946

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Adsorption of Na and Hg on the Ice(Ih) Surface: A Density-Functional Study Abu Md. Asaduzzaman and Georg Schreckenbach* Department of Chemistry, UniVersity of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 ReceiVed: July 30, 2009; ReVised Manuscript ReceiVed: January 11, 2010

The adsorption of Na and Hg atoms on the ice(Ih) surface has been studied using first principles densityfunctional calculations. Apart from the stoichiometric surface, a defective surface, created by removing a hydrogen atom from the surface, is also investigated. The adsorption energy for both Na and Hg is low on the stoichiometric surface. The calculated adsorption energies of Hg are qualitatively similar with different theoretical approaches, e.g., a generalized-gradient approximation (GGA) functional, a hybrid functional, and MP2. However, for Na, the GGA calculations reveal a favorable adsorption process, whereas the more accurate B3LYP and MP2 calculations favor the desorption of Na on the stoichiometric ice surface. The adsorption of Hg on the defective surface is stronger (double) than that of the stoichiometric surface. Na adsorbs very strongly on the defect site by forming Na-O bonds. The structures and energetics of all possible adsorption sites of Na and Hg on both the stoichiometric and defective surfaces are analyzed and discussed. I. Introduction Water is one of the few substances that occur naturally in all three phases. Its solid phase, named ice, occurs as an amorphous or crystalline solid. In the crystalline solid, ice has more than a dozen different lattice structures (crystalline phases), depending on the external pressure and temperature.1 The flexibility of the hydrogen bonds along with the tetrahedral coordination of the water molecules facilitates such a wide variety of crystallographic phases. However, under ambient conditions, ice appears as the Ih phase. The oxygen atoms in Ih ice form a regular hexagonal lattice. The two hydrogen atoms belonging to a given oxygen atom are situated between two of the four oxygen neighbors, obeying the ice rule.2 The proton configuration is somewhat disordered. The bulk properties of Ih ice are rather well understood.3-5 Water ice surfaces are abundant in the Polar regions of the Earth and on small ice particles in the atmosphere. When water freezes, other species dissolved in it will be embedded in the resulting ice. Molecules or atoms can also be adsorbed on an ice surface. Therefore, it is evident that ice surfaces in the Polar regions and ice particles in the atmosphere serve as a sink for trace gases and pollutants present in the air. Molecules on these highly reactive surfaces undergo processes like physisorption, chemisorption, dissociation, recombination, phonon excitation, and electron-hole pair generation.6-9 Mercury (Hg) is a global contaminant and has increasingly become a concern in the North due its high toxicity, ability to biomagnify, and ability to be transported over long distances. A recent study suggests that there is a very high level of Hg in marine mammals in the Arctic Ocean.10 Atmospheric Hg depletion events provide a possible pathway of Hg deposition from the atmosphere to the aquatic system. However, the extent to which this atmospherically deposited Hg impinges on the underlying ocean through ice remains unknown.11 It is essential to know the various steps involved in the whole deposition processes. * To whom correspondence should be addressed. E-mail: schrecke@ cc.umanitoba.ca.

In a bid to better understand the overall Hg deposition process, we will initially consider a fraction of the whole deposition process, applying an idealized model system. In the current study, we have carried out an atomic-level investigation of the adsorption of Hg on the ice (Ih) surface. We have also considered Hg deposition on a defective ice surface (that was created by removing a surface hydrogen atom) to investigate how the defect in the surface influences the adsorption. Other than Hg, the most abundant element in the ocean is Na. Therefore, we have also chosen the Na atom for our adsorption study since surface adsorption of metal atoms depends on the electronic configuration of the adsorbed atom.12 II. Computational Procedure The majority of the calculations have been performed applying approximate density-functional theory (DFT) using plane wave basis sets, as implemented in VASP (Vienna ab initio simulation package),13,14 version 4.6. The exchangecorrelation contribution to the total energy is modeled using the GGA functional due to Perdew and Wang (PW91).15 The electronic interactions are described by Vanderbilt ultra-soft pseudopotentials (US-PP)16 provided by VASP. The use of pseudopotentials also ensures that scalar relativistic effects are included in the calculations. The cutoff energy for the plane wave expansion is set to 400 eV. Regarding the number of k-points, we have used a 4 × 4 × 1 Mankhorst-Pack k-points grid for the surface calculations and a 4 × 4 × 8 grid for bulk calculations. The surface is modeled by a periodically repeated slab. Figure 1 shows a side view of the slab that is used in these calculations. All calculations are performed in a simulation box using periodic boundary conditions, i.e., the supercell approach. The bulk ice is optimized in an orthorhombic supercell containing 32 water molecules in four bilayers. The ice structure in the supercell is generated by placing the oxygen atoms using crystallographic data17 and then adding hydrogen atoms obeying the ice rule. Both the cell dimensions and atomic positions are optimized to their local energy minima. The convergence criterion for local energy minima is that all atomic forces be smaller than 0.02 eV/Å. The ice surface is then created by extending the supercell along the Z axis by 10 Å. Extending

10.1021/jp9073202  2010 American Chemical Society Published on Web 01/28/2010

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Asaduzzaman and Schreckenbach In addition to the calculations described so far, we have also employed the molecular Priroda18,19 code for single point energy calculations. We have employed the PBE functional20 and MP2 theory in Priroda calculations with triple-ζ polarized quality basis sets.19 Priroda applies a scalar four-component relativistic method with all-electron basis sets. Moreover, we have also performed single point energy calculations using VASP5.2 with the PBE20 and B3LYP21,22 functionals using the projector plane wave23 potential. Only the gamma point is used in these single point energy calculations. III. Results and Discussion

Figure 1. Side view of one of the slabs used to model the ice surface (optimized structure). Red (green) circles denote O (H) atoms.

Figure 2. Top view of the optimized ice surface; (a) and (b) for stoichiometric and defective surfaces, respectively. The position of the defect is denoted by V in panel b. Three different adsorption sites are denoted by A (on top of an oxygen atom), B (on top of a hydrogen atom), and C (at the center of the hexagon) in panel a. The same atom representation as in Figure 1 has been used.

the vacuum space (by 4 Å) between repeating slabs amounts to a negligible (0.01 eV) change of adsorption energy. A top view of the surface is shown in Figure 2. For both naked and adsorbed surfaces, atoms forming the upper three bilayers are allowed to relax whereas atoms from the remaining bilayer are fixed at their bulk positions. Shown in Figure 2b is a defective surface where a surface hydrogen atom has been removed to create the defect. We have chosen to create the defect in this manner (as opposed to the alternative possibility of removing a proton, creating a charged defect) in order to (i) avoid technical issues related to a net charge in the supercell and (ii) allow for direct comparison of the calculated adsorption energies between the ideal and defective surfaces. An optimization of a free water molecule has also been performed, in order to further assess the accuracy of our approach. The same supercell as for the bulk calculations has been used. Both non spin-polarization (Non-Sp) and spin-polarization (Sp) have been considered for surface and adsorption calculations.

Our study starts off with the optimization of bulk ice and a single water molecule in the same orthorhombic box. Key features of the optimized ice and water structures are summarized in Table 1. The structural parameters for bulk ice are in very good agreement with the reported experimental values and other theoretically calculated values.25 The calculated O-H-O angle is 177.17°. This means that the hydrogen bonds in the ice crystal are not linear which confirms the previous experimental findings.1 The structural parameters for the water molecule are also in very good agreement with the experimentally reported values and better than other25 theoretically calculated values using comparable computational methods (specifically plane wave/US-PP). In our calculations, we have obtained a cohesive energy of 0.69 eV per molecule, somewhat larger than the experimental value of 0.61 eV per molecule.1 The present results, however, are in excellent agreement with previous calculated values of 0.69 and 0.70 eV, respectively, in refs 26 and 27. Such overbinding in the ice crystal is typical for DFT calculations. Although the unit cell used in refs 26 and 27 is different from the current one, the results, however, have not changed significantly. The accurate determination of the structure and energetics of ice is a challenge for GGA methods. Hermann and Schwerdtfeger28 as well as Pisani et al.29 recently attempted to accurately calculate the structure and energetics of ice, by going beyond the GGA approximation. Hermann and Schwerdtfeger28 calculated the lattice energy by adding twobody correlation contributions to the energy on top of the periodic Hatree-Fock calculations. Pisani et al.,29 on the other hand, concluded that the B3LYP21,22 hybrid functional is the best method among those studied to describe the structure and energetics of ice. They have further confirmed the validity of the earlier GGA calculations of Hirsch and Ojama¨e.30 While it is evident that GGA overestimates the cohesive energy (by about 0.10 eV28), we are more interested in calculating the structures (that DFT predicts well) and the relative adsorption energies of Na and Hg on the ice surface, along with the influence of the electronic structure of the different adsorbates on the adsorption process. The adsorption energy is calculated as the difference in the total energy between the metal-ice complex on the one hand, and the ice and the bare metal on the other, see below. Thus, it is reasonable to assume that there is substantial cancellation of any GGA-induced errors in the energetics of the ice. Nevertheless, we have also provided some results on the weakly interacting system using empirical dispersion corrections31 to the GGA20 calculated adsorption energy (DFTD) and using the more accurate methods B3LYP and MP2, see below. Three possible adsorption sites have been identified, i.e., on top of an oxygen atom (site A), on top of a hydrogen atom

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TABLE 1: Key Structural Parameters for Optimized Bulk Ice and Water Moleculesa materials

structural parameters

this study

A B C r(O-H) θ(O-H-O) θ(H-O-H) r(O-O) r(O-H) θ(H-O-H)

4.440 7.720 7.310 0.996 177.16 107.28 2.732 0.967 105.05

ice

water a

exp.b

previous plane wave /US-PP resultsc

4.465 7.858 7.292 1.006

4.529 7.800 7.363 0.998

109.10 2.749 0.957 104.51

107.70 2.761 0.964 107.00

Bond lengths in Å; angles in degrees. b Reference 24. c Obtained from the theoretical work of ref 25.

TABLE 2: Adsorption Energy (∆Ead; PW91) for Na and Hg Atoms on the Ice Surface (eV) Na Non-Sp Sp

Hg

site A

site B

site C

defect (site V)

site A

site C

defect (site V)

0.63 0.54

0.64 0.52

0.64 0.51

2.72 2.41

0.16 0.16

0.15 0.14

0.31 0.23

(site B), and at the center of the hexagon (site C) as shown in Figure 2. The adsorption energy of the metal atom is calculated as

∆Ead ) E(M) + E(Ice) - E(M/Ice)

(i)

with E(M), E(Ice), and E(M/Ice) being the total energy for the metal atom, the ice slab, and the metal on the ice surface, respectively. For the defective surface, the term E(Ice) refers to the defective surface. The calculations on the bare metal atoms were performed in the same simulation box. The calculated adsorption energies (PW91) for the Na and Hg atoms are shown in Table 2. The adsorption energy of Na on the nondefective surface is lower than on the defective surface. Na is a strongly electropositive element. It tends to bind in situations where the binding partners are strongly electronegative. Consequently, the electropositive Na atom will not bind strongly with the hydrogen atom on site B. At first glance, it seems that site A is much more suitable for Na adsorption as the sodium atom will bind with an oxygen atom. However, three hydrogen atoms surround this adsorption site. These three hydrogen atoms and the oncoming Na atom are repulsive to each other. This will put a barrier between the Na and O atoms. On site C, three hydrogen atoms again push the oncoming Na atom to prevent it from coming close to the oxygen atoms. Such repulsions between Na and surface hydrogen atoms lead to long bond distances (3.8-4.0 Å) between them, which can be found in the Supporting Information. They confirm the above discussion. Effectively, this repulsion results in similar adsorption energies for sites A, B, and C, Table 2. The Na and surface H atoms are both strongly electropositive elements. Bringing the Na atom close to the surface exerts repulsive interactions with the H atoms, which push the Na atoms away, resulting in a long distance between Na and surface atoms. On the other hand, the adsorption energy of sodium is very high on the defective surface (larger by about 2.0 eV). At the defect site, the Na atom has easy access to the surface oxygen atom because the previously attached hydrogen atom has been removed due to the defect creation. This oxygen atom is unsaturated in terms of bonding as it lost one of its hydrogens. Therefore, there is a strong driving force for this oxygen atom to become saturated by forming a bond with the adsorbate. Thus, both the unsaturated bonding of the oxygen and the easy access

for the Na atom lead to the formation of a strong ionic bond, resulting in a much higher adsorption energy. Qualitatively, the bonding process could be viewed as donation of an electron from the metal atom to the surface oxygen. The resulting bonding interaction amounts to a strong ionic bond between a Na+ cation and an -O- anionic surface defect. The strong bond formation can be confirmed from the Na-O bond distance. The bond distance between Na and O is 2.11 Å at the defective surface. The adsorption energy of adsorbed metals at the defect site can also be represented by

∆Ead_def ) E(M) + E(def) - E(M/def)

(ii)

1 ∆Edef ) E(def) + *E(H2) - E(Ice) 2

(iii)

subtracting eq iii from ii gives

1 ∆EM_H ) E(M) + E(Ice) - E(M/def) - *E(H2) 2

(iv) where ∆EM_H ) ∆Ead_def - ∆Edef, is a measure for the energy gain of replacing a H atom by an adsorbed metal. E(def) is the energy of the defect surface, E(M/def) is the energy of the adsorbed systems in the defect site, and E(H2) is the energy of hydrogen molecule. The value for the Na atom that we obtained is 1.30 eV, which implies that the replacement of a hydrogen atom from the ice surface by a Na atom is an energetically favorable process. Such observations can be rationalized from the simple fact that the strongly electropositive Na atom binds stronger to the surface oxygen atom than the hydrogen atom. The Bader charge analysis32,33 on the adsorbed system also confirms the above explanations. At the defective site, the charge on the Na atom is +0.89. That means that, at the defect site, the Na atom almost completely donates its valence electron to the surface oxygen atom, in accordance with the qualitative discussion above. Hence, the two atoms form indeed a strong ionic bond. On the other hand, charges on the Na atom at sites A, B, and C are only +0.12, +0.08 and +0.09, respectively. The Na atoms at these adsorption sites (A, B, and C) are able to donate only a small portion of charge. They are only slightly

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Figure 3. Density of states (DOS) of Na, Hg, and their adsorbed systems (a and b) for elemental Na and Hg, respectively, and (c and d) for their adsorption (site A) systems, respectively. The vertical dotted lines in panels c and d mark the Fermi level.

polarized and hence form only weak van der Waals type or dipole-induced dipole bonds. The calculated adsorption energies on all sites are approximately 0.10 eV lower for spin-polarized calculations than for non spin-polarized calculations. The defective surface and the adsorbate atom both have unpaired electrons. The exchange splitting energies for these unpaired electrons are responsible for the lower adsorption energy for spin-polarized calculations. Figure 3 shows the density of states for both adsorbed and elemental Na. It is clear from Figure 3, panels a and c, that there is a small exchange splitting energy due to the unpaired electrons of the Na and surface atoms. The adsorption energies of Hg on the ice surface are much lower than those of Na, Table 2. For Hg, we have not found any local energy minima at site B. The adsorption energies on site A and site C are again very close (within 0.02 eV) to each other. As discussed in the previous section, the metal atoms tend to bind to the electronegative parts of the systems. Accordingly, the Hg atom approaching the oxygen at sites A and C gets repelled by the three electropositive hydrogen atoms surrounding the adsorption sites. Hence the adsorption energies on these two sites are very small. (The repulsion is even stronger for site B were the Hg approaches a hydrogen atom directly.) The Hg-H bond distance is in the range of 3.65-3.75 Å for Hg adsorption. More structural parameters can be found in the Supporting Information. The electronic configuration of the Hg atom is more of a closed-shell type. The repulsive interactions between Hg and surface atoms are not as strong as those of Na and hence the Hg-H distance is shorter than the Na-H distance. However, on the defective site, the Hg atom can bind to the oxygen atom directly and hence it has a higher adsorption energy. Being the less electropositive element, Hg (compared to Na) does not form as strong a bond with the oxygen atom at the defective site as does Na. This can be further confirmed from the charge analysis, which shows that the charge on Hg at the defective site is only +0.16. Due to having paired electrons both, in the Hg and the nondefective surface, the

adsorption energies for spin-polarized and non spin-polarized calculations for sites A and C are similar. However, an unpaired electron in the defective surface leads to a lower adsorption energy for the Sp case. The density of states plots (Figure 3, panels b and d) further clarify the point that the d-electrons of the Hg atom are paired and no exchange splitting and hence no influence of spin-polarization occurs. The ∆EM_H value for the Hg atom that we obtain is -1.11 eV. The negative value of ∆EM_H demonstrates that the replacement of a H atom on the ice surface by a Hg atom is not an energetically (thermodynamically) favorable process. This can be understood such that the H-O bond in the ice surface is stronger than the Hg-O bond. Na and Hg are at the two opposite ends in the electropositive scale. (The Pauling electronegativities are 0.93 and 2.00, respectively.) Due to its high electropositive nature, Na has a strong tendency to bind with electronegative counterparts. On the other hand, Hg, although being a metal, is weak on the electropositive scale and has a much lower tendency to bind with electronegative counterparts. Rather, it tends to bind through electron sharing (covalent bonds). Na, being a strongly electropositive element, binds to the ice surface if there is any opportunity to bind with oxygen atoms. Hg, on the other hand, has less binding tendency with surface oxygen atoms. From the adsorption energies of Na and Hg on the stoichiometric surface and the bond distance between adsorbate and surface, one might wonder about the higher adsorption energies of Na. In addition, the structural features (long distance between adsorbate and surface) and the small adsorption energies certainly point to weak interactions between Na/Hg and the ice surface. GGA functionals cannot describe these properly as we stated previously. In order to address the issue of weakly interacting systems, we have performed single point energy calculations on the optimized geometries with more accurate methods and with another computational tool, Priroda.18,19 With VASP we have employed the hybrid functional B3LYP. Due to the extremely high computational cost, we have employed gamma-point-only calculations in these B3LYP calculations. To

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TABLE 3: Adsorption Energy (∆Ead) in eV for Na and Hg Atoms on the Site A Using Different Theoretical Approachesa

a

methods

Hg

Na

PW91 PBE B3LYP MP2 PBE-D

0.16 0.22 0.16 0.11 0.10

0.63 0.68 -0.30 -0.52

See the text for details of the computational approaches.

compare with the GGA calculations, we have also performed single point energy and gamma-point-only calculations with the PBE functional.20 The adsorption energies for Na and Hg on the site A with PBE are 0.68 and 0.22 eV, respectively, which are in qualitative agreement with our previous results as shown in the Table 3. However, the adsorption energies for Na and Hg with B3LYP are -0.30 and +0.16 eV. Although both GGA and B3LYP calculations provide a similar adsorption energy for the Hg atom, the adsorption energies of Na with GGA and B3LYP are opposite to each other. To further elucidate and clarify this point, we have also calculated the adsorption energy of Hg by introducing Grimme’s empirical dispersion correction31 to PBE (PBE-D) into the energy calculations and by applying the MP2 level of theory using the molecular code Priroda.18,19 The adsorption energies of Hg with PBE-D and MP2 are 0.10 and 0.11 eV. Now, if we compare the adsorption energies of Hg calculated with the various different methods, we can find them to be very close to each other. The slightly smaller values for PBE-D and MP2 might be due to the fact that we have performed a molecular calculation on a periodic slab. Such agreement of the adsorption energy of Hg from several different theoretical approaches gives us confidence with regards to the accuracy of these values. On the other hand, for the adsorption energy of Na with MP2, we obtained a value -0.52 eV. (PBE-D calculations of the Na system did not converge.) With the oppositely signed adsorption energies of Na with different methods, one must take care and use chemical intuition in describing the actual chemical process. Recalling the bond distance between Na and the surface atoms and the nature of the interacting atoms (Na and H both are electropositive), one can reasonably assume that adsorption of Na on the stoichiometric surface is very unlikely. This simple chemical picture is also supported by the calculated values (both are negative, i.e., desorption) using the B3LYP and MP2 levels of theory, which are believed to be the more accurate methods than GGA. In a nutshell, Hg can be adsorbed on the stoichiometric ice surface by weak interactions (0.10-0.16 eV) but this is very unlikely for Na. In a real-case scenario, both Na and Hg or any other metal atoms might not exist in their elemental form, although elemental Hg is well-known to be transported in the atmosphere.34 The ionized form of a metal atom has a smaller covalent radius, which might have some sort of influence on the adsorption on sites A and C. However, from an electrostatic point of view, whether in its elemental or ionized form, metal adsorption on the ice surface occurs only if an oxygen atom is available for binding. IV. Conclusion The adsorption of Na and Hg atoms on the ice(Ih) surface has been studied by plane-wave based density-functional theory calculations. The structural and energetic parameters of bulk ice are well reproduced. The calculations reveal that Na and

Hg adsorptions occurs at a site where there is a chance to form metal-oxygen bonds (e.g., the defect site V in Figure 2). The surface hydrogen atoms, on the other hand, inhibit the metal adsorption process. Due to its higher electropositive nature, the adsorption of a Na atom on the stoichiometric surface is unlikely. The adsorption energies of Hg on the stoichiometric surface are qualitatively similar with different theoretical approaches including GGA, B3LYP, MP2, and PBE-D. However, the calculated adsorption energies of Na on the same surface with GGA (favoring adsorption) are opposite to those with B3LYP and MP2 (favoring desorption). The latter results are considered to be the qualitatively correct ones, based on both chemical arguments and the known features of the different methods. We note that, compared to the rather complex naturally occurring systems that are relevant to the environmental fate of mercury,34 our current study employs a highly idealized model system. For instance, there are various types of defects1 that can occur on the ice surface, in addition to the one considered. Moreover, the generally held view of natural ice surfaces is that of a quasi-liquid layer at the interface. Furthermore, mercury may occur in various compounds other than its elemental form. We plan to address some of these complexities in subsequent studies. Acknowledgment. We are grateful to Fei Wang, Manitoba, for the inspiration to this study and for valuable discussions. We like to thank Tom Woo, Ottawa, for help with the chargedsupercell problem. We also would like to acknowledge funding from The EJLB Foundation (http://www.ejlb.qc.ca/), the Natural Sciences and Engineering Research Council of Canada (NSERC), and the University of Manitoba (University Research Grants Program, URGP). All calculations were performed using WestGrid computing resources and the Atlantic Computational Excellence Network (ACEnet). Westgrid is funded in part by the Canada Foundation for Innovation, Alberta Innovation and Science, BC Advanced Education, and the participating research institutions, and ACEnet is supported by CANARIE. Supporting Information Available: Cartesian coordinates for the optimized geometries; metal-oxygen/hydrogen bond distances (Table S1). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Petrekno, V. F.; Whitworth, R. W. Physics of Ice; Oxford University Press: Oxford, 1999. (2) Bernal, J. D.; Fowler, R. H. J. Phys. Chem. 1933, 1, 515. (3) Hahn, P. H.; Schmidt, W. G.; Seino, K.; Preuss, M.; Bechstedt, F.; Bernholc, J. Phys. ReV. Lett. 2005, 94, 037404. (4) Hamann, D. R. Phys. ReV. B 1997, 55, R10157. (5) Pauling, L. J. Am. Chem. Soc. 1935, 57, 2680. (6) Wolf, E. W. Antartic Sci. 1990, 2, 189. (7) Tuomi, R.; Jones, R. L.; Pyle, J. A. Nature 1993, 365, 37. (8) Solomon, S. Nature 1990, 347, 347. (9) Molina, M. J.; Tso, T.-L.; Molina, L. T.; Wang, F. C.-Y. Science 1988, 238, 1253. (10) Lockhart, W.; Stern, G.; Wagemann, R.; Hunt, R.; Metner, D.; DeLaronde, J.; Dunn, B.; Stewart, R.; Hyatt, C.; Harwood, L.; Mount, K. Sci. Total EnViron. 2005, 351, 391. (11) Outridge, P. M.; Macdonald, R. W.; Wang, F.; Stern, G. A.; Dastoor, A. P. EnViron. Chem. 2008, 5, 89. (12) Asaduzzaman, A. M.; Kru¨ger, P. J. Phys. Chem. C 2008, 112, 19616. (13) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (14) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (15) Perdew, J. P. , Electronic Structure of Solids ′91; Ziesche, P., Eschrig, H., Eds.; Akademie-Verlag: Berlin, 1991. (16) Kresse, G.; Hafner, J. J. Phys.: Condens. Matter. 1994, 6, 8245. (17) Goto, A.; Hondoh, T.; Mae, S. J. Chem. Phys. 1990, 93, 1412. (18) Laikov, D. N. Chem. Phys. Lett. 2005, 416, 116. (19) Laikov, D. N.; Ustynyuk, Y. A. Russ. Chem. Bull. 2005, 54, 820.

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(20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (21) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (22) Lee, C.; Yong, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (23) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (24) Line, C. M. B.; Whitworth, R. W. J. Chem. Phys. 1996, 104, 10008. (25) Hara, Y.; Hashimoto, N. T.; Nagaoka, M. Chem. Phys. Lett. 2001, 348, 107. (26) Koning, M. d.; Antonelli, A.; Silva, A. J. R. d.; Fazzio, A. Phys. ReV. Lett. 2006, 96, 075501. (27) Thierfelder, C.; Hermann, A.; Schwerdtfeger, P.; Smith, W. G. Phys. ReV. B 2006, 74, 045422.

Asaduzzaman and Schreckenbach (28) Hermann, A.; Schwerdtfeger, P. Phys. ReV. Lett. 2008, 101, 183005. (29) Erba, A.; Casassa, S.; Maschi, L.; Pisani, C. J. Phys. Chem. B 2009, 113, 2347. (30) Hirsch, T. K.; Ojama¨e, L. J. Phys. Chem. B 2004, 108, 15856. (31) Grimme, S. J. Comput. Chem. 2006, 27, 1787. (32) Henkelman, G.; Arnaldsson, A.; Jonsson, H. Comput. Mater. Sci. 2006, 36, 354. (33) Bader, R. F. W. Atoms in Molecules - A Quantum Theory; Oxford University Press: Oxford, 1990. (34) Schroeder, W. H.; Munthe, J. Atmos. EnViron. 1998, 32, 809.

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