Supporting Information
Interaction of Alkylamines with Cu Surfaces: A Metal-Organic Many-Body Force Field Shih-Hsien Liu† and Kristen A. Fichthorn∗,†,‡ †Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡Also in the Department of Physics E-mail:
[email protected] Phone: +1-814-863-4807. Fax: +1-814-865-7846
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Details of the DFT Calculations The bulk Cu lattice constant we used is 3.615 ˚ A from experiment. 1 The corresponding bulk Cu cohesive energy is Ebulk = -4.146 eV by using a face-centered cubic (fcc) primitive cell and agrees with PAW-PBEsol DFT calculations. 2 We considered two Cu surfaces that could occur during HDA-mediated colloidal syntheses: Cu(100) and Cu(111), and we per√ formed calculations for HDA layers with the following patterns: (5 × 3)-Cu(100) and ( 3 √ √ √ × 3)R30◦ -Cu(111). For (5 × 3)-Cu(100) and ( 3 × 3)R30◦ -Cu(111), we used (5 × 3 × √ 26) and ( 3 × 3 × 23) supercells, respectively. The unit to describe supercell geometries in x and y is the nearest-neighbor distance, and that in z is the interlayer spacing. Our supercells have six layers of Cu with HDA molecules adsorbing on the top side of the slabs, and we left a vacuum spacing of ∼12 ˚ A between the top of the molecular layer and the top of the supercell, as we did in recent DFT studies. 3–5 The cutoff radius for van der Waals (vdW) interactions is 40 ˚ A. Wave functions were expanded using a kinetic energy cut-off of 400 eV, and the Brillouin zone was sampled with a Monkhorst-Pack k-point grid and with √ √ a Methfessel-Paxton smearing of 0.1 eV. For (5 × 3)-Cu(100) and ( 3 × 3)R30◦ -Cu(111), we used (4 × 6 × 1) and (10 × 6 × 1) k-point grids, respectively.
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Force-Field Test on c(2 × 6)-Cu(100) Table S1: The FF- and DFT(in parentheses 5 )-optimized properties defined in the main text for c(2 × 6)-Cu(100) with uniform γ and different θ. Ebind (eV)
error
1.71(1.71) 1.71(1.74) 1.84(1.84) 1.96(1.97) 1.94(1.96)
0.05% 1.63% 0.15% 0.34% 1.38%
EHDA-HDA (eV) EHDA-Cu (eV) ⟨dN-Cu ⟩ (˚ A) 1.10(1.16) 1.09(1.16) 1.23(1.26) 1.32(1.40) 1.31(1.41)
0.61(0.55) 0.62(0.57) 0.61(0.58) 0.64(0.56) 0.63(0.55)
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2.22(2.16) 2.19(2.17) 2.35(2.18) 2.28(2.21) 2.20(2.23)
⟨θ⟩ 3.5◦ (1.7◦ ) 10.1◦ (8.5◦ ) 23.2◦ (20.5◦ ) 31.4◦ (30.8◦ ) 31.7◦ (35.9◦ )
Force-Field Test on p(2 × 2)-Cu(100) Table S2: The FF- and DFT(in parentheses 5 )-optimized properties defined in the main text for p(2 × 2)-Cu(100) with uniform γ and different θ. Ebind (eV)
error
1.36(1.33) 1.40(1.36) 1.38(1.44) 1.94(1.72) 1.92(1.89) 1.93(1.94) 1.93(1.96)
2.71% 3.30% 4.42% 12.31% 1.82% 0.86% 1.47%
EHDA-HDA (eV) EHDA-Cu (eV) ⟨dN-Cu ⟩ (˚ A) 0.59(0.61) 0.61(0.62) 0.59(0.70) 1.11(0.98) 1.10(1.15) 1.10(1.23) 1.07(1.24)
0.77(0.71) 0.79(0.73) 0.79(0.74) 0.82(0.74) 0.82(0.74) 0.82(0.71) 0.86(0.72)
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2.01(2.14) 2.00(2.15) 2.06(2.21) 2.17(2.20) 2.41(2.23) 2.36(2.26) 2.14(2.25)
⟨θ⟩ 4.3◦ (4.1◦ ) 13.1◦ (9.7◦ ) 22.4◦ (22.7◦ ) 46.8◦ (40.3◦ ) 50.8◦ (46.8◦ ) 50.7◦ (50.8◦ ) 50.6◦ (50.8◦ )
√ √ Force-Field Test on ( 3 × 3)R30◦-Cu(111) Table S3: The FF-√and √ DFT(in parentheses 5 )-optimized properties defined in the main text for ( 3 × 3)R30◦ -Cu(111) with uniform γ and different θ. Ebind (eV)
error
1.86(1.83) 1.82(1.82) 1.89(1.78) 1.90(1.79) 1.86(1.78)
1.45% 0.38% 6.17% 6.28% 4.39%
EHDA-HDA (eV) EHDA-Cu (eV) ⟨dN-Cu ⟩ (˚ A) 1.43(1.39) 1.40(1.36) 1.45(1.32) 1.45(1.32) 1.40(1.33)
0.42(0.44) 0.42(0.46) 0.44(0.47) 0.45(0.46) 0.45(0.45)
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2.40(2.30) 2.36(2.26) 2.43(2.26) 2.43(2.26) 2.38(2.26)
⟨θ⟩ 2.6◦ (2.6◦ ) 4.7◦ (4.6◦ ) 1.8◦ (7.1◦ ) 1.4◦ (7.6◦ ) 5.8◦ (9.7◦ )
Force-Field Test on p(2 × 2)-Cu(111) Table S4: The FF- and DFT(in parentheses 5 )-optimized properties defined in the main text for p(2 × 2)-Cu(111) with uniform γ and different θ. Ebind (eV)
error
1.42(1.51) 1.46(1.55) 1.67(1.67) 1.68(1.72) 1.82(1.89) 1.72(1.57)
6.25% 6.33% 0.10% 1.99% 3.86% 9.32%
EHDA-HDA (eV) EHDA-Cu (eV) ⟨dN-Cu ⟩ (˚ A) 0.89(0.90) 0.89(0.92) 1.08(1.04) 1.06(1.08) 1.20(1.28) 1.10(0.95)
0.53(0.61) 0.57(0.63) 0.59(0.63) 0.62(0.64) 0.62(0.62) 0.62(0.62)
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2.25(2.20) 2.27(2.20) 2.35(2.23) 2.24(2.24) 2.33(2.25) 2.32(2.26)
⟨θ⟩ 1.6◦ (1.6◦ ) 14.3◦ (11.3◦ ) 29.7◦ (25.2◦ ) 32.4◦ (30.6◦ ) 38.5◦ (38.8◦ ) 33.0◦ (32.8◦ )
Details of Constructing HDA Binding Patterns on Cu for MD Simulations For each of the proposed HDA patterns, one nitrogen was initially placed on a high-symmetry site, while others were evenly spaced hexagonally in the supercell. We considered that the molecules could have uniform γ, and their initial tilt angles were zero since we found small √ √ tilt angles for (5 × 3)-Cu(100) and ( 3 × 3)R30◦ -Cu(111) in our recent DFT study. 5 The sizes of surface planes for various HDA patterns are shown in Table S5, and they are at least twice the size of the unit cell size and the vdW cutoff radius. These ensure that the periodicity of the pattern is not constrained by the supercell size in MD simulations. Table S5: The sizes of surface plane for the proposed HDA patterns on Cu(100) and Cu(111) in MD simulations. The unit to describe the x and y supercell axes in the surface plane is the nearest-neighbor distance. Pattern
Surface plane
(13 × 3)-Cu(100) (5 × 3)-Cu(100) (12 × 3)-Cu(100) (19 × 3)-Cu(100) (26 × 3)-Cu(100) (33 × 3)-Cu(100) (7 × 3)-Cu(100) (16 × 3)-Cu(100) (17 × 3)-Cu(100) √ √ ( 3 × 3)R30◦ -Cu(111)
(26 × 12) (15 × 12) (24 × 12) (38 × 12) (52 × 12) (66 × 12) (14 × 12) (32 × 12) (34 × 12) √ (7 3 × 12)
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√ √ Radial Distribution Functions for ( 3 × 3)R30◦-Cu(111)
Figure S1: Radial distribution functions atoms projected onto the x − y √ for nitrogen √ (g(r)) ◦ plane with standard error bars for ( 3 × 3)R30 -Cu(111) at a temperature of 373 K. Vertical lines show g(r) at 0 K as a reference.
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Nitrogen Locations for (17 × 3)-Cu(100)
Figure S2: Top-down view of the equilibrated nitrogen configurations and underlying Cu surface atoms for (17 × 3)-Cu(100) at 373 K. Nitrogen is blue.
Figure S3: Top-down view of the optimized nitrogen configurations and underlying Cu surface atoms for (17 × 3)-Cu(100) at 0 K. The red rectangle is the unit cell of the pattern. Nitrogen is blue.
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Details of MD Simulations on Water/HDA/Cu System We used the TIP3P water model 6 implemented in CHARMM36 force field files 7 to describe water-water interactions and the CHARMM-Metal force field 8 for water-Cu interactions. To model aqueous HDA adsorption on cu surfaces, we first built a face-centered cubic (fcc) (10 × 10 × 10) cell for Cu with a lattice constant of 3.615 ˚ A, 9,10 and we performed NPT simulations at 373 K and 1 bar using the Nos´e-Hoover barostat to maintain constant pressure. The system was equilibrated for 5 ns, and its corresponding average lattice constant is 3.636 √ ˚ A, which was employed as our Cu lattice constant to construct (5 × 3)-Cu(100) and ( 3 √ × 3)R30◦ -Cu(111). We then placed water molecules in simple cubic packing at a density of ∼1 g/cm3 on top of HDA monolayer structures, and in the surface normal, we left ∼20 ˚ A , where water molecules do not interact with HDA and Cu, to model solvent behavior in the bulk phase. We performed NPT simulations of the water/HDA/Cu systems at 373 K and 1 bar only in the surface normal to equilibrate the size of supercell in the z axis for 5 ns. Subsequently, we performed NVT simulations of the water/HDA/Cu systems with the average equilibrated supercell size from NPT simulations.
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