Supporting information for: Simulating Ensemble-Averaged. Surface-Enhanced Raman Scattering

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1 Supporting information for: Simulating Ensemble-Averaged Surface-Enhanced Raman Scattering Dhabih V. Chulhai, Xing Chen, and Lasse Jensen Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park, 16802, United States. S1

2 Ag-pyridine force field details The force field responsible for the Ag-pyr interactions were parameterized through the embedded-atom-method (EAM) potential modified by a Morse potential and DFT-D2. S1 S3 In the EAM-like potential, the total electron density is written in terms of Ag-Ag electron density and Ag-N electron density. Ag ρ β (r ij ) = ρ Ag Ag (r ij )+ i j N ρ N Ag (r ij ). (1) i j It is assumed that ρ N Ag is proportional to ρ Ag Ag. Accordingly, a scaling factor f is applied to evaluate ρ N Ag. N ρ N Ag (r ij ) = fρ Ag Ag (r ij ). (2) i j The Morse potential is written as φ morse (r ij ) = D 0,Ag L [ e 2α Ag L (r ij r 0,Ag L ) 2e α Ag L(r ij r 0,Ag L ) ], (3) where D 0,Ag L, α Ag L and r 0,Ag L are the parameters describing the short-range interactions between Ag and pyridine molecules. The parameterization is carried out in the same way as reported in our previous work. S4 The parameters of morse potential and the scaling factor are collected in Table S1. Table S1: Morse potential parameters and the scaling factor in electron-density function of EAM potential. D 0,Ag L (ev) α Ag L (Å 1 ) r 0 (Å) f Ag-C Ag-N Ag-H Ag-H a a H s nearest to N The reference data used for the parametrization of the EAM-like potential were generated S2

3 from the DFT calculations. The model system consists of pyridine and a Ag 56 cluster. Two configurations were considered: pyridine both perpendicular and parallel to the Ag(111) facet. The geometry optimizations were performed on the ADF program package, S5 using the Becke-Perdew (BP86) XC-potential S6,S7 and the triple-ζ with one polarization function (TZP) Slater type basis set from the ADF basis set library (keeping the 1s 3d core frozen for Ag). Scalar relativistic effects were taken into account by adopting the zeroth-order regular approximation (ZORA) S8 S10 and dispersion effects were accounted for by the DFT- D3 approach. S11 The interaction energies as the function of the Ag-N distance obtained from DFT and the force field are compared in in Figure S1. The binding energies predicted by force field well match with the DFT results, indicating the force field correctly describe the pyridine and Ag cluster interactions. Figure S1: The interaction energy as a function of the Ag N distance as calculated by DFT (in blue) and the force field (in red) for pyr bound both (a) perpendicular and (b) parallel to the Ag(111) facet. S3

4 Enhancement Distributions Table S2: Signal contribution from the different nanoparticle systems enhancement sm. monomer lg. monomer dimer % mol. % sig. % mol. % sig. % mol. % sig Figure S2: TPD analysis for the DIM and DDA models with a homogeneous field (E) or both a field and gradient (E+FG). S4

5 Figure S3: TPD analysis for actual and random sampling using both the DIM and DDA models. Table S3: Signal contribution from the different models enhancement DIM DDA DIM - random DDA - random % mol. % sig. % mol. % sig. % mol. % sig. % mol. % sig > S5

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