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# Theoretical modeling of surface and tip‐enhanced Raman spectroscopies

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Raman spectroscopy is a powerful technique in molecular science because of the ability of providing vibrational ‘finger‐print’. The developments of the surface‐enhanced Raman spectroscopy (SERS) and tip‐enhanced Raman spectroscopy (TERS) have significantly improved the detection sensitivity and efficiency. However, they also introduce complications for the spectral assignments, for which advanced theoretical modeling has played an important role. Here we summarize some of our recent progresses for SERS and TERS, which generally combine both solid‐state physics and quantum chemistry methods with two different schemes, namely the cluster model and the periodic boundary condition (PBC) model. In the cluster model, direct Raman spectra calculations are performed for the cluster taken from the accurate PBC structure. For PBC model, we have developed a quasi‐analytical approach that enables us to calculate the Raman spectra of entire system. Under the TERS condition, the non‐uniformity of plasmonic field in real space can drastically alter the interaction between the molecule and the light. By taking into account the local distributions of the plasmonic field, a new interaction Hamiltonian is constructed and applied to model the super‐high‐resolution Raman images of a single molecule. It shows that the resonant Raman images reflect the transition density between ground and excited states, which are generally vibrational insensitive. The nonresonant Raman images, on the other hand, allow to visualize the atomic movement of individual vibrational modes in real space. The inclusion of non‐uniformity of plasmonic field provides ample opportunities to discover new physics and new applications in the future. WIREs Comput Mol Sci 2017, 7:e1293. doi: 10.1002/wcms.1293

Calculated Raman images by EFG method with the plasmonic size set to 5, 10, and 20 Å (from top to bottom) for H2TBPP adsorbed on the Ag(111) surface with the concave, plane, and convex configurations (from left to right), respectively. The solid lines represent the skeleton of H2TBPP.
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Calculated moduli of induced dipole by the EFG ($μ z E F G$, black solid line) and the analytical ($μ z P$, red solid line) methods with the full width at half‐maximum of α x,y,z set to be 5, 10, 20, and 50 Å (from top to bottom) for H2TBPP adsorbed on the Ag(111) surface with the concave configuration along the scanning line (red dashed line) shown in the inset figure. The inset figure also shows the geometry of the concave extracted from Ref .
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(a) Calculated Raman images for bending (v 2), symmetrical stretching (v 1), and asymmetrical stretching (v 3) modes (from left to right) of a water molecule adsorbed on the Au(111) surface with the plasmonic size set to 1 Å. (b) Calculated Raman images for hydrogen bonding stretching modes of a water dimer and trimer adsorbed on the Au(111) surface with the plasmonic size set to 1 Å. The values are the corresponding frequencies in cm−1. The solid and dotted lines represent the skeleton of the water molecules and hydrogen bonds, respectively. (Reprinted with permission from Ref . Copyright 2016, Wiley‐VCH Verlag GmbH & Co.)
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Calculated nonlinear (top) and total (bottom) Raman images for the concave, plane, and convex configurations (from top to bottom) with the plasmonic size at xy plane set to 20 Å. The solid lines represent the skeleton of H2TBPP. (Reprinted with permission from Ref . Copyright 2015, American Chemical Society)
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Calculated linear Raman images with the plasmonic size at xy plane set to 5, 10, 20, and 30 Å (from top to bottom) for H2TBPP adsorbed on the Ag(111) surface with the concave, plane, and convex configurations (from left to right). Only the topmost slab layer of the substrate is shown for clarity. The inset shows the experimental Raman image extracted from Ref . The solid lines represent the skeleton of H2TBPP. (Reprinted with permission from Ref . Copyright 2015, American Chemical Society)
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(a) Four optimized configurations (flat, vertical, tilting, and broken from left to right) of 4,4′‐bpy sandwiched in Au junctions with different electrode distances in the periodic boundary condition (PBC) model. Only the outermost slab layers of substrates are depicted for clarity. (b) Calculated Raman spectra by the quasi‐analytical method for the four configurations in (a). (c) Three types of experimental surface‐enhanced Raman spectroscopy (SERS) spectra at different electrode distances extracted from Ref . (Reprinted with permission from Ref . Copyright 2015, American Chemical Society)
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Analytical (black), quasi‐analytical (red), and experimental (blue) Raman spectra of isolated 4,4′‐bpy. The experimental spectrum is extracted from Ref . (Reprinted with permission from Ref . Copyright 2015, American Chemical Society)
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(a) Optimized geometries of p‐aminobenzenethiol (PATP) and 4,4′‐dimercaptoazobenzene (DMAB) adsorbed on the Ag(111) surface in the periodic boundary condition (PBC) model. Only the topmost slab layer of the substrate is shown for clarity. (b) Extracted cluster models from optimized structures in (a) for Raman calculations. (c) Calculated Raman spectra of the cluster models in (b). The experimental surface‐enhanced Raman spectroscopy (SERS) spectra of PATP and DMAB extracted from Refs and , respectively, are also included for comparison. (Reprinted with permission from Ref . Copyright 2014, American Chemical Society)
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