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This study integrates atomic Raman tensors and atomic Raman Intensity Densities (RIDs) to provide a comprehensive framework for understanding the contributions of individual atoms to Raman intensities. By demonstrating that weak Raman bands can result from destructive interference among strong atomic contributions, the authors reveal the significance of phase relationships in determining Raman signal strength. The methodology is applied to experimental data from surface-enhanced Raman spectroscopy (SERS), highlighting how substituent changes affect Raman intensities through variations in atomic phase rather than global polarizability alterations.
Weak Raman bands can arise from strong atomic contributions canceling each other out, challenging traditional interpretations of Raman intensity.
Raman spectroscopy is commonly reduced to molecular fingerprint sensing, neglecting Raman intensities. Atomic Raman intensity contributions trace Raman intensities back to their microscopic origin and act as local electronic structure descriptors; however, a both physical but intuitive framework is missing by now. Therefore, in this work, we combine the two main lines of decomposing Raman intensities: atomic Raman tensors and atomic Raman Intensity Densities (RIDs). The former are used to define atomic Raman intensities which quantify both the magnitude and the phase of each atom's contribution to the global Raman signal, demonstrating that weak Raman bands may arise from destructive interference of individually strong atomic contributions. The latter build on redefined atomic Raman Polarizability Densities, RPDs, and are defined in analogy to our atomic Raman intensities. They show how the motion of an individual atom modulates the polarizability of the entire molecule. Atomic RIDs thus show local interferences of different atomic contributions. They integrate to the atomic Raman intensities bridging the two main lines. Additional (atomic) Charge Density Differences (CDDs) extend the RIDs to electronic structure effects. Finally, we apply the methodology to experimental surface-enhanced Raman spectra of substituted 2-mercaptobenzothiazole derivatives and discuss substituent-induced Raman intensity changes. We show that such changes do not necessarily stem from globally altered polarizabilities but from changes in the relative phase of atomic contributions. However, this method is not limited to SERS but widely applicable to all kinds of Raman, SERS or picocavity TERS experiments offering a basis for atomically resolved investigations of molecular processes such as adsorption, catalysis, and chemical reactions
