Theoretical treatment of single‐molecule scanning Raman picoscopy in strongly inhomogeneous near fields

Abstract

Tip‐enhanced Raman spectroscopy (TERS) of a single molecule is commonly described by considering the change in the polarizability of the molecule with respect to a normal coordinate induced by homogeneous illumination. However, the local fields induced by nanoscale and atomic‐scale features at the surface of metallic clusters and nanogaps show strong inhomogeneities in their spatial distribution, which induces breaking of Raman selection rules. In this context, the spatial extension of the molecular electronic states subjected to strongly varying local fields challenges the validity of the point–dipole approximation as an adequate description of TERS in such configurations. Here, we introduce a general treatment to simulate single‐molecule TERS spectra and their energy‐filtered vibrational fingerprints maps, in which the polarization properties of the single molecule and that of the optical enhancing nanoresonator can be calculated separately and then conveniently combined to obtain the total Raman cross section of the molecule under the strongly inhomogeneous field. We apply the general method to study tip‐enhanced scanning Raman picoscopy of a 4,4′‐bipyridine and biphenyl molecules in the proximity of a silver icosahedral cluster with a few atoms at the tip apex mimicking an enhancing picocavity. The polarization of the molecules is calculated within density functional theory (DFT), and the optical response of the tip is calculated within a classical atomistic discrete–dipole approximation. The Raman spectra are found to be extremely sensitive to the spatial distribution of the local fields and to the orientation of the molecule. Our calculations show that the spatial mapping of molecular vibrational fingerprints, as probed by a tip with atomic protrusions, is capable to reveal intramolecular features of a single molecule in real space and thus establish a robust basis for scanning Raman picoscopy.

Locating Single-Atom Optical Picocavities Using Wavelength-Multiplexed Raman Scattering

“…For the single molecule interacting with this atomic-scale plasmonic feature, SERS is further amplified by its extra enhancement of the local field E nano in the NPoM gap (E/E nano ) 4 ∼ 10 1 −10 4 while also inducing a strong field gradient over the molecule leading to broken selection rules. 26 This leads to the characteristic appearance of nominally dark SERS modes in picocavity spectra and allows for the single molecule SERS to be spectrally isolated from the persistent signal from all other molecules. This transient SERS is used to probe the underlying nanocavity field profiles through simultaneous continuous wave excitation using two wavelengths (λ 1 = 633 nm, λ 2 = 785 nm).…”

Challenges in Plasmonic Catalysis

“…144 A recent theoretical work combined DFT and classical calculations to map the Raman behavior of single molecules in strongly inhomogeneous fields, and demonstrated that picocavities are capable of probing and revealing "intramolecular features of a single molecule in real space". 145 Hence, picocavities provide unprecedented access to specific chemical bonds within a single molecule, opening pathways to modulate and to control optically specific intramolecular bonds and siteselective chemistry. 141 Although thus far picocavities have been used to access vibrational modes at the submolecular level, they have the potential to offer extraordinary control over catalytic reactions at the single-molecule level as well.…”

“…Since then, other tip-based techniques with atomic light confinement have been reported, achieving angstrom resolution for imaging the normal modes and intramolecular charges/currents in single molecules, using either the Raman signal emerging from specific chemical bonds , or photoluminescent measurements at the submolecular level . Recent theoretical work combined DFT and classical calculations to map the Raman behavior of single molecules in strongly inhomogeneous fields and demonstrated that picocavities are capable of probing and revealing “intramolecular features of single molecules in real space” . Hence, picocavities provide unprecedented access to specific chemical bonds within a single molecule, opening pathways to modulate and to control optically specific intramolecular bonds and site-selective chemistry …”

Preface to the special issue dedicated to Professor Richard P. Van Duyne (1945–2019)

“…Aizpurua et al introduce a general treatment to simulate single‐molecule TERS spectra and the corresponding energy‐filtered vibrational fingerprint maps, wherein the polarization properties of the single molecule and that of the optical enhancing nanoresonator can be calculated separately and then conveniently combined to obtain the total Raman cross section of the molecule when there is a strongly inhomogeneous field. [ 4 ]…”

“…[3] Aizpurua et al introduce a general treatment to simulate single-molecule TERS spectra and the corresponding energy-filtered vibrational fingerprint maps, wherein the polarization properties of the single molecule and that of the optical enhancing nanoresonator can be calculated separately and then conveniently combined to obtain the total Raman cross section of the molecule when there is a strongly inhomogeneous field. [4] Reich et al review a number of experimental studies examining the predictions of the electromagnetic enhancement theory of SERS and focusing on the results that require going beyond simple electromagnetic enhancement theory. The authors argue that the results of these experiments reveal the need to develop the theory of SERS further, especially the exact role of plasmonic enhancement in inelastic light scattering.…”