Charge-transfer theory of surface enhanced Raman spectroscopy: Herzberg–Teller contributions

Abstract

A comprehensive development of the charge-transfer theory of surface enhanced Raman scattering (SERS) is presented. We incorporate the Herzberg–Teller mixing of zero-order Born–Oppenheimer electronic states by means of vibronic interaction terms in the Hamiltonian. This is similar to the theory of Tang and Albrecht12 except that we include metal states as part of a molecule–metal system. When this is done we may no longer discard a term involving mixing of ground-state vibrations. The theory is comprehensive in that both molecule-to-metal and metal-to-molecule transfer is considered. Furthermore, both Franck–Condon and Herzberg–Teller contributions to the intensity are obtained. The former, however, contribute only to the intensity of totally symmetric vibrations, while the latter contribute to nontotally symmetric vibrations as well. Since overtones are observed in SERS only weakly if at all, the Herzberg–Teller terms are most consistent with experimental findings. The resulting formulas may be interpreted as a type of resonance Raman effect in which intensity for the charge transfer transitions is borrowed from an allowed molecular transition. We may also carry out the sum over metal states. This procedure predicts a logarithmic resonance at the Fermi level of the metal. We thus predict intensity vs voltage profiles such as I ∝ ‖ln(ωFI−ω+iΓ)‖2 which fits the experimental curves quite well.

Metal−Molecule Schottky Junction Effects in Surface Enhanced Raman Scattering

“…Though, the CT mechanism has been widely studied and fairly gives an intuitive picture of the chemical enhancement, it mostly relies on phenomenological parameters [16,24]. In this context, it is increasingly important to understand the microscopic nature of SERS using first principle modeling [43].…”

Theory of Raman enhancement by two-dimensional materials: Applications for graphene-enhanced Raman spectroscopy

“…The enhancement of the Raman intensity is usually explained as a * ebarros@fisica.ufc.br combination of two effects, the first, and most important one, is the enhancement of the electromagnetic field by the light interaction with plasmons in the metallic surface (known as EM-SERS) [20]. The other process, with a magnitude that is usually smaller, is related to the chemical interaction between the molecule and the rough metallic surface, and is usually referred to as chemical-SERS or charge-transfer-SERS (which we will here refer to as CT-SERS) [13,21]. The first and most prominent effect is strongly based on the geometry of the surface and requires no chemical interaction between the molecule and the surface, such that, in principle, any molecule can be enhanced by any metallic surface provided that the experimental conditions for exciting the plasmon are met and provided that the molecule sits in a location where the electromagnetic field is enhanced.…”

“…[13,21], which has its foundations in Albrecht's theory for vibronic coupling [22]. Albrecht's theory is deemed to be appropriate to describe systems for which the electronic and vibrational coordinates are strongly coupled, such that the excitations of the system can no longer be separated into these categories, but are instead a mix between electronic excitations and vibrations.…”

“…Furthermore, since Albrecht's theory [22] is mainly based on a semiclassical approximation, it lacks the mathematical rigor necessary for further developing our understanding of this interesting process. For example, within Lombardi's theory for the CT-SERS effect [13,21], the Fermi level dependence of the SERS effect is included, a posteriori, after all the electron-vibration interactions are taken into account, disregarding the possible interactions between the vibration and the holes left behind in the valence band.…”

Synthesis of size tunable monodispersed silver nanoparticles and the effect of size on SERS enhancement

“…The EM enhancement is due to the coupling of the incident and Raman electromagnetic field with the SERS substrate, while the CE origins are still controversial [16]. The most widely accepted mechanism for the latter is through a charge transfer mechanism [17]. The EM enhancement factor is thought to be the dominant contribution, however it is not necessary to know the exact origin to measure the overall enhancement factor.…”