Surface-enhanced Raman scattering of M2 -pyrazine-M2 (M = Cu, Ag, Au): Analysis by natural perturbation orbitals and density functional theory functional dependence.

Here, we propose a new method to analyze various electronic properties of molecules based on natural perturbation orbitals (NPOs). We applied the proposed method to chemical enhancement of the surface-enhanced Raman scattering (SERS) intensity of M2 -pyrazine-M2 (M = Cu, Ag, Au) complexes. The SERS intensity can be effectively decomposed into the contributions of four NPO pairs (1σ-1σ*, 2σ-2σ*, 1π-1π*, and 2π-2π*), so NPO analysis makes the SERS intensity much easier to understand than by conventional canonical molecular orbitals. Moreover, we analyzed the dependence of the density functional theory functional on the SERS intensity. For the Ag2 -pyrazine-Ag2 complex, the BP86 functional overestimates the Raman intensity by about 23 times compared with coupled-cluster singles and doubles level of theory, while the CAM-B3LYP functional gives moderately accurate values. This overestimation arises from the inaccuracy of the energy derivative along the normal vibrational mode.