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

Abstract

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 M 2 -pyrazine-M 2 (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 Ag 2 -pyrazine-Ag 2 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. K E Y W O R D S DFT functional dependence, NPO, pyrazine, Raman intensity, SERS 1 | INTRODUCTION Decomposition of molecular properties into canonical molecular orbitals (CMOs) or atomic orbitals (AOs) frequently fails to capture the essence of the electronic mechanisms of calculated molecular properties, because the decomposed values are distributed into manyCMOs and/or AOs, and no leading term can be found even for medium-sized molecules. In this study, we demonstrate a new strategy to analyze electronic molecular properties, which are expressed as a response by various external perturbations. The method is based on the singular value decomposition/transformation, and therefore the transformed molecular orbitals (MOs) can be called natural perturbation orbitals (NPOs). The NPOs can be applied to various molecular properties, such as the NMR chemical shift, molecular polarizability, and infrared and Raman intensities.Surface-enhanced Raman scattering (SERS) is a great tool for studying molecules adsorbed on metal surfaces. The enhancement mechanisms in SERS can be divided into chemical, resonance, charge transfer, and electromagnetic mechanisms. 1 The electromagnetic mechanism arises from the plasmon resonance of metal surfaces, and therefore the SERS enhancement is usually the largest. Conversely, the chemical mechanism is because of variation of the electronic states caused by interaction between molecules and metal surfaces, and it sometimes shows high enhancement under specific conditions, such as molecules and molecular environments. Analysis of these factors is important to understand the origin of SERS.One of the typical model systems to analyze the chemical mechanism in SERS is the metal-pyrazine-metal junction system. A few studies of metal-pyrazine-metal junction systems have been performed, including for Ag, 2 Au, 3 and Au-Pd 4 junction structures. In particular, high enhancement of about 10 5 has been estimated using the Ag 20 -pyrazine-Ag 20 cluster as a model by density functional theory (DFT) calculation. 2 However, in DFT cal...