Analytic high-order energy derivatives for metal nanoparticle-mediated infrared and Raman scattering spectra within the framework of quantum mechanics/molecular mechanics model with induced charges and dipoles

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au-18 and Au-32) at varying intersystem distances of 3, 4, and 5 A are used as the test systems, and Raman spectra of 4,4'-bipyridine in the proximity of Au-2057 and Ag-2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs.

Automated summary

This work focuses on deriving and implementing analytic energy derivatives with respect to nuclear coordinates and an external electric field within the framework of the QM/DIM method. These derivatives are used to efficiently calculate vibrational frequencies, infrared and Raman spectra of molecules near noble metal clusters/nanoparticles. The results demonstrate the validity and accuracy of the analytic approach, especially when considering the hyperpolarizability of the metal cluster to improve the prediction of Raman spectral intensities. Additionally, the potential impact of charge migration between the adsorbate and MNPs is addressed.