Abstract
Vibrational spectroscopy techniques are some of the most-used tools for materials characterization. Their simulation is therefore of significant interest, but commonly performed using low cost approximate computational methods, such as force-fields. Highly accurate quantum-mechanical methods, on the other hand are generally only used in the context of molecules or small unit cell solids. For extended solid systems, such as defects, the computational cost of plane wave based quantum mechanical simulations remains prohibitive for routine calculations. In this work, we present a computational scheme for isolating the vibrational spectrum of a defect in a solid. By quantifying the defect character of the atom-projected vibrational spectra, the contributing atoms are identified and the strength of their contribution determined. This method could be used to systematically improve phonon fragment calculations. More interestingly, using the atom-projected vibrational spectra of the defect atoms directly, it is possible to obtain a well-converged defect spectrum at lower computational cost, which also incorporates the host-lattice interactions. Using diamond as the host material, four point-defect test cases, each presenting a distinctly different vibrational behaviour, are considered: a heavy substitutional dopant (Eu), two intrinsic point-defects (neutral vacancy and split interstitial), and the negatively charged N-vacancy center. The heavy dopant and split interstitial present localized modes at low and high frequencies, respectively, showing little overlap with the host spectrum. In contrast, the neutral vacancy and the N-vacancy center show a broad contribution to the upper spectral range of the host spectrum, making them challenging to extract. Independent of the vibrational behaviour, the main atoms contributing to the defect spectrum can be clearly identified. Recombination of their atom-projected spectra results in the isolated spectrum of the point-defect.
Highlights
Quantum mechanical modeling of such experimental spectra starts from the calculated vibrational spectrum of the system, with the appropriate intensities for the individual spectral modes determined depending on the target experimental technique (e.g., Infra-Red, Raman,...).[2]
In contrast to solid state modeling, where the phonon spectra are generally only considered for small unit cell systems,[10,13] several approaches have been developed to deal with large systems within the context ofmolecular structure investigations,[14]
The remainder of the system is considered, but to reduce the computational cost, the atoms outside the fragment of interest are grouped in rigid blocks, which have no internal degrees of freedom, only 6 external degrees of freedom
Summary
Vibrational spectroscopy is an important tool for the structural investigation and characterization of solids.[1,2,3,4,5,6,7] Quantum mechanical modeling of such experimental spectra starts from the calculated vibrational spectrum of the system, with the appropriate intensities for the individual spectral modes determined depending on the target experimental technique (e.g., Infra-Red, Raman,...).[2]. The resulting fragment properties are recombined again as approximation of the original system.[20] Yamamoto et al.[21,22] showed this method reproduces spectra of large molecules faithfully as long as suitable fragments were selected They note that the force field transfer accounted for nearly half of the observed error.[21] Hanson-Heine et al.[23] presented a local mode approach which can be used within the context of 2DIR spectroscopy of large systems, where it provides a platform for the parameterization of site frequencies and coupling maps with regard to the geometry of different functional groups. Within the context of the partial Hessian approximations, having a quantitative measure of the defect nature of an atom, would allow for more targeted selection of Hessian sub-blocks In both cases, small supercells can be used to identify specific defect-atoms, and partial Hessian calculations on large supercells to obtain the spectrum of interest, reducing the computational cost of obtaining an accurate quantum mechanical vibrational spectrum in a periodic solid
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