The phonon modes of molecular crystals in the terahertz frequency region often feature delicately coupled inter- and intra-molecular vibrations. Recent advances in density functional theory such as DFT-D(*) have enabled accurate frequency calculation. However, the nature of normal modes has not been quantitatively discussed against experimental criteria such as isotope shift (IS) and correlation field splitting (CFS). Here, we report an analytical mode-decoupling method that allows for the decomposition of a normal mode of interest into intermolecular translation, libration, and intramolecular vibrational motions. We show an application of this method using the crystalline anthracene system as an example. The relationship between the experimentally obtained IS and the IS obtained by PBE-D(*) simulation indicates that two distinctive regions exist. Region I is associated with a pure intermolecular translation, whereas region II features coupled intramolecular vibrations that are further coupled by a weak intermolecular translation. We find that the PBE-D(*) data show excellent agreement with the experimental data in terms of IS and CFS in region II; however, PBE-D(*) produces significant deviations in IS in region I where strong coupling between inter- and intra-molecular vibrations contributes to normal modes. The result of this analysis is expected to facilitate future improvement of DFT-D(*).
We present the N-doping induced atomic-scale structural deformation in N-doped carbon nanotubes by using density functional theory calculations. For substitutional N-doped nanotube clusters, the N dopant with an excess electron lone pair exhibits the high negative charge, and the homogeneously distributed dopants enlarge the tube diameter in both zigzag and armchair cases. On the other hand, in pyridine-like N-doped ones, the concentrated N atoms result in a positively curved graphene layer and, thus, can be responsible for tube wall roughness and the formation of interlinked structures.
This paper presents a theoretical analysis of the low-frequency phonons of L-alanine by using the solid-state density functional theory at the Γ point. We are particularly interested in the intramolecular vibrations accessing low-frequency phonons via harmonic coupling with intermolecular vibrations. A new mode-analysis method is introduced to quantify the vibrational characteristics of such intramolecular vibrations. We find that the torsional motions of COO(-) are involved in low-frequency phonons, although COO(-) is conventionally assumed to undergo localized torsion. We also find the broad distributions of intramolecular vibrations relevant to important functional groups of amino acids, e.g., the COO(-) and NH3(+) torsions, in the low-frequency phonons. The latter finding is illustrated by the concept of frequency distribution of vibrations. These findings may lead to immediate implications in other amino acid systems.
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