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WIREs Comput Mol Sci
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# Mixing of intermolecular and intramolecular vibrations in optical phonon modes: terahertz spectroscopy and solid‐state density functional theory

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Advances in terahertz (THz) spectroscopy and solid‐state density functional theory (DFT) have enabled a better understanding of low‐frequency molecular phonon modes in the region that includes intermolecular interactions. Normal modes in this region, in particular, may have contributions under the harmonic approximation from both intermolecular and intramolecular nuclear motions. A newly developed mode analysis allows us to characterize molecular optical phonon modes in terms of intermolecular and intramolecular vibrational mixing for the C60 , anthracene, adenine, α‐glycine, and l‐alanine crystals. Through systematic investigation, two forms of the vibrational mixing have been identified. One is strong mixing within similar characteristic frequency regions, while the other is weak mixing of distinct characteristic frequency regions separated by a large gap. The former is predictable from classical mechanics and appears in molecular systems having structural flexibility. The latter is nonclassical and has been illustrated in amino acids. This finding provides new insights into the nature of molecular optical phonon modes and related physical and/or chemical processes such as energy transfer between internal and external modes with large energy separation. WIREs Comput Mol Sci 2016, 6:386–409. doi: 10.1002/wcms.1256

• Structure and Mechanism > Molecular Structures
• Electronic Structure Theory > Density Functional Theory
• Theoretical and Physical Chemistry > Spectroscopy
Structural information for C60 (a), anthracene (b), adenine (c), α‐glycine (d), and l‐alanine (e) crystals. The left side in each panel shows the three principal axes x, y , and z of the irreducible molecular unit(s), while the right side shows the spatial packing structures of all molecules in the unit cell. The red, green, and blue lines represent the three unit cell vectors a, b, and c, respectively. For the cubic C60 and orthorhombic l‐alanine systems, the three Cartesian coordinate axes X, Y, and Z are coincidental with the directions of the three unit cell vectors a, b, and c, respectively. For the other three monoclinic systems, the directions of X and Y are coincidental with that of a and b, while Z points away from c. Their relationships are shown explicitly. Intermolecular CH/π and hydrogen bonds are shown. Molecules in different layers of the anthracene and adenine crystals are shown in different colors for clarity. The dipole moments of C60 and anthracene are zero because of high symmetry. The dipole moments are 0.17 D for both adenine #1 and #2, and 1.05 and 1.01 for glycine and l‐alanine, respectively.
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Frequency distribution of vibration (FDV) patterns of the total intermolecular translation and libration and the two intramolecular skeletal and NH3 + torsions. The results are shown for (a) α‐glycine and (b) l‐alanine.
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Construction of the bases for internal modes. The nine internal modes of an irreducible molecule in the unit cell are shown for (a) α‐glycine and (b) l‐alanine. All vibrational schemes have been amplified equally.
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All inner products of intramolecular vibrational vectors $Q # 1 n , i n t r a$ for all optical phonon modes of α‐glycine in the 0–1050 cm−1 region.
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Mode analysis of crystalline l‐alanine. (a) Simulated IR‐active phonon modes in the 0–800 cm−1 region. Lorentzian line shapes with HWHM = 2.0 cm−1 were convolved into all modes for visualization. All optical modes are categorized into nine groups in terms of frequencies. The mode range in each group is labelled. (b) Percentage contributions of the three intermolecular translations, the three intermolecular librations, and the total intramolecular vibration in each mode. (c) Percentage contributions of the nine elementary intramolecular vibrations as well as the residual motion in the total intramolecular vibration in each mode.
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Mode analysis of crystalline α‐glycine. (a) Simulated IR‐active phonon modes in the 0–1050 cm−1 region. Lorentzian line shapes with HWHM = 2.0 cm−1 were convolved into all modes for visualization. All optical modes are categorized into nine groups in terms of frequencies. The mode range in each group is labelled. (b) Percentage contributions of the three intermolecular translations, the three intermolecular librations, and the total intramolecular vibrations in each mode. (c) The percentage contributions of the nine elementary intramolecular vibrations as well as the residual motion in the total intramolecular vibration in each mode.
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Mode analysis of crystalline adenine. (a) Simulated IR‐active phonon modes in the 0–1000 cm−1 region. Lorentzian line shapes with HWHM = 2.0 cm−1 were convolved for visualization. The mode numbers of the representative IR/Raman bands are labelled. (b) Characteristics of optical phonon modes of adenine in the same spectral region. Each irreducible unit in the unit cell is composed of an adenine dimer; thus, in certain modes, one molecule can be in motion, while the other one is at rest. The percentage contributions of translations, librations, and the total intramolecular vibration in each phonon mode are calculated by averaging their RMSMWDs in the irreducible molecules.
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Mode analysis of crystalline anthracene. (a) Simulated IR‐active phonon modes in the 0–1000 cm−1 region. Lorentzian line shapes with HWHM = 2.0 cm−1 were convolved for visualization. The mode numbers of the representative IR bands are labelled. (b) Characteristics of optical phonon modes in the same spectral region. The upper, middle, and bottom panels show the percentage contributions of the three intermolecular translations, the three intermolecular librations, and the total intramolecular vibration in each mode, respectively.
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Mode analysis of crystalline C60. (a) Simulated IR‐active phonon modes in the 0–300 cm−1 region. Lorentzian line shapes with a half‐width at half‐maximum (HWHM) = 2.0 cm−1 were convolved for visualization. The mode numbers of the two IR bands are labelled. (b) Characteristics of all the optical phonon modes in this region. The upper, middle, and bottom panels show the percentage contributions of the three intermolecular translations, the three intermolecular librations, and the intramolecular vibrations in each mode, respectively.
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