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Intramolecular Vibrations in Low-Frequency Normal Modes of Amino Acids: L-Alanine in Neat Solid State Feng Zhang, Houng-Wei Wang, Keisuke Tominaga, and Michitoshi Hayashi J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp512164y • Publication Date (Web): 27 Feb 2015 Downloaded from http://pubs.acs.org on March 4, 2015

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The Journal of Physical Chemistry

Intramolecular Vibrations in Low-Frequency Normal Modes of Amino Acids: LAlanine in Neat Solid State

Feng Zhang,† Houng-Wei Wang,‡ Keisuke Tominaga, *, † and Michitoshi Hayashi, *, ‡

†

Molecular Photoscience Research Center, Kobe University, Kobe 657-8501, Japan

†

Center for Condensed Matter Sciences, National Taiwan University, 1 Roosevelt Rd. Sec. 4,

Taipei 10617, Taiwan

Corresponding Authors: *E-mail: [email protected] (K. Tominaga). *E-mail: [email protected] (M. Hayashi).

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ABSTRACT

This paper presents a theoretical analysis of the low-frequency phonons of L-alanine by using the solid-state density functional theory at the gamma 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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1. INTRODUCTION Weak interactions occur in all forms of matter, and such interactions ultimately determine the properties of everyday things.1 These weak interactions particularly play an important role in biological systems; for example, weak interactions enable macromolecules to fold into various conformations and packing structures, and mediate important low-frequency vibrations that normally take place in the frequency region of 0.1–10 THz. At low temperatures, such vibrations can be harmonic with small amplitudes; with an increase in temperature, anharmonicity takes effect, thus, giving rise to large-scale slow atomic motions that are functionally relevant.2-4 Global structural transformations of biomolecules, such as allosteric transformations, most likely occur via low-frequency modes.5-7 In contrast, vibrations in the mid-IR region can barely be excited at ambient temperature and may play a restricted role in the generation of biological functions. Although a comprehensive elucidation of the low-frequency vibrations of proteins at the ab initio level remains a challenging task, investigations of their building blocks, i.e., amino acids, have been enabled by recent advances in the solid-state density functional theory (DFT).8-13 It has been found that the average packing densities of amino acid crystals are the same as those of proteins.14 Important functional groups, such as NH3+ and COO− in amino acid crystals and proteins, may be affected by similar environments,15-18 and undergo similar vibrations. Thus, amino acid crystals provide a model system for studying the vibrational dynamics of localized functional groups that are relevant to biological functions. Amino acids in a crystalline state vibrate in the form of phonon modes; therefore, we anticipate that 3



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understanding the nature of low-frequency phonons associated with amino acids is the first step toward elucidating some of the low-frequency vibrational properties of proteins at the ab initio level. Conventionally, intermolecular vibrations dominate the low-frequency molecular phonons due to their small force constants and large reduced mass. In contrast, intramolecular vibrations, which have a relatively large force constant and small reduced mass, always appear in the high-frequency phonons.19 However, recent ab initio simulations of amino acid systems have shown that the low-frequency phonon modes actually result from a mixture of the two types of vibrations.8-11, 13, 20-29 In other words, by coupling with intermolecular vibrations, certain intramolecular vibrations access the low-frequency modes. Consequently, they can be excited at ambient temperature and assume large amplitudes. Before proceeding further, it is convenient to define two terminologies we will frequently use to avoid ambiguity. We refer to the simultaneous appearance of intermolecular and intramolecular vibrations in a single normal mode as harmonic coupling, and refer to the interaction between different normal modes thought the anharmonic mechanism as anharmonic coupling.30-33 From now on, the terminology of coupling specifies the situation of harmonic coupling if without further statement. Intramolecular low-energy vibrations can cause collective atomic motions in which many structural segments vibrate coherently to give rise to, e.g., stretching, bending, or torsional vibrations of backbones. However, this coupling of intermolecular vibrations with intramolecular vibrations makes it difficult to understand the nature of the intramolecular vibrations. Thus, a quantitative mode-analysis method is necessary to characterize the 4


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underlying intramolecular vibrations of a phonon mode of interest at the level of experimental accuracy. In general, two mode-analysis methods have been employed for amino acid systems. One method relies on the Eckart axis conditions10-11,

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to decouple intermolecular and

intramolecular vibrations, as well as on the variations of important internal coordinates, such as bond and dihedral angles, to characterize intramolecular vibrations. The other is the potential energy distribution (PED) method.8-9 These approaches have been successful in separating intermolecular and intramolecular motions in the normal modes of small molecules. However, these methods have a certain limitation in representing intramolecular vibrations. The former, i.e., measuring variations of bond and dihedral angles, is essentially a qualitative approach; thus, it cannot reflect the complete features of intramolecular vibrations. The latter represents intramolecular vibrations as a superposition of a set of linearly independent local-mode coordinates. In fact, PED analysis is specially developed for small molecular systems with few vibrational entities. Regarding the low-frequency intramolecular vibrations undergoing collective atomic motions, the quality of PED analysis depends strongly on the introduced set of coordinates related to the degrees of freedom for the nuclei; as the molecule size increases, the PED analysis becomes increasingly unfeasible. In addition, it is inefficient to reconstruct a three-dimensional image of collective motion based on a list of prominent local-mode coordinates. The above-mentioned methods do not help reveal the nature of intramolecular collective vibrations, which can often be made clear once the interference of intermolecular vibrations is removed. The collective vibrations may be better represented in a “collective” 5



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manner by introducing a set of proper collective-mode coordinates onto which intramolecular vibrations can be projected. Previously, we introduced a mode-analysis method and elucidated its effectiveness by using crystalline anthracene as an example.28 This material represents a molecular system of high-order symmetry, and its molecular structure does not vary significantly from the gas phase to the solid phase. This allows us to presume that all gas-phase vibrations of anthracene are preserved in the solid phase; thus, we can use the degrees of freedom of the coordinates of the nuclei that form the low-frequency gas-phase modes to define the collective-mode coordinates in the solid phase. In contrast to the case of anthracene, amino acid solids represent a general molecular system with low symmetry. Their structures often change dramatically from neutral configurations in the gas phase to zwitterions in the solid phase. For such a case, it is necessary to generalize the previous method. Here, we propose a new mode-analysis method for general molecular crystal systems. This method decomposes a normal mode of interest as a linear superposition of a set of intermolecular and intramolecular vibrational coordinates (VCs). We introduce a comprehensive approach to define these VCs, particularly the intramolecular collective VCs required for a complete reflection of the characteristics of intramolecular vibrations in the lowfrequency region. We then apply the resulting formula to analyze the low-frequency vibrations of crystalline L-alanine as an example. L-alanine is one of the smallest amino acids, having only a CH3 side group. The lowfrequency vibrations of crystalline L-alanine have been studied intensively using far-IR,35-37 6


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THz,38-42 Raman,9,

43-53

, neutron scattering9,

36, 46-47, 54-56

, NMR57-58, piezoelectric and

dielectric59 spectroscopy. High-quality far-IR35-36 and Raman9, 52 spectra have been recorded at temperatures below 15 K. The thermal energy at 15 K corresponds to 10.5 cm−1. IR and Raman spectra beyond this frequency limit thus result from only the fundamental transitions of gamma-point phonons, thereby providing a rigorous comparison for theoretical calculations performed at 0 K. Through a demonstration in the L-alanine system, we aim to provide a solid basis using which low-frequency normal mode analysis can be applied to other amino acids. Such analysis results may lead to immediate solutions to several unsettled problems in molecular solid systems. For instance, if a certain type of vibration can appear in a number of normal modes over a frequency region via the vibration coupling mechanism, then it has a frequency distribution. As the coupling possibility increases, the frequency distribution broadens. First, the frequency distribution may contribute to a new frequency splitting mechanism for intramolecular vibrations, in addition to the traditional viewpoint of correlation field splitting (or factor group splitting).60-63 Moreover, intramolecular vibrations are typically regarded as more localized motions with characteristic frequencies and small dispersion relationships. Intermolecular vibrations, on the other hand, are more delocalized, which leads to a larger frequency dispersion. and consequently, the vibrational density of state. Thus, any intramolecular vibrations allowed to mix into intermolecular vibrations will receive broad frequency distributions in the same frequency region, which would have important implications in many aspects. 7



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2. METHODOLOGY Solid-state DFT calculations implemented with a periodic boundary condition were performed using the CRYSTAL09 software package64-65 on clusters of Intel Xeon E5530 & E5620 (2.4 GHz) processors and 48 GB memory. The Grimme dispersion correction term66-67 D* (whose parameters were re-optimized by Civalleri et al.68 for the application in the solid molecular systems) was used to augment the PBE and B3LYP functionals to construct the PBED* and B3LYP-D* models, respectively. All calculations were performed using the 6-311G(d,p) basis set.69 The geometry was optimized by relaxing both the atomic coordinates and the unit cell parameters. The orthorhombic crystal structure of L-alanine, measured by the X-ray diffraction method at 23 K,70 was used as the starting point (P212121 space group symmetry; cell parameters: a = 5.9279 Å, b = 12.2597 Å, and c = 5.7939 Å). A global scaling factor

s6

was used to adjust the strength of the dispersion correction term such that the simulated unit cell volume was used as a scaling criterion. We consider that a balance between the dispersion correction term and the corresponding DFT functional was achieved once the simulation could produce a unit cell volume with a shrinking rate

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