Article pubs.acs.org/JPCA
Vibrational Spectroscopy and Phonon-Related Properties of the L‑Aspartic Acid Anhydrous Monoclinic Crystal A. M. Silva,† S. N. Costa,‡ F. A. M. Sales,‡ V. N. Freire,‡ E. M. Bezerra,§ R. P. Santos,∥ U. L. Fulco,⊥ E. L. Albuquerque,⊥ and E. W. S. Caetano*,# †
Universidade Estadual do Piauí, 64260-000 Piripiri, Pi Brazil Departamento de Física, Universidade Federal do Ceará, Centro de Ciências, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, CE Brazil § Departamento de Análises Clínicas e Toxicológicas, Universidade Federal do Ceará, Campus do Porangabuçu, 60430-270 Fortaleza, CE Brazil ∥ Engenharia de Computaçaõ , Universidade Federal do Ceará, 62042-280 Sobral, CE Brazil ⊥ Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN Brazil # Instituto Federal de Educaçaõ , Ciência e Tecnologia do Ceará, 60040-531 Fortaleza, CE Brazil ‡
S Supporting Information *
ABSTRACT: The infrared absorption and Raman scattering spectra of the monoclinic P21 L-aspartic acid anhydrous crystal were recorded and interpreted with the help of density functional theory (DFT) calculations. The effect of dispersive forces was taken into account, and the optimized unit cells allowed us to obtain the vibrational normal modes. The computed data exhibits good agreement with the measurements for low wavenumbers, allowing for a very good assignment of the infrared and Raman spectral features. The vibrational spectra of the two lowest energy conformers of the L-aspartic molecule were also evaluated using the hybrid B3LYP functional for the sake of comparison, showing that the molecular calculations give a limited description of the measured IR and Raman spectra of the L-aspartic acid crystal for wavenumbers below 1000 cm−1. The results obtained reinforce the need to use solid-state calculations to describe the vibrational properties of molecular crystals instead of calculations for a single isolated molecule picture even for wavenumbers beyond the range usually associated with lattice modes (200 cm−1 < ω < 1000 cm−1).
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INTRODUCTION Vibrational spectroscopy techniques such as infrared absorption and Raman scattering measurements are essential tools in characterizing amino acid-based systems, being applied to both amino acid molecules in vacuum and solvated as well as to their crystal structures.1 The interpretation of vibrational features (normal mode assignments, for instance) has an invaluable aid from density functional theory calculations (DFT) that provide a quantum-mechanical description of the electronic energies and forces involved. Perturbation theory allows one to obtain the vibrational normal modes by estimating the derivatives of the Kohn−Sham energy with respect to atomic displacements.2−4 In the case of molecular crystals, however, it is common practice to perform DFT calculations only for isolated molecules to estimate the vibrational properties and interpret the experimental data accordingly. This approach, unfortunately, has some pitfalls. For example, long-range Coulombic forces and charge polarizations induced by intermolecular interactions are not taken into account, and the impact of hydrogen bonds on the molecular © XXXX American Chemical Society
elastic constants is neglected. There is general agreement that the far-infrared vibrational spectra (lattice modes with ω < 200 cm−1) of amino acid crystals in general cannot be adequately described when intermolecular forces are not properly addressed during theoretical modeling.6−8,34 Notwithstanding that, it is a general belief that the isolated molecule picture can give a good description for wavelengths >200 cm−1 (above the so-called lattice modes). This assumption is interesting as it allows a more economical approach in order to decrease the computational cost of quantum-level methods. Nevertheless, advances in computer hardware and software have allowed the simulation of increasingly complex systems using DFT. For amino acid crystals, DFT methods were applied by Chisholm et al.,9 who pursued the relative stabilities of the four known crystalline phases of glycine. The structural and Received: September 8, 2015 Revised: November 16, 2015
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DOI: 10.1021/acs.jpca.5b08784 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A electronic properties of L-amino acids alanine, leucine, isoleucine, and valine were investigated within the generalized gradient approximation (GGA) for the exchange-correlation functional,10 with the result that the amino acid molecules adopt zwitterionic configurations with estimated band gaps close to 5.0 eV. Molecular signatures in the photoluminescence of α-glycine, Lalanine, and L-asparagine crystals were detected11 and explained using DFT calculations, while Tulip and Clark12 presented pioneering results of DFT computations to describe the lattice dynamics and the dielectric properties of L-amino acids alanine, leucine, and isoleucine. These pioneering investigations were soon followed by other papers.13−19 In a recent work, Dunitz and Gavezotti20 have investigated the stabilities of proteogenic amino acids employing an array of semiempirical and ab initio methods, showing that the crystal stability tends to increase for smaller crystal densities, which is probably due to hydrogen bond directionality effects. Aspartic acid (Asp, D, chemical formula C4H7NO4) was one of the most abundant amino acids in the primitive earth, being found in the Murchison meteorite.21 For the gaseous aspartic acid phase, ab initio studies have found a total of 139 canonical conformers22 (none of them zwitterionic), from which 6 were conclusively identified by their distinct rotational 14N nuclear quadrupolar coupling constants23 using laser ablation and supersonic jets on solid samples. In water solution, a total of 22 zwitterion conformers were found.22 In the solid state, aspartic acid can be crystallized as D- and L-enantiomorphs at room temperature24 with the following crystal forms: L-Asp anhydrous monoclinic, space group P21, and Z = 2,25−28 as shown in Figure 1; L-Asp monohydrated orthorhombic, space group P212121, and Z = 4;29 and DL-Asp anhydrous monoclinic, space group C2/c, and Z = 8.30−32 Previous papers on the vibrational properties of aspartic acid presented IR and Raman spectra of solid samples33−36 as well as in aqueous environments.35,37 All supporting DFT calculations in these works, however, were performed for the aspartic acid molecule, i.e., with the lattice modes (ω < 200 cm−1) neglected. As a matter of fact, Navarrete et al.33 have measured the IR and Raman spectra of L-aspartic acid, L-aspartic-d4 acid, and Laspartic-15N acid as solid samples, and their vibrational assignments were based on the isotopic shifts measured and by establishing correlations with published data for other amino acids and related molecules. On the other hand, Matei et al.34 performed far-infrared absorption measurements in polycrystalline samples of 18 amino acids (including aspartic acid) in the spectral range of 10−650 cm−1 with assignments based on the spectra of different amino acids and molecular normal mode calculations available in the literature. Zhu et al.35 measured the Raman spectra of amino acids solid samples and their aqueous solutions in the 600−1700 cm−1, but no normal mode assignments were accomplished in the case of aspartic acid. Anharmonic vibrational studies of L-aspartic acid using HF and DFT molecular calculations were carried out by Alam and Ahmad,36 who recorded the FTIR spectrum of that crystal in the 700−4400 cm−1 wavenumber range. Finally, Wolpert and Hellwig37 presented the infrared spectra and molar absorption coefficients of the 20 α-amino acids (including the aspartic acid) in aqueous solutions (varying the pH) in the spectral range 500− 1800 cm−1, with tentative experimental mode assignments. In order to investigate noncovalent chemical bonds that are relevant to biochemistry, it is interesting to perform a good characterization of the vibrational properties of amino acid crystals. Another very important reason to describe and
Figure 1. (a) Anhydrous monoclinic unit cell of L-aspartic acid. All four hydrogen bonds (η11, η52, η42, and η63) occurring between the L-aspartic acid molecules of the crystal are depicted. (b) Top view of the two ab planes formed by L-aspartic acid molecules. Both planes are related through a screw axis transformation. Hydrogen bonds η11 (interlayer) and η52 (intralayer) occurring between are shown. (c) lateral view of two ac crystal planes showing hydrogen bonds η42 (interlayer) and η63 (intralayer).
understand the vibrational spectra of amino acid crystals is the usual publication of papers presented as novel amino acid compounds that, at the end, because of poor experimental data, are just the pristine amino acid crystals used at the beginning of the synthesis process.38−41 In view of this, our work can be useful as a support material to avoid mistakes when investigating molecules derived from chemical reactions that use aspartic acid as a reagent. Besides, vibrational characterization can also help in the interpretation of the physical properties of new materials based on the integration of amino acids in mixed crystals such as L-asparagine monohydrate crystals doped with L-aspartic acid, which produce a polar system able to induce the freezing of supercooled water.42 By the way, the salification of antibiotics, nonsteroidal anti-inflammatory drugs, and antiarrythmic agents using aspartic acid, lysine, or arginine is commonly employed to B
DOI: 10.1021/acs.jpca.5b08784 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A improve their physical, chemical, and solid-state properties.43 In this type of process, vibrational spectroscopy can provide important clues to assess the role of noncovalent interactions in the product cocrystals, and its interpretation can benefit from theoretical simulations such as those that we present here. In this work, we show how the typical approach used in DFT calculations to obtain the vibrational spectra of molecular crystals, which consists of extrapolating the molecular vibrational simulations to describe the corresponding solid-state system, fails to account for the measured spectra in the case of the L-aspartic acid anhydrous crystal. With this end in mind, we have calculated the IR and Raman spectral curves of the two lowest energy conformers of the L-aspartic molecule for the sake of comparison with the crystal computations in an attempt to understand how electrostatic effects, hydrogen bonds, and dispersive interactions affect lattice motion. The phonon dispersion and the phonon density of states were obtained as well for the first time for this material, together with its specific heat and Debye temperature.
O3). The O2 atom is involved in two hydrogen bonds (η42, interlayer, and η52, intralayer), whereas O1 and O4 take part in the η11 interlayer bond. Atoms O3 and N1 form the η63 bond of the intralayer zigzag backbone. There are no intramolecular hydrogen bonds in the crystal because the lattice structure prevents the formation of the internal N1−H4···O2 bond exhibited by the lowest-energy molecular conformers of Laspartic acid (Figure 2).
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MATERIALS AND METHODS Structural Aspects and Hydrogen Bonding. In a molecular crystal, the total interaction energy is given by the average value of the Hamiltonian of the crystalline system and can be separated into contributions arising from Coulomb interactions, polarization effects, dispersion interactions, and repulsive forces. The Coulomb interaction can be repulsive or attractive depending on the way electric charge is distributed inside the unit cell, being strongly dependent on the relative orientation of each molecular species. Polarization, on the other hand, is always stabilizing because induced dipoles tend to align with the electric field along the stabilizing direction. Dispersion interactions are due to fluctuating dipoles inducing dipoles in their electronic neighborhoods, while repulsive contributions arise, for example, from the Pauli exclusion principle. In systems where molecules exhibit a permanent charge separation (such as the zwitterions in an amino acid crystal), Coulomb and polarization effects are large and essential for stabilization20 and help to promote the formation of hydrogen bonds. Lattice energy calculations for crystals of zwitterionic L-alanine employing a semiempirical strategy with predictive power close to that exhibited by the more sophisticated DFT-D approach have predicted that the attractive Coulomb energy is mainly responsible for the stabilization of the unit cell, while the polarization and dispersion energies are practically canceled by intermolecular repulsive forces.44 The L-aspartic acid molecule in the anhydrous phase crystal has its four carbon atoms constrained to the same plane (average deviation from planarity smaller than 0.01 Å) as depicted in Figure 1, which also shows the atom labels used in this work. A network of hydrogen bonds is essential to stabilizing the anhydrous monoclinic L-aspartic acid crystal.26−28 The hydrogen bonds between two molecules inside a unit cell are shown in Figure 1(a). Two layers of L-aspartic acid molecules can be distinguished in the anhydrous crystal (Figure 1(b)), being related to one another by a screw axis transformation. Two hydrogen bonds connect the layers, and intralayer zigzag chains are formed by the other two hydrogen bonds. This configuration gives rise to important anisotropies in the electronic and optical properties of the L-aspartic acid anhydrous crystal, as showed by Silva et al.,17 and also influences its vibrational properties. Figure 1(b,c) reveals that the stability of anhydrous L-aspartic acid crystals is partially due to four distinct hydrogen bonds, denoted as η11 (H1···O1), η42 (H4···O2), η52 (H5···O2), and η63 (H6···
Figure 2. (Top) Scan of 729 possible configurations for the L-aspartic acid zwitterionic molecule using the water PCM model. There are only two conformers with formation energies smaller than kT at room temperature (blue overlapped squares). (Bottom) L-Aspartic molecular zwitterionic configurations mc1 and mc2. The lowest formation energy configuration, mc1, is used as a reference to measure the relative formation energy of mc2. Hydrogen bond lengths are shown.
IR and Raman Measurements. Powder consisting of Laspartic acid anhydrous crystals with 98% minimal purity was purchased from Sigma-Aldrich. Its crystalline structure was confirmed to be monoclinic through X-ray diffraction (data not presented here). Its FTIR spectra were recorded on a KBr pellet (100 mg, 1 wt %) that was dried under vacuum in desiccators for 24 h to reduce water absorption (water can induce spectral noise around 1630 and 3400 cm−1). The spectra were collected along 120 scans at a resolution of 2 cm−1 . The absorption measurements were all performed using an FTLA 2000 series laboratory instrument (ABB Bomem). Baseline corrections were made in the spectral window from 400−4000 cm−1 to allow for a better comparison with the DFT theoretical calculations. The IR spectrum in the 10−400 cm−1 region was obtained from the literature.34 The FT Raman spectrum, on the other hand, was recorded using a Bruker Vertex 70/RAM2 with a Raman attachment. A 1064 nm Nd:YAG laser excitation source and a liquid-nitrogen-cooled Ge detector line were used to record the Raman spectrum in the 80−4000 cm−1 region. The measurements were performed in samples inside the hemispheric bore of an aluminum sample holder. The Raman curve was acquired along 512 scans at a laser power of 500 mW with a spectral resolution of 4 cm−1. DFT Computational Details. Quantum-mechanical firstprinciples computations were carried out using the CASTEP code45,46 to minimize the unit cell total energy. Lattice parameters and atomic positions of anhydrous crystals of Laspartic acid as measured by Bendeif and Jelsch for a crystal at C
DOI: 10.1021/acs.jpca.5b08784 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A 100 K28 were used to prepare the input structure for the calculations. It was reported that these crystals are monoclinic with space group P21 and lattice parameters a = 5.1135 Å, b = 6.9059 Å, c = 7.5925 Å, β = 100.662 °C, and Z = 2. Our DFT calculations47,48 were carried out using the Cerpeley−Alder−Perdew−Zunger 49,50 parametrization (CAPZ) for the LDA exchange-correlation functional (only for the sake of comparison of the lattice parameters; see Table 1) and
constant pressure and the Debye temperature were also estimated. To optimize the structure of the aspartic acid molecule, a relaxed potential energy surface scan (RPESS)57 was performed. The RPESS method performs a search for the best conformations through the rotation of molecular dihedral angles followed by geometry optimization. In the case of L-aspartic acid, three dihedral angles were selected: θ1 (C1−C2−C3−C4, rotation of the lateral chain), θ2 (N1−C2−C1−O1, rotation of the carboxyl group), and θ3 (C3−C4−O4−H1, rotation of the O4H1 hydroxyl about the C4O4 axis); these were varied in steps of 45° between 0 and 360°, generating 729 distinct configurations. The top of Figure 2 depicts the total energy values for all 729 conformations generated after this procedure. The only two conformers stable below room temperature (blue squares) were labeled mc1 and mc2 and are depicted at the bottom of Figure 2. The calculations were carried out using the Gaussian 09 code58 with exchange-correlation functional B3LYP and the 6-311+G(d,p) basis set using the polarizable continuum model (IEFPCM model with default parameters in Gaussian 09) to simulate water solvation, which is required to stabilize the zwitterionic state of the L-aspartic acid molecule. The following convergence thresholds were applied: maximum force per atom smaller than 1.5 × 10−5 Ha Å−1, RMS force per atom smaller than 1.0 × 10−5 Ha Å−1, self-consistent-field energy variation smaller than 10−7 Ha, and maximum atomic displacement smaller than 6.0 × 10−5 Å. Vibrational properties (normal modes and infrared and Raman intensities) were obtained after a frequency calculation. The full width at half maximum (fwhm) to generate the theoretical vibrational spectra was set to 6 cm−1. Normal mode assignments and potential energy distribution (PED) analysis were carried out using the VEDA code.59 The local contribution with the largest value was taken into account to make the normal mode assignments and was eventually corrected by direct visual inspection of the animated molecular vibrations using Gaussview for the molecular structures and Accelrys Materials Studio Visualizer for the crystals (Figures 9 and 10).
Table 1. Lattice Parameters (Å), Unit Cell Volume (Å3), and α Angle (deg) of the Anhydrous L-Aspartic Acid Crystal Unit Cell as Calculated at the LDA, GGA, and GGA+TS Levelsa a b c β V Δa Δb Δc Δβ ΔV
LDA
GGA
GGA+TS
EXP
4.9719 6.6925 7.4401 101.609 242.50 −0.142 −0.213 −0.152 0.947 −20.98
5.2605 7.3159 7.7191 96.415 295.21 0.147 0.410 0.127 −4.247 31.73
5.1176 6.9529 7.6406 99.457 268.17 0.004 0.047 0.048 −1.205 4.69
5.1135 6.9059 7.5925 100.662 263.48
a
Deviations from experimental (EXP) values for a crystal at 100 K28 are also shown.
the Perdew−Burke−Ernzerhof (PBE)51 GGA approach. The latter also included the dispersion correction scheme proposed by Tkatchenko and Scheffler52 (TS). The PBE functional leads to results close to the ones obtained by using the PW91 functional,53 whereas dispersion corrections avoid the need to use high-level quantum methods to describe van der Waals forces. We also have adopted pseudopotentials to replace the core electrons in each atomic species: norm-conserving pseudopotentials54 were used in both the LDA and GGA+TS calculations with valence electronic shells C 2s22p2, N 2s22p3, and O 2s22p4, leading to 104 valence electrons per unit cell. A 4 × 4 × 4 Monkhorst-Pack55 sampling was employed to evaluate all integrals in the reciprocal space, which is more than enough to give a well-converged electronic structure. Lattice parameters, angles, and atomic positions were optimized by searching a total minimum for the electronic energy. In order to perform the geometry optimization, the following convergence thresholds were considered along successive self-consistent steps: total energy change smaller than 0.5 × 10−5 eV/atom, maximum force per atom below 0.01 eV/Å, pressure smaller than 0.02 GPa, and maximum atomic displacement not larger than 0.5 × 10−3 Å. The BFGS minimizer56 was employed to carry out the unit cell optimization. For each self-consistent field step the electronic minimization convergence parameters were a total energy/atom variation smaller than 0.5 × 10−6 eV, electronic eigenenergy below 0.1250 × 10−6 eV, and a convergence window of three cycles. A planewave basis set was adopted to represent the Kohn−Sham orbitals with a cutoff energy of 830 eV, selected after convergence studies (Table 1). This value was used for both the LDA and GGA (with and without the TS correction) computations. The quality of this basis set was kept fixed notwithstanding unit cell volume changes during the geometry optimization. After finding the minimumenergy structures, we obtained the infrared and Raman spectra as well as the phonon dispersion curves and the partial phonon density of states for the GGA+TS structure. The heat capacity at
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RESULTS AND DISCUSSION Table 1 shows the lattice parameters and unit cell volume for the L-aspartic acid anhydrous crystal at three levels of calculation in comparison with the experimental data of Bendeif et al.28 for anhydrous aspartic acid crystals at 100 K. In the case of the LDA functional, the lattice parameters estimated with a plane wave cutoff energy of 830 eV were significantly smaller than the X-ray diffraction data, especially in the case of b (3.1% smaller), and the unit cell volume is almost 8% below the measured value. Using the pure GGA functional with an 830 eV cutoff energy, the calculated unit cell volume is larger by 12%, with a worse figure for the b parameter as well (5.9% larger than experiment). After the GGA functional is corrected using the TS dispersion scheme, the calculated structural features improve significantly, with the unit cell volume being smaller than experiment by only 1.8%. For the β angle, the best agreement with the measurements occurs at the LDA level (only 0.94% larger). These results suggest the need to employ dispersion correction approximations in order to describe accurately the structure of amino acid crystals. Because of its overall better agreement with the experimental lattice parameters, the unit cell as converged at the GGA+TS level was used to evaluate the vibrational properties, including phonon dispersion curves/density of states, and the thermodynamic properties, as described in the following text. D
DOI: 10.1021/acs.jpca.5b08784 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
wagging; σ, scissoring; ν, bond stretching; β, bending; and ϕ, out of plane. The s and a subscripts denote symmetric and antisymmetric movements, and the out and in subscripts denote outward and inward motions with respect to a plane defined by a functional group or by the molecule. In Figure 3 one can see the 0−1000 cm−1 wavenumber range of the infrared spectra for the crystal experimental (EXP), mc1 (MC1), mc2 (MC2), and crystal theoretical (CRYS) data. For wavenumbers below 400 cm −1 (dashed line), the IR experimental curve was taken from Matei et al.34 because our equipment did not allow us to explore this interval (the infrared spectrum we measured was scaled to match theirs at 400 cm−1). This region corresponds to normal modes characterized by torsions, rocking, and deformations across the entire molecular structure. There is good agreement between the experimental curve and the theoretical curve for the crystal. The spectral curves obtained for the single molecules, however, do not agree very well with the measured crystalline spectrum. As a matter of fact, the difference is not only remarkable in the case of lattice modes (ω < 200 cm−1) but also very important for modes around 400, 600, and even 800−1000 cm−1. This result is consistent with the work of Lopes et al.,60 who performed a study of solid-state anhydrous adenine using vibrational spectroscopy and DFT computations and concluded that it is necessary to use DFT periodic approaches to describe the low-energy region of the vibrational spectrum (
