l-Serine Anhydrous Crystals ... - American Chemical Society

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L‑Serine

Anhydrous Crystals: Structural, Electronic, and Optical Properties by First-Principles Calculations, and Optical Absorption Measurement

S. N. Costa,† F. A. M. Sales,† V. N. Freire,† F. F. Maia, Jr.,‡ E. W. S. Caetano,*,§ L. O. Ladeira,∥ E. L. Albuquerque,⊥ and U. L. Fulco⊥ †

Departamento de Física, Universidade Federal do Ceará, Centro de Ciências, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza-CE, Brazil ‡ Universidade Federal Rural do Semi-Á rido, UFERSA, Campus Angicos, 59515-000 Angicos-RN, Brazil § Instituto de Educaçaõ , Ciência e Tecnologia do Ceará, 60040-531 Fortaleza-CE, Brazil ∥ Instituto de Ciências Exatas, Departamento de Física, Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627, Pampulha, 31340-550 Belo Horizonte-MG, Brazil ⊥ Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil S Supporting Information *

ABSTRACT: The X-ray diffraction data of L-serine anhydrous crystals was taken into account to initialize the total energy minimization process of their unit cell through density functional theory (DFT) computations, which were performed within both the local density and generalized gradient approximations with dispersion, LDA, and GGA+D, respectively. The calculated lattice parameters are in good agreement with the experimental results for the dispersion corrected generalized gradient approximation functional, with a unit cell volume larger by only about 0.32%; the Mulliken and Hirschfield charges show the zwitterionic state of the L-serine molecules in the DFT converged crystals. The electronic (band structure, density of states) and optical absorption properties were calculated to explain the light absorption of the L-serine anhydrous crystalline powder we have measured at room temperature. The optical absorption related to transitions between the top of the valence band and the bottom of the conduction band involves O-2p valence states and H-1s conduction states. The LDA (4.74 eV) and GGA+D (4.75 eV) estimated energy gaps are about 1 eV below the estimated value from optical absorption measurements (5.90 eV). Small values were obtained for the electron effective masses, which are almost isotropic, whereas large anisotropic values were found for hole effective masses, suggesting that the Lserine anhydrous crystal behaves like an n-type wide gap semiconductor. Different dielectric function profiles obtained for some of the most important symmetry directions also demonstrate the optical anisotropy of L-serine anhydrous crystals.

1. INTRODUCTION

After pioneer works on the low-energy conformers of unionized serine,3,4 Gronert and O’Hair5 have spanned 51 serine conformers in vacuum at the highest theoretical ab initio level (up to MP2/6-31+G*) of that moment. The conformational equilibria of neutral serine was studied by Lambie et al.6 through experimental matrix-isolation Fourier transform infrared spectroscopy in combination with density functional theory (DFT) calculations. Besides, the multiple serine conformations of serine in the gas phase has been demonstrated with microwave Fourier transform spectroscopy and pulsed supersonic expansion and laser ablation (LA-MB-FTMW).7 On the other hand, Upadhyay et al.8 performed an ab initio and density functional study of the L- and D-forms of serine in the gas phase

Serine (Ser, S, pKa = 2.21 for the α-carboxylic acid group, 9.15 for the α-ammonium ion, isoelectric point pI = 5.68, MW = 87.08), chemical formula C3H7NO3, is one of the 20 natural amino acids (a nonessential one since can be synthesized from metabolites, including glycine) whose polymerization gives rise to the proteins, biochemical compounds that rule the liferelated biological functions. Among the 10 amino acids that can be formed in Miller’s atmospheric discharge experiments, it is ranked the sixth in order of decreasing abundance in prebiotic contexts, as predicted by thermodynamic arguments, which was likely reflected in the composition of the first proteins at the time the genetic code originated.1 In respect to its abiotic synthesis, serine is found in meteorites, spark discharge experiments, and cyanide polymerization experiments.2 It has two enantiomeric modifications: L-serine and D-serine. © XXXX American Chemical Society

Received: January 19, 2013 Revised: May 15, 2013

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dx.doi.org/10.1021/cg400111w | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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dominant rule to the dipolar and hydrogen-bonding interactions. L-alanine and glycine, on the other hand, exhibit more dispersion in their valence and conduction bands probably due to their closer packaging, as their electronic wave functions are localized as well.14,16 In this work, the focus is on the serine anhydrous monoclinic crystal. By taking full advantage of its X-ray diffraction data,11 a monoclinic (P21) unit cell is constructed and its geometry optimized with respect to its total energy within the DFT scope, the structural, electronic, and optical properties being obtained afterward. Optical absorption measurements of Lserine anhydrous crystals were performed, from which it is estimated a wide indirect energy band gap of 5.90 eV, which is close to the theoretical GGA+D value, as suggested by the calculated band structure, 4.75 eV involving an S → Γ transition. Together with the carriers’ effective masses obtained from the bottom of the main valence and conduction bands, the results suggest that serine anhydrous crystals can have semiconducting properties at least for the electrons, as alanine and glycine.14,16 Finally, the dielectric functions along some symmetry directions are calculated and show important optical anisotropies.

and bulk aqueous medium (using the Polarized Continuum Model - PCM), suggesting that both L- and D-forms are somewhat compressed in the aqueous medium, and despite being almost isoenergetic, they have significant differences in the dipole moments and polarizabilities. However, geometrical features obtained using an improved explicit water model demonstrated that solvated noncompact conformers are able to stabilize as the water molecules prevent the formation of intramolecular hydrogen bonds, an effect that cannot be seen if one uses a homogeneous continuous model, such as PCM.9 On the other hand, in the solid state, serine can be crystallized as Dand L-enantiomorphs under ambient temperature, being known nowadays as the following crystal forms: L-Ser anhydrous monoclinic, P212121, and Z = 4;10−12 L-Ser monohydrated orthorhombic, P212121, and Z = 4;12 and DL-Ser anhydrous monoclinic, P21/a, and Z = 4.11,13 In the solid state, biomolecules, such as nucleotide bases, amino acids, and medicinal drugs (to mention a few), form molecular crystals, which are stabilized by hydrogen bonds, van der Waals, and dipolar electrostatic interactions (known as salt bridges).14 The interest of these crystals remains mainly on characterizing experimentally their polymorphs by infrared, Raman, nuclear magnetic resonance (NMR), and electron paramagnetic resonance (EPR) spectroscopies, which is very useful in the pharmaceutical domain, for example. On the theoretical side, the computational complexity required to study such systems within the density functional theory (DFT) approach strongly limited the development of this field, as stated by Tulip and Clark.14 As a matter of fact, even the numerous spectroscopic measurements on molecular crystals were explained with the calculated spectra of the individual biomolecules; that is, lattice effects were disregarded. However, advances in computer hardware (and more friendly free and commercial DFT codes) are meaning that, increasingly, complex systems are now falling within the remit of ab initio methods.14 As our group has advanced,15,16 there are efforts to take advantage of amino acid films in biosensors and optoelectronic devices, and the adhesion of amino acids on a series of inorganic surfaces, including insulators and semiconductors, was already investigated (being amply cited).17 Oda and Nakayama18,19 have proposed to control electrically the amino acid ionization and the conformation of proteins arranged on semiconductor surfaces, which might produce new types of biodevices. Stroscio and Dutta20 have described advances in man-made nanostructures integrated with biological molecules and systems, their properties, characteristics, and functions. Consequently, it is of paramount importance to understand the fundamental aspects (in particular, electronic and optical characteristics) of amino acid crystals and films for the future development of bio-optoelectronic devices.16 Recently, it was demonstrated that anhydrous crystals of DNA bases are wide gap semiconductors;21 in the case of amino acid crystals, only a few were investigated, with results suggesting that alanine and glycine14,16 are wide band gap semicondutors, whereas valine, leucine, isoleucine, and cysteine could be small band gap insulators.14,22 For the latter, the valence bands exhibit little dispersion, which means that the electronic Kohn−Sham states must resemble the localized molecular orbitals, with small differences being due to the action of van der Waals forces, hydrogen bonding, and dipolar interactions. The nonzero molecular dipole moment and the polar functional groups (which tend to form hydrogen bonds) seem to indicate a

2. MATERIALS AND METHODS 2.1. Experiment. Anhydrous serine powder with at least a 99% purity was purchased from Sigma-Aldrich, being determined to be monoclinic through X-ray diffraction (data not presented here), and mixed separately with KBr to form anhydrous L-Asp-KBr pellets. Light absorption measurements were carried out in these pellets using a Varian Cary 5000 UV−visible NIR spectrophotometer equipped with solid sample holders. The absorption spectra of the samples were recorded in the 200−800 nm wavelength range (6.21−1.55 eV). The optical absorption measurements were performed by transmittance, with background removal and baseline corrections being made when necessary. 2.2. Computational Details. The anhydrous monoclinic serine crystal (space group P212121) lattice parameters and atomic coordinates from ref 11 were optimized within the density functional theory formalism23,24 using the plane-wave CASTEP code.25 Two distinct exchange-correlation functionals were employed: the local density approximation (LDA) and the generalized gradient approximation (GGA) plus dispersion correction (D). The LDA parametrization proposed by Cerpeley, Alder, Perdew, and Zunger26,27 was adopted, whereas the GGA functional is the one proposed by Perdew, Burke, and Ernzerhof (PBE).28 The dispersion correction scheme of Tkatchenko and Scheffler29 was taken into account in the GGA computations to include the effect of van der Waals forces; PBE functional results have the same quality of the well-known PW91 functional.30 Norm-conserving pseudopotentials31 are employed for each atomic species with the following valence configurations: C2s22p2, N-2s22p3, and O-2s22p4. Thus, each unit cell has 224 electrons (56 core and 168 valence electrons). To evaluate integrals in reciprocal space, a Monkhorst−Pack32 2 × 2 × 3 sampling grid was used to achieve a well- converged electronic structure. We note that increasing the sampling to 4 × 4 × 6 using the 2 × 2 × 3 optimized geometry does not lead to significant changes in the unit cell total energy, which varies by less than 0.04%, while the Kohn−Sham band structures remain essentially the same. Geometry optimization was performed by varying the unit cell size, angles, and internal atomic coordinates in order to obtain a total energy global minimum. The structure was taken to be converged after the following criteria were satisfied after two successive self-consistent energy iterations: total energy variation smaller than 0.5 × 10−5 eV/ atom, maximum force acting on each atom smaller than 0.01 eV/Å, pressure less than 0.02 GPa, and maximum atomic displacement smaller than 0.5 × 10−3 Å. In these calculations, the Broyden− Fletcher−Goldfarb−Shanno (BFGS) minimizer,33 a quasi-Newton B



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eV is observed. The onset of the optical absorption α(ℏω) as a function of the energy in an indirect gap crystalas our DFTGGA+D calculations indicate that the anhydrous serine crystals have several close indirect band gapsis related to the incident photon energy by α = C(hν − Eg ∓ ℏΩ)1/2, where C is a constant, Eg is the indirect band gap, and ∓ ℏΩ is the energy of the absorbed or emitted phonon.34,35 Accordingly, in the region where the light absorption of the anhydrous L-serine-KBr pellets increases strongly, the indirect band gap was estimated by carrying out a linear fit of the square of the absorbance, being found a band gap energy of about 5.90 eV. This value is much higher than the band gap energies measured previously by our research group for monoclinic (P21/n, Z = 4) α-glycine crystals, 5.11 ± 0.02 eV,16 and for orthorhombic (P212121, Z = 4) cysteine crystals, 4.68 ± 0.02 eV.22 The estimated errors are related to the inhomogeneity and defects (low density) of the samples due to the growth process. Figure 2 shows (i) the L-serine zwitterion molecular structure, (ii) the monoclinic unit cell for the anhydrous crystal, and (iii) the pattern of hydrogen bonds around a single molecule inside the crystal, as well as (iv) a view of molecular stackings along the b axis. The total energy variation for the Lserine anhydrous crystal as the lattice parameters are varied near the optimal values is depicted in the Supporting Information, revealing that the structure is harder for stresses applied along the a and c directions, where the total energy variation is more pronounced in comparison with the b direction. This is due to the weaker character of the hydrogen bonds between the L-serine molecules at distinct molecular layers in comparison with the in-plane interactions; see Figure 2(iv). The LDA total energy values are larger than the GGA+D corresponding data by about 0.17 kcal/mol, but both functionals have qualitatively the same behavior as the unit cell lengths are changed. Table 1 indicates the lattice parameters calculated within both approaches, with the best agreement with experiment being obtained for the GGA+D data, mainly for the c lattice parameter, which is only 0.021 Å larger than the X-ray diffraction measurements. The GGA+D unit cell, as a matter of fact, is only 0.32% larger than the

approach in which a starting Hessian is recursively corrected, was employed. For each self-consistent field step, convergence was achieved if the total energy variation was less than 0.5 × 10−6 eV within a convergence window of three cycles. Kohn−Sham orbitals were depicted using a plane-wave basis set with a cutoff energy of 830 eV. The electronic structure (Kohn−Sham bands) with the electronic density of states, including total and partial contributions of each orbital and each atomic species, was obtained within both the LDA and the GGA+D frameworks, together with the complex electronic dielectric function and optical absorption using the same scheme of ref 16 for polarized light and in the case of a polycrystalline sample. Carrier effective masses at the band extrema were estimated through parabolic curve fittings.

3. RESULTS AND DISCUSSION The spectra for the optical absorption (squared) of the anhydrous L-Asp-KBr pellets are depicted in Figure 1. The

Figure 1. Square of the optical absorption of serine anhydrous powder measured at 300 K with nonpolarized incident radiation. The straight dashed line points to the 5.90 eV estimated energy gap.

optical absorption increases weakly for small energies, after which a pronounced absorbance increase beginning around 5.6

Figure 2. (i) The L-serine zwitterionic molecule. (ii) The anhydrous L-serine monoclinic unit cell. (iii) A view of the independent hydrogen bonds of the crystal. (iv) View of molecular stackings along the b axis. The atom bonded to the hydrogens H4, H5, and H6 is the nitrogen atom N1. C



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Table 1. Lattice Parameters (in Å), Unit Cell Volume (in Å3), and Angle β (in deg) of the Anhydrous L-Serine Crystal Unit Cell As Calculated at the LDA and GGA+D Levels. Their Deviations from the Experimental Values of Kistenmacher et al.11 Are Also Shown LDA GGA+D exp

a

Δa

b

Δb

c

Δc

V

ΔV

8.280 8.471 8.599

−0.319 −0.128

8.958 9.482 9.348

−0.390 0.134

5.490 5.639 5.618

−0.128 0.021

407.172 452.938 451.500

−44.328 1.438

Table 2. The (xLDA,yLDA,zLDA) LDA and (xGGA,yGGA,zGGA) GGA+D Calculated Fractional Atomic Coordinates in the Unit Cell, and the (xexp,yexp,zexp) Experimental Values of Kistenmacher et al.11 C1 C2 C3 N1 O1 O2 O3 H1 H2 H3 H4 H5 H6 H7

xexp

yexp

zexp

xLDA

yLDA

zLDA

xGGA+D

yGGA+D

zGGA+D

0.115 0.084 0.080 0.201 0.227 0.026 0.229 −0.017 0.054 0.002 0.303 0.162 0.214 0.274

0.194 0.243 0.403 0.182 0.114 0.243 0.462 0.203 0.428 0.445 0.216 0.192 0.080 0.488

−0.141 0.115 0.139 0.280 −0.178 −0.296 0.078 0.163 0.324 0.028 0.267 0.449 0.262 0.212

0.110 0.075 0.071 0.193 0.233 0.012 0.225 −0.047 0.031 −0.017 0.309 0.140 0.216 0.273

0.188 0.243 0.411 0.183 0.111 0.227 0.474 0.203 0.445 0.453 0.235 0.198 0.068 0.498

−0.144 0.111 0.124 0.286 −0.178 −0.309 0.073 0.162 0.308 −0.010 0.276 0.462 0.263 0.233

0.144 0.081 0.078 0.197 0.229 0.022 0.228 −0.037 0.043 −0.010 0.308 0.146 0.219 0.274

0.186 0.241 0.402 0.183 0.104 0.229 0.463 0.204 0.435 0.441 0.232 0.196 0.076 0.496

−0.144 0.108 0.120 0.284 −0.173 −0.306 0.061 0.160 0.299 −0.006 0.276 0.454 0.258 0.210

experimental value, whereas the LDA unit cell is about 10% smaller (an effect of the well-known tendency of LDA to overestimate the strength of binding interactions). The calculated fractional atomic coordinates are shown in Table 2, and some selected bond lengths, bond angles, and hydrogen bond lengths and angles are included in the Supporting Information. Again, one can see that the GGA+D results are overall closer to the experimental values than LDA. For the internal atomic coordinates, however, the LDA estimates for the z coordinates are slightly better, on average, than the GGA+D values. For the bond lengths, the A−BE (C− C and C−N bonds) LDA estimates are, on average, a little bit better than the GGA+D values, whereas the A−CE bond lengths (mostly C−H and N−H bonds) in the GGA+D approach are in better agreement with the experimental parameters. Lastly, the GGA+D bond angles are on average much better than the LDA values, the last exhibiting an undervaluation trend. GGA+D hydrogen bond lengths are much closer to the experimental values than LDA, with the largest discrepancy being observed for the N1−H5−O2 hydrogen bond (0.16 Å larger than the X-ray diffraction measurements). The corresponding LDA figure is 0.23 Å, which is 43% larger than GGA+D. The O3−H7−O3 angle, by the way, is 1.5° (3.1°) larger in the GGA+D (LDA) calculation than the experimental measurement, while the other hydrogen bond−covalent bond angles eventually agree better with the experimental data if one uses the LDA (N1−H6−O1, N1− H5−O2) or GGA+D (N1−H4−O2) functional. Finally, in Table 3, we show a few selected torsion angles for the L-serine molecule in the anhydrous crystal. The GGA+D results, again, are closer to the experiment than the LDA ones, with the mean absolute difference between then being about 2.2°, while the LDA mean absolute difference is 3.1°, about 41% larger. The χ1 (χ2) GGA+D angle is 0.5° (1°) larger than the X-ray data, while the corresponding value for the LDA computation is 2° (6.4°).

Table 3. Torsion Angles in the Anhydrous L-Serine Crystal Unit Cell As Calculated at the LDA and GGA+D Levels. The Experimental Values of Kistenmacher et al.11 Are Also Shown for the Sake of Comparison torsion

LDA

GGA+D

exp

N1−C2−C3−O3 (χ1) C2−C3−O3−H7 (χ2) O1−C1−C2−N1 O2−C1−O1−C2 O3−C3−C2−C1 N1−C2−C1−C3 H1−C2−C1−O1 H2−C3−C2−C1 H3−C3−C2−C1 H4−N1−C2−C1 H5−N1−C2−C1 H6−N1−C2−C1

59.2 −99.6 0.460 178 −62.3 −123 −115 178 55.9 69.0 −165 −50.0

61.7 −105 −4.15 178 −65.3 −124 −124 173 55.3 74.5 −163 −45.0

61.2 −106 −0.840 179 −63.4 −125 −118 175 56.6 76.8 −161 −42.5

Overall, one can say that the combination of the generalized gradient approximation with dispersion corrections leads to sensibly improved figures for the structural features of L-serine anhydrous crystals in comparison with the local density approximation functional, mainly if one contrasts the lattice parameters and unit cell volume obtained from both levels of theory. The results of charge population analysis per atom and per functional group (carboxyl, lateral chain, amine) for the L-serine molecule in the anhydrous crystal are shown in Table 4. Two distinct methods of charge evaluation were adopted: Mulliken36 and Hirshfeld population analysis (HPA).37 The Mulliken approach is more limited, as it divides the electron population in an arbitrary way, which sometimes makes Fukui function indices estimated using these charges unpredictable.38 In contrast, Hirshfeld charges (HPA) tend to be more accurate with respect to the Fukui function indices,39,40 being able to D



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symmetry points depicted. The LDA full band structure is shown at the top part of Figure 3, together with the partial (per

Table 4. Mulliken and Hirshfeld Atomic Charges of the LSerine Molecule in the Anhydrous Monoclinic Crystal As Calculated at the LDA and GGA+D Levels atom

MullikenLDA

MullikenGGA

HirshfeldLDA

HirshfeldGGA

C1 C2 C3 O1 O2 O3 N1 H1 H2 H3 H4 H5 H6 H7 carboxyl CH2OH Lat amine

0.64 −0.18 −0.25 −0.66 −0.65 −0.75 −0.77 0.31 0.25 0.28 0.42 0.42 0.43 0.52 −0.67 0.05 0.50

0.65 −0.18 −0.24 −0.68 −0.68 −0.76 −0.77 0.30 0.25 0.28 0.43 0.43 0.44 0.52 −0.71 0.05 0.53

0.16 0.00 −0.02 −0.20 −0.19 −0.16 −0.09 0.05 0.04 0.03 0.10 0.09 0.10 0.12 −0.23 0.01 0.20

0.16 0.01 −0.01 −0.24 −0.23 −0.18 −0.06 0.05 0.04 0.03 0.11 0.10 0.11 0.13 −0.31 0.01 0.26

predict reactivity trends better than Mulliken, natural bond orbital (NBO) analysis,41 and adjusted electrostatic potentials.42 Besides, the Hirshfeld charges exhibit a smaller degree of loss of information due to the formation of chemical bonds.43,44 However, its values are, in general, too small45,46 as Hirshfeld atoms behave much like neutral atoms.47,48 Nevertheless, such an undesirable effect can be corrected using an iterative technique,46 which has led to good results for the solid state49 and to the study of Fukui functions.50 In the charge analysis we will present here, Hirshfeld charges will be preferred. In general, Hirshfeld charges calculated using the GGA+D exchange-correlation potential have larger absolute values than the LDA ones. For example, the GGA+D carboxyl group has a Hirshfeld charge of −0.31 fundamental charge units, whereas the LDA calculated charge is −0.230. Both functionals agree that O1, O2, and O3 are the most negatively charged species, with GGA+D (LDA) charges of −0.24, −0.23, and −0.18 (−0.20, −0.19, −0.16), whereas the nitrogen atom has a small negative charge of −0.060 (−0.090). The amine group hydrogen atoms, H4, H5, and H6, have the largest positive charges and with approximately the same value: 0.11 (0.10) in the GGA+D (LDA) calculation level. The C1 atom, which belongs to the carboxyl group, also has a relatively wellpronounced positive charge, 0.16, the same value for both the GGA+D and LDA approaches. The remaining atoms (C2, C3, H1, H2, H3), on the other hand, are practically neutral, as well as the lateral chain. Mulliken charges, on the other hand, have larger absolute values than the Hirshfeld results, even for the Hirshfeld almost neutral atoms, but keeping the lateral chain practically devoid of net charge. All in all, we may conclude that the serine molecule in the anhydrous crystalline structure exhibits a remarkable degree of polarization due to its zwitterionic state, with a dipole moment pointing from the carboxyl group to the amine group. The net charges at the carboxyl and amine groups contribute strongly to the formation of the hydrogen bonds that stabilize L-serine anhydrous crystals. 3.1. Electronic Structure. The Kohn−Sham electronic band structure was evaluated taking into account a specific path inside the Brillouin zone of the anhydrous L-serine crystals, which is included in the Supporting Information with its high

Figure 3. LDA calculated band structure of serine anhydrous crystals: (a) in the −21.5 to 13 eV range; (b) in the region around the band gap energy. The partial density of states for the orbitals s (dotted) and p (solid) are shown in the right for each case.

type of orbital) density of states (PDOS). From it, one can see a set of five deep s-like bands between −21.5 and −12.0 eV. Above them, we have the top valence bands, which are mainly p-like in character. The bottom of the conduction band is originated from p orbitals as well (see sharp peak of the PDOS near 5 eV), but s-like contributions are relevant for energies above 6 eV. At the bottom part of Figure 3 there is a close-up of the band structure near the Kohn−Sham band gap, where we can see that both the valence band maximum and the conduction band minimum occur at the Γ point. Thus, Lserine anhydrous crystals are direct band gap materials according with the LDA computations. The direct gap is 4.74 eV, with secondary indirect gaps displaying slightly larger energies: 4.75 eV between the S point at the valence band (VB) and Γ at the conduction band, and 4.76 eV between X (VB) and Γ (CB) and between U (VB) and Γ (CB). The four lowest conduction bands are clearly dominated by contributions from p orbitals, but with a small contribution from s levels. The eight highest valence bands, on the other hand, are strongly p-like, with a very small amount of s-orbital character. Qualitatively, the GGA+D band structure (top part of Figure 4) looks very similar to the LDA band structure. The main difference appears when you look to the smallest band gap between the valence and conduction bands, which is not direct, but indirect, being 4.75 eV between the S point in the valence band and the Γ point in the conduction band. Secondary indirect gaps with similar energies are 4.76 eV (Y → Γ) and 4.77 eV (X → Γ). The direct Γ → Γ energy gap is 4.80 eV. The E



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Figure 5. LDA (up) and GGA+D (down) estimated electron and hole effective masses (in free electron mass mo unit). The fittings are performed at high and low symmetry points, as shown in Figure 4.

+D; 1.02, LDA) me in comparison with the electron effective mass range for the remaining directions (1.36−1.48 me). One can say that the electron effective mass is almost isotropic for Lserine anhydrous crystals and that its electrons are more suitable for charge transport applications due to their improved mobility in comparison with holes, which are much heavier. To analyze the most relevant contributions to the electronic states from each atomic species and each functional group of the serine molecule, we have plotted the per atom partial density of states (PDOS) in Figures 6 (LDA results) and 7 (GGA+D). A direct comparison shows that both functionals provide qualitatively the same PDOS information, so we will focus on the GGA+D data (Figure 7). Looking to the top of the valence band, one can see that the electronic energy levels have a strong O-2p character, with a much smaller contribution from the C-2p levels. The bottom of the conduction band, in contrast, is dominated by C-2p levels, but with a significant amount of contribution from O-2p orbitals. For energies higher than 5 eV, H-1s states, together with C-2p states, form the conduction bands. These s-like contributions come mainly from the hydrogen atoms at the lateral chain for energies below 7.50 eV, and from the amine group for energies between 7.50 and 12.0 eV. The sharp PDOS peaks of the carboxyl group at the top of the valence band and the bottom of the conduction band are related to the localization of the wave functions corresponding to the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the zwitterionic serine molecule. 3.2. Optical Properties. A comparison between the experimental onset of the optical absorption in L-serine anhydrous crystals and the theoretical DFT calculations can be performed by looking to Figure 8. In it, the LDA and GGA +D optical absorption curves for a polycrystalline sample reveal three peak structures between 4.50 and 6.50 eV. The GGA+D peaks occur at 5.65, 5.90, and 6.25 eV, whereas the LDA peaks are centered at 5.67, 6.15, and 6.40 eV. The differences between the optical absorption features of the LDA and GGA+D curves are due mainly to the sensitivity of the optical absorption

Figure 4. GGA+D calculated band structure of serine anhydrous crystals: (a) in the −21.5 to 13 eV range; (b) in the region around the band gap energy. The total density of states for the orbitals s (dotted) and p (solid) are shown in the right for each case.

results we obtained for the band gap of L-serine anhydrous crystals can be compared with previous reports for crystals of glycine,16 cysteine,22 and anhydrous aspartic acid,51 with GGA main band gaps of 4.95 eV (monoclinic glycine), 4.06 eV (monoclinic cysteine), 4.52 eV (orthorhombic cysteine), 4.54 eV (monoclinic aspartic acid), and experimental gap estimates of 5.11 eV (monoclinic glycine), 4.62 eV (orthorhombic cysteine), and 5.02 eV (monoclinic aspartic acid). As one could expect from pure DFT calculations, DFT estimates for the band gaps are smaller than the experimental values52−56 (recently, however, a nonempirical scaling correction method for molecules and solids was proposed to deal with such a problem57). Figure 5 depicts the LDA and GGA+D electronic band structures at the valence and conduction band edges for a few selected high symmetry directions, together with a set of quadratic fits (red dots) used to estimate the corresponding hole and electron effective masses (effective mass is inversely proportional to the parabolic curvature). The largest hole effective mass is associated with the S → Γ direction, being 94.3 (29.4) free electron masses (me) in the GGA+D (LDA) approach, while the smallest effective mass occurs for the U → Γ direction, 8.68 (8.45) me using the GGA+D (LDA) exchange-correlation energy. One can note that the S → Γ transition corresponds to the smallest energy band gap of the GGA+D band structure and that the Γ → Y, S → Γ, and Γ → X directions have flat valence bands, which leads to large hole effective masses. The electron effective mass, on the other hand, does not vary very much as we switch from one direction to another starting always at the Γ point, the largest discrepancy being observed for the Γ → X direction, which is 1.09 (GGA F



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Figure 6. C, O, N, and H contributions to the density of states of serine anhydrous crystals calculated at the LDA level: s (dotted, red) and p (solid, black) orbitals.

Figure 7. Carboxyl, COOH lateral chain, and amine contributions to the density of states of serine anhydrous crystals calculated at the GGA+D level: s (dotted, red) and p (solid, black) orbitals.

polarized light (the number stands for the crystal plane with which the polarization plane aligns), there is a sharp peak at 8.50 eV, which is much smaller than the 010 and 100 cases. The optical absorption peak structure at 6.00 eV observed for the 100 direction is much smaller for the 001 case. The real and imaginary parts of the dielectric function ε(ω) are shown, for the LDA and GGA+D calculations, in Figures 10 and 11, respectively, for light polarized along the 100, 010, and 001 directions and for a polycrystalline sample. As the imaginary part is closely related to the optical absorption, which we already discussed, we will focus now only in the real part, ε1 = Re(ε). If we compare the behavior of ε1 along

formula to the Kohn−Sham interband energy gaps and the shape of the electronic wave functions, which are distinct for each exchange-correlation functional. These peak structures are due to optical transitions between the O-2p uppermost valence bands and the lowest H-1s conduction bands just above the main band gap. The theoretical onset of optical absorption starts at about 5.10 eV for the LDA computations, whereas, for the GGA+D, it begins at about 4.90 eV. It seems also that the GGA+D plot resembles more closely the experimental data. If we analyze the optical absorption curves for distinct incident light polarizations (Figure 9), we can see that there is a strong degree of optical anisotropy. For example, in the case of 001 G



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at ω = 0 for the 001 and 010 polarizations, and about 2.20 for the 100 polarization. For the most part of the 0−23.0 eV energy range, ε1 is positive, except for the 14.0−19.0 eV region, where it becomes slightly negative, but always larger than −1.

4. CONCLUSIONS In this work, we have presented results of density functional simulations, including geometry optimization, electronic band structure and density of states, optical absorption and dielectric function, as well as experimental measurements of optical absorption for L-serine anhydrous crystals. Two distinct exchange-correlation functionals were adopted: the local density approximation (LDA) and the dispersion corrected generalized gradient approximation (GGA+D). The calculated structural properties are in better agreement with the experimental data for the GGA+D functional, which predicts a unit cell volume only slightly larger (+0.32%) than the X-ray diffraction estimates, whereas the LDA functional predicts a unit cell with a volume about 10% smaller. Hirshfeld and Mulliken charges for each atom of serine in the unit cell were obtained, with the carboxyl group having a Hirshfeld charge of −0.23e (−0.31e), the amine group with +0.20e (+0.26e), and the lateral chain with +0.010e (+0.010e) at the LDA (GGA+D) level. The Kohn−Sham electronic band structure exhibits a 4.73 eV direct band gap in the case of the LDA computation, and an indirect band gap of about 4.75 eV between the S point at the valence band and the Γ point in the conduction band (the GGA+D direct gap is 4.80 eV). The optical absorption measurement, on the other hand, allows one to estimate the band gap of L-serine crystals to be around 4.90 eV; thus, notwithstanding the well-known inaccuracy of DFT to estimate excitation energies, the theoretical estimates are close to the experiment. The top of the valence band originates mainly from O-2p states with a smaller contribution from C-2p levels, whereas the bottom of the conduction band has its strongest contribution from C-2p orbitals, with an almost equivalent contribution from C-2p orbitals. Above 5 eV, the H-1s states have a significant contribution, and O-2p → H-1s interband transitions should be responsible for the sharp increase of optical absorption at about 6.00 eV obtained in our measurements. Effective masses for electrons are almost isotropic and smaller than 2 free electron masses, while hole masses are large, reaching as much as 94.3 free electron masses

Figure 8. Comparison between the optical absorption of the anhydrous serine crystal measured with nonpolarized incident radiation at 300 K (black bullets) and the LDA (dotted red line) and the GGA+D (solid black line) calculated (for the polycrystal).

Figure 9. GGA+D (solid black line) and LDA (dotted red line) calculated optical absorption of the anhydrous serine crystal along the directions 001, 010, and 100 for the former, and 001, 010, and 100 for the latter. The optical absorption for the polycrystal is also shown.

different polarization directions, we can see some degree of anisotropy. While the 010 and 100 directions share many similarities, the 001 direction has some remarkable differences in comparison with the other two. For example, the minimum (maximum) near 6.30 eV (5.90 eV) observed for the 010 and 100 cases seems to be shifted upward to 8.30 eV (8.10 eV) for the 001 polarized light ε1. The real part of ε is just a bit above 2

Figure 10. Real (solid black line) and imaginary (dotted red line) components of the GGA+D calculated dielectric function of the anhydrous serine crystal along the directions 001, 010, and 100. The dielectric function components for the polycrystal are also shown. H



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Figure 11. Real (solid black line) and imaginary (dotted red line) components of the LDA calculated dielectric function of the anhydrous serine crystal along the directions 001, 010, 100, 51̅9, and 2̅21. The dielectric function components for the polycrystal are also shown.

(GGA+D, S → Γ direction). One can then conclude that the electron transport in L-serine anhydrous crystals should be more favorable than hole transport, the crystal behaving as an n-type band gap semiconductor and as an insulator for holes except for a few electric field directions. The calculated polarization-dependent dielectric function, on the other hand, reveals a certain degree of optical anisotropy for L-serine anhydrous crystals, with the 100 polarization plane exhibiting distinctive features in comparison with the 010 and 001 planes.

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ASSOCIATED CONTENT

S Supporting Information *

Structural features (bond lengths, angles, hydrogen bond lengths, hydrogen bond angles) are included in the Supporting Information of the paper, together with a figure of the L-serine crystal unit cell energy as a function of the lattice parameters and its first Brillouin zone. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS E.L.A. and V.N.F. are senior researchers from the Brazilian National Research Council (CNPq) and would like to acknowledge the financial support received during the development of this work from the Brazilian Research Agencies CAPES-PROCAD and Rede Nanobiotec, CNPq-INCT-Nano(Bio)Simes project 573925/2008-9, and FAPERN-CNPq (Pronex). E.W.S.C. received financial support from CNPq projects 304283/2010-0 and 474734/2011-0.

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