Journal Pre-proofs
DFT Calculations of the Structural, Electronic, Optical and Vibrational
Prop-erties of Anhydrous Orthorhombic L-Threonine Crystals
Roniel L. Araújo, Manoel S. Vasconcelos, Carlos A. Barboza, José X. Lima
Neto, Eudenilson L. Albuquerque, Umberto L. Fulco
PII:
S2210-271X(19)30317-2
DOI:
https://doi.org/10.1016/j.comptc.2019.112621
Reference:
COMPTC 112621
To appear in:
Computational & Theoretical Chemistry
Received Date:
16 August 2019
Revised Date:
14 October 2019
Accepted Date:
15 October 2019
Please cite this article as: R.L. Araújo, M.S. Vasconcelos, C.A. Barboza, J.X. Lima Neto, E.L. Albuquerque, U.L.
Fulco, DFT Calculations of the Structural, Electronic, Optical and Vibrational Properties of Anhydrous
Orthorhombic L-Threonine Crystals, Computational & Theoretical Chemistry (2019), doi:
https://doi.org/
10.1016/j.comptc.2019.112621
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DFT Calculations of the Structural, Electronic, Optical
and Vibrational Properties of Anhydrous Orthorhombic
L-Threonine Crystals
Roniel L. Ara´ujoa, Manoel S. Vasconcelosb, Carlos A. Barbozac, Jos´e X. Lima
Netoc, Eudenilson L. Albuquerquec, Umberto L. Fulcoc,∗
aDepartamento de F´ısica Te´orica e Experimental, Universidade Federal do Rio Grande do
Norte, 59072-970, Natal-RN, Brazil.
bEscola de Ciˆencias e Tecnologia, Universidade Federal do Rio Grande do Norte,
59072-970, Natal-RN, Brazil.
cDepartamento de Biof´ısica e Farmacologia, Universidade Federal do Rio Grande do Norte,
59072-970, Natal-RN, Brazil.
Abstract
The structural, electronic, optical, vibrational and thermodynamic properties of the anhydrous orthorhombic L-threonine crystals are investigated by ab initio simulation using a pseudopotential approach within the density functional the-ory (DFT) method. We have considered both the generalized gradient approx-imation with dispersion correction (GGA+TS) and the local density approxi-mation (LDA), respectively, as our exchange functionals. Within the GGA+TS calculations, an excellent agreement between the measured X-ray and our the-oretical unit cell parameters was obtained, with deviations ∆a, ∆b, ∆c of -0.08 ˚
A, 0.12 ˚A, and 0.01 ˚A, respectively, for an 830 eV cutoff energy. Besides, a direct-band gap E(Γ → Γ)=5.06 eV, was found in agreement with the experi-mental 4.96 eV result. The optical properties have been calculated considering [001] as the incidence direction of polarization of the incident light. The normal vibration’s modes, the infrared and Raman spectra of L-threonine, as well as the thermodynamic properties were also obtained and analyzed.
Keywords: DFT, Anhydrous orthorhombic L-threonine, Electronic properties, Optical properties, Vibrational properties
2010 MSC: 00-01, 99-00
1. Introduction
A large proportion of our cells, muscles, and tissues are composed of amino acids. There are 20 canonical amino acids [1], classified according to the type
∗Corresponding author
of the central structural functional groups. They also play a key role in the transport and the storage of nutrients, with a great influence on the function of 5
organs, tendons and arteries, being essential for healing wounds and repairing tissue, as well as for the removal of all kinds of waste deposits produced in connection with the metabolism [2].
L-threonine (L-Thr, chemical formula C4H9N O3) is one (and the last
discov-ered) of the essential proteinogenic amino acids for humans, being an important 10
component in the protein metabolism chain and contributing to the formation of enzymes and hormones [3, 4]. As an essential amino acid, it needs to be in-gested for a healthy, balanced life since their absence or deficiency could trigger intestinal infections, difficulty in absorbing nutrients, and fatty liver [5]. Fortu-nately, most proteins contain threonine, and therefore a deficiency is unlikely. 15
High concentrations of L-Thr are found in the skeletal muscles and the central nervous system, been also used as a partial treatment for mental health and emotional agitation. Its DNA codons are ACT, ACC, ACA, and ACG.
L-threonine is a polar amino acid with a crystalline state in the zwitterionic form, arising from the transfer of a proton from the carboxyl to the amino 20
group, whose stabilization in the condensed phases is essentially due to the dipole interaction and intermolecular hydrogen bonds. It presents nonlinear optical properties [6] and two chiral centers in the carbons C2 and C3, the former being an alpha carbon atom bonded to the amino group, the carboxyl group, and the side chain, while the latter is located in the side chain. The non-25
linear amino acids have particular characteristics such as the molecular chirality and great transparency in the visible and ultra-violet regions [7, 8].
Recently, there are efforts to employ amino acid molecules and crystals in biosensors and optoelectronic devices [9]. The possibility of using C60-derived nanobaskets bonded to L-alanine was presented by dos Santos et al. [10]. As 30
far as the crystalline L-serine form is a concern, studies related to its electronic (band structure, density of states) and optical absorption properties were calcu-lated to explain the light absorption measured at room temperature [11]. The role of water on the monohydrated L-aspartic acid crystal, as well the inves-tigation of its phonon-related properties considering its monoclinic P 21 phase
35
through Raman and infrared spectroscopy were also discussed recently [12, 13]. Furthermore, biomolecules such as medicinal drugs used for a varied of diseases including cancer, forming molecular crystals stabilized by hydrogen bonds, van der Waals interactions, and dipolar electrostatic interactions (known as salt bridges) were recently investigated [14]. Notwithstanding the interest in molecu-40
lar crystals remained focused mainly on the characterization of their polymorphs by, for instance, nuclear magnetic resonance, and electron paramagnetic reso-nance spectroscopies, very useful in the pharmaceutical domain, few relevant information are being released about their electronic, spintronic and optoelec-tronic properties. The use of computer simulation to overcome this problem 45
by using a quantum chemistry methodology has imposed stringent limits, as stated by Tulip and Clark [15]. However, advances in computer hardware and more efficient density functional theory (DFT) codes are allowing the simula-tion of increasingly complex systems [16, 17, 18, 19]. Recent works by Oda and
Nakayama [20, 21], as well as Stroscio and Dutta [22] proposed new types of 50
biodevices tailored by man-made biological molecules nanostructures.
Despite its relevance, however, only few amino acid crystals had their op-toelectronic properties measured so far, with results suggesting that some of them are wide band gap semiconductors, while others could be small band gap insulators [15, 23, 24]. It was also demonstrated, by using a DFT framework, 55
that anhydrous crystals of the DNA bases present a wide band gap semicon-ductor aspect [25]. Thus, it is of paramount importance to understand these fundamental physical aspects of the amino acids looking for the development of sustainable bio-organic electronic and optoelectronic devices [26].
The crystal structure of L-threonine in the room temperature was deter-60
mined originally by Shoemaker et al. in 1950 [27] through X-ray diffraction. However, due to the lack of information on the geometry of hydrogen bonds, as well as the location of the hydrogen atoms, Janczak et al. [28] re-determined its crystal structure at a temperature equal to 12 K, also using X-ray diffrac-tion technique, finding an orthorhombic crystalline structure composed by four 65
molecules per unit cell (68 atoms), whose space group is P 212121. Its lattice
parameters (angles) of the unit cell were: a=13.63 ˚A, b=7.62 ˚A, and c=5.11 ˚
A(α = β = γ = 90◦), giving a unit cell volume equal to 530.5 ˚A3.
The L-threonine zwitterionic molecule is depicted in Fig. 1(a), while the orthorhombic unit cell of anhydrous L-threonine crystals is shown in Fig. 1(b). 70
Observe the absence of water molecules. Parallel layers of L-threonine molecules can be distinguished, connected through hydrogen bonds occurring between the charged groups (COO−, NH+3 and COO), as can be inferred from Fig. 1(c). Finally, a perspective view of the supercell of L-threonine orthorhombic crystal is shown in Fig. 1(d).
75
In this work, we intend to present a pseudopotential approach within the density functional theory computations by using the local-density approxima-tion (LDA) and the generalized gradient approximaapproxima-tion with scatter correcapproxima-tion (GGA+TS), to investigate the structural, electronic, optical, vibrational, and thermodynamic properties of L-threonine anhydrous crystals. The electronic 80
(band structure and density of states) and optical absorption properties were discussed to interpret the calculated light absorption performed at room temper-ature. The real and imaginary parts of the dielectric function are also presented, as well as the absorption spectrum, refractive index, conductivity, reflectivity, and loss function. The infrared and Raman spectra of L-threonine were also 85
obtained and their normal modes assigned. Our motivation was to study the amino acid L-threonine in an attempt to understand how electrostatic effects, hydrogen bonds, and dispersive interactions affect lattice motion.
2. Materials and Methods
2.1. Crystal Structures and DFT Computational Approach 90
Lattice parameters, angles, and atomic positions of L-threonine orthorhom-bic unit cell obtained by Janczak et al. [28] were fully taken into account to
Figure 1: (color online) The L-threonine orthorhombic crystal structure: (a) its molecular structure in the zwitterionic form; (b) the unit cell; (c) parallel layers connected by hydrogen bonds; (d) a perspective view.
prepare the input structure, and the CASTEP code (version 6.0) was used to perform the DFT calculations [29]. Two exchange-correlation functionals were
adopted for almost all steps of simulation: the local density approximation 95
(LDA) exchange-correlation functional developed by Ceperley-Alder-Perdew-Zunger [30, 31] (CAPZ), and the Perdew-Burke-Ernzerhof (PBE) [32] gener-alized gradient approximation (GGA). We have chosen these two exchange-correlation functionals over hybrid methods due to a two-fold arguments: i) it shows a good performance for non-covalently bound systems, and ii) it is robust 100
and mainly proposed as a quantum efficient and accurate chemical method for large systems where the forces of dispersion are of great importance. For in-stance, they were already used in a number of nanomaterial-ligand systems [33], as well as in the evaluation of a large number of data sets proposed by Li et al., presenting a best performance over some of the hybrid methods applied in their 105
work, including the largely used hybrid functional B3LYP [34]. Besides, taking into account the good comparison with experimental data, we see no reason to increase the computational cost without a comparable gain.
In order to improve the description of non-covalent interactions in GGA-PBE calculations, the Tkatchenko and Scheffler semi-empirical dispersion correction 110
scheme was applied (GGA+TS) [35]. To replace the core electrons in each atomic species, we adopted norm-conserving pseudopotentials [36] for both LDA and GGA+TS calculations. The valence electronic configurations considered were O - 2s22p4, N - 2s22p3, C - 2s22p2and H - 1s1. A plane-wave basis set was
adopted to represent the Kohn-Sham orbitals, with cutoff energy chosen, after 115
convergence studies, to be 830 eV, and Monkhorst-Pack [37] grid was fixed in 1 × 2 × 3 for the Brillouin zone to perform reciprocal space integrations.
By searching for a minimum total energy, the L-threonine structure was opti-mized through a plane-wave DFT calculation by using both LDA and GGA+TS functionals [38, 39, 40]. The optimization of the geometry was obtained con-120
sidering a tolerance of 0.5 × 10−6eV/atom for the self-consistency calculations. Besides, the following convergence thresholds along successive self-consistent steps were adopted: total energy change smaller than 5×10−6eV/atom, max-imum force per atom below 0.01 eV/˚A, pressure smaller than 0.02 GPa, and maximum atomic displacement below 0.5×10−3˚A. These parameters were also 125
applied to perform further calculations.
After obtaining the geometries optimization, we evaluated the Kohn-Sham electronic band structure and the density of states (total and partial per or-bital and per atom), as well as the dielectric function, the optical absorption, the refractive index, the optical conductivity and loss function for light polar-130
ized along the [001] crystal direction, following Refs. [41, 42]. The optical and electronic properties of the L-threonine crystal were individually obtained for both LDA (from LDA optimized structure) and GGA+TS (from GGA one) functionals, adopting a cutoff energy of 830 eV. On the other hand, infrared (IR) and Raman properties were calculated only by the GGA+TS functional, 135
adopting a cutoff of 1000 eV. Similarly, we adopt a cutoff energy of 1000 eV for thermodynamic calculations, as well as a k-point set of 2×2×3.
3. Results and Discussion 3.1. Unit Cell Optimization
The optimized lattice and volume parameters, as calculated with the func-140
tionals LDA and GGA+TS, are shown in Table I. For the sake of comparison, the experimental values of the parameters measured by Janczak et al. [28] are also included. In the LDA approximation, where the values found are generally smaller than the experimental ones, the lattice parameter a (b) (c) showed a decrease of 0.51 ˚A, (1.14 ˚A) (0.35 ˚A), which corresponds to 3.73%, (14.95%) 145
(6.75%) of the experimental result. The volume obtained was 405.17 ˚A3, less
23.62% than the experimental one. The differences in the lattice parameters are caused by an overestimation of the forces between the atoms, causing a decrease in the lengths of the connections and volume of the crystal. On the other hand, values of lattice parameters were obtained closer to the experimental one when 150
the functional GGA+TS was applied, although an increase of the volume esti-mate was found. The margin of error found for the lattice parameters a, b and c were 0.61%, 1.59%, and 0.18% respectively. The volume obtained was 536.76 ˚
A3, higher 1.18% than the experimental one. Unlike the LDA functional, the application of the GGA+TS for geometry optimization usually provides higher 155
values than the experimental data, since it underestimates the forces of inter-atomic connections, causing an increase in the length of the connections. These results show that the GGA functional corrected with the TS dispersion scheme was significantly better than the LDA functional.
Table 1: Unit cell lattice parameters (in ˚A) and volume V (in ˚A3) of the orthorhombic
L-threonine crystal obtained with the functionals LDA and GGA + TS levels for a 830 eV cutoff energy. Their deviations ∆ from the experimental values of Janczak et al. [28] are also shown.
approximation a(˚A) ∆a(˚A) b (˚A) ∆b(˚A) c(˚A) ∆c(˚A) V (˚A3) ∆V (˚A3) LDA 13.120 -0.508 6.479 -1.139 4.765 -0.345 405.174 -125.326 GGA+TS 13.545 -0.083 7.739 0.121 5.119 0.009 536.759 6.259 Experimental 13.628(2) — 7.618(1) — 5.110(1) — 530.5(1) —
In order to better describe the structure of the L-threonine crystal, we also 160
calculate the dielectric function, the optical absorption, the refractive index, the optical conductivity, and the polarized light loss function incident on a polycrystalline sample, using the same functionals as before, as described in the following text.
3.2. Electronic and Optical Properties 165
In order to understand better the electronic states at the valence and con-duction band of the L-threonine orthorhombic crystal structure, we determine in this section the Kohn-Sham electronic band structure as an image of the electronic self-energies E(k), k being a wave vector in the first Brillouin zone
(BZ). Points of high symmetry were selected in the reciprocal space form-170
ing a path within the Brillouin zone of the orthorhombic L-threonine crys-tal, namely: Γ(0, 0, 0), Y(-1/2,0,0), T(-1/2,0,1/2), Z(0,0,1/2), S(-1/2,1/2,0), X(0,1/2,0), U(0,1/2,1/2) and R(-1/2,1/2,1/2).
The CASTEP code was employed to achieve the band structure characteris-tics of the orthorhombic L-threonine crystal using the exchange and correlation 175
functionals GGA+TS and LDA, respectively. To do that, a plane wave basis set and atomic pseudopotentials were employed, as described in the previous section, allowing one to easily improve the quality of the calculations without concern with a typical basis set superposition errors found in other codes for dis-sociation energy estimations. Figure 2 (left) depicts the Kohn-Sham electronic 180
band structures, together with the respective partial density of states (PDOS) per orbital (right), of the orthorhombic L-threonine crystal near its main band gaps. Energy values were defined to ensure that the highest energy for a valence electron is equal to zero eV. At the top of Figs. 2a and 2b, we have plotted the GGA+TS and the LDA contributions, respectively, to the energy bands within 185
the range from -22.5 to 12.5 eV, and defining bands whose features are assigned to specific s and p atomic orbitals. For both contributions, the upper valence bands are dominated by the orbital p states, while the deepest one is mainly due to the s atomic orbitals. Furthermore, the bottom of the conduction band has a strong p-like in character, although the levels above have similar contributions 190
from the s and p atomic orbitals.
The bottom of Figs. 2a and 2b show a zoom of the region of the energy gap, separating the conduction band from the valence band. For the GGA+TS contribution, one can see a direct gap of 5.06 eV formed between the Γ point in the valence band and the Γ point in the conduction band, indicating a good 195
agreement with the experimental 4.96 eV result [43]. On the other hand, for the LDA functional, it was observed four indirect gaps ranging from 4.91 to 5.0 eV. The smallest indirect gap (4.91 eV) is between the X point of the valence band and the S point of the conduction band, 2.97% smaller than those found for the functional GGA+TS. These results indicate that the orthorhombic L-threonine 200
crystal resembles a wide gap semiconductor. It is worth noting that previous analysis of other amino acid crystals shown similar behavior. By studying the monoclinic crystal of glycine, it was obtained, through DFT calculations (ex-perimentally estimated), a band gap of 4.95 eV (5.11 eV) [44]. Likewise, the calculated monoclinic aspartic acid band gap was 4.54 eV (5.02 eV), while the 205
evaluation of the L-serine crystal shown a band gap of 4.75 eV (5.90 eV) [45, 46]. All of these structures also presented a wide gap semiconductor behavior, such as the L-threonine evaluated in this work. On the other hand, calculations of orthorhombic crystal of proline and cysteine, as well as the monoclinic crystal of cysteine have presented a band gap of 5.50 eV (experimental gap of 5.54 eV), 210
4.52 eV (experimental gap of 4.62 eV) and 4.06 eV, respectively, with cysteine shown a small gap insulators behavior [47, 48].
Notwithstanding their qualitative agreements, the GGA+TS and LDA ap-proaches predict band structures with some differences in the calculated energy band gaps of the L-threonine crystal, the most notable one being the predic-215
- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 0 2 0 3 0 - 1 . 0 - 0 . 5 0 . 0 4 . 6 4 . 8 5 . 0 5 . 2 1 0 2 0 3 0 s p ( a ) Y Γ X S Γ U R Γ Z T Γ 5 . 0 6 e V E n er g y ( eV ) E n er g y ( eV ) 5 . 0 6 e V Y Γ X S Γ U R Γ Z T Γ 5 . 0 6 e V D O S ( e l e c t r o n s / e V ) s p - 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 0 2 0 3 0 - 1 . 0 - 0 . 5 0 . 0 4 . 6 4 . 8 5 . 0 5 . 2 1 0 2 0 3 0 Y Γ X S Γ U R Γ Z T Γ Y Γ X S Γ U R Γ Z T Γ s p E n er g y ( eV ) E n er g y ( eV ) 5 . 0 0 e V 4 . 9 9 e V 4 . 9 5 e V 4 . 9 1 e V ( b ) D O S ( e l e c t r o n s / e V ) s p
Figure 2: (color online) Electronic band structures (left) and the respective partial density of states (PDOS) per orbital (right) of the orthorhombic L-threonine crystal along high symmetry directions in the Brillouin zones: (a) the GGA+TS, and (b) the LDA exchange-correlation functionals.
tion of a direct band gap of 5.06eV for the former, and four indirect band gaps ranging from 4.91 to 5.0 eV for the latter. It is then necessary a further in-vestigation, now considering its optical properties, helping us to obtain a clear concept about its electronic structure.
To do that, let us consider different photons energies to calculated some 220
optical properties of the anhydrous orthorhombic L-threonine crystal, starting with the complex frequency-dependent dielectric function, ε(ω) = ε1(ω)+iε2(ω),
for the incident light polarized along the direction [001]. The dielectric function, ε(ω), is a fundamental optical parameter that describes the absorption and polarization properties of the material, where ε1(ω) and ε2(ω) are respectively
225
for the GGA+TS functional (left panel) and the LDA approach (right panel). The imaginary part ε2(ω) of the dielectric function ε(ω) (shown as a solid red
line in Fig. 3) can be obtained from the momentum matrix elements between the occupied and unoccupied electronic states, which is given by [49]:
230 ε2(ω) = 2e2π V ε0 X k,v,c |hψc k|u · r|ψ v ki| 2δ(Ec k− E v k− ¯hω) , (1)
where u is the vector that provides the polarization of the electric field of the incident electromagnetic radiation, V is the volume of the unit cell, e is the electronic charge, and ψv
k (ψ c
k) represents the wave function of the valence
(con-duction) band at the wavevector k. On the other hand, the real part ε1(ω) of
the dielectric function ε(ω) (shown as a solid black line in Fig. 3) is calculated 235
from the imaginary part of ε2(ω) according to Kramers-Kronig relations [50]:
ε1(ω) = 1 + 2 πP Z ∞ 0 ω0ε2(ω 0 )dω0 (ω02− ω2) , (2)
where P represents the principle value of the integral.
The dielectric constant ε1(0) was found to be 2.33 for GGA+TS functional
and 2.87 for the LDA one. For energies above 20eV, ε2(ω) → 0, while ε1(ω → ∞)
is 0.84 for GGA+TS and 0.78 for LDA. 240
Through ε1(ω) and ε2(ω) it is possible obtain all other optical properties,
including the refractive index n(ω), optical conductivity σ(ω), absorption coef-ficient α(ω), reflectivity R(ω) and loss function L(ω) by the following equations [41, 42]: n(ω) = √1 2[ q ε2 1(ω) + ε22(ω) + ε1(ω)] 1 2 (3) σ(ω) = ωε2 4π (4) α(ω) =√2ω[ q ε2 1(ω) + ε22(ω) − ε1(ω)] 1 2 (5) R(ω) = pε(ω) − 1 pε(ω) + 1 2 (6) L(ω) = ε2(ω) ε2 1(ω) + ε22(ω) (7)
0 5 1 0 1 5 2 0 2 5 - 6 - 4 - 2 0 2 4 6 8 1 0 1 2 0 5 1 0 1 5 2 0 2 5 - 6 - 4 - 2 0 2 4 6 8 1 0 1 2 D ie le ct ri c F u n ct io n E n e r g y ( e V ) R e I m ( a ) G G A + T S D ie le ct ri c F u n ct io n E n e r g y ( e V ) R e I m L D A 0 5 1 0 1 5 2 0 2 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 0 5 1 0 1 5 2 0 2 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 R ef ra ct iv e In d ex E n e r g y ( e V ) R e ( n ) I m ( n ) ( b ) G G A + T S R ef ra ct iv e In d ex E n e r g y ( e V ) R e ( n ) I m ( n ) L D A 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 - 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 0 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 - 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 0 4 . 8 5 . 0 5 . 2 - 0 . 1 0 - 0 . 0 5 0 . 0 0 0 . 0 5 C o n d u c ti v it y E n e r g y ( e V ) R e 4 . 9 1 e V C o n d u ct iv it y E n e r g y ( e V ) R e I m L D A ( c ) 4 .9 1 e V 4 . 8 5 . 0 5 . 2 5 . 4 - 0 . 1 0 - 0 . 0 5 0 . 0 0 0 . 0 5 C o n d u c ti v it y E n e r g y ( e V ) R e 5 . 0 6 e V C o n d u ct iv it y E n e r g y ( e V ) R e I m G G A + T S 5 .0 6 e V
Figure 3: (color online) Real (solid black line) and imaginary (solid red line) components of the calculated a) dielectric function; b) refractive index; c) optical conductivity of the orthorhombic L-threonine crystal along the direction [001]. (inset) Close-up of the optical conductivity near to the main band gaps of the structures. Left panel: GGA + TS functional; Right panel: LDA functional.
The refractive index n is a dimensionless complex number that describes 245
in Fig. 3b along the direction [001] of the L-threonine crystal. The refractive index n(0) is 1.52 (GGA+TS) and 1.69 (LDA).
The optical conductivity is an optoelectronic phenomenon in which the elec-trical conductivity of a given material increases through the absorption of the 250
electromagnetic radiation. The real part of the optical conductivity begins with the photon energy ∼ 5.06 (∼ 4.91) eV, corresponding to the direct (indirect) energy gap found above for the GGA+TS (LDA) functional, as depicted in Fig. 3c (inset). The electrical conductivity due to the energy absorption of the pho-tons decreases in the energy range between 20 and 30 eV, being zero when the 255
photon energy is greater than 30eV.
The absorption coefficient provides important information about the solar energy conversion and indicates in which region of the electromagnetic spectrum the material absorbs energy. Fig. 4a depicts the optical absorption spectrum of the L-threonine along the polarization direction [001] for the GGA+TS (solid 260
black line) and LDA (solid red line) approaches. Therefore, in results obtained for both functionals, L-threonine crystal absorbs photon energy in the range 5 to 25 eV (see the inset of Figure 4a), i.e. in the ultraviolet region, and is therefore transparent. Kumar et al. [51] (Rodrigues et al. [8]), has obtained a transparency of approximately 85% in the range of 250 to 900 (250 to 1500) 265
nm, which corresponds to the energy range of 4.9 to 17.64 (4.9 to 29.40) eV, in a fairly good agreement with our theoretical prediction. This is an important characteristic of the L-threonine crystal, because crystals that do not show op-tical absorption in the visible region are suitable materials for second harmonic generation [7]. It is remarkable that by comparing the absorption energy range 270
in this work to previous studies for aspartic acid, serine, and proline crystals, it is possible to observe a similar behavior, where these amino acids begin to absorb photonic energy from ∼5 eV to ∼20 eV [45, 46, 47].
The reflectivity spectra as a function of photon energy are shown in Fig. 4b. It starts with a value of ∼ 0.04 (0.06) for the GGA + TS (LDA) functional. 275
From there, it increases up to a maximum intensity of ∼ 0.74 (0.49) in the energy range of 5.3 − 6.3 eV. It presents another peak of ∼ 0.48 (0.64) in the range of 17.5 − 18.2 (18.8 − 19.6) eV, indicating that the L-threonine crystal is a good candidate to coating material in these energy ranges. It goes to zero at E=30 eV.
280
The energy loss function as a function of photon energy is shown in Fig. 4c. This function is related to the energy loss of an electron crossing a material [52]. It is related to the plasma frequency ωp, occurring when ε2 > 1 and
ε1 approaches to zero. The energy loss function plotted within the GGA+TS
(LDA) calculation considers the effective plasma frequency ωp as 17.94 (19.69)
285
eV. From this figure, we can conclude that the material becomes transparent (the loss function tends to zero) when the incident photon frequency is greater than ωp at both functionals.
We used the GGA + TS functional to evaluate these properties, due to the overall better agreement with the experimental lattice parameters, as follows. 290
0 5 1 0 1 5 2 0 2 5 3 0 3 5 0 . 0 5 . 0 x 1 04 1 . 0 x 1 05 1 . 5 x 1 05 2 . 0 x 1 05 2 . 5 x 1 05 3 . 0 x 1 05 L D A 4 . 7 4 . 8 4 . 9 5 . 0 5 . 1 5 . 2 5 . 3 0 1 x 1 03 2 x 1 03 3 x 1 03 A b so rp ti o n ( c m -1) E n e r g y ( e V ) 4 .9 1 eV 5 .0 6 eV A b so rp ti o n ( cm -1) E n e r g y ( e V ) G G A + T S ( a ) 0 5 1 0 1 5 2 0 2 5 3 0 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 L D A ( b ) G G A + T S R ef le ct iv it y E n e r g y ( e V ) 0 5 1 0 1 5 2 0 2 5 3 0 0 2 4 6 8 1 0 G G A + T S L o ss F u n ct io n E n e r g y ( e V ) L D A ( c )
Figure 4: (color online) The GGA+TS (solid black line) and LDA (solid red line) calculated a) absorption function; b) reflectivity; c) loss function of the orthorhombic L-threonine crystal. (inset) Close-up of the optical absorptions near to the main band gaps of the structures.
3.3. Infrared and Raman Spectrum
Infrared and Raman spectroscopies are very useful tools to investigate the vibrational, rotational, and other low-frequency modes in molecules, thin films, biological materials, solids, etc., being also complementary techniques used for fingerprinting of molecules and solids [53]. Both come from changes in their 295
vibration modes. In particular, the infrared (IR) spectroscopy provides infor-mation on the percentage of the radiation transmission as a function of its wave-length, considering only those vibration modes which result in changes in the dipole moment. The peaks in an infrared spectroscopy plot, called absorption bands, are associated with the energy absorption for a particular wavelength. 300
On the other hand, Raman spectra result from the inelastic scattering of light by vibrating molecules due to changes in their polarizability and are commonly used in physics and chemistry to provide a structural fingerprint by which molecules can be identified.
The diversity of hydrogen bonds observed in molecular crystals gives rise 305
to vibrational signatures, which can be related to the particular way in which intermolecular interactions occur in the lattice. However, the coupling of inter-molecular excitons to intrainter-molecular vibrations and the oscillator strength for emission processes in crystals can be very different from those of an isolated molecule [54]. Hydrated crystals, on the other hand, are more likely to display 310
hydrogen bonding patterns and electronic structure changes related to their presence in comparison with the isolated molecules. On the other hand, an-hydrous crystals, as the orthorhombic L-threonine crystal considered here, can modify the vibrational spectra by altering the effective strength of the covalent bonds, increasing its stretching elastic constant and shifting the corresponding 315
normal-mode frequency to higher values.
Table II depicts the normal modes together with their respective irreducible representations, as well as the assignment of IR and Raman active modes, for the orthorhombic L-threonine anhydrous crystal. There are 204 normal modes of vibration at the wave vector k = 0, three of them being acoustic (inac-320
tive) modes (the modes 1, 2, and 3 shown in Table II). The remaining 150 (201) are IR (Raman) active modes, according to the irreducible representation ΓIR=50B1+50B2+50B3(ΓRaman=51A+50B1+50B2+50B3).
The infrared and Raman spectroscopy plots obtained for the orthorhombic L-threonine crystal is shown in Fig. 5, considering the wavelength range λ = 0 325
to 4000 cm−1. In what follows, the assignments of the IR and Raman active
modes of vibration are described according to: τ torsion, ρ balance, δ -deformation, w - wagging, and ν - stretching.
In the range 0 to 400 cm−1, it is possible to observe the formation of ab-sorption bands in the infrared spectrum. In this interval, apparently, there are 330
no explicit Raman modes. However, the existence of active modes in this re-gion can be found with the help of Table II. From there, we can identify the formation of IR absorption bands and active Raman modes, with a common peak corresponding to the wavelength 68 cm−1 related to the molecular skeletal balance (ρskel) (see the inset of Figure 5). In the IR spectrum, ρskel is respon-335
Table 2: Normal modes of orthorhombic L-threonine crystal at k = 0. Irreducible representa-tions (Irrep) are indicated, as well as the active IR and Raman modes.
N λ(cm−1 ) Irrep IR Raman N λ(cm−1 ) Irrep IR Raman N λ(cm−1 ) Irrep IR Raman N λ(cm−1 ) Irrep IR Raman
1 -0.06 B3 N N 52 399.03 B3 Y Y 103 1084.67 B1 Y Y 154 1478.75 B3 Y Y 2 -0.05 B1 N N 53 417.51 B2 Y Y 104 1086.54 A N Y 155 1483.89 A N Y 3 -0.03 B2 N N 54 423.29 B1 Y Y 105 1089.24 A N Y 156 1492.46 B2 Y Y 4 42.55 A N Y 55 449.54 B3 Y Y 106 1093.03 B1 Y Y 157 1529.06 A N Y 5 55.23 B3 Y Y 56 451.04 A N Y 107 1095.26 B3 Y Y 158 1529.76 B2 Y Y 6 56.57 A N Y 57 474.21 B2 Y Y 108 1098.81 A N Y 159 1590.60 B3 Y Y 7 68.02 B3 Y Y 58 474.45 B1 Y Y 109 1100.06 B1 Y Y 160 1591.61 B1 Y Y 8 69.06 B1 Y Y 59 476.16 A N Y 110 1101.56 B2 Y Y 161 1601.82 B3 Y Y 9 75.87 B2 Y Y 60 477.26 B3 Y Y 111 1104.01 B3 Y Y 162 1601.93 B1 Y Y 10 77.66 A N Y 61 497.90 B1 Y Y 112 1110.12 B2 Y Y 163 1613.61 A N Y 11 87.69 B2 Y Y 62 499.70 B3 Y Y 113 1179.30 B3 Y Y 164 1614.80 B2 Y Y 12 91.37 B1 Y Y 63 501.93 A N Y 114 1182.58 B2 Y Y 165 1638.80 B1 Y Y 13 91.45 B3 Y Y 64 506.33 B2 Y Y 115 1190.97 B1 Y Y 166 1642.67 B3 Y Y 14 98.26 A N Y 65 546.87 B1 Y Y 116 1191.19 A N Y 167 1644.24 A N Y 15 104.59 B2 Y Y 66 549.25 B3 Y Y 117 1225.86 B1 Y Y 168 1652.22 B2 Y Y 16 105.49 B1 Y Y 67 552.68 B2 Y Y 118 1230.06 A N Y 169 2860.91 A N Y 17 107.03 B2 Y Y 68 559.81 A N Y 119 1235.28 B3 Y Y 170 2861.14 B2 Y Y 18 107.93 A N Y 69 679.43 B3 Y Y 120 1236.46 B2 Y Y 171 2884.71 B1 Y Y 19 110.52 B3 Y Y 70 683.45 A N Y 121 1287.34 A N Y 172 2887.32 B3 Y Y 20 116.64 B1 Y Y 71 684.99 B2 Y Y 122 1292.82 B1 Y Y 173 2896.20 A N Y 21 131.76 B3 Y Y 72 689.68 B1 Y Y 123 1295.86 B3 Y Y 174 2896.58 B1 Y Y 22 131.79 A N Y 73 726.31 B2 Y Y 124 1303.84 B2 Y Y 175 2896.71 B3 Y Y 23 132.76 B2 Y Y 74 729.87 A N Y 125 1314.30 A N Y 176 2897.54 B2 Y Y 24 136.63 A N Y 75 733.40 B3 Y Y 126 1318.99 B2 Y Y 177 2964.15 B2 Y Y 25 161.85 B1 Y Y 76 737.00 B1 Y Y 127 1320.48 B1 Y Y 178 2964.27 B3 Y Y 26 170.98 B3 Y Y 77 834.71 B3 Y Y 128 1320.89 B3 Y Y 179 2966.16 A N Y 27 181.92 B1 Y Y 78 839.47 B1 Y Y 129 1325.25 B2 Y Y 180 2966.31 B1 Y Y 28 183.19 B2 Y Y 79 844.67 B2 Y Y 130 1327.82 A N Y 181 2971.60 A N Y 29 192.13 B3 Y Y 80 845.93 A N Y 131 1328.71 B3 Y Y 182 2974.55 B2 Y Y 30 198.73 B1 Y Y 81 858.24 B3 Y Y 132 1333.17 B1 Y Y 183 2982.83 B3 Y Y 31 201.47 A N Y 82 866.16 B2 Y Y 133 1363.01 B1 Y Y 184 2991.94 B1 Y Y 32 214.27 B2 Y Y 83 868.61 B1 Y Y 134 1363.21 A N Y 185 3012.23 A N Y 33 214.73 B1 Y Y 84 868.63 A N Y 135 1366.26 B2 Y Y 186 3020.43 B3 Y Y 34 215.83 A N Y 85 886.54 A N Y 136 1372.37 B3 Y Y 187 3035.92 B2 Y Y 35 225.32 B2 Y Y 86 890.05 B2 Y Y 137 1372.51 A N Y 188 3040.51 B2 Y Y 36 226.81 B3 Y Y 87 898.70 B1 Y Y 138 1374.01 B2 Y Y 189 3040.65 B3 Y Y 37 247.93 A N Y 88 902.78 B3 Y Y 139 1379.31 B1 Y Y 190 3040.83 B1 Y Y 38 252.13 B1 Y Y 89 911.09 A N Y 140 1381.76 B3 Y Y 191 3041.20 A N Y 39 252.98 B2 Y Y 90 911.51 B1 Y Y 141 1389.59 B3 Y Y 192 3048.61 B1 Y Y 40 255.90 B3 Y Y 91 918.12 B2 Y Y 142 1397.67 B2 Y Y 193 3060.35 A N Y 41 313.52 B2 Y Y 92 919.15 B3 Y Y 143 1408.38 A N Y 194 3061.24 B2 Y Y 42 314.04 A N Y 93 1015.29 A N Y 144 1410.42 B1 Y Y 195 3061.36 B3 Y Y 43 314.57 B1 Y Y 94 1020.43 B1 Y Y 145 1441.02 A N Y 196 3061.71 B1 Y Y 44 315.15 B3 Y Y 95 1021.72 B3 Y Y 146 1442.41 B1 Y Y 197 3066.77 B1 Y Y 45 334.89 A N Y 96 1023.00 A N Y 147 1445.55 B2 Y Y 198 3066.83 A N Y 46 338.83 B3 Y Y 97 1024.13 B2 Y Y 148 1445.90 B3 Y Y 199 3067.47 B3 Y Y 47 352.61 B1 Y Y 98 1024.94 B1 Y Y 149 1451.45 B3 Y Y 200 3069.98 B2 Y Y 48 354.50 B2 Y Y 99 1031.33 B2 Y Y 150 1458.86 B1 Y Y 201 3166.58 B3 Y Y 49 373.95 B2 Y Y 100 1031.62 B3 Y Y 151 1460.23 A N Y 202 3175.49 A N Y 50 376.27 A N Y 101 1079.78 B3 Y Y 152 1460.61 B2 Y Y 203 3176.39 B1 Y Y 51 386.20 B1 Y Y 102 1081.18 B2 Y Y 153 1467.39 B1 Y Y 204 3182.18 B2 Y Y
hand, in the wavelength range from 181 to 198 cm−1, there are IR absorption bands attributed to the torsion of the COO− (τ COO−) and CC (τ CC) groups, respectively. The molecular skeleton balance (ρskel), the torsion CH3 (τ CH3)),
deformation CNH3 (δCNH3), and CCH3 (δCCH3), and the vibration mode of
340
molecular skeletal deformation (δskel) are responsible for the absorption bands at λ = 214, 255, 252, 315, 338, 354 and 399 cm−1. Regarding the active Raman modes, there are peaks at λ = 110 and 170 cm−1, respectively, due to the ρskel and the torsion of the carboxyl group (τ COO−). Besides, vibration modes due to ρskel, δCCH3 and δskel are assigned to the respective wavelengths at 215,
345
334 and 376 cm−1.
In the region corresponding to the wavelength λ between 400 and 1000 cm−1, there are IR absorption bands due to the δskel, δCOH, δCCH3and τ NH3
vibra-tions for the frequencies 423, 449, 474 and 497 cm−1, respectively. The torsion of the NH3 group was found for the wavelength corresponding to 489.9 cm−1
350
0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 2 0 0 4 0 0 6 0 0 8 0 0 In te n si ty ( a. u .) I R 3 1 6 6 3 0 6 6 3 0 2 0 2 9 9 2 2 8 6 1 1 5 9 1 1 4 6 7 1 0 9 5 1 2 9 5 W a v e n u m b e r ( c m - 1) R a m a n 3 1 8 2 3 0 6 6 3 0 1 2 2 9 6 6 2 8 9 6 1 3 1 4 1 1 1 0 1 4 4 1 I n te n si ty ( a .u .) W a v e n u m b e r ( c m - 1 ) 9 1 1 8 4 5 7 2 9 6 8 3 5 5 9 4 7 6 4 5 1 3 3 4 2 1 5 1 7 0 1 1 0 6 8 3 7 6 I n te n si ty ( a .u .) W a v e n u m b e r ( c m- 1 ) 6 8 10 5 1 6 1 2 1 4 2 2 5 31 5 3 3 8 3 9 9 44 9 4 7 4 5 5 2 6 7 9 7 3 3 8 3 9 8 6 8 9 1 9
Figure 5: Infrared and Raman spectra of orthorhombic L-threonine crystal in the 0 to 4000
cm−1range. The numbers correspond to the most important normal modes. The insets show
the infrared and Raman spectra in the low-frequency range 0-1000 cm−1.
active Raman modes correspond to the vibration modes δCOH, δCOH, δCCH3
and δCNH3 for λ = 417, 451, 476, and 559 cm−1. The IR (Raman) peak at
λ = 679 (683) cm−1is associated with the CH-oscillation vibration mode (ρCH), while the IR (Raman) peak at λ = 733 (729) cm−1 is attributed to the wagging 355
mode w of CO−2 (wCO−2). The active IR modes for wavelengths 839, 868, and 898 (919) cm−1 correspond to the vibration modes wOH (the antisymmetric balance CH3 - ρaCH3). In the Raman spectrum, the active modes at 845 and
911 cm−1 are assigned to wOH and ρaCH3, respectively.
From λ = 1000 to 1400 cm−1, the Raman peaks at the wavelengths 1110, 360
1021, 1031, 1182 and 1191 cm−1 are assigned to the modes ρNH3, CN strain
(νCN), CH strain (δCH) and CH balance (ρCH), respectively. Besides, modes associated with ρCH appear also in the Raman spectrum, at λ = 1230, 1314 and 1372 cm−1. In the IR spectrum, the wavelengths and their respective modes of vibration are: 1225 cm−1 due to ρCH; 1295 cm−1 related to δCH; 1320 cm−1
365
assigned to δCH; 1333 cm−1by ρCH; 1363 cm−1corresponding to the symmetric
balance vibration mode CH3 (δsCH3); and 1389 cm−1 related to ρOH.
From λ = 1400 to 2000 cm−1 there are identified absorption bands in the infrared absorption spectrum and more discrete Raman activities. This region is usually formed due to the double bonds. Between 1400 and 1600 cm−1we have, 370
for the IR absorption spectra: the vibration mode of symmetric deformation CH3 (δsCH3) which is responsible for the peak at 1458 cm−1; the 1467 cm−1
wavelength peak, associated to the antisymmetric deformation vibration mode of the CH3 group (δaCH3); the wavelength 1591 cm−1, associated with the
antisymmetric deformation vibration of the group N H3 (δaNH3). On other
375
hand, in the Raman spectrum, more intense modes occur for wavelengths λ = 1408 (ρOH) and 1441 (δaCH3).
The wavelength range from 2000 to 2500 cm−1 is attributed to triple bonds [57] absent in the L-threonine crystal, explaining the absence of peaks in this region.
380
Finally, the formation of peaks in the wavelength range between 2500 and 4000 cm−1of the IR spectrum are usually attributed to the functional groups of the material, where the stretching ν-vibration modes of hydrogen bonds occur. The peaks corresponding to λ = 2861, 2887, 2982, 2992 and 3166 cm−1, related to the absorption of the IR spectroscopy, are associated with the antisymmetric 385
stretching of the N H3(νaNH3) group, with a contribution due to the stretching
of the OH (νOH) group to form the peak corresponding to the wavelength 2982 cm−1. In the Raman side, the 2860 cm−1 peak is attributed to the νaNH3
group, and the peak at 2896 cm−1 is related to the OH stretch. Also, the peak at λ = 2966 cm−1 is associated to the symmetrical stretching of the CH3
390
group. The peak 3020 cm−1is attributed to the νOH and to the νaNH3groups,
while the peak at 3035 cm−1 (3066 cm−1) is formed by the νOH (νCH) group. Besides, peaks appear due to the OH and CH stretches at wavelengths 3012 and 3066 cm−1, respectively, and by the antisymmetric NH
3 stretch at 3182 cm−1.
3.4. Thermodynamic Properties 395
The thermodynamic properties are closely related to the vibrational prop-erties of a material, providing a guidance for insights about their atomic lattice behavior, as well as essential information for modeling technological processes [58, 59]. It is well known that by increasing the temperature of a material, there is an expansion in its volume, which usually softens the lattice vibrations and 400
enhances (reduces) its entropy (lattice energy) [59, 60, 61]. Besides, this effect is most significant in weakly bound crystals, such as organic crystals.
In this sense, to obtain a better understand about the thermal effect over the anhydrous orthorhombic L-threonine crystal, some thermodynamic properties were obtained by means of phonon calculations within the quasi-harmonic ap-405
proximation framework. They include the enthalpy (E), entropy (S), free energy (F), lattice heat capacity (CV) and the Debye temperature (ΘD), in the range
of 7 to 2000 K, using a norm-conserving pseudopotential for the GGA-PBE+D functional and the Baroni relation [62]. They are depicted in Fig. 6.
Fig. 6(a) shows the profiles of the calculated thermodynamic potentials’ 410
enthalpy, free energy and the temperature (T) times the entropy (T*Entropy) term, TS = U - F (U being the internal energy), as a function of the temperature (in K), for the anhydrous orthorhombic L-threonine crystal. From there one can see that at a temperature below 100 K, the enthalpy, free energy, and the T*Entropy values are almost zero. After that (T> 100 K), T*Entropy and the 415
enthalpy values increase as a function of T, with the latter showing a most linear behavior. On the other hand, the free energy decreases as the T increases.
In Fig. 6(b) we depict the constant lattice heat capacity (CV), as a function
0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0 4 0 5 0 E n e rg y ( e V ) T e m p e r a t u r e ( K ) E n t h a l p y F r e e E n e r g y T * E n t r o p y ( a ) 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 H e a t C a p a c it y ( C a l/ c e ll .K ) T e m p e r a t u r e ( K ) H e a t C a p a c i t y ( b ) 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 D e b y e t e m p e ra tu re ( K ) T e m p e r a t u r e ( K ) D e b y e t e m p e r a t u r e ( c )
Figure 6: Anhydrous orthorhombic L-threonine crystal (a) enthalpy (black solid line), free
energy (red solid line) and T*Entropy (blue solid line), (b) lattice heat capacity (CV), and
(c) Debye temperature (ΘD), as a function of the temperature.
the temperature increases, reaching the Dulong-Petit limit at around 380 K. 420
According with the Dulong-Petit law, the atoms of a solid crystal vibrate in three-dimensional space with an energy of kBT, at room temperature (300 K)
[61]. In this work, the calculated CV at room temperature was 143.06 cal/cell·K.
Finally, the variation of the Debye temperature as a function of T until 2000 K is depicted in Fig. 6(c). One can observe that ΘD shows a higher variation
425
at temperatures until 1000 K, becoming smaller for temperatures higher than that.
The above analysis shows that L-threonine crystal exhibits some instabil-ity in thermodynamic properties. These results can be either compared with the experimental data, or used to predict the phase stability for its different 430
structural modifications.
4. Conclusions
As a new contribution to obtain a complete picture of the properties of amino acids in the solid state, the anhydrous orthorhombic L-threonine crystal was investigated in this work by means of the calculated structural, electronic and 435
optical properties using both the DFT-GGA+TS and DFT-LDA approaches, taking advantage of its X-ray diffraction pattern as measured by Janczak et al. [28].
The lattice parameters a, b, c obtained from LDA calculations are 3.73, 14.95 and 6.75 % smaller than the experimental result (see Table I) due to 440
overestimation of the forces between atoms in the LDA approach. On the other hand, for GGA+TS calculations, where we have underestimate the forces of interatomic connections, we have obtained lattice parameters showing a good agreement among the lattices parameters a, b and c (-0.61, 1.59 and 0.18 %) when compared to the experimental results.
445
The band structure reveals that the L-threonine crystal have a direct (in-direct) band gap semiconductor for GGA+TS (LDA), with top valence band at the point Γ (X) and bottom of conduction band at point Γ (S). The band gap value is 5.06 eV (4.91 eV) according to the GGA+TS (LDA) calculations. Therefore, the result for GGA+TS and LDA approaches are in good agreement 450
with the 4.96 eV experimental estimation of the band gap for L-threonine crystal [43]. Regarding the DOS spectra obtained in both approaches, we can observe that the upper valence bands are dominated by the p states, while the deepest valence bands are mainly originated from the s atomic orbitals.
The calculated complex electronic dielectric constant along the direction 455
[001] of the L-threonine crystal yielded a refractive index n(0) equal to 1.52 (GGA+TS) and 1.69 (LDA). For both functionals, L-threonine crystal absorbs photon energy in the range of 5 to 25 eV, i.e., in the ultraviolet region, an important result since crystals that do not show optical absorption in the visible region are suitable materials for second harmonic generation [7].
460
The infrared spectrum of L-threonine crystal has its most intense absorption peaks near 1467 (3020) cm−1 of its lower (higher) frequency range. On the other hand, active Raman modes are more intense near 1314 (3012) cm−1 of its lower (higher) frequency interval. Finally, the thermodynamic properties of these crystal systems are presented by its enthalpy, entropy, free energy, heat 465
capacity and Debye temperature.
We hope this work will stimulate further experimental efforts to unveil the rich role of the structural, optoelectronic, vibrational and thermodynamic prop-erties of biomolecules systems in the solid state.
Declaration of Competing Interest 470
The authors have not conflict of interest to declare.
Acknowledgement
This work was partially financed by the Brazilian Research Agencies CAPES (PNPD) and CNPq.
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Title: DFT Calculations of the Structural, Electronic, Optical, Vibrational and Thermodynamic Properties of
Anhydrous Orthorhombic L-Threonine Crystals
Authors: Roniel L. Araújo, Manoel S. Vasconcelos, Carlos A. Barboza, José X. Lima Neto, Eudenilson L.
Albuquerque and Umberto L. Fulco
Highlights:
Characterization of the orthorhombic L-Threonine Crystals.
A quantum chemistry approach within the density functional theory computations by using the
local-density approximation (LDA) and the generalized gradient approximation with scatter correction (GGA+TS).
Analysis of the electronic, structural, thermodynamical, optical, and vibrational spectra of the
orthorhombic L-Threonine crystals.
