Experiment and Density Functional Theory - ACS Publications

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Structural, Electronic, and Optical Properties of Bulk Boric Acid 2A and 3T Polymorphs: Experiment and Density Functional Theory Calculations M. Bezerra da Silva,† R. C. R. dos Santos,‡ A. M. da Cunha,‡ A. Valentini,‡ O. D. L. Pessoa,§ E. W. S. Caetano,*,∥ and V. N. Freire†,‡ †

Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60440-900 Fortaleza-CE, Brazil Departamento de Química Analítica e Físico-Química, Universidade Federal do Ceará, 60440-554 Fortaleza-CE, Brazil § Departamento de Química Orgânica e Inorgânica, Universidade Federal do Ceará, 60021-970, Fortaleza-CE, Brazil ∥ Instituto Federal de Educaçaõ , Ciência e Tecnologia do Ceará, DEMEL, Campus Fortaleza, 60040-531 Fortaleza-CE, Brazil ‡

S Supporting Information *

ABSTRACT: Boric acid (H3BO3) is being used effectively nowadays in traps/baits for the management of Aedes aegypti L. and Aedes albopictus Skuse species of mosquitos, which are the main spreading vectors for diseases like malaria, dengue, and zika worldwide. Due to its renewed importance, we have studied in this work the structural, electronic, and optical properties of its molecular triclinic H3BO3-2A and trigonal H3BO3-3T polymorphs within the framework of density functional theory (DFT) at the local density and generalized gradient levels of calculations, LDA and GGA, respectively, improving and extending previously published theoretical results on triclinic boric acid structural properties. In addition, the optical absorption of the 2A polymorph was measured in this work for the sake of comparison with our DFT estimate. In comparison to published X-ray diffraction data, unit cell deviations as small as Δa ∼ −0.13 Å (−0.12 Å), Δb ∼ −0.13 Å (−0.12 Å), Δc ∼ 0.18 Å (−0.31 Å), and interplanar distance deviation Δd ∼ −0.11 Å (−0.10 Å) for H3BO32A (H3BO3-3T) were obtained using a Tkatchenko and Scheffler dispersion corrected GGA functional. The properties of the polymorphs are shown to be ruled by an interplay between in-plane hydrogen bonds and interplanar van der Waals interactions. However, the molecular stacking pattern, AB for H3BO3-2A and ABC for H3BO3-3T, does not lead to significantly distinct electronic and optical properties. Both polymorphs are suggested to be insulators with indirect bang gaps of about 6.26 ± 0.01 eV, which is in close agreement with the 5.98 eV indirect band gap we have measured for triclinic boric acid by optical absorption. Notably the usual DFT gap underestimation is not observed due to the extra shrinking of the unit cell caused by the inclusion of van der Waals forces in the geometry optimization. The complex dielectric function and optical absorption of both boric acid polymorphs were characterized as well. Skuse,3,4 insect vectors responsible for the spreading of malaria, dengue, and zika.5−7 Knowledge of boric acid solid state chemistry, however, is very limited.8,9 The first information about an approximate boric acid crystal structure was published by Zachariasen in 1934,10 being one of the first molecular crystals to be examined using X-ray diffraction. Cowley11 found in 1953 a disordered layer stacking with a hydrogen-bonding scheme very different from the original one suggested by Zachariasen10 who, in 1954,12 determined a triclinic boric acid crystal structure with four molecules in the unit cell and P1̅ space group. The triclinic

1. INTRODUCTION Boric acid, chemical formula H3BO3 or B(OH)3, also named orthoboric acid, boracic acid, hydrogen borate, and acidum boricum, has been used since classic Greece for cleaning and preserving food. Nowadays many other applications can be listed for this compound,1,2 such as in the manufacture of fiberglass and glass for LCD flat panel displays, in the jewelry industry, as an additive in nuclear reactor coolants, as a buffer against rising pH in swimming pools, and as a lubricant and flame retardant.1,2 It also works as an antiseptic, acaricide, herbicide, and fungicide, and since 1948 it has been registered in the US as a stomach poison affecting insect metabolism.1,2 Low concentrations (∼1%) of boric acid have been used recently as an effective control agent for the eggs and immature/adult stages of Aedes aegypti L. and Aedes albopictus © XXXX American Chemical Society

Received: August 31, 2016 Revised: September 30, 2016

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DOI: 10.1021/acs.cgd.6b01297 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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boric acid crystal picture was improved by Craven and Sabine13 in 1966 and Gajhede et al.14 in 1986, while Dorset15 in 1992 was able to perform a structural analysis of triclinic boric acid, estimating more accurately hydrogen atom positions and finding stacking planes in the repeating sequence AB···. Later, in 2003, a trigonal polytype of boric acid was discovered by Shuvalov and Burns,16 with three sheets stacked in the repeating sequence ABC···. Accordingly, the boric acid triclinic and trigonal structures were labeled H3BO3-2A and H3BO3-3T, respectively, in agreement with the recommendations of the international Union of Crystallography. For the sake of completeness, it is worth mentioning that a recently nonconventional hexagonal structure for boric acid was also proposed by Harabor et al.17 in 2014, but it will not be studied here. In the theoretical domain there is only a single work, by Zapol et al.,18 where periodic ab initio calculations for triclinic boric acid were performed (this is the single published work on DFT-calculated structural properties of the triclinic H3BO32A), mainly focusing on its structural and electron density properties using the Becke exchange19 and Lee, Yang, and Parr gradient-corrected correlation functional (BLYP),20 and a standard 6-31G* basis set.21 The unit cell structure was not fully optimized since the fractional coordinates of the atoms were kept fixed, varying only the lattice constants, which were adjusted to a = 6.976 Å, b = 6.976 Å, and c = 6.150 in order to reach a total energy minimum. The deviations in comparison to the experimental data of Gajhede et al.14 were Δa = −0.043 Å, Δb = −0.059 Å, Δc = −0.197 Å. Moreover, the atomic charges were shown to increase upon interlayer bond formation revealing that the crystalline environment significantly affects the molecular electron density distribution.18 The boric acid crystal polymorphs H3BO3-2A and H3BO3-3T have their structures due to intra- and interplane attractive noncovalent interactions (hydrogen bonding and van der Waals dispersion interactions) between B(OH)3 units. Improvements in computational performance during the last two decades have made DFT-based electronic structure modeling of molecular crystals feasible,22 our research group having several contributions to the field.23−32 Nevertheless, within the framework of the density functional theory,33,34 which now can incorporate van der Waals dispersion forces,35 it remains a challenge to find the best description for dispersive interactions.36 Here, we present the results of our DFT computations of the structural, electronic, and optical properties of the H3BO3-2A and H 3 BO 3 -3T crystal polymorphs performing a full optimization of their unit cells (lattice parameters and internal atomic coordinates). Our DFT-converged structure for the 2A polymorph is shown to be as good (for the a, b lengths) or better (c length) than thosenot fully optimizedby Zapol et al.18 In addition, we show that the stackings AB··· for H3BO32A and ABC··· for H3BO3-3T cause subtle differences in their physical properties. We also disclose the results of an optical absorption measurement for H3BO3-2A samples estimating an 5.98 eV energy gap. This result can be contrasted with the 6.25 eV indirect gap found after our DFT computations (unfortunately we were unable to perform optical absorption measurements for the 3T polymorph due to lack of samples), indicating the insulating character of both H3BO3-2A and H3BO3-3T crystals. From the theoretical point of view, the H3BO3 polymorphs are also shown to be interesting stacked molecular crystals to probe actual DFT-based descriptions of hydrogen and van der Waals interactions.

2. MATERIALS AND METHODS 2.1. H3BO3-2A Optical Absorption Measurement. H3BO3-2A powder of 99.5% purity was purchased from VETEC, its X-ray diffraction pattern being measured to ensure its quality (see Figure S1 in the Supporting Information), after which it was used with no further purification mixed with KBr to form H3BO3-2A:KBr pellets. A Varian Cary 5000 UV−visible NIR spectrophotometer equipped with solid sample holders was used to carry out the light absorption measurements. The absorption spectra of the pellet samples were recorded in the 200−800 nm wavelength range (6.21−1.55 eV), as shown in Figure 1.

Figure 1. Square of the optical absorption (α2) measured for H3BO32A:KBr pellets at 300 K with nonpolarized incident radiation. The red dotted line provides an estimate for the indirect band gap of this material, Eg = 5.98 eV. 2.2. H3BO3-2A and H3BO3-3T Crystallographic Data. Cumulated X-ray diffraction data show that (i) the H3BO3 molecule is very symmetric, with in-plane interactions due to six hydrogen bonds with three neighbors, as shown in Figure 2a,b; (ii) the H3BO3-2A polymorph has triclinic structure, space group P1,̅ and stacked planes with relative displacements following the repeating sequence AB···,15 3.18 Å apart (see Figure2c); (iii) the H3BO3-3T polymorph trigonal structure belongs to the P32 space group, with stacked planes displaced relative to each other following the repeating sequence ABC···,16 3.19 Å apart (Figure 2d). The two (three) H3BO3 basic planes for the 2A (3T) polymorph are shown in Figure 2c (Figure 2d). The H3BO3-2A (3T) polymorph has four (six) H3BO3 molecules in its unit cell, whose experimental lattice parameters parameters a, b, c and angles α, β, γ are given in Table 11, and have been used to prepare the input structures for the DFT calculations. Finally, a plane depicting the hexagonal arrangement of the H3BO3 molecular units is shown in Figure 2e. 2.3. DFT Computational Details. All crystal geometry optimizations were performed using the plane-wave CASTEP code.37 Two distinct approximations for the exchange-correlation functional were employed: the local density approximation (LDA) and the generalized gradient approximation (GGA) with dispersion correction. The LDA parametrization proposed by Ceperley, Alder, Perdew, and Zunger38,39 was adopted, whereas the GGA functional is the one due to Perdew, Burke, and Ernzerhof (PBE),40 which is qualitatively similar to the well-known PW91 functional.41 The dispersion correction scheme of Tkatchenko and Scheffler42 (TS) was taken into account in the GGA computations to include van der Waals forces43 due to electron density fluctuations44 (GGA+TS). These forces are expected to contribute substantially to the interaction between the H3BO3 polymorph planes, as is the case with other twodimensional materials.45,46 Norm-conserving pseudopotentials47 replace the core electrons of the non-hydrogen atoms, with valence configurations 2s22p1(B) and 2s22p4(O). The unit cells of the H3BO3B



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Figure 2. (a) H3BO3 molecule; (b) in-plane hydrogen bonds between H3BO3 molecules in a polymorph; (c) unit cell of the H3BO3-2A polymorph with experimental interplanar distance 3.18 Å; (d) unit cell of the H3BO3-3T polymorph with experimental interplanar distance 3.19 Å; (e) plane of boric acid molecular units common to both polymorphs: the in-plane hexagonal pattern is easily seen.

Table 1. Lattice Parameters and Planar Distances Calculated at the LDA, GGA, and GGA+TS Levels for Triclinic H3BO3-2A and Trigonal H3BO3-3T Polymorphsa H3BO3-2A 12

Exp LDA500 GGA500 GGA+TS500 LDA830 GGA830 GGA+TS830 LDA1100 GGA1100 GGA+TS1100 H3BO3-3T Exp16 LDA500 GGA500 GGA+TS500 LDA830 GGA830 GGA+TS830 LDA1100 GGA1100 GGA+TS1100 a

a

Δa

b

7.04 6.83 7.26 7.08 6.67 6.99 6.92 6.67 6.99 6.92 a

−0.21 +0.22 +0.04 −0.37 −0.05 −0.12 −0.37 −0.05 −0.12 Δa

7.05 6.85 7.26 7.08 6.67 6.99 6.92 6.67 6.99 6.92

7.05 6.83 7.29 7.43 6.67 6.98 6.93 6.67 6.98 6.93

−0.22 +0.24 +0.39 −0.37 −0.07 −0.12 −0.37 −0.07 −0.12

Δb

b 7.05 6.83 7.29 7.43 6.67 6.98 6.93 6.67 6.98 6.93

−0.20 +0.20 +0.04 −0.38 −0.07 −0.13 −0.38 −0.07 −0.13 Δb −0.22 +0.24 +0.39 −0.37 −0.07 −0.12 −0.37 −0.07 −0.12

c

Δc

6.58 5.88 7.77 6.30 5.96 8.03 6.40 5.95 8.03 6.40

−0.70 +1.19 −0.98 −0.62 +1.46 −0.18 −0.63 1.46 −0.18 c 9.56 8.69 11.78 10.03 8.69 11.55 9.26 8.68 11.55 9.26

Δα

β

Δβ

γ

Δγ

d

Δd

−0.79 +0.13 +0.17 −0.57 −0.27 −0.10 −0.67 −0.27 −0.10

101.1 100.3 102.2 102.2 100.9 99.14 101.9 101.1 99.14 101.9

−0.84 +1.06 +1.10 −0.26 −2.03 0.74 −0.04 −2.03 0.74 Δβ

119.8 120.0 120.1 119. 119.8 120.0 119.8 119.8 120.0 119.8 γ

0.25 0.24 0.00 0.04 0.20 0.01 0.04 0.20 0.01 Δγ

3.18 2.85 3.73 3.07 2.87 3.92 3.07 2.86 3.92 3.07 d

−0.33 +0.55 −0.11 −0.31 +0.74 −0.11 −0.32 +0.74 −0.11 Δd

120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0

-

a 92.58 91.79 92.71 92.75 92.01 92.31 92.48 91.91 92.31 92.48 Δc −0.87 2.22 +0.47 −0.87 +1.99 −0.31 −0.88 +1.99 −0.31

α

Δα

β

90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0

-

90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0

-

-

3.19 2.80 3.93 3.34 2.80 3.85 3.09 2.80 3.85 3.09

−0.39 +0.74 +0.15 −0.39 +0.66 −0.10 −0.39 +0.66 −0.10

Lengths a, b, c and planar distances d are given in Å, while angles α, β, γ are in degrees.

C



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2A and H3BO3-3T crystals have 128 electrons (32 core and 96 valence electrons) and 192 electrons (48 core and 144 valence electrons), respectively. In order to ensure a well converged structure, optimized lattice parameters were obtained for plane wave cutoff energies of 500, 830, and 1110 eV. The following geometry optimization thresholds were followed through successive self-consistent field steps: total energy variation smaller than 0.50 × 10−5 eV/atom, maximum force per atom below 0.01 eV/Å, pressure smaller than 0.02 GPa, and maximum atomic displacement smaller than 0.10 × 10−3 Å. The BFGS minimizer48 was employed to perform the unit cell optimizations and the self-consistent field convergence was achieved when the following criteria were satisfied: total energy/atom varying by less than 0.50 × 10−5 eV and electronic energy varying by less than 0.125 × 10−6 eV in a convergence window of three cycles. The best computational cost-benefit was found for a plane wave energy cutoff of 830 eV, since the unit cell parameters calculated using a higher value (1100 eV) have not changed significantly (see Table 1). The absence of imaginary vibrational frequencies for both boric acid polymorphs (data not presented here) confirmed the accuracy of the final geometries. A Monkhorst−Pack49 2 × 2 × 3 sampling grid was employed to evaluate integrals in reciprocal space. For the optical properties, however, this sampling was increased to 10 × 10 × 10, as it is necessary to use more k-points in the Brillouin zone (BZ) when running optical matrix element estimates, which are more sensitive to the Brillouin zone sampling than electronic energies. In order to compare the boric acid molecular orbitals in a single molecule and in the crystals, electronic structure calculations were performed for both molecule and GGA+TS optimized crystals using the DMOL3 code50 with the same exchange-correlation functional and a Double Numerical plus Polarization (DNP) basis set with convergence thresholds similar to the values adopted for the CASTEP computations. The Kohn−Sham electronic band structure and electron density of states were evaluated for the optimized GGA+TS unit cells with a plane wave cutoff of 830 eV (GGA+TS830), as well as the dielectric function and optical absorption for polarized light along a set of chosen crystalline planes and in the case of a polycrystalline sample. The optical absorption α(ω) and the complex dielectric function ϵ(ω) = ϵ1 + iϵ2(ω) of the H3BO3-2A and H3BO3-3T polymorphs were calculated at the GGA+TS830 level following the same scheme described in previous work.24,27,29−31

observe that computations at the LDA level do not lead to good unit cell parameters since their deviations Δa, Δb, Δc, and so forth (differences between theoretical and experimental data) for the lattice lengths, angles, and volumes are in general considerably larger in magnitude than those found at the GGA level. This occurs because the LDA functional tends to overestimate interatomic forces (hydrogen bonds in the case). In contrast, pure GGA functionals are able to provide a good description of hydrogen bonds, but tend to underestimate the strength of interatomic interactions. The GGA+TS lattice parameters, by the way, reproduce the experimental data more accurately than the pure GGA calculations, especially for the c lattice parameter for which the GGA predictions are much worse than LDA. Indeed, a recent report using DFT with a semiempirical dispersion correction scheme was presented by Zhu and Gao53 for the TiO2 polymorphs anatase, brookite, and rutile, showing that the inclusion of dispersion effects improves the lattice parameter estimates. For a 830 eV plane wave cutoff, all normal modes obtained for the crystal geometry of both H3BO3 polymorphs using the GGA+TS functional exhibited positive frequencies, indicating that a total energy minimum was reached (in a work to be published soon we intend to present the results of the normal modes, infrared and Raman spectra of H3BO3-2A and H3BO3-3T). Consequently, the converged unit cell parameters for the H3BO3-2A and H3BO33T polymorphs considered in this work for the electronic and optical properties calculations are those obtained at the GGA +TS830 level. In this case, we also have the best estimate for the planar distances, with Δd ∼ −0.1 Å. The fractional atomic coordinates, bond lengths and angles thus obtained are included in the Supporting Information (see Tables S1 and S2). In order to compare the stiffness of the H3BO3 crystal polymorphs, single point energy calculations were performed by taking the GGA+TS optimized structures and varying their lattice parameters near to their optimal values a0, b0, and c0. Total energy values E (Δa/a0), E (Δb/b0), and E (Δc/c0) were obtained, as shown in Figure 3. For both polymorphs the total energy change for E (Δc/c0) is much smaller than changes of E (Δa/a0) and E (Δb/b0). This is due to the weak van der Waals forces that bind the crystal planes to each other, while in-plane intermolecular hydrogen bonds are much stronger. This weakness explains the small sliding friction and lubricating characteristics of colloidal suspensions of boric acid nanoparticles. One can also note that H3BO3-2A and H3BO3-3T polymorphs should have similar lubricant properties since their E (Δc/c0) curves are similar. 3.3. Electronic Structure. The symmetry of the H3BO3 molecule and its neighborhood in the crystalline polymorphs (see Figure 2a and b) must lead to similar amounts of negative charge being transferred from the boron atom (electronegativity 2.04) to the oxygen atoms O1, O2, and O3 (electronegativity 3.44). To confirm this supposition, Hirshfeld population analysis54 was performed on the DFT results, a method that generates improved Fukui function indices estimates55,56 in comparison to the more usual Mulliken analysis,57 natural bond orbital analysis,58 and charges fitted to the electrostatic potential.59 The Mulliken and Hirshfeld atomic charges for the acid boric polymorphs are given in Table S3 of the Supporting Information. At the GGA+TS830 level of calculation, Hirshfeld charges of 0.27 for B1; −0.21 for O1, O2, O3; and 0.12 for H1, H2, H3 were obtained, confirming our expectations (see Figure 2a for a description of the atomic labeling).

3. RESULTS AND DISCUSSION 3.1. H3BO3-2A Energy Gap from Optical Absorption Measurements. The H3BO3-2A optical absorption spectrum measured in this work is shown in Figure 1. The corresponding spectrum for the 3T polymorph was not obtained since we were unable to synthesize it or to buy its powder. The optical absorption of an indirect band gap material is related to the incident photon energy according to the equation E(ℏω) = C(ℏω − Eg ± ℏΩ)1/2, where C is a constant, Eg is the indirect band gap energy, and ± ℏΩ is the energy of the emitted (minus signal) or absorbed (plus signal) phonon contributing to the optical absorption of the photon with energy ℏω51,52 required to ensure momentum conservation. As the DFT-based electronic calculations of the present work point to an indirect gap for the H3BO3-2A polymorph (see Figure 5), one can obtain an experimental value for the indirect band gap of the polymorph H3BO3-2A through a linear fit of the square of the absorbance in the energy range. where it increases more sharply. From this procedure, the H3BO3-2A indirect energy gap was found to be 5.98 eV (see dotted red line in Figure 1). 3.2. Structural Features of the H3BO3 Polymorphs. Table 1 shows the optimized unit cell parameters for both boric acid polymorphs obtained at the LDA, GGA, and GGA+TS levels for each tested plane wave cutoff energy. One can D



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The GGA+TS830 calculated band structures, partial and total electron densities of states for triclinic H3BO3-2A and trigonal H3BO3-3T are shown at the left and right sides of Figures 5 and

Figure 3. DFT calculated (GGA+TS830 level) total energy E of the triclinic H3BO3-2A (top) and trigonal H3BO3-3T (bottom) unit cells as a function of lattice parameter deviations Δa/a0, Δb/b0, and Δc/c0 relative to the converged optimal parameters a0, b0, and c0, respectively.

Figure 5. Band structure and electron densities of states of the H3BO32A polymorph. Top: Full electronic band structure in the −20−20 eV energy range (left) and the s, p, and total densities of states (right). Bottom: close-up of the band structure (left) and s H, s B, p B, s O, and p O electron densities of states (right) near the main band gap.

The Kohn−Sham electronic band structure gives the electronic eigenenergies E as a function of a set of quantum numbers that form the components of a wave vector k in the first Brillouin zone (BZ) of the crystal. For the boric acid polymorphs, the paths in the BZ used for band structure computations are formed by straight lines connecting a set of selected high-symmetry/special points, as shown in Figure 4.

6, respectively. Electron energies were gauged to ensure that the highest valence band has its maximum at 0.0 eV. At the top of the band structure plots for both boric acid polymorphs, the

Figure 4. First Brillouin zones of the boric acid polymorph H3BO32Aand H3BO3-3T. High-symmetry points are indicated: Z(0.00, 0.00, 0.50), Γ(0.00, 0.00, 0.00), Q(0.00, 0.50, 0.50), F(0.00, 0.50, 0.00), B(0.50, 0.00, 0.00), β1(0.00, 0.00, 0.19), and β2(0.0, 0.35, 0.00) for 2A; Z(0.00, 0.00, 0.50), Γ(0.00, 0.00, 0,00), Q(0.00, 0.50, 0.50), F(0.00, 0.50, 0.00), K(−0.33, 0.67, 0.00), H(−0.33, 0.67, 0.50), α1(0.00, 0.33, 0.00), and α2(−0.33, 0.67, 0.23) for 3T.

For H3BO3-2A, these points are Z(0.00, 0.00, 0.50), Γ(0.00, 0.00, 0.00), Q(0.00, 0.50, 0.50), F(0.00, 0.50, 0.00), B(0.50, 0.00, 0.00), β1(0.00, 0.00, 0.19), and β2(0.0, 0.35, 0.00). For the H3BO3-3T polymorph, we have Z(0.00, 0.00, 0.50), Γ(0.00, 0.00, 0,00), Q(0.00, 0.50, 0.50), F(0.00, 0.50, 0.00), K(−0.33, 0.67, 0.00), H(−0.33, 0.67, 0.50), α1(0.00, 0.33, 0.00), and α2(−0.33, 0.67, 0.23).

Figure 6. Band structure and electron densities of states of the H3BO33T polymorph. Top: Full electronic band structure in the −20−20 eV energy range (left) and the s, p, and total densities of states (right). Bottom: close-up of the band structure (left) and s H, s B, p B, s O, and p O electron densities of states (right) near the main band gap. E



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full energy range of calculated electron energies, from −20.0 to 20.0 eV, is shown. The right panels depict the contributions of the s and p orbitals to the density of states, as well as the total density of states (a more detailed description of them is included in the Supporting Information, Figure S2). The valence bands between −7.5 and 0.0 eV (−17.5 eV and −20.0 eV) are dominated by contributions of p (s) orbitals from oxygen, while the conduction bands between 6.0 and 17.5 eV have significant contributions from both s and p orbitals, but with the prevalence of the former (s from H − the strongest contribution, s from O, and s from B) for the conduction band energy minima at the symmetry point Γ. At the bottom of Figures 5 and 6 for both boric acid polymorphs, close-ups of the band structures near the main band gap are shown, revealing the most relevant electronic transitions between the top of the valence band and the bottom of the conduction band (see left side), while the contributions of the total s, p orbitals and hydrogen, boron, and oxygen orbitals to the partial density of states near the main energy gap are displayed at the right side, as well as the total density of states. For H3BO3-2A, Figure 5 shows that the smallest band gap corresponds to the valence-conduction band transition Q(0.00, 0.50, 0.50) → Γ(0.00, 0.00, 0.00), being 6.25 eV. There are, however, two close transitions with 6.28 eV energy: β2(0.0, 0.35, 0.00) → Γ(0.00, 0.00, 0.00) and B(0.50, 0.00, 0.00) → Γ(0.00, 0.00, 0.00). All these estimates are remarkably close to the measured 5.98 eV value obtained from optical absorption. It is important to note that H3BO3-2A also exhibits indirect Z(0.00, 0.00, 0.50)) → (0.00, 0.00, 0.00) and direct Γ(0.00, 0.00, 0.00) → Γ(0.00, 0.00, 0.00) transitions with energies of 6.34 and 6.35 eV, respectively. For the H3BO3-2T polymorph, Figure 6 reveals that the smallest indirect gap is also 6.25 eV, which is assigned to the transition α2(−0.33, 0.67, 0.23) → Γ(0.00, 0.00, 0.00); there are also indirect transitions Q(0.00, 0.50, 0.50) → Γ(0.00, 0.00, 0.00) (6.26 eV) and α1(0.00, 0.33, 0.00) → Γ(0.00, 0.00, 0.00) (6.27 eV), and a 6.31 eV direct transition Γ(0.00, 0.00, 0.00)) → Γ(0.00, 0.00, 0.00). Both boric acid polymorphs are predicted to be insulators since their highest valence and lowest conduction bands are very flat, and the energy gap is large. In addition, one can note that the measured energy gap estimated for the H3BO3-2A polymorph is a little bit smaller than the theoretical value, which is unexpected as DTF calculations tend to underestimate gap energies in contrast with more accurate approaches such as the GW method.60 This can be explained by the decrease of the unit cell lattice parameters caused by the inclusion of the van der Waals interactions in the system (a smaller cell size implies in a larger main band gap due to quantum confinement). Although smaller lattice constant values affect band gap, it is surprising that a shrinkage of about 3% in comparison with the experiment (for the c lattice parameter) can produce a difference so unexpected in the band gap value. In order to check for this result, we have also carried out band structure calculations using the experimental lattice parameters of both 2A and 3T polymorphs without any optimization using both the GGA+TS approach and the pure GGA functional, as well as the Kohn−Sham band structures optimizing the unit cells using the GGA approximation without the dispersion energy term. The resulting band structures are presented in the Supporting Information of the paper (Figures S3 and S4). After performing the calculations using the experimental lattice parameters, we have found that the theoretical band gaps are increased to 6.44 eV (2A) and 6.27 eV (3T) at the GGA+TS level, while the pure

GGA values are essentially the same. Using the GGA optimized unit cell, however, the band gap of the 2A polymorph decreases to 5.98 eV, matching precisely the optical absorption experimental estimate. In this case, as the c lattice parameter is increased by 22% when switching from the experimental to the optimized geometry, the main band gap decreases by about 8%. For the GGA+TS functional, the c parameter decreases by about 3% as we switch from the experimental unit cell to the optimized case, while the band gap decreases by approximately the same amount. As a matter of fact, in previous published work,24,25,27,30 the authors have obtained the DFT electronic band structure of some molecular crystals of amino acids (namely, α-glycine, orthorhombic cysteine, monoclinic Laspartic acid, and L-serine) and also have observed that the calculated gaps were close to experimental estimates from optical absorption measurements. However, in the case of anhydrous DNA nucleobase crystals (guanine, adenine, cytosine, and thymine), differences as large as 40% between the DFT-calculated at the LDA level and the optical absorption measurements of energy band gaps were found.26 With the purpose of better understanding the relationship between the band gaps of the boric acid polymorphs and the electronic structure of the H3BO3 molecule, DFT calculations for the isolated boric acid molecules were also performed using the GGA+TS exchange-correlation functional. Figure 7 shows

Figure 7. GGA+TS calculated HOMO and LUMO orbitals for a single H3BO3 molecule.

the HOMO and LUMO orbitals for the H3BO3 molecule. The HOMO−LUMO gap was estimated to be 7.75 eV. For the HOMO, one can clearly see a strong contribution from 2p O states, while the LUMO has a strong contribution from 1s H orbitals and a smaller contribution from 2p O states. The boron atom does not contribute significantly to any of the frontier molecular orbitals. When the H3BO3 is embedded in the crystal, the uppermost valence band retains its 2p O molecular character. This can be confirmed by looking at the highest occupied valence band (HOVB) orbitals shown in Figure 8. The HOVB, which corresponds to the HOMO state in the molecule, clearly shows a strong p contribution from the oxygen atoms inside the unit cell, with a small degree of intermolecular interaction within and between the crystal planes. In contrast, for the lowest unoccupied conduction band (LUCB) orbital, one can see 2s B and 2p B as strong contributions (which do not occur in the isolated molecule), as well as a strong superposition of 1s H orbitals and a smaller contribution from 2s O orbital levels, with a region contributing significantly to the electron probability density between adjacent hydrogen bonds. Interactions can be easily pointed out between molecular units within a given crystal plane for both polymorphs due to the 1s H overlap, and between molecular units at adjacent crystal planes due to the overlap of 2s B and 2p B orbitals, mostly for the 2A polymorph. F



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scattering, decreasing broadening effects. A well pronounced peak at about 16.0 eV is observed for both structures, which involves mainly transitions due to p-like O orbitals at −7.5 to −5.0 eV to p-like B orbitals at 7.5−10.0 eV, as shown in Figure S2. For the 3T polymorph, the 001 absorption curve exhibits a broad structure between 8.0 and 12.0 eV, and a sharp peak at 16.0 eV. The polycrystalline absorption resembles more closely 010 and 100 absorption features. The absorption spectrum of the 3T polymorph is less broadened around 16.0 eV than for the 2A one, with a minimum at about 18.0 eV. A direct comparison between theory and experiment for the optical absorption of the H3BO3-2A polymorph is presented in Figure 10, where one can see curves for the unshifted (see red solid

Figure 8. GGA+TS calculated highest occupied valence band (HOVB, left) and lowest unoccupied conduction band (LUCB, right) orbitals of the triclinic H3BO3-2A (top) and hexagonal H3BO3-3T (bottom) polymorphs.

3.4. Optical Absorption and Dielectric Function of the H3BO3 Polymorphs. The GGA+TS830 optical absorption curves calculated for both H3BO3-2A and 3T polymorphs are shown in Figure 9 for three cases of polarized light incidence

Figure 10. Experimental optical absorption of the H3BO3-2A crystal (black solid curve). Theoretical GGA+TS830 unshifted (red solid curve) and shifted by −0.3 eV (red dashed curve) absorption curves for the polycrystal are also shown for the sake of comparison. Straight lines indicate the indirect energy band gaps.

curve in Figure 10) and ∼0.3 eV rigidly shifted theoretical absorption to match the experimental curve (see red dashed and black solid curves in Figure 10, respectively). The real and imaginary parts of the dielectric function ϵ(ω) = ϵ1(ω) + iϵ2(ω), of the boric acid polymorphs are shown in Figure 11. As the imaginary part ϵ2(ω) of the dielectric function is proportional to the optical absorption we already discussed, we focus our analysis here only on the real part ϵ1(ω). For incident light with 001 polarization, the value of ϵ1(ω = 0) is approximately 2.0 for the 2A and 1.8 for the 3T structure. As the energy increases, ϵ1(ω) gets larger, reaching a maximum at approximately 9 eV and then falling sharply, with the 010 and 100 polarization curves becoming negative for both polymorphs. Also between 10.0 and 16.0 eV, ϵ1(ω) exhibits a set of broad peaks in the 010 and 100 plots for the 2A and 3T polymorphs, while the 001 curve has two well-defined maxima at 10 0.0 and 11.5 eV. At 15.6 eV, the 001 curve shows a sharp decrease. For the polycrystalline case, the qualitative behavior of ϵ1(ω) for the H3BO3 0crystals is very similar. The minima at 16.0 eV are mainly due to transitions from 2p O orbitals at −7.5 to −5.0 eV to 2p B orbitals at 7.5−10.0 eV, as one can see from Figure S2 in the Supporting Information.

Figure 9. Calculated optical absorption for the H3BO3-2A (left) and 3T (right) crystals considering incident polarized light along the 001, 010, and 100 crystal planes and a polycrystalline (POLY) sample.

(polarization along the 001, 010, and 100 crystal planes) and for a polycrystalline sample. The 010 and 100 absorption curves are remarkably similar to each other for each crystal structure, with small peaks near 8.0 eV, a pronounced peak at about 9.0 eV, and a broad set of peaks between 12.0 and 24.0 eV. For the 001 polarization in the 2A polymorph, on the other hand, there are a set of three absorption bands at 9.0, 10.0, and 11.5 eV, more pronounced than in the 3T structure, which is probably due to the fact that in the former case the existence of only two displaced acid boric molecular planes produces less optical

4. CONCLUSIONS In summary, the optical absorption of the 2A boric acid crystal was measured and DFT calculations were performed to obtain G



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Figure 11. Calculated complex dielectric function ϵ(ω) = ϵ1(ω) + iϵ2(ω) for the H3BO3-2A (left) and 3T (right) crystals considering incident polarized light along the 001, 010, and 100 crystal planes and a polycrystalline (POLY) sample. The red curves depict the real part ϵ1(ω), while the black curves depict the imaginary part ϵ2(ω).

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the structural, electronic, and optical properties of the 2A and 3T polymorphs. Both systems are formed by the stacking of molecular planes with hydrogen bonds connecting in-plane boric acid molecular units in a hexagonal pattern, van der Waals forces being responsible for holding the planes together. These structures, besides their biological applications, are also interesting as models to study two-dimensional materials held by noncovalent forces. The optimized unit cells revealed that the best approach to describe planar distances and lattice parameters in comparison to experiment is to use a GGA functional with the dispersion correction scheme of Tkatchenko and Scheffler,42 GGA+TS, as an LDA (pure GGA) functional tends to strongly underestimate (overestimate) the size of the unit cell, especially along the stacking axis. The total unit cell energy as a function of the lattice parameters was shown to behave practically in the same way for both 2A and 3T polymorphs, while their electronic structures have subtle differences: the main band gap of the 2A phase is indirect (Q → Γ) and equal to 6.25 eV, while the direct gap (Γ → Γ) is 6.35 eV. In comparison, the H3BO3-2A energy gap estimated from optical absorption was 5.98 eV, about 0.4 eV smaller. In the case of H3BO3-3T, the Q → Γ transition gap is also 6.25 eV and the Γ → Γ is 6.31 eV. The uppermost valence bands of both polymorphs were shown to be relatively flat, originating mainly from 2p O states, while the bottom of their conduction bands have some dispersion and are mostly due to 1s H and 2s B orbitals. The calculated optical properties revealed that for polarized incident light along the 100 and 010 crystal planes, the optical absorption and complex dielectric functions behave in a very similar way for both polymorphs, with distinct spectral features being observed in the case of 001 polarized incident light across the full photon energy range of the simulation (6.0−26.0 eV). Finally, our results indicate that in the case of the boric acid polymorphs the description of the van der Waals interactions using the TS scheme leaves room for improvement.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b01297. X-ray diffraction patterns; GGA+TS partial electron densities of states; Kohn−Sham band structures; tables with structural features and charge populations for both boric acid polymorphs (PDF)

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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 V. N. F., A. Valentim, and O. D. L. Pessoa 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. E. W. S. C. received financial support from CNPq through the project 307843/2013-0.

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