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Article pubs.acs.org/molecularpharmaceutics

Exploring the Molecular-Level Architecture of the Active Compounds in Liquisolid Drug Delivery Systems Based on Mesoporous Silica Particles: Old Tricks for New Challenges Jiri Brus,*,† Wolfgang Albrecht,‡ Frank Lehmann,‡ Jens Geier,‡ Jiri Czernek,† Martina Urbanova,† Libor Kobera,† and Alexand Jegorov§ †

Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky sq. 2, 162 06 Prague 6, Czech Republic ‡ Ratiopharm GmbH, Graf-Arco-Str. 3, 89079 Ulm, Germany § Teva Czech Industries s.r.o., Branisovska 31, 370 05 Ceske Budejovice, Czech Republic S Supporting Information *

ABSTRACT: A general, easy-to-implement strategy for mapping the structure of organic phases integrated in mesoporous silica drug delivery devices is presented. The approach based on a few straightforward solid-state NMR techniques has no limitations regarding concentrations of the active compounds and enables straightforward discrimination of various organic phases. This way, among a range of typical arrangements of the active compounds and solvent molecules, a unique, previously unknown organogel phase of the selfassembled tapentadol in glucofurol as a solvent was unveiled and clearly identified. Subsequently, with an aid of 2D 1H−1H MAS NMR and high-level quantum-chemical calculations this uncommon low-molecular-weight organogel phase, existing exclusively in the porous system of the silica carrier, was described in detail. The optimized model revealed the tendency of tapentadol molecules to form hydrophobic arrangements through −OH···π interactions combined with π−π stacking occurring in the core of API aggregates, thus precluding the formation of hydrogen bonds with the solvent. Overall, the proposed experimental approach allows for clear discrimination of a variety of local structures of active compounds loaded in mesoporous silica drug delivery devices in reasonably short time being applicable for advancement of novel drug delivery systems in pharmaceutical industry. KEYWORDS: Liquisolid systems, drug-delivery, Solid state NMR, Organogels

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technology.5−10 Although the synthesis of these systems has been well investigated, little is known about the interfaceaffected architecture of their organic phases. In particular, due to the complex pathway of weak, mostly reversible interactions, a range of local arrangements can be expected including the formation of crystalline, amorphous and partially ordered protocrystalline and organogel phases.11−15 Full exploitation of these systems, however, requires their precise characterization. This is a stringent requirement, as these systems naturally exist at the borderline between solids and liquids, and high-quality diffraction data are inherently unavailable. In this respect, solidstate nuclear magnetic resonance spectroscopy (ss-NMR) has evolved into a powerful tool for studying the structures of a broad range of materials. Complex multicomponent MSN-

INTRODUCTION

An increasing number of currently known compounds with desirable biological activity may never reveal their true potential due to their unfavorable physicochemical properties. In particular, for poorly water-soluble drugs comprising ca. 40% of newly discovered chemical entities, oral administration in common dosage forms is problematic. Recent efforts to optimize their therapeutic efficacy have, however, resulted in the development of liquisolid drug delivery systems1−4 (LSS), which are based on the incorporation of a liquid film of the active compound on the surface of mesoporous silica (nano)particles (MSNs). These systems enable to control the release of the active compound and combine the advantages of solid dosage forms, such as the comfort of oral administration, with the efficient absorption of liquid drugs in the gastrointestinal tract. Besides pharmaceutical applications, MSN-based functional materials have currently received attention also in the fields of targeted nanocatalysis, nanomedicine, and advanced sensor © XXXX American Chemical Society

Received: Revised: Accepted: Published: A

March 3, 2017 April 10, 2017 May 9, 2017 May 9, 2017 DOI: 10.1021/acs.molpharmaceut.7b00167 Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Article

Molecular Pharmaceutics based hybrids,16 aluminosilicate frameworks,17 and drug delivery systems18−23 have been successfully characterized. However, a comprehensive methodology suitable for exploring liquisolid systems at atomic resolution is still required, which represents a crucial obstacle to the advancement of nextgeneration hybrid drug delivery devices. To bridge this gap, we propose and demonstrate in this contribution an easy-toimplement strategy for determining the structure of organic phases incorporated into the variable liquid/solid environments of MSNs.

Table 1. Composition of the Reaction Mixtures Used for the Synthesis of Liquisolid Systems solvent (mL) GLF PRO DMI BUT PRO PEG PRO PRO BUT DHN

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MATERIALS AND METHODS Chemicals and Materials. Active pharmaceutical ingredients (API) tapentadole (TAP) and ivabradine (IVB) in their hydrochloride forms were used. Tapentadol and tapentadol· HCl is a centrally acting opioid analgesic of the benzenoid class with a dual mode of action as an agonist of the μ-opioid receptor and norepinephrine reuptake inhibitor (NRI). Ivabradine·HCl is an active compound used for symptomatic management of stable heart related chest pain and heart failure not fully managed by beta blockers. As dissolving agents glycofurol (GLF, tetrahydrofuranyl alcohol polyethylene glycol ether), decahydronaphtalene (DHN), dimethyl isosorbid (DMI); 1,2-propanediol (PRO), 2,2-butanediol (BUT), and PEG200 (PEG) all purchased from Sigma-Aldrich were used. The following porous materials were used as model carriers: Neusilin (Fuji Chemical Industries Co., Ltd.) is a synthetic amorphous form of magnesium alumino-metasilicate (with pore size diameter ca. 15 nm, NEU); AEROPERL 300 Pharma (Evonik (SEA) Pte. Ltd.) is a granulated form of colloidal silicon dioxide (pore size diameter cc 37 nm, AER); Bentonit (Sigma-Aldrich Co. LLC.) is an absorbent aluminum phyllosilicate clay consisting mostly of montmorillonite (BEN); Celite (Sigma-Aldrich Co. LLC.) is a registered trademark of calcined or flux diatomaceous earth (Imerys Minerals California Inc.; with average pore size diameter ca. 5000 nm, CEL). MCM-48 (ca. 3 nm, MCM), SBA-15 (ca. 10 nm, SBA), and MSU-F (ca. 15 nm, MSU) (Sigma-Aldrich Co. LLC.) are typical mesoporous silica systems. Synthesis of Liquisolid Systems. The liquisolid systems were prepared by a standard procedure involving initial dissolution of the API in the selected solvent (saturated solutions were prepared) followed by the subsequent impregnation of the selected silica carrier. The API was dissolved in solvent at 80 °C under stirring. The carrier material was added in portions of 0.05 g at 80 °C, and the mixture was manually stirred with a spatula until a free-flowing homogeneous powder was obtained. The product was then cooled to room temperature under ambient conditions and dried. Typically, tapentadol·HCl (200 mg) was dissolved in methanol (1 mL). Neusilin (500 mg) was added in portions of 0.05 g, and the mixture was manually stirred with a spatula until a freeflowing homogeneous powder was obtained. The solvent was then removed under vacuum (10 mbar) at room temperature. Composition of reaction mixtures is listed in Table 1. For other details see Supporting Information S1. NMR Spectroscopy. The proposed experimental approach to explore the architecture of active compounds in liquisolid mesoporous silica particles is based on the combination of three straightforward ss-NMR techniques:24 (i) 1H magic angle spinning (MAS) NMR, (ii) T1(13C)-filtered 13C MAS NMR, and (iii) 13C cross-polarization (CP) MAS NMR spectroscopy

0.2 1.0 0.2 0.5 0.2 0.4 0.2 0.2 0.4 0.1

API (mg) TAP TAP-HCl TAP TAP-HCl IVB.HCl IVB.HCl IVB.HCl IVB.HCl IVB.HCl TAP-HCl TAP-HCl

carrier (mg) 100 200 100 100 100 100 100 100 100 200 200

AER NEU BEN MSU CEL SBA MSU NEU MCM NEU NEU

150 500 500 250 300 200 100 150 150 500 500

(Figure 1). Each of these techniques provides specific structural and motional information, and in combination, the obtained data facilitate the reconstruction of a surprisingly complex picture of the internal architecture of liquisolid systems. All solid-state NMR spectra were measured at 11.7 T using a Bruker AVANCE III HD WB/US NMR spectrometer (Karlsruhe, Germany, 2013) in a double-resonance 4 mm probehead at spinning frequencies ωr/2π = 10 kHz. In all cases finely powdered, macroscopically dry, samples were placed into 4 mm ZrO2 rotors. 1H MAS NMR spectra were recorded using the single-pulse experiment with the repletion delay of 8 s and the number of scans of 512. T1-filtered 13C MAS NMR spectra were recorded using the single-pulse experiment with a highpower dipolar decoupling (SPINAL-64). The applied short repetition delay (1−4 s, T1-filter) was used to suppress the 13C magnetization of rigid molecules and molecular segments. The number of scans was 4−8k. A standard cross-polarization pulse sequence was used to measure 13C CP/MAS NMR spectra. The length of cross-polarization contact time was usually set to 100 μs to preferentially detect the strongly immobilized segments. The applied nutation frequency of B1(13C) and B1(1H) fields during the cross-polarization period was ω1/2π = 62.5 kHz, and repetition delay was 5 s. During data acquisition the high-power dipolar decoupling SPINAL-64 was applied. The applied nutation frequency of B1(1H) field was ω1/2π = 89.3 kHz. The number of scans was 4−8k. The site-specific measurement of one-bond 1H−13C dipolar couplings under the Lee−Goldburg condition25 was achieved by the 2D PILGRIM experiment26 (Supporting Information S2, Scheme S1). The length of polarization-inversion period was 1 ms. Lee− Goldburg cross-polarization was found in the range 50 to 5170 μs with 20 μs increments. The experiments were performed at spinning frequency ωr/2π = 10 kHz. The recycle delay was 4 s, t1 evolution period consisted of 256 increments each made of 512 scans. Cross-polarization kinetics was measured using a standard cross-polarization pulse program with a cross-polarization period from 50 to 8050 μs with an increment of 150 μs. The 2D 1H−1H MAS NMR correlation spectra were measured using the standard three-pulse (NOESY-type) pulse sequence (Supporting Information S2, Scheme S2) at spinning frequency of ωr/2π = 10 kHz; and recycle delay of 4 s. The t1 evolution period consisted of 128 increments each made of 256 scans. All experiments were conducted at 303 K, and frictional heating was compensated.27 The 13C NMR scale was calibrated with glycine as an external standard (176.03 ppm low-field carbonyl signal). Complete set B

DOI: 10.1021/acs.molpharmaceut.7b00167 Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Article

Molecular Pharmaceutics

Figure 1. Schematic representation of the proposed three-step experimental strategy for mapping the internal architecture of liquisolid mesoporous silica drug delivery systems.

atomic31 and auxiliary32 basis functions. The TURBOMOLE V6.5 program package was used with default settings.33

of experimental parameters is described in detail in Supporting Information S2. Quantum Chemical Calculations. The geometrical optimization of all the complexes employed the RI-MP2 (the resolution-of-the-identity integral approximation to the secondorder Møller−Plesset perturbation theory) method28 combined with the SVP (single-valence plus polarization) atomic29 and auxiliary30 orbital basis sets. The counterpoise-corrected interaction energies were obtained by combining the RI-MP2 method with the TZVP (triple-ζ valence plus polarization)

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RESULTS AND DISCUSSION

Experimental Strategy of the Analysis of Liquisolid Systems. 1H MAS NMR spectroscopy is the first step in exploring the structure of LSSs (Figure 1) because signals measured at a moderate frequency (ca. 5−10 kHz) are strongly receptive to changes in molecular dynamics. Broad, featureless 1 H MAS NMR signals accompanied by strong spinning C


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Figure 2. 1H MAS (blue), 13C MAS (green), and 13C CP/MAS NMR (red) spectra of tapentadol·HCl/2,3-butanediol/MCM-48 (a); tapentadol· HCl/1,2-propanediol/Neusilin (b); ivabradine·HCl/2,3-butanediol/MCM-48 (c); and tapentadol·HCl/decahydronaphthalene/Neusilin (d) systems.

filtered 13C MAS NMR spectra measured with a short repetition delay (D1 = 0.5−2 s) preferentially detect signals of mobile segments (Supporting Information S3, Figure S3). If the signals are narrow (ca. 40−10 Hz), the corresponding molecules undergo fast motions. Unrestricted mobility is evidenced by 1J(CH) spin−spin interaction patterns in the 1Hundecoupled 13C MAS NMR spectra. In this case, the typical 3 J(HH) signal splitting is also detected in 1H MAS NMR spectra (Supporting Information S3, Figures S2 and S4). The loss of the multiplet pattern combined with signal broadening observed in 1H-decoupled 13C MAS NMR spectra indicates reduced molecular dynamics and the existence of a broad

sidebands (ssb’s) indicate rigid organic solids in the crystalline or amorphous state, which are below the glass transition temperature (Tg; see Supporting Information S3; Figures S1 and S2). Narrowing of the signals toward the line width of ca. 2 kHz to 500 Hz and the disappearance of ssb’s indicate partially released motions typical for amorphous solids above Tg and near the critical fusion temperature Tc. The resolved 1H MAS spectra with signals ca. 500−50 Hz reflect soft amorphous phase or gels, whereas diluted solutions produce narrowed signals below 50 Hz. In the second step (Figure 1), the regularity of the molecular arrangements is assessed using 13C NMR spectra. The T1D


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Figure 3. 1H MAS (blue), 13C MAS (green), and 13C CP/MAS NMR (red) spectra of tapentadol/dimethyl isosorbid/bentonit (a) and tapentadol/ Neusilin (b) systems.

spectrum). The multicomponent nature of this organic phase is further evidenced by distinctly different types of signals in the T1-filtered 13C MAS and CP/MAS NMR spectra. The intensive T1-filtered 13C MAS NMR signals reflect mobile solvent molecules, whereas the considerably weaker signals show a partially dissolved fraction of the API. Broad and narrow 13C CP/MAS NMR signals then reveal the coexistence of rigid amorphous and crystalline phases, respectively (Figure 2d, red spectrum; the reference spectra of solution state, crystalline, and amorphous modifications of tapentadol·HCl are demonstrated in Supporting Information S6, Figure S17). The increasing strength of the API−solvent interactions induces the formation of homogeneous phases in which API and solvent molecules adopt uniform, more or less restricted, dynamics. The absence of fast high-amplitude jumps and translation motions are reflected by signal broadening and the loss of spectral resolution (Figure 3a and Supporting Information S4 Figure S13). The simultaneous absence of 13 C CP/MAS NMR signals reflecting fast T1ρ(1H) relaxations shows that these molecules undergo midkilohertz motions34,35 (Figure 3a, red spectrum). With the decreasing amount of solvent molecules, these midkilohertz motions gradually disappear as the resulting amorphous phase converts to the glassy state. Under these conditions terminal silanol groups covering the surface of SiO2 particles start to play a key role for silica−drug interactions and subsequent amorphization. Typically, hydrogen bonding interactions between the acid and amide functional groups of an API and surface Si−OH groups was found to support encapsulation of the API in amorphous state.36 In general, the high surface free energy (due to the large surface area) allows the system to transfer to a lower free energy state upon adsorption of drug molecules. The adsorbed drug molecules then lose their crystalline structure. Consequently, due to the decreased Gibbs free energy, the amorphous system is physically stable.37 From the spectroscopic point of view, the frozen segmental motion of the API leads to an increase in T1(13C) relaxation times, which suppress

distribution of molecular assemblies typical of amorphous phases close to the critical temperature Tc. Rigid fractions are then preferentially detected in 13C CP/MAS NMR spectra. If these signals are narrow (100 Hz), the corresponding molecules adopt the disordered nature of amorphous solids. Typical Constitution of Organic Phases in Liquisolid Systems. To demonstrate the proposed strategy, we explored a set of liquisolid systems provided by a pharmaceutical company Ratiopharm GmbH, which covered a range of silica carriers, active pharmaceutical ingredients (APIs), and dissolving agents (for complete composition of the systems see Supporting Information S1, Tables S1 and S2; for complete spectroscopic data see Supporting Information S4 and S5, Figures S5−S16). An ideal liquisolid system is demonstrated in Figure 2a. The narrow signals (20−50 Hz) detected in the 1H MAS and T1filtered 13C MAS NMR spectra reflect fast motions of the completely dissolved API and solvent molecules forming a homogeneous liquid phase, whereas the signal-free 13C CP/ MAS NMR spectra confirm the absence of immobilized organic fractions. However, even in these systems, slight solvent− surface interactions probably mediated by hydrogen-bonding with surface hydroxyls can be present, as indicated by the weak solvent signals in the 13 C CP/MAS NMR spectrum demonstrated in Figure 2b (red spectrum), which reflect the existence of residual 1H−13C dipolar couplings. Systems with the liquid phase contaminated by phase-separated fractions are demonstrated in Figure 2c,d. For low contamination, the 1H and 13C MAS NMR spectra are still predominated by the narrow signals of the liquid phase, while the separated rigid amorphous phase is detected as broad lines in the 13C CP/MAS NMR spectra (Figure 2c, red spectrum). An increase in the liquid-phase contamination is clearly visible in the 1H MAS NMR spectra in which the broad lines reflect the phase-separated API, while the narrow signals correspond to free solvent molecules (Figure 2d, blue E


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Figure 4. (a) 1H MAS (blue), 13C MAS (green), and 13C CP/MAS (red); (b) 2D 1H−13C PILGRIM; (c) 1H−13C cross-polarization build-up dependences; and (d) 1H−1H MAS NMR spectra of the tapentadol/glycofurol/Aeroperl-300 system.

the signals in T1-filtered 13C MAS NMR spectra. Simultaneously, the efficiency of 1H−13C cross-polarization increases and leads to signal enhancement in 13C CP/MAS NMR spectra (Figure 3b and Supporting Information S4, Figure S14). Low-Molecular-Weight Organogel Phases. As demonstrated above, by the consecutive application of three straightforward ss-NMR experiments, typical arrangements of organic phases in liquisolid systems can be easily recognized (Figure 1). However, due to the complex pathways of API− solvent−surface interactions, the spectroscopic responses of some systems may deviate from the expected behavior. These deviations then indicate the presence of extra phases such as low-molecular-weight organogels,11−15 and although these phases can be unveiled using the presented strategy, clearly identifying them and describing them in detail require additional NMR techniques. The typical behavior of one such exotic system is demonstrated in Figure 4. The narrow 1H and 13C MAS NMR signals suggest fast, unrestricted molecular motions typically occurring in solution. Surprisingly, however, the 13C

CP/MAS NMR experiment provides exactly the same spectrum with identical frequencies and signal line widths as those recorded by the 13C MAS NMR technique (Figure 4a; for detailed comparison see Supporting Information S7, Figure S18). This finding thus demonstrates the presence of residual 1 H−13C dipolar interactions in the organic phase. Although these interactions are weaker than those in typical organic solids, as indicated by the slow buildup of 1H−13C CP signals (Supporting Information S9, compare Figures S21 and S22), the preserved static part of 1H−13C dipolar interactions shows that the molecular motions in this phase are significantly anisotropic. Measurements of 1H−13C dipolar spectra then revealed motionally averaged one-bond dipolar couplings (DCH) ranging from 2.7 to 5.7 ± 0.5 kHz (Figure 4b and Supporting Information S10, Figures S23 and S25), which represent ca. 10−25% of the value typical for rigid C−H segments (23 kHz). The smallest DCH couplings were found for CH2−O units of the solvent; CH and CH2 units in the API alkyl chain exhibit DCH ≈ 3.0−4.5 kHz; while the aromatic CH− groups show F


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Molecular Pharmaceutics values reaching 4.5−5.7 kHz. Although the molecular weights of the API and solvent are comparable (MAPI = 221 and Msolv ≈ 190−234), the obtained DCH couplings indicate nonuniform molecular dynamics in the organic phase with reduced mobility of the API, particularly in its aromatic region. This fact was further indicated by the distorted multiplet patterns in 1Hundecoupled 13C MAS NMR spectra (Supporting Information S8, Figures S19 and S20) and was confirmed by the 1H−13C CP build-ups (Figure 4c), showing more rapid CP transfer for API molecules. All these findings thus reflect the presence of high-amplitude motions, with a constrained geometry and a reduced number of the degrees of freedom. Such behavior is, however, typical for weakly cross-linked polymer gels and liquid−crystalline phases.38−41 Therefore, for further information about the molecular assembly of this system, we recorded and analyzed 1H−1H NOESY MAS NMR spectra in which we found a complete set of resolved API/API and API/solvent correlations (Figure 4d). All these signals evolved within 50 ms of the polarization transfer; however, with decreasing mixing times, the API/solvent correlations disappeared more rapidly than the API/API correlations. The last API/solvent contact found at 5 ms involved the CH2−O and −OH side-chain protons of glycofurol and the aromatic unit of tapentadol, whereas at shorter mixing times, only API/API correlations were detected. Among them, the signals involving aromatic and −OH protons and methyl groups located at molecular peripheries were particularly evolved. In this regard it is worthy to note that much purer correlation spectra, without clear API/solvent correlations, were recorded for liquisolid systems with completely dissolved API (see Supporting Information S11, Figure S28). All these findings thus suggest tight and regular packing of API and solvent molecules in the tapentadol/glycofurol/Aeroperl-300 system with preferential API/API clustering. Bearing in mind all the obtained experimental findings, we applied the high-level quantum-chemical calculations (as detailed in Supporting Information S12) to elucidate the stabilizing features of the aggregations processes described here. Thus, the single-chain trimer model was created and subjected to the RI-MP2/SVP geometrical optimization, and for the resulting structure (which was verified to be the minimum of the potential energy surface (PES) and is shown in Figure 5) the supermolecule interaction energy was obtained at the RIMP2/TZVP level of theory.42 In order to obtain the quantitative comparison of the interactions involved, the global MP2 minima of the phenol···benzene dimer and of the water dimer were described in an analogous way. The optimized trimer model revealed the tendency to form the hydrophobic arrangements (through the −OH···π interactions occurring in the core of an aggregate of the API molecules, thus precluding the formation of hydrogen bonds with the solvent and/or surface silanols). The enthalpic gain of the formation of such structures is significant: the average interaction energy of the three respective dimers present in the trimer model amounts to 24.0 kJ/mol, which surpasses both the phenol···dimer and the water dimer values of 15.3 and 19.2 kJ/mol, respectively. However, only a local minimum of the trimer PES was considered. Consequently, tapentadol molecules are expected to stack into fibrils with a rigid core formed by the aromatic rings, surrounded by alkyl substituents adopting a columnar morphology. This arrangement also exhibits close proximity between aromatic rings and methyl units (Figure 5), which is in agreement with the obtained 1H−1H MAS NMR data. Mutually

Figure 5. RI-MP2/SVP optimized geometry of tapentadol trimer proposed in tapentadol/glycofurol/Aeroperl-300 (a), and the visualization of the LUMO orbitals in the stacked region (b).

interacting solvent molecules then form a medium for these aggregates. In this regard also the existence of slight interactions between solvent and surface silanols can be supposed; however, detailed analysis of solvent−surface interactions is beyond the scope of this contribution. Although further structure refinements must be performed the amphiphilic properties of the solvent and API molecules suggest that the obtained results are consistent with Flory’s conclusions43 on low-molecular-weight organogels, wherein continuous macroscopic phases with lamellar morphology consist of a gel skeleton body surrounded by solvent molecules.44 Analogously, we thus suppose that tapentadol molecules within the large pores of Aeroperol-300 (30−40 nm) form an embryonic, protocrystalline phase or well-ordered lowmolecular-weight organogel structures. Detailed structural investigation of the discovered tapentadol/glycofurol superstructure is currently in progress.

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CONCLUSIONS In summary, we present here an efficient strategy to probe the development of the local architectures of organic phases in liquisolid mesoporous silica drug delivery systems. The proposed ss-NMR strategy is not significantly limited by the concentrations of active compounds or the physical state of organic phases. The proposed approach enables clearly discriminating various local structures of loaded active compounds in a reasonably short time, thus facilitating the advancement of novel drug delivery systems in the pharmaceutical industry. The described strategy also enables clearly identifying uncommon low-molecular-weight organogels G


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and opens new avenues for the exploration of chemical processes and structural changes occurring in the porous systems of framework materials.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.molpharmaceut.7b00167. Methodology, experimental, and computational details; cross-polarization build-up dependences; full-size spectra (PDF) Fully optimized model of trimer (PDB)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jiri Brus: 0000-0003-2692-612X Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Grant Agency of the Czech Republic (#GA 16-04109S) and the Ministry of Education, Youth and Sports of the CR within the National Sustainability Program I (NPU I), Project LO1507 POLYMAT, for their financial support. Computational resources were partially provided under the program LM2010005 and at the Centre CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, reg. no. CZ.1.05/ 3.2.00/08.0144.

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REFERENCES

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