A First-Principles Study of the Interaction of Aspirin with Nitrogen-Doped TiO2 Anatase Nanoparticles

Document Type : Original Research Article

Authors

1 Molecular Simulation laboratory (MSL), Azarbaijan Shahid Madani University, Tabriz, Iran

2 Computational Nanomaterials Research Group (CNRG), Azarbaijan Shahid Madani University Tabriz, Iran

3 Department of Chemistry, Faculty of Basic Sciences, Azarbaijan Shahid Madani University Tabriz, Iran

Abstract

Objective(s): First-principles calculations have been carried out to investigate the interaction of aspirin molecule with nitrogen-doped TiO2 anatase nanoparticles using the density functional theory method in order to fully exploit the biosensing capabilities of TiO2 particles.
Methods:
For this purpose, we have mainly studied the adsorption of the aspirin molecule on the fivefold coordinated titanium atom site of the TiO2 nanoparticles because of the more reactivity of this site in comparison with the other sits. The complex systems consisting of the aspirin molecule positioned toward the undoped and nitrogen-doped nanoparticles have been relaxed geometrically.
Results: The obtained results include structural parameters such as bond lengths and energetic of the systems. The electronic structure and its variations resulting from the adsorption process, including the density of states, molecular orbitals and the Mulliken charge transfer analysis have been discussed. We found that the adsorption of aspirin molecule on the nitrogen-doped TiO2 nanoparticles is energetically more favorable than the adsorption on the undoped ones.

Conclusions: These results thus provide a theoretical basis and overall understanding on the interaction of TiO2 nanoparticles with aspirin molecule for applications in modeling of efficient nanomedicine carriers, biosensors and drug delivery purposes.

Keywords


INTRODUCTION

Titanium dioxide has been identified as an important semiconductor metal oxide, which has different applications in many fields such as photo-catalysis [1], gas sensor devices, heterogeneous catalysis [2] and photovoltaic cells [3]. This physically well-organized material has involved numerous academic and industrial attentions because of its exceptional properties such as lack of toxicity, chemical stability, large band-gap and so on. These unique properties make it possible the TiO2 could be considered as a fascinating material [4-8]. Many academics have investigated some of the important properties of TiO2 [8-15]. Anatase phase of TiO2 has a wide band-gap of 3.2eV, and can be utilized only for absorbing a few portion (3–5%) of the incoming solar irradiation. A convenient method to expand the photo-catalytic properties and adsorption abilities of TiO2 should satisfy the improvementson the behaviors of TiO2 and be utilized in wide range of investigations. Doping of TiO2 with some non-metal elements such as nitrogen is such a process, which has a reinforcing effect on the activities of TiO2 [16-19]. N-doped TiO2 anatase nanoparticles have been studied by numerous researchers over the past years. For example, Liu et al. [20] reported that the N-doped TiO2 anatase can adsorb NO molecules more strongly, compared to the undoped ones. Additionally, doping of TiO2 nanoparticles with nitrogen atom developed its electronic and structural properties and makes the TiO2 particle as an effective candidate to be utilized in gas sensor devices [20-25]. Nevertheless, the effects of N-doping on band structure of TiO2 anatase and the photo-catalytic activity have been investigated in some other works [26, 27]. For exhibiting the enhancements of the efficiency of TiO2 nanoparticles in the surface phenomena, some researchers have evaluated its electronic properties such as density of states (DOS), band structures and also its structural properties such as bond lengths and adsorption energies [14,19,28]. Density functional theory (DFT) is based not on the wavefunction, but rather on the electron density function, usually named the electron density or charge density, labelled by. This is a probability per unit volume; the probability of finding an electron in a volume element dxdydz. The electron density function is the basis not only of DFT, but of an entire set of methods of regarding and reviewing atoms and molecules, and, unlike the wavefunction, is measurable, e.g. by X-ray diffraction. The electronic density is a function of position only, that is, of just three variables (x, y, z). Today, DFT calculations on molecules are based on the Kohn–Sham approach, the stage for which was set by two theorems suggested by Hohenberg and Kohn. The first Hohenberg–Kohn [24] theorem says that all the properties of a molecule in a ground electronic state are calculated using the ground state electron density function. The second theorem declares that any trial electron density function will give energy higher than (or equal to, if it were exactly the true electron density function) the true ground state energy.

Aspirin or acetylsalicylic acid (ASA), is a medication, which has been utilized to treat pain, fever, and inflammation. Aspirin at lower doses has also been considered to help inhibit heart attacks and blood clotting in people who are of the subject of great risk of emerging blood clots.[29] Aspirin could be applied as an effective material in preventing certain types of cancer, particularly colorectal cancer. The stability of drugs in the presence of solid additives has attracted substantial consideration in the field of pharmaceutics. Aspirin is a drug that hydrolyses to salicylic acid and acetic acid in the vicinity of moist media or water. In this research, the interaction of aspirin molecule with N-doped TiO2 anatase nanoparticles was investigated using the DFT computations. The electronic and structural properties of the considered non-adsorbed and adsorbed structures and the adsorption energies in adsorbed complexes were computed and analyzed. Moreover, the effects of doping of nitrogen on total density of states (DOS) and band structure of TiO2 were investigated in detail.

 

COMPUTATIONAL DETAILS

Methods of computations

All of DFT calculations [30,31] have been performed using the Open source Package for Material eXplorer (OPENMX) version 3.7 [32] which has been verified to be a well-organized package for simulation of large atomic systems, specially solid state substrates. The same outer electrons of Ti atom were considered as valence electrons in the self-consistent field iteration. Pseudo atomic orbitals (PAO's) centered on atomic sites have been used as basis sets in order to expand the wave functions in a KS schema with a cutoff energy of 150 Ry (Rydberg) [32, 33]. Pseudo atomic orbitals were generated via the basis sets (two-s, two-p, one-d) for Ti atom, two-s and two-p for O, N and C atoms and two-s for H atom according to the cutoff radii set to the values of 7 for Ti, 5.5 for H, 5 for O and N and 4.5 for C (all in Bohrs) in generation by a confinement scheme. The cutoff radius (a.u.) is an important parameter for the generation of pseudopotentials. Although an optimum cutoff radius is determined so that the generated pseudopotentials has a smooth shape without distinct kinks and a lot of nodes, however, the selection includes somewhat an empirical factor. The accuracy and efficiency of the calculations can be controlled by two parameters: a cutoff radius and the number of basis functions. In general, one can get the convergent results by increasing the cutoff radius and the number of basis functions. However, it is noted that the use of a large number of basis orbitals with a large cutoff radius requires an extensive computational resource such as memory size and computational time [33]. The generalized gradient approximation functional (GGA) in the Pedrew-Burke-Ernzerhof (PBE) form, which treat the exchange correlation in an approximate manner was used in the calculations [34]. An efficient open-source program (XCrysDen), which is a crystalline and molecular structure visualization program [35] was utilized in display of isosurfaces such as molecular orbitals, contours and other Figures present in this study. The adsorption energy was calculated via the following formula:

Ead = E (particle + drug) - E particle – E drug                                                    (1)

Where E( particle + drug ), E particle and E drug are the energies of the complex system, the free TiO2 nanoparticle without any adsorbed molecule and the free aspirin molecule in an non-adsorbed state respectively. The more negative the Ead is, the more energy favorable the adsorbed structure is.

 

Models of nanoparticles

          The studied TiO2 anatase nanoparticles were modeled via setting a 3×2×1 supercell of TiO2 anatase along x, y and z axis, respectively. The constructed supercell has been shown in Fig 1. The unit cell was taken from "American Mineralogists Database" webpage [36] and reported by Wyckoff [37]. The schematic geometric structure of TiO2 anatase has been displayed in Fig 2. N-doped TiO2 anatase nanoparticles were constructed by replacement of two surface oxygen atoms by nitrogen atoms. The substitution of oxygen atom by nitrogen atom in the TiO2 nanoparticle leads to the introducing of a hole in the particle. The generated empty state (hole) can be observed either on the top of the valence band or mixed inside the band gap of TiO2[20]. In one doping configuration, a nitrogen atom substitute an oxygen atom in the middle (3f-O substitution site) of the particle and the other is a nitrogen atom substitute an oxygen atom at 2f-O position. The chosen N-doped nanoparticles were separately optimized to obtain the energy minimized and stable structures for studying the adsorption behaviors of complex systems. The substituted oxygen atoms were found that to be of great importance in calculating and obtaining the optimum parameters of TiO2. The reason is that the crystal structure of TiO2 anatase includes two types of oxygen atoms (twofold coordinated oxygen atom, 2f-O, and threefold coordinated oxygen or middle oxygen, 3f-O) and the modification of TiO2 nanoparticle through substituting these representative oxygen atoms by other atoms has a significant effect on the structural and energetic properties of TiO2. These effects also comprise the variations in the electronic DOS or appearing and changing of some new bands in the electronic band structure. The aspirin adsorbed complexes were made by the help of the geometrically optimized N-doped nanoparticles. N-doped nanoparticles were displayed in Fig. 3 from the front view. We investigated the adsorption on the active fivefold coordinated titanium sites of the considered TiO2 anatase nanoparticles due to their relatively high activity in adsorption process in comparison with the other oxygens. Moreover, the structure of aspirin molecule has been illustrated before the adsorption (Fig. 4).

 RESULTS AND DISCUSSION

Bond lengths and bond angles

Studied formaldehyde molecule has been adsorbed on the fivefold coordinated titanium site of TiO2 from two orientations relative to TiO2 nanoparticles. In one orientation, aspirin's oxygen was laid toward the nanoparticle in parallel orientation (orientation 1) and in other it was located perpendicularly with respect to the nanoparticle resulting in the adsorption on the nanoparticle with slightly distortion but with the same orientation (orientation 2). Theses interactions both include N-doped nanoparticles in the middle oxygen position and N-doped ones in the twofold coordinated oxygen atom sites. Fig 5 represents the considered TiO2-aspirin complexes in parallel configuration optimized using the DFT method. This Figure includes the aspirin-adsorbed complexes named A to C for the adsorption in the parallel configuration. Each complex of Fig 5 differs in substituted oxygen atom of TiO2 nanoparticle and/or adsorbed aspirin positioning from the others. For instance, complex A was made from OC-substituted TiO2 nanoparticle and aspirin molecule with parallel arrangement towards the nanoparticle (orientation 1). The undoped TiO2 interacts with aspirin molecule in both configurations. The optimization of the complexes formed from the aspirin orientation with carbon atom towards the nanoparticle leads to the complexes with lower degree of stability and favorability. Then, the most favorable configurations (namely parallel and perpendicular) have been studied in this work. Fig 6 also presents three configurations for perpendicular adsorptions of aspirin on the nanoparticle, which have been denoted by D to F complex types. It has been found that the perpendicular interaction of aspirin with nanoparticles results in the most stable configurations, compared to the parallel orientation of aspirin. The optimized values of some bond lengths before and after the adsorption on the nanoparticle have been listed in table 1. The bond lengths given in this table are included Ti-O bond of TiO2 nanoparticle, nearest C-O bond of aspirin molecule and newly-formed Ti-O bond between titanium atom nanoparticle and nearest oxygen atom of aspirin. The results of this table show that the Ti-O bond and C-O bond of aspirin molecule are stretched after the adsorption process. These variations of the bond lengths are mostly due to the transfer of electronic density from Ti-O bond of TiO2 and C-O bond of the adsorbed aspirin molecule to the newly formed Ti-O bond at the interface of aspirin molecule and TiO2 anatase nanoparticle. Therefore, the C-O bond of the aspirin molecule is weakened after the adsorption. The smaller the bond formed between the oxygen atom of aspirin molecule and the fivefold coordinated titanium atom of nanoparticle (Ti-O), the more powerful the adsorption of aspirin on TiO2 anatase nanoparticle. As can be seen from Table 1, although the configuration B has the smaller newly formed Ti-O bond length than the configuration A (2.14 Ǻ versus 2.20 Ǻ), it has the higher adsorption energy than the configuration A (-3.53 eV versus -3.45eV). Since higher adsorption energy gives rise to a strong binding between adsorbate and the nanoparticle, we can see that there is a stronger interaction between aspirin and TiO2 nanoparticle in configuration B compared to the interaction in configuration A. Also the adsorption energy of configuration D is higher than that of configuration E (while configuration D has the lower Ti-O bond length than the configuration E), which indicates a strong interaction between aspirin and nanoparticle in configuration D. On the other hand, lower Ti-O distance in configuration B in comparison with configuration A corresponds to the higher value of Mulliken charge transferred from TiO2 to aspirin. This increasing of the charge transfer could be a useful feature for sensing of aspirin molecule by TiO2 nanoparticle.

 

Adsorption Energies

The adsorption energies for the undoped and N-doped TiO2 anatase nanoparticles have been tabulated as table 1 as the Eads reported results.These results show that the adsorption of aspirin molecule on the N-doped nanoparticle is energetically more favorable than the adsorption on the pristine one. It means that the N-doped nanoparticle interacts with aspirin molecule more effectively in comparison with the undoped one. In both adsorption configurations, the N-doped complexes have been clarified as the most stable ones from the energetics point of view. For parallel configuration, the calculated adsorption energy of complex B is more negative (higher) than that of complex A, suggesting the more stability of this complex. The calculated adsorption energy of complex D in perpendicular configuration is higher than that of complex E, which indicates that the complex D interacts with the molecule strongly.. These results indicate that the N-doping could strengthen the interaction of aspirin over the TiO2 anatase nanoparticles. The improvement of both adsorption energy and structural properties of the adsorption of aspirin on TiO2 nanoparticles resulted by N-doping proposes us that the TiO2 can be used for sensing of aspirin molecule. The increasing of efficiency of the TiO2 nanoparticles by the doping of nitrogen atom is an effective property to help in the development of more efficient and consequently more demanding biosensors for aspirin detection.

 

Electronic structures

Fig. 7 displays the total density of states (TDOS) for the interaction of pristine and the N-doped anatase TiO2 particles with aspirin molecule in both configurations before and after the adsorption process. The biggest difference is the creation a small peak in the DOS of N-doped TiO2 at the energy values close to -12 eV. Fig.7 also presents a comparison of the DOS of N-doped particles (panels’ a-f) before and after the adsorption for clear comparison. These panels show that the DOSs of N-doped particles before and after the adsorption have small differences with each other. The whole DOSs of studied systems show that the differences between DOS of doped and undoped TiO2 are increased by adsorption of CH2O. These variations are comprised both growing shift of energies of peaks and formation of some peaks in the DOS of the pristine TiO2. These impacts are also included of small shifts in energies of the states and generating some small peaks at energies between -5 to -15 eV. A closer inspection of this Figure reveals that the adsorption process changes the energies of the states and the density of the states. So, these changes in energy gap of DOS would affect the electronic transport properties of the nanoparticles and this feature can be beneficial for sensing of aspirin by TiO2 nanoparticles. The projected density of states (PDOSs) and key molecular orbitals (HOMOs, LUMOs) were computed to additional analysis the aspirin adsorption on TiO2 nanoparticles. The titanium and oxygen projected DOSs (Ti-PDOS and O-PDOS) after the adsorption were shown in Fig. 8 as panels (a-c for parallel configuration) and (d-f for perpendicular configuration) respectively. These panels indicate the bond formation between the titanium atom of nanoparticle and oxygen atom during the adsorption process. The large overlap between the PDOS of these two atoms is a good electronic reason which could take into account for the formation of chemical bond. It means that the aspirin molecule is chemisorbed on the nanoparticle in most stable configurations. Fig. 9 has been contained the isosurfaces of HOMO and LUMO molecular orbitals of the isolated non-adsorbed aspirin molecule respectively. The isosurfaces of molecular orbitals for TiO2/aspirin complexes have been also shown for two complexes of both parallel and perpendicular configurations (Figs 10 and 11). These Figures show that the HOMO's and LUMO's are mainly localized on the TiO2 nanoparticle and the aspirin molecule describes a negligible state of localization. We have also investigated the band structures for pristine and N-doped TiO2 anatase. The computed band structures are represented as Fig. 12 (Top and Down) for pristine and N-doped TiO2 respectively. One can see from Fig. 12 that the valence band of pristine TiO2 mainly includes the 2p states of oxygen while the conduction band mainly consists of 3d states of titanium. Band structures for the considered N-doped TiO2 contained an impurity state as the 2p states of nitrogen inside the band-gap, and the valence band consists of the mixed 2p states of oxygen and 2p states of nitrogen while the conduction band was mainly composed of 3d states of titanium 26. Due to the interaction between nitrogen’s 2p and titanium’s 3d states, electrons of the nitrogen’s 2p states would be transferred to the conduction band more easily in comparison to the pristine TiO2. In addition, the increasing the rate of the electron transfer from the valence band to the conduction band extends photo-catalytic activity of the N-doped TiO2 to the low-energy region, again, in comparison with the undoped one [21, 23]. Further analysis of the band structures and total density of states shows that the band-gap for N-doped TiO2 at Γ point is much narrower than that of undoped one. It is probably due to the mixing of nitrogen’s 2p states with oxygen’s 2p states in the N-doped TiO2.

Charge transfer analysis

To further explain the charge transfer between aspirin molecule and TiO2 nanoparticle, we report in table 1 the charge analysis based on Mulliken charges. The charge difference for the particle j after and before adsorption was calculated using the following equation:

∆Qj = Qj (in complex) – Qj (in vacuum)                                                               (2)

Where Qj is the value of Mulliken charge of the j. Subscript "j" signifies the TiO2 nanoparticle or aspirin molecule. The charge difference, ∆Qj, is a measure of the amount of charge transferred to, or, from the studied nanoparticles from, or, to the aspirin molecule. For example, the computed charge value for TiO2 nanoparticle in configuration A is about +0.48 e and that of aspirinmolecule is -0.48 e. This means that TiO2 nanoparticle acts as an electron donor to aspirin molecule. In other words, aspirin molecule accepts electrons from TiO2. This could be an effective property to help in the designation and improvement of TiO2-based biosensors for aspirin recognition.

 

CONCLUSIONS

We studied the adsorption energy and geometry configurations of aspirin on the fivefold coordinated titanium atom of undoped and two types of N-doped TiO2 anatase nanoparticles using first-principles DFT calculations. The results indicate that the interaction of aspirin molecule with nanoparticles causes the stretching of the Ti-O bond of TiO2, as well as C-O bond of aspirin, leading to the bond lengths of aspirin molecule getting smaller. Analyzing of the adsorption energies shows that the N-doped nanoparticles have a higher efficiency to interact with aspirin molecule, compared to the pristine TiO2. The density of states for pristine and N-doped TiO2 have been also presented before and after adsorption and the effect of adsorption of aspirin on these properties have been discussed and it was suggested that TiO2 can be used for sensing of aspirin. The interaction of aspirin over the N-doped nanoparticles is energetically more favorable than the interaction over the undoped ones. The band structure calculations suggest that the band gap of N-doped TiO2 is narrower than that of pristine one, resulting in the improvements on the capabilities of TiO2. Based on the obtained results, it can be inferred that the N-doped nanoparticles have higher adsorption ability than the undoped ones.

 

ACKNOWLEDEMENT

This work has been supported by Azarbaijan Shahid Madani University.

 

 

1. Linsebigler AL, Lu G, Yates Jr JT. Photocatalysis on TiO2 surfaces: principles, mechanisms, and selected results. Chem Rev. 1995;95(3):735-58.
2. Diebold U. The surface science of titanium dioxide. Surface science reports. 2003;48(5):53-229.
3. Fujishima A, Zhang X, Tryk DA. TiO2 photocatalysis and related surface phenomena. Surf Sci Rep. 2008;63(12):515-82.
4. Henderson MA. A surface science perspective on photocatalysis. Surf Sci Rep. 2011;66(6):185-297.
5. Banfield JF, Veblen DR. Conversion of perovskite to anatase and TiO2 (B): A TEM study and the use of fundamental building blocks for understanding relationships among the TiO2 minerals. Am Mineral. 1992;77(5-6):545-57.
6. Grätzel M. Photoelectrochemical cells. Nature. 2001;414(6861):338-44.
7. Fujishima A. Electrochemical photolysis of water at a semiconductor electrode. Nature. 1972;238:37-8.
8. Dutta PK, Ginwalla A, Hogg B, Patton BR, Chwieroth B, Liang Z, et al. Interaction of carbon monoxide with anatase surfaces at high temperatures: optimization of a carbon monoxide sensor. J Phys Chem B. 1999;103(21):4412-22.
9. Garfunkel E, Gusev E, editors. Fundamental Aspects of Ultrathin Dielectrics on Si-based Devices. Netherlands: Springer Science & Business Media; 2012.
10.Liu H, Zhao M, Lei Y, Pan C, Xiao W. Formaldehyde on TiO2 anatase (101): A DFT study. Comput Mater Sci. 2012;51(1):389-95.
11.Erdogan R, Ozbek O, Onal I. A periodic DFT study of water and ammonia adsorption on anatase TiO2 (001) slab. Surf Sci. 2010;604(11):1029-33.
12.Onal I, Soyer S, Senkan S. Adsorption of water and ammonia on TiO2-anatase cluster models. Surf Sci. 2006;600(12):2457-69.
13.Wei Z, Mei W, Xiyu S, Yachao W, Zhenyong L. Electronic and optical properties of the doped TiO2 system. J Semicond. 2010;31(7):072001.
14.Liu J, Dong L, Guo W, Liang T, Lai W. CO adsorption and oxidation on N-doped TiO2 nanoparticles. J Phys Chem C. 2013;117(25):13037-44.
15.Zhao D, Huang X, Tian B, Zhou S, Li Y, Du Z. The effect of electronegative difference on the electronic structure and visible light photocatalytic activity of N-doped anatase TiO2 by first-principles calculations. Appl Phys Lett. 2011;98(16):162107.
16.Tang S, Cao Z. Adsorption of nitrogen oxides on graphene and graphene oxides: insights from density functional calculations. J Chem Phys. 2011;134(4):044710.
17.Rumaiz AK, Woicik JC, Cockayne E, Lin HY, Jaffari GH, Shah SI. Oxygen vacancies in N doped anatase TiO2: Experiment and first-principles calculations. Appl Phys Lett. 2009;95(26):262111.18.Chen Q, Tang C, Zheng G. First-principles study of TiO2 anatase (101) surfaces doped with N. Physica B Condens Matter. 2009;404(8):1074-8.
19.Jia L, Wu C, Li Y, Han S, Li Z, Chi B, et al. Enhanced visible-light photocatalytic activity of anatase TiO2 through N and S codoping. Appl Phys Lett. 2011;98(21):211903.
20.Liu J, Liu Q, Fang P, Pan C, Xiao W. First principles study of the adsorption of a NO molecule on N-doped anatase nanoparticles. Appl Surf Sci. 2012;258(20):8312-8.
21.Li Y-F, Aschauer U, Chen J, Selloni A. Adsorption and reactions of O2 on anatase TiO2. Acc Chem Res. 2014;47(11):3361-8.
22.Berger T, Sterrer M, Diwald O, Knözinger E, Panayotov D, Thompson TL, et al. Light-induced charge separation in anatase TiO2 particles. J Phys Chem B. 2005;109(13):6061-8.
23.Mirzaei M, Ahadi H, Shariaty-Niassar M, Akbari M. Fabrication and Characterization of Visible Light active Fe-TiO2 Nanocomposites as Nanophotocatalyst. Int J Nanosci Nanotechnol. 2015;11(4):289-93.
24.Zarei H, Zeinali M, Ghourchian H, Eskandari K. Gold nano-particles as electrochemical signal amplifier for immune-reaction monitoring. Int J Nano Dimens. 2013;4(1):69.
25.Zuas O, Budiman H, Hamim N. Anatase TiO2 and mixed M-Anatase TiO2 (M= CeO2 or ZrO2) nano powder: Synthesis and characterization. Int J Nano Dimens. 2013;4(1):7.
26.Otoufi M, Shahtahmasebebi N, Kompany A, Goharshadi E. A systematic growth of Gold nanoseeds on Silica for Silica@ Gold core-shell nanoparticles and investigation of optical properties. Int J Nano Dimens. 2014;5(6):525.
27.Rastkar Ebrahimzadeh A, Abbasi M, Jahanbin Sardroodi J, Afshari S. Density functional theory study of the adsorption of NO2 molecule on Nitrogen-doped TiO2 anatase nanoparticles. Int J Nano Dimens. 2014;6:11-7.
28.Sardroodi JJ, Afshari S, Ebrahimzadeh AR, Abbasi M. Theoretical computation of the quantum transport of zigzag mono-layer Graphenes with various z-direction widths Int J Nano Dimens. 2015;6(1):105.
29.Abbasi A, Nadimi E, Plänitz P, Radehaus C. Density functional study of the adsorption of aspirin on the hydroxylated (001) α-quartz surface. Surf Sci. 2009;603(16):2502-6.
30.Hohenberg P, Kohn W. Inhomogeneous electron gas. Physical review. 1964;136(3B):B864.
31.Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. PhysRev. 1965;140(4A):A1133.
32.Ozaki T, Kino H, Yu J, Han MJ, Kobayashi N, Ohfuti M et al (2011) The code, OpenMX, pseudo-atomic basis functions, and pseudopotentials is available as user manual on a web site: http://www.openmx-square.org/
33.Ozaki T. Variationally optimized atomic orbitals for large-scale electronic structures. Phys Rev B. 2003;67(15):155108.
34.Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev lett. 1996;77(18):3865.
35.Kokalj A. Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale. Comput Mater Sci. 2003;28(2):155-68.
36. Available from: http://rruff.geo.arizona.edu/AMS/amcsd.php.
37.Wyckoff RWG, Wyckoff RW. Crystal structures: Interscience New York; 1960.