Titanium dioxide has been identified as an important semiconductor metal oxide, which has different applications in many fields such as photo-catalysis , gas sensor devices, heterogeneous catalysis  and photovoltaic cells . 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.  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  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. 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.
Methods of computations
All of DFT calculations [30,31] have been performed using the Open source Package for Material eXplorer (OPENMX) version 3.7  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 . 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 . An efficient open-source program (XCrysDen), which is a crystalline and molecular structure visualization program  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  and reported by Wyckoff . 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. 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.