QUANTUM-CHEMICALLY COMPUTED INTEGRAL CHARACTERISTICS OF COMPLEX NANOMATERIALS

Development of theoretical tools to analyze electronic structure of complex nanomaterials depending on features of spatial and chemical organizations of different phases is of interest from both practical and theoretical points of view. Therefore, in this work, an approach based on computations of the atomic charge distribution functions (CDF) in parallel to calculations of the distribution functions of the chemical shifts (SDF) of protons is developed to be applied to a set of complex oxide and carbon nanomaterials. Binary nanooxides (alumina/silica, titania/silica), 3d-metal-doped anatase, activated carbon, carbon nanotube, fullerene C 60 , graphene oxide, and N-doped Kagome graphene are considered here as representatives of different classes of nanomaterials. The analyses of the CDF and SDF as nonlocal characteristics of certain kinds of atoms in complex systems provide a deeper insight into electronic structure features depending on composition of the materials, guest phase-doped host phase at various amounts of dopants, structure of O- and OH-containing surface sites, amounts and organization of adsorbed water, formation of neutral and charged surface functionalities, bonding of solvated ions, etc. The CDF of metal and hydrogen atoms (electron-donors) are more sensitive to the mentioned factors than the CDF of O, N, and C atoms (electron acceptors) in various systems. As a whole, the use of the CDF and SDF in parallel expands the tool possibility in detailed analysis of the structural and interfacial effects in dried and wetted complex nanomaterials.

There are several aspects related to the models and methods used in quantum chemical modeling of complex materials [18][19][20][21][22]. First, it is of importance to select methods (ab initio, density functional theory (DFT), semiempirical, etc.) appropriate to solve the tasks. Second, the use of adequate basis sets (narrow or extended, optimal, maximum appropriate), correct account of electron correlation and exchange (perturbation theory in ab initio, various functionals in DFT, additional tools), as well as corrections on the basis set superposition errors (BSSE), temperature, zero-point energy, and vibrations are quite important. Third, accurate selection of appropriate models (clusters, nanoparticles, primitive or expanded cells used with periodic boundary conditions (PBC), etc.) is necessary. Additionally, taking into account solvation, kinetic and dynamic aspects and some others could be important on the analyses of the phenomena occurring at a surface of complex nanostructured systems under various conditions [18][19][20][21][22]. Therefore, in the present work, several aspects related mainly to the sizes of particulate models, their phase compositions, structure of the host and gest phases, bound water effects, as well as the types of the materials (e.g., metal and metalloid oxides, various carbons) are analyzed. It has been done using ab initio (6-31G(d,p) and DGDZVP basis sets), DFT (functional ωB97XD with the ccpVDZ basis set) [23][24][25]. Some calculations have been performed using a solvation model with the SMD method [26] and gauge-including-atomic-orbital (GIAO) method [27,28] to compute 1 H NMR spectra. Semiempirical PM7 and PM6 methods [29,30] have been applied to large models.

CALCULATION METHODS
Individual materials (oxide and carbon nanoparticles) and complex models hydrated by water clusters or interfacial water layer located at a solid surface are analyzed using the Gaussian 09 [27], GAMESS 2020 R2 [28], and MOPAC 2016 [29,30] program suits. The DFT calculations have been done using a hybrid functional ωB97XD with the ccpVDZ basis set. The GIAO method (with DFT) has been used to compute the chemical shifts of the proton resonance ( H ) [27,28]. The solvation effects have been analyzed with the SMD method [26][27][28] implemented in the Gaussian and GAMESS program suits. The calculations have been carried out taking into account zero-point and thermal corrections to the Gibbs free energy in the gas phase and for solvated molecules and solids clusters using the geometry optimized with ωB97XD/ccpVDZ (with or without SMD). Note that ωB97XD introduces empirical damped atom-pairwise dispersion terms into the functional containing range-separated Hartree-Fock (HF) exchange for better description of vander-Waals interactions [24,25]. Therefore, ωB97XD has been selected to obtain more adequate results for the gas and liquid phases interacting with nanoparticles. The distribution functions of various parameters have been calculated with a simple equation [31][32][33][34] where j is the number of a certain type (n) of atoms,  2 is the distribution dispersion, and X j is atoms [34]. To decrease small details (e.g., small excess peaks) in the distribution functions, the distribution dispersion could be increased, e.g., up to the values corresponding to experimental peaks (i.e., full width at the half-height, FWHH) [10,35]. , graphene oxide (GO), fullerene C 60 (fullerite), and nitrogen-doped Kagome graphene (NKG)) are modelled using the PM7 and PM6 methods. Note that NKG was recently described in detail [36].

RESULTS AND DISCUSSION
Practically in all the models of complex nanooxides calculated using the ab initio and DFT methods with different basis sets, the CDF demonstrate significant changes in peak positions and band width due to doping of the main (host) phase (SiO 2 or TiO 2 ) by various metal (Al, Ti  (Fig. 7), the CDF strongly differ in the shape and peak positions in comparison to nanooxides due to lower polarity of the skeletal bonds in carbon materials, which are, therefore, mainly hydrophobic (especially, nonfunctionalized carbons). Therefore, for all the carbons modelled, the q C CDF are located around q C = 0. However, for all atoms in oxides, the CDF are located far from q = 0 at q > 0 (metals, H) or q < 0 (oxygen).
In the anatase clusters (22 units with ten surface hydroxyls) doped by silica, the bond polarity decreases with increasing number of the Si atoms. There is a tendency of a decrease in the atomic charges of Ti (Fig. 1 c) and Si ( Fig. 1 d), as well as in excess electron density located on the O atoms ( Fig. 1 b), with decreasing Ti/Si ratio. For the H atoms, there is the opposite tendency with increasing charges upon decreasing Ti/Si (Fig. 1 a). This is typical for the Brønsted acidity of complex oxides vs. their composition. Note that the q H CDF shape changes with doping. The H atoms with maximal charges of 0.42-0.44 a.u. are absent in the doped clusters, but the main peak of q Ti CDF for the former is located at minimal q Ti values ( Fig. 1 a, curve 1). This is in agreement with increasing Brønsted acidity of the bridging hydroxyls SiO(H)Ti in comparison to the hydroxyls in the individual silica and titania phases. Note that the Brønsted acidity of SiO(H)Al is greater than that of SiO(H)Ti ( Fig. 2 a) due to a lower number of valence electrons in Al than in Ti. Not only the Ti/Si or Al/Si ratio affects the surface hydroxyl acidity but also solvation evaluated using the supercluster approach or SMD method. It enhances the OH bond polarity and possibility of the appearance of mobile protons forming Eigen (H 3 O + ) (q H  0.32 a.u. in Fig. 2 a) or Zundel (H 5 O 2 + ) cations. Enhancement of this effect due to the surroundings for the Si, Al, and Ti atoms in larger clusters (as well as due to solvation) causes broadening of the CDF peaks (Fig. 2 c, d). All these changes affect the properties of complex nanooxides in heterogeneous acid-base reactions, in which Brønsted and Lewis acid and base sites can play the main role. Not only particle compositions (e.g., Al/Si or Ti/Si ratio) but also particle sizes and shapes can affect the characteristics of active surface sites taking part in the adsorption of reagents with subsequent catalysis of various chemical transformation.
Anatase as a photocatalyst is active in redox reactions. However, its bandgap (E g ) is relatively large (E g  3.2 eV corresponding to ultraviolet light). Therefore, it cannot be used upon activation by visible light. To improve titania as a photocatalyst, it is doped by various dopants (metals and nonmetals) to provide E g < 2-3 eV. The effects of dopants of several types on the CDF are analyzed here (Figs. 3-6). Note that the effects on the bandgap were previously studied using quantum chemical methods and various approaches (e.g., cluster or PBC), but the CDF were not yet computed for similar complex systems [34,37]. Besides the appearance of excess electrons or holes, additional polarization of the oxygen-metal bonds can affect the band gap. The appearance of excess electron density caused by weakly bound electrons (number of valence electron in dopant metal atoms n X > 4 = n Ti ) characterized by energy levels located higher than the top of the upper valence band of a pure host phase, as well as the holes (n X < 4, located lower the conductive band bottom). In the electron-hole subsystem for the host/guest phases or for dopants embedded into the host phase and characterized by larger or smaller numbers of valence electrons than metal in a host phase (e.g., Ti), their behavior may reflect in changes in the CDF (Figs. 3-6). The computing results show that the atomic charge distribution functions depend on the ratio of the guest/host phases and a kind of metal atoms (i.e., metal oxide) embedded into a host phase. Typically, the positive effects (i.e., diminution of the E g value) are observed for a small guest/host ratio (not greater than several atomic percent without formation of individual guest phase) [38][39][40][41][42][43][44]. Note that the CDF of metals in doped titania are more sensitive (and more important) to the mentioned ratio than that of other atoms (H and O). This is well visible on the 3D CDF surfaces for Fedoped anatase (Fig. 6), since for the H and O atoms these functions are characterized by relatively smooth surfaces (Fig. 6 c, d) in contrast to that for the Fe and Ti atoms (Fig. 6 a, b). At small changes in the X/Ti ratio (e.g., 2/20 and 3/19 for Sn/Ti, Fig. 5), the changes in the CDF for Sn and Ti are better visible than that for H and O. At relatively large X/Ti values (Figs. 3, 4, and 6), this tendency remains; however, changes in the H and O CDF become well visible, but the position of their main CDF peaks does not practically change.
The structural effects in carbon nanomaterials on the atomic charge distribution functions of the C, H, O, and N atoms are well visible (Fig. 7) for activated carbon (Fig. 7 a), capped carbon nanotube (Fig. 7 b), graphene oxide (GO) with two layers with bound water (Fig. 7 c) or single layer GO, wetted fullerite with fullerene C 60 (Fig. 7 a, e) and nitrogen-doped Kagome graphene (NKG) (Fig. 7 d). Note that NKG with an open-work structure [36] remains plane upon the geometry optimization with the PM7 method (Fig. 7 d, insert). The behavior of the C CDF for pure or modified or functionalized carbon materials is characterized by a location of the main peak around q C = 0 (Fig. 7). Oxidizing or doping (e.g., by N or O) of carbons may lead to broadening or even splitting of the C CDF [45]. This corresponds to a decrease in the hydrophobicity of modified and functionalized carbons. There is an effect of 5-member rings in C 60 and CNT resulting in broadening of the C CDF in comparison to graphite.
The effects of bound water (as real clusters or solvation shells or in the SMD model) lead to additional polarization of the O-H bonds in surface hydroxyls and bound water molecules, especially located in the first adsorption layer, that even may lead to generation of the Eigen and Zundel cations (Figs. 8 and 9). An increase in the number of bound water molecules leads to the stabilization of these cations and a certain downfield shift in the 1 H NMR peak at  H = 15-16 ppm (Fig. 8, Eigen cation).  (Fig. 8), however, the  H value is slightly greater (16.1 ppm) for the Eigen cation bound to Al 2 O 3 /SiO 2 (Fig. 8 a, curve 7) than  H = 15.4 ppm for TiO 2 /SiO 2 (Fig. 8 b, curve 2). Appearing of water bound to -Al 2 O 3 nanoparticle results in a significant downfield shift of the 1 H NMR lines of the OH groups (Fig. 8 a, curves 1 and 2). However, the acidity of surface sites and polarized hydroxyls is greater for alumina/silica, AS (Figs. 8 and 9) than for pure alumina (Fig. 8 a,   curves 1 and 2). Greater values of  H are observed for bound water (molecules directly interacting with surface sites, Fig. 9, curves 3 and 4) than that for surface hydroxyls (curves 5 and 6). The use of the SMD method (with water as a solvent) results in insignificant changes in the 1 H NMR spectra of bound water and surface hydroxyls (Figs. 8 and  9). These changes are greater at a smaller number of water molecules bound to oxide nanoparticles since a relative number of the H atoms with the hydrogen bonds is smaller than at a larger number of bound water molecules.