Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices

Accepted Manuscript Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices T.G. Díaz Rodríguez, J.A. Reyes Nava, M. Pacio, H. Juárez, Jesús Muñiz PII: DOI: Reference:

S2210-271X(16)30499-6 http://dx.doi.org/10.1016/j.comptc.2016.12.013 COMPTC 2330

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Computational & Theoretical Chemistry

Please cite this article as: T.G. Díaz Rodríguez, J.A. Reyes Nava, M. Pacio, H. Juárez, J. Muñiz, Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices, Computational & Theoretical Chemistry (2016), doi: http://dx.doi.org/10.1016/j.comptc.2016.12.013

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Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices T. G. D´ıaz Rodr´ıgueza , J. A. Reyes Navab , M. Pacioa , H. Ju´areza , Jes´ us c,d Mu˜ niz a

Centro de Investigaci´ on en Dispositivos Semiconductores, Benem´erita Universidad Aut´ onoma de Puebla, 4 Sur Num. 104 Col. Centro C.P. 72000, Mexico b Facultad de Ingenier´ıa, Universidad de Ciencias y Artes de Chiapas, 1ra Sur Poniente 1460, Centro, 29000 Tuxtla Guti´errez, Chiapas, Mexico c Instituto de Energ´ıas Renovables, Universidad Nacional Aut´ onoma de M´exico, Priv. Xochicalco s/n, Col. Centro, Temixco, Morelos. CP 62580, Mexico d CONACYT-Universidad Nacional Aut´ onoma de M´exico, Priv. Xochicalco s/n, Col. Centro, Temixco, Morelos. CP 62580, Mexico

Abstract A theoretical study was carried out for the first time in a series of two nanocomposite semiconducting systems (PbS)4 @(TiO2 )38 . We stabilized two structures of TiO2 using a simulated annealing procedure with Molecular Dynamics as a first approach and the second model was optimized at the PBE level of theory, as benchmarking. An amorphous and anatase structures were found for both methodologies, respectively. We adopted the cubic structure of the (PbS)4 quantum dot as suggested by experimental data. The DOS of the isolated systems were assessed and also those of the composites (PbS)4 @(TiO2 )38 . Adsorption energies on both systems were estimated and an attraction with a certain degree of covalency was found for the (PbS)4 at the TiO2 anatase model system. A weaker interaction of the electrostatic-

Preprint submitted to Comp. Theor. Chem.

December 7, 2016

type was found with the TiO2 amorphous configuration. In both systems, the attraction is favored in S-Ti bond pairs. The DOS for the composite sytems presents a different nature for the amorphous and anatase cases that is evidenced in the size of the band gaps. The (PbS)4 @(TiO2 )38 anatase composite systems results in a more favorable electronic structure that may readily provide fundamental data to develop and design photocatalytic devices for hydrogen production, energy storage and photovoltaic applications. Keywords: Renewable energy, Molecular Dynamics, DFT, Quantum Dot, PbS@TiO2 , Energy storage 1. Introduction TiO2 is an active semiconductor used in photocatalysis, solar cells devices[1, 2, 3] and energy storage applications[4]. It is efficient adsorbing UV radiation, but it only harnesses 4% of the total irradiated sunlight[5]. For this reason, recents efforts have focused to design semiconductor nanostructures with the aim to approach tunable response to visible and infrared light. In the last decades, metal oxides such as TiO2 and metal calcogenides Quantum Dots (CdS, CdSe, PbSe and PbS), also known as QDs have been the subject of intensive research, suggesting that it is possible to tune the band gap for hybrid systems (QDs@TiO2 )[6, 7] due to size effects and electronic structure modification[8]. Photocatalytic studies concentrate on the net photoconversion efficiency with the goal to understand the several electron-transfer steps

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at the fundamental level. Recently, Trevisant et al[6] developed a device for H generation by using a QD based heterostructure. Mesoporous TiO2 electrodes were synthesized with in situ deposited PbS/CdS QDs in order to harvest light in both, the visible and the near-infrared for hydrogen generation. The heterostructure presents a remarkable photocurrent of 6mA/cm2 , leading to 60 mL/(cm2 day) of hydrogen generation. Furthermore, the conformation of infrared photons to H2 generation is confirmed in this work. On the other hand, previous studies have shown that small semiconductor TiO2 and PbS nanoparticles present different optical and electronic properties. For instance, Lundqvist et al [9] performed an exhaustive DFT study at the B3LYP and PW levels, on a series of (TiO2 )n cluster models, where n=1-68 and with no periodic conditions. It was found that the band gap for these systems is highly sensitive to the implemented functional and basis set. Band gaps ranging from 3.37 to 6.00 eV were found. This discrepancy is essentially attributed to the size of the TiO2 cluster model used in the calculations. The larger model systems present a nanocrystal-like character with a defect-free band gap; i.e., the rising of trapped states between a completely filled valence band and a completely empty conduction band. Furthermore, Auvinen et al [10] used DFT at the PBE level with periodic conditions to simulate a series of (TiO2 )n models, with n=1,2,8,18,28 and 38. Band gaps ranging from 0.37 to 2.86 eV were found in the series of model systems, while in the calculations for the anatase and rutile structures, band gaps of 2.12 and 1.75 eV were obtained, respectively. In the case of the model systems, 3

the larger band gaps correspond to the smallest particles. This behavior was assigned to the transformation of the electron structure and breaking of the crystal symmetry as the size of the particle is reduced[10]. Kim et al[11] showed that the impact of PbS QD stoichiometry on the electronic structure may be significant, and suggested that control on the overall stoichiometry in the QD may play a critical role for improving the efficiency of optoelectronic devices based on PbS QDs. Particularly, it was found that for bare PbS QDs: (i) stoichiometric PbS QDs are free from midgap states even without ligand passivation and independent of the geometry, (ii) off-stoichiometry in PbS QDs introduces new states in the gap that are highly localized on certain surface atoms, and (iii) further deviations in stoichiometry lead to QDs with metallic behavior, with a dense number of energy states near the Fermi level. Azpiroz et al[12] performed a theoretical study on the interaction between a (101) and a (001) TiO2 slab model (with no periodic conditions) and a (PbS)n QD with n = 4, 16, 28, 44 and 68. They found the strongest attraction for the (PbS)68 system adsorbed on the TiO2 (101) surface model, which corresponds to the anatase phase. They proposed a methodology to estimate the injection rates found experimentally and they found a reasonable agreement with experiment. It was found that the (101) slab is more susceptible to faster electron recombination with the valence band of the QD, which may reduce injection efficiencies, than those found on the (101) surface. Nevertheless, all calculations were performed by considering cluster models, which may be subjected to present border effects, giving as a consequence 4

unrealistic properties. In this respect, no theoretical study is available based upon a Molecular Dynamics approach or a DFT study with periodic conditions that avoid border effects on TiO2 surfaces and the corresponding interaction with PbS QDs. The inclusion of periodic conditions with both methodologies may be of fundamental interest in order to elucidate the role of the structural parameters at the molecular level, as it given by the DFT approach, and the role of temperature effects, as it is provided by the MD methodology. Furthermore, a systematic study with both methodological contributions may accelerate the assisted-design of PbS QD deposited on TiO2 substrates for subsequent synthesis at the experimental level. The aim of this work is to give insights by using a combined Density Funcional and Molecular Dynamics approach into the electronic structure properties of extended (PbS)4 @TiO2 systems and their correlation with optical properties of interest on photovoltaic and renewable energy applications.

2. Computational Details 2.1. DFT Calculations Density Functional calculations were performed with VASP computational code[13, 14, 15], which uses a based-PAW (Projector Augmented) method. In order to model the TiO2 substrate, we fully relaxed the anatase structure with periodic conditions. This configuration was built with (101) planes of truncated anatase symmetry in bulk phase. It was performed by using a conjugate gradient algorithm to converge. The accuracy requirement 5

is that all forces in the final structures are smaller than 0.05 eV/˚ A. The unit cell size presents a dimension of 30x30x30˚ A, in order to consider the periodic boundary conditions. We used a 3x3x1 Monkhorst-Pack of k-point sets. All calculations were performed using a plane wave gradient approach (GGA) of Perdew-Burke-Ernzerhof for the exchange-correlation energy, namely the PBE functional[16]. Spin-orbit effects were also included in the calculations, which may have an influence in the interaction with heavy metals such as Pb. Besides, the same calculations were also carried out using atomic-based functions, with the ’tier1’ basis set for Pb atoms and ’tier2’ for the rest of the species. We included relativistic effects in these calculations (which may be relevant in heavy-metal atoms as Pb) with the Zeroth-order relavistic approach (ZORA), as implemented in the FHI-aims computational code[17, 18], in order to compare if the management of plane-waves and atomic-based functions may play a role in the description of electronic structure properties. We found that no further effect is present, since virtually all the computed values led to the same results. We also quantified the strength of the interaction between the TiO2 substrate and the PbS QD in accordance to the adsorption energy (∆Ea ) equation as given by

∆Ea = ET − EP bS − ET iO2 ,

(1)

where ET stands for the total energy of the relaxed system PbS@TiO2 , including periodic boundary conditions, EP bS and ET iO2 are the total energies

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of the isolated PbS QD and TiO2 substrate with exactly the same periodic conditions, as performed in the geometry relaxations. 2.2. Molecular Dynamics simulations The model structures of the TiO2 substrate was allowed to relax in order to find the ionic configuration of mechanical equilibrium, using simulated annealing, as implemented in the Molecular Dynamics code DL POLY[19]. We used the Matsui-Akaogi-Collins force field[20], since this model potential is the most suitable for classical molecular dynamics simulations of bulk TiO2 polyphorms for a wide range of temperatures. The model potential describes the interaction among Ti and O ions through the Buckingham[21] potential U SR (ij) and the electrostatic potential U LR . In this model, we considered that the cohesive energy can be decomposed into the energy of pair atoms i, P j, Ucoh (tot) = ij Ucoh (ij). Therefore, the energy between a pair of atoms i and j may be written as:

Ucoh (ij) = U SR (ij) + U LR (ij)

(2)

Further, the Buckingham potential U SR (ij) (Eq. 3) describes short range interactions among atoms. The first term corresponds to repulsive interactions and the second term to the attractive attractions.

U

SR

(ij) =

X i6=j

  rij C Aexp − − ρ (rij )2

7

(3)

The electrostatic potential U LR (ij) (Eq. 4), corresponds to the Coulombic interaction.

U LR (ij) =

X 1 qi q j 4πε0 rij i6=j

(4)

After substituting Eq. 3 and 4 into Eq. 2, we obtain:

Ucoh (ij) =

X i6=j



rij Aexp − ρ

 −

C 1 qi qj + 2 (rij ) 4πε0 rij

(5)

Where A is the number of electrons, ρ corresponds to the electronic density and Cij is the interaction between two atoms. All parameters are reported in Table 1. rij is the interatomic distance between i and j ions. The O and Ti ions have partial charges(q) of +2.196 and −1.098, respectively. Constant temperature MD simulations were also carried out using Ion-Ion A, kcal/mol Ti-Ti 717654 Ti-O 3910553 O-O 271719

ρ,◦ A C, kcal◦ A6 /mol 0.154 120.997 0.194 290.392 0.234 696.941

Table 1: Interaction Parameters for the Matsui-Akaogi Force Field for T iO2

DL POLY code version 2.13[19]. DL POLY uses Velocity−Verlet algorithm with the multiple time step method to integrate Newton law of motion over time. Each simulation considers a unit cell with periodic boundaries in the x−, y− and z− directions. The unit cell is a cubic box with 30˚ A, which is larger than geometrical diameter of the nanoparticle under study. The

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latter, avoids spurious results coming from replication of the unit cell. The simulated annealing was implemented to reach a high energy (-12 eV/atom) and a temperature of 2300 K. It was dynamically represented by a trajectory of 4 ns. The temperature was increased and decreased at intervals at 100 K, and freezing velocity at 18 K/ns.

3. Results and discussion 3.1. Equilibrium configurations of TiO2 nanoparticles We explored the equilibrium configurations of TiO2 nanoparticles using Molecular Dynamics simulations as described in the Computational Details section. In Fig.1, we present the final configuration as obtained through quenching and a slow freezing. We found that most of the members in the collective present cohesive energies of -37.15, and -37.16 (eV/Formula unit). We also observed that three members present the lowest-energy at -37.16 (eV/Formula unit). We selected one of these geometries to determine the electronic structure properties at the ground state and we also performed a structural analysis with a coordination study. This study was performed with a ’home-made’ code to count the number of first neighbors around a certain atom located in the molecular ensemble. The number of atoms with respect to the number of nearest neighbor atoms is depicted in Fig.2. It was found that 8 is the largest number of nearest neighbor atoms for O and Ti, and 3 is the number with more incidence of nearest neighbors. 9

We can find in the nanoparticle 76 O atoms and 38 Ti atoms. O atoms have 3 Ti atoms as nearest neighbors and Ti atoms have 6 O atoms as nearest neighbors. This coordination is representative of rutile and anatase geometries [2]. However, no symmetry was identified in this ’amorphous’ cluster. On the other hand, a geometry optimization was performed on a periodic structure of (101) TiO2 anatase by using the DFT methodology, as described in the Computational Details section. The TiO2 extended model contains 3 planes that were all allowed to relax during the geometry optimization. Despite a large unit cell was considered in the calculations (to avoid border effects that may lead to unphysical results), the TiO2 (101) anatase model presents some structural modifications. Such modifications have been evidenced from the RDF diagrams depicted in Fig.3 (a), where it is presented the Ti−O bonding density distribution over all the TiO2 substrate model, and it may be seen that the majority of Ti−O bonds present in the substrate have a localized bond length of 2˚ A. A small amount of Ti−O pairs present a weak bonding at 4˚ A. The RDF for the amorphous TiO2 substrate presents an analogous behavior with a high peak located at about 2˚ A and also a weak bonding density at 4˚ A. Furthermore, a distribution around 4˚ A is raised, indicating that some Ti−O bonding pairs inside the substrate are elongated, giving as a result the structural morphology presented in Fig.3 (a). This indicates that the optimization of TiO2 substrate at the PBE level, preserves the nature of anatase, only with some bond lengths elongation found after 10

the geometry relaxation. We also present the RDF results (see Fig.3 (c)) for the amorphous phase of TiO2 performed with Molecular Dynamics. It was found an analogous behavior to that observed with the anatase phase after geometry relaxation using DFT. The only difference is the rising of new Ti−O pairs around 4˚ A, which appear to be larger than those found at the optimized anatase. This may be readily understood from the deformation observed after the temperature quenching process performed using Molecular Dynamics. Nevertheless, the latter does not alter significantly the nature of anatase found at the optimized structure using DFT, as presented in the RDF pattern depicted in Fig.3 (a). Besides, the RDF pattern for the PbS@TiO2 model is presented in Fig.3 (b), and we found that the characteristic peak located at 2˚ A is preserved, while the presence of Ti-O bonding pairs around 4˚ A are significantly attenuated. 3.2. Electronic structure properties of PbS, TiO2 and nanocomposite PbS@TiO2 We performed DOS calculations at the DFT/PBE level of theory and in accordance with the methodology presented in the Computational Details. It was found that the band gap of (TiO2 )38 is 0.6 eV, which is in close agreement with the band gap of 0.37 eV found by Auvinen et al [10]. This may be due to a number of localized states in the gap area and it may also be involved with the fact that Lundqvist et at [9] reported a defect-free fundamental band gap for (TiO2 )38 structure.

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As depicted in Fig.4, the anatase nanoparticle (see Fig.4 (a)) presents a band gap of 0.6 eV, while the ’amorphous’ cluster presents a band gap of about 1.6 eV (see Fig.4 (b)). By comparison, bulk TiO2 has a band gap of about 3.6 eV [2]. The band gap of anatase nanopaticle is smaller than that found for the ’amorphous symmetry’. This may be due to the rising of new energy levels coming from the defects of the ionic configurations. This may also be evidenced from the peak and shoulder depicted in Fig.4(a) and located at -6.09 eV and -4.87 eV, respectively. The rising of the new Ti-O bonds at the amorphous substrate alters the electronic structure of the overall system, giving as a consequence the opening of the band gap, which is increased 1.0 eV from that of the anatase symmetry. The latter is shown in the DOS of the amorphous TiO2 presented in Fig.4(b). On the other hand, we present the electronic structure properties at the ground state geometry of the PbS QD model, which were found at the DFT/PBE level of theory and in accordance to the methodology given in the computational Details. We found that the Pb-S bond length for the relaxed structure is 275 pm, which is in reasonable agreement with experimental bond length of 280pm[22] . The calculations performed with VASP (including spin-orbit coupling) and FHI-aims (scalar relativistic effects) led in both cases to the same qualitative results, indicating that the relativistc effects in the size of the PbS QD under study are not necessarily relevant. Nevertheless, it may have an influence for larger PbS QDs. A systematic study regarding the size of the QD is currently in process by our group. 12

The DOS of (PbS)4 QD is presented in Fig.5.

The Projected DOS

(PDOS) are also depicted for the Pb and S atoms of the QD. From the DOS integral, we are able to find the total number of Molecular Orbitals (MO) for each of the energy peaks along the distribution. Consequently, the energy peak 1 in Fig.5 corresponds to 2 orbitals, the energy peak 2 corresponds to 6 orbitals, while peaks 2 and 4 correspond to 4 and 2 orbitals, respectively. Energy peaks 1, 2, 6 and 7 present the largest contribution of the S atomic orbitals. Energy peaks 3, 4, 8, 9 and 10 present the largest contributions of the Pb atomic orbitals, while peak 5 is made of similar contributions from the atomic oribitals of Pb and S. As show in Fig.5, the (PbS)4 nanoparticle presents a band gap of about 1.9 eV, while a band gap of 0.37 eV for bulk PbS has been reported elsewhere [10]. The presence of new energy levels and band gap broadening is attributed to a strong quantum confinament effect of electrons in this nanoparticle. This is also in agreement with the nanoparticle size of 2˚ A, which is smaller than the Bohr exciton radius (Re = 20 nm) [23]. Volume densities of electronic charge are depicted in Fig.6 for some of the representative MOs of (PbS)4 . The MOs correspond to contributions coming from the lowest energy peaks up to energy peak 2, as presented in Fig.5, where the contributions of the S atomic orbitals are the greatest. That is, MO 3 presents larger contributions of S atomic orbitals, while MO 6 is mainly composed of Pb orbitals. Finally, MO 10 is representative of a combined distribution of S and Pb atomic orbitals (see Fig.6) 13

According to Fig.5, the energy peak for the Pb atom corresponds to two s orbitals; energy peak 2 corresponds to two p orbitals, and energy peak 3 presents 4 occupied orbitals. The peaks 4 and 5 correspond to antibondingtype orbitals. Therefore, the 4 Pb valence electrons are distributed in the 2 s and p orbitals in an energy range from -12.988 eV to the Fermi level at -3.0043 eV. On the other hand, the S atomic orbitals are distributed in energy peaks 1 and 2, representing s orbitals, while peaks 3 and 4 are both p orbitals. Energy peaks 5 and 6 represent non-bonding orbitals. Furthermore, the 6 S valence electrons are distributed in 2 s orbitals, 3 p orbitals and one of the electrons in another p-orbital. Such electrons range in the energy interval from -18.0 eV to -5.836 eV. We further studied the interaction between the PbS quantum dot and our TiO2 substrate model. We fully relaxed the anatase TiO2 structure (previously optimized at the PBE level ) in the presence of the PbS QD in accordance to the same methodology. The ground state geometry is shown in Fig.7. It was found that the PbS QD is tighty bonded to the TiO2 surface with an adsorption energy (computed in accordance to Eq.1) of -13.5 eV, which may be due to a strong interaction with a certain degree of covalency. The PbS system is attached to the TiO2 substrate through a S-Ti bonding, with a bond length of 236.8 pm. This is also in agreement with the results found by Azpiroz et al[12]. Such degree of covalency may also be inferred from a charge transfer mechanism. The latter was evidenced with the computation of ∆Q (as presented in Table 2) from a M¨ ulliken analysis at the 14

Density Functional level of theory as reported in the Computational Details. In this scheme, ∆Q refers to the charge transferred from the PbS QD to the substrate. The positive values of ∆Q at Pb and S suggest a clear charge transfer coming from the PbS QD to the TiO2 substrate, since a residual electronic charge populates the Ti and O atoms, as it shown in Table 2. The PbS fragment loses charge in an oxidation process, migrating to the TiO2 surface. The small amount of charge donated from the QD to the substrate shows that the covalent bonding plays only a modest role in the interaction mechanism, but it may certainly not be neglected. Fig.8 shows the DOS of the optimized (PbS)4 @(TiO2 )38 nanohybrid system. This nanocomposite configuration was obtained simulating the adsorption process implemented with First-principles Molecular Dynamics simulation at constant energy, using a dynamic trajectory of 1160 fs. The evolution of the system started from an arbitrary geometry by reorienting all atoms through the simulation. A slight modification of the TiO2 nanoparticle was found at the end of the simulation. No. Atoms ∆Q 1 Ti -0.2194 2 O -0.3601 3 Pb +0.4194 4 S +0.1601 Table 2: ∆Q M¨ ulliken analysis as computed from the total charges at PbS@TiO2 , substracted to the M¨ ulliken charges of the PbS and TiO2 isolated fragments, previous to the nanocomposite attraction

The band gap of this system was estimated at the PBE level from the 15

equilibrium configuration found from Molecular Dynamics. It was found that the band gap of the system is ∼ 2 eV. Besides, the interaction between both systems shifts the energy to more negative values. This is evident in the adsorbed particle and it indicates that the electrons are more tied up in the composite system than they are in the isolated nanoparticle. The (PbS)4 @TiO2 (amorphous) system was fully optimized at the PBE level in order to compare the adsorption energy of the composite system with that of the (PbS)4 @TiO2 (anatase). We found that the adsorption energy (∆Ea ) (computed according to Eq.1) corresponds to -1.3 eV, which may be due to a non-covalent attraction of the electrostatic type. As it was already stated, the (PbS)4 @TiO2 (anatase) system presents a band gap of about 2 eV, which allows it to be readily implemented in applications of photovoltaic materials, where the adsorption of light at that energetic range is of particular interest. Consequently, it may be readily implemented in photovoltaic applications. Nevertheless, as it is depicted in Fig.9, the PbS@TiO2 (amorphous) presents a small band gap of 0.202 eV, which falls out of the range of the visible light. This may be assigned to the bond length found in this configuration, which is 195.2 pm larger than that found for the anatase structure. The Ti-S bond length also adopts the preferential orientation of interaction. This bonding may be ascribed to an electrostatictype interaction, which may also be ruled by a dispersive attraction of the London-type and may also activate the rising of novel electronic states. As a consequence, the band gap falls outside the range of visible light (see Fig.9). 16

We can also conclude that the excess of peaks in the RDF distribution, located at around 4˚ A in the amorphous TiO2 structure, plays also a role when the surface interacts with another system, such as the PbS QD. The density of states is destabilized and the redistribution of charge density due to the presence of the PbS cluster, changes dramatically the electronic structure configuration of the nanocomposite (PbS)4 @TiO2 (amorphous). We finally propose that the (PbS)4 @TiO2 (anatase) substrate is the most promising material to be implemented in a photovoltaic application, despite the intrinsic TiO2 analogous behavior of the amorphous as compared with that of the anatase in the calculations. For larger (PbS)n QDs with n > 4, an analogous effect may be expected and calculations for QDs of this size are being performed by our group in order to to have a wider scope on the role of (PbS)n size and stoichiometry. Such results will be presented in a future work.

4. Conclusions A combined Density Functional and Molecular Dynamics study on a series of (PbS)4 @(TiO2 )38 system models was carried out for the first time. The TiO2 substrate was simulated as a slab and it was fully optimized using a DFT methodology on the one hand, and a Molecular Dynamics approach, on the other. The first scheme reveals a relaxed nanoparticle that presents the structural features of anatase, while the second scheme yields an amorphous configuration. This geometry preserves at a certain degree, the symmetry of anatase. The DOS of both configurations differ from that found 17

in bulk, due to the size of the model. The (PbS)4 system was considered as a small quantum dot model, which presents structural parameters that are in close agreement with those found in experiment. Furthermore, the nanocomposite (PbS)4 @TiO2 model was studied, and we found that a strong attraction is present between the QD and the TiO2 substrate with anatase symmetry. It was found an intermolecular interaction energy that may be comparable with that of a covalent bonding. The energy of the attraction for the QD at the amorphous substrate was identified as a weak interaction of the electrostatic-type. As a consequence, the band gap found for the first nanocomposite model lies around 2 eV, which makes it suitable to be implemented as a semiconductor material in photovoltaic devices, since it would adsorb most of the solar radiation. It represents a potentially suitable material in solid-state for the design and development of photocatalysts for water-splitting, electrodes in energy storage devices, artificial photosynthesis, water dissociation for Hydrogen production, biomedical materials, among other.

5. Acknowledgements J.M. wants to acknowledge the support given by C´atedras-CONACYT (Consejo Nacional de Ciencia y Tecnolog´ıa) under Project No. 1191; DGTIC (Direcci´on General de C´omputo y de Tecnolog´ıas de Informaci´on y Comunicaci´on) and the Supercomputing Department of Universidad Nacional Aut´onoma de M´exico for the computing resources under Project No. SC1618

1-IR-29. T.G.D.R. wants to acknowledge the PhD. Scholarship provided by CONACYT with No.287914. The authors would also like to acknowlegde the computing time provided by Laboratorio Nacional de Superc´omputo of Benem´erita Universidad Aut´onoma de Puebla (LNS-BUAP) under Project No.O-2016/005. The authors want to acknowledge the technical support given by Alfredo Guill´en L´opez to provide RDF spectra.

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[19] K. T. I.T. Todorov, W. Smith, M. Dove, DL POLY 3: new dimensions in molecular dynamics simulations via massive parallelism, J. Mater. Chem. 16 (2006) 1911–1918. URL http://dx.doi.org/10.1039/B517931A [20] M. Matsui, M. Akaogi, Molecular Dynamics Simulation of the Structural and Physical Properties of the Four Polymorphs of TiO2 , Mol. Simul. 6 (1991) 239–244. [21] R. A. Buckingham, The classical equation of state of gaseous helium, neon and argon, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 168 (933) (1938) 264–283. arXiv:http://rspa.royalsocietypublishing.org/content/168/933/264.full.pdf, doi:10.1098/rspa.1938.0173. URL http://rspa.royalsocietypublishing.org/content/168/933/264 [22] N. O. Boadi, P. D. McNaughter, M. Helliwell, M. A. Malik, J. A. M. Awudza, P. O’Brien, The deposition of PbS and PbSe thin films from lead dichalcogenoimidophosphinates by AACVD, Inorg. Chim. Acta 453 (2016) 439–442. [23] X. Zhao, I. Gorelikova, S. Musikhin, S. Cauchi, V. Sukhovatkin, E. H. Sargent, , E. Kumacheva, Synthesis and Optical Properties of ThiolStabilized PbS Nanocrystals, Langmuir 21 (2005) 1086–1090.

22

16 14

Ucoh = -37.1632 eV

12

Clusters

-37.1500

10 8 6 -37.1474

4 2 0

-37.1632

-37.1421

-37.1605

-37.1395

-37.1342

-37.1105

-37.1079

Cohesive energy (eV/Formular unit) Figure 1: TiO2 nanoparticles distribution with respect to cohesive energy

23

-37.0474

50

Nearest neighbor Ti 3

O atoms

40 30 20 10 0 50

Ti atoms

40 Nearest neighbor O 6

30 20 10

8

0 50

Atoms

40 30 20 10 0

0

2

4 8 10 12 6 Number of nearest neighbor atoms

14

Figure 2: Number of atoms in the TiO2 nanoparticle with respect to the number of first neighbors

24

RDF O-Ti 10

a) Anatase symmetry

8 6 4 2

RDF Ti-O

0 10

b) Anatase symmetry PbS4@TiO2

8 6 4 2 0 10

c) Amorphous model

8 6 4 2 0

0

1

2

3

4

5

6

7

8

9

10

r(Å) Figure 3: RDF distribution of the Ti-O bonding. (a) anatase symmetry, (b) (PbS)4 @TiO2 (anatase), (c) amorphous model

25

250

a) 200

EF= -4.5201 eV Eg= 0.6 eV

150

100

DOS

50 Eg

0 200

b) EF= -5.7995 eV Eg= 1.6 eV

150

100

50 Eg

0 -30

-25

-20

-15 Energy (eV)

-10

-5

0

Figure 4: Density states of (a) anatase and (b) amorphous nanoparticles of TiO2

26

25

(PbS)4 Pb S

20 15

EF= -4.2291 eV Ubond= -1.903 eV 3

2

6 66

6

10

7

6 6

9

5

5

1 2

4

2

2

8

EF

0 30

EF= -3.0043 eV

25

DOS

10

4

20 15

4p

10 2p

2s

5

EF

0 30 EF= -5.8361 eV

25 20 15 10 5 0 -20

3p

1s

1s

3p

EF

-15

-10 Energy (eV)

-5

0

Figure 5: DOS of (PbS)4 QD and PDOS of Pb and S atoms

27

Molecular orbital 3

Molecular orbital 6

Figure 6: Representative MO isosurfaces of (PbS)4 QD

28

Molecular orbital 10

Figure 7: Configuration of mechanical equilibrium of the nanocomposite (PbS)4 @TiO2

29

250 (PbS)4@TiO2 DOS TiO2 PDOS (PbS)4 PDOS

200

DOS

150

100

50

0 -30

-25

-20

-15 Energy (eV)

-10

Figure 8: DOS of the nanocomposite (PbS)4 @TiO2 (anatase). PDOS of (PbS)4 and TiO2

30

-5

0

80

PbS4@TiO2 (amorphous) DOS TiO2 PDOS PbS PDOS

70 60

DOS

50 40 30 20 10 0 -10

-8

-6

-4

-2

Energy (eV) Figure 9: DOS of the nanocomposite (PbS)4 @TiO2 (amorphous). PDOS of (PbS)4 and TiO2

31

0

2

Graphical Abstract

25

(PbS)4 Pb S

20 15

EF= -4.2291 eV Ubond= -1.903 eV 3

2

6 66

6

10

7

6 6

9

5

5

1

4

2

4

2

2

8

EF

0 30

EF= -3.0043 eV

25

DOS

10

20 15

4p

10 2p

2s

5

EF

0 30 EF= -5.8361 eV

25 20 15 10 5 0 -20

3p

1s

1s

3p

EF

-15

-10 Energy (eV)

-5

0

Highlights

Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices T. G. Díaz Rodríguez, J. A. Reyes Nava, M. Pacio, H. Juárez and Jesús Muñiz Highlights

   

A combined DFT and MD study was performed on a series of PbS@TiO2 nanocomposites A TiO2 amorphous phase was identified from the quenching performed with MD The calculated band gap of PbS@TiO2 appears in the range of visible light The PbS QD is adsorbed on the TiO2 substrate with an electrostatic-type attraction