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. 2021 Jun 17;6(25):16612–16622. doi: 10.1021/acsomega.1c02016

Role of Dispersion Interactions in Endohedral TM@(ZnS)12 Structures

Elisa Jimenez-Izal †,‡,*, Iker Ortiz de Luzuriaga §, Eloy Ramos-Cordoba †, Jon M Matxain †
PMCID: PMC8246693  PMID: 34235333

Abstract

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II–VI semiconducting materials are gaining attention due to their optoelectronic properties. Moreover, the addition of transition metals, TMs, might give them magnetic properties. The location and distance of the TM are crucial in determining such magnetic properties. In this work, we focus on small hollow (ZnS)12 nanoclusters doped with TMs. Because (ZnS)12 is a cage-like spheroid, the cavity inside the structure allows for the design of endohedral compounds resembling those of C60. Previous studies theoretically predicted that the first-row TM(ZnS)12 endohedral compounds were thermodynamically unstable compared to the surface compounds, where the TM atom is located at the surface of the cluster. The transition states connecting both structure families were calculated, and the estimated lifetimes of these compounds were predicted to be markedly small. However, in such works dispersion effects were not taken into account. Here, in order to check for the influence of dispersion on the possible stabilization of the desired TM(ZnS)12 endohedrally doped clusters, several functionals are tested and compare to MP2. It is found that the dispersion effects play a very important role in determining the location of the metals, especially in those TMs with the 4s3d shell half-filled or completely filled. In addition, a complete family of TM doped (ZnS)12 nanoclusters is explored using ab initio molecular dynamics simulations and local minima optimizations that could guide the experimental synthesis of such compounds. From the magnetic point of view, the Cr(7S)@(ZnS)12 compound is the most interesting case, since the endohedral isomer is predicted to be the global minimum. Moreover, molecular dynamics simulations show that when the Cr atom is located at the surface of the cluster, it spontaneously migrates toward the center of the cavity at room temperature.

1. Introduction

II–VI semiconductors have been extensively studied in the last decades due to the optoelectronic properties that make them suitable for important applications in photocatalysis,1 solar cells,2,3 or quantum devices.4,5 Likewise, the use of II–VI semiconductor nanomaterials in biological investigations has increased notably due to their unique optical properties and to recent advances in biofunctionalization.6 The addition of transition metals, TMs, can change the structural and electronic properties of these materials7−10 and even give them magnetic properties.11,12 The resulting magnetic and optoelectronic properties are assorted and dependent on the particular transition metal atom.13−19

II–VI nanomaterials often exhibit new and exciting properties, arising from the quantum confinement and their high surface to volume ratio. Moreover, nanoclusters composed of a few atoms are treatable by first-principles computational protocols allowing the study of their properties at the atomic level, that would otherwise be extremely difficult to explore in larger nanoparticles. For instance, the endohedral doping of (ZnS)12, that has spherical symmetry, can be considered as equivalent to the interstitial doping in bulk. A recent review highlights the importance of such endohedrally doped nanoclusters.20

Several TM doped (ZnS)12, (CdS)12, and (ZnO)12 clusters have been studied theoretically in the past.9,21−27 Previously some of us theoretically characterized the first- and second-row TM endohedrally doped (ZnS)12 and (ZnS)16 nanoclusters.11,28,29 From all the compounds, the most promising ones were predicted to be those endohedrally doped with silver. Although metastable, Ag@(ZnS)i were predicted to have sufficiently large lifetimes and show interesting magnetic properties and coupling when forming Ag@(ZnS)i dimers, directly related to the Ag–Ag distance. Indeed, for the Ag@(ZnS)12 dimer, Ag atoms exhibit an antiferromagnetic coupling, while for the larger Ag@(ZnS)16 dimer, ferromagnetic and antiferromagnetic states are degenerate.11 Unfortunately, in the rest of the TM doped clusters (except for Zn and Cu that do not have magnetic properties), it was found that the metal atom moves toward the surface of the nanocluster, breaking it and forming the more stable surface doped structure (see Figure 1).

Figure 1.

Figure 1

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General picture for TM@(ZnS)12 structures, where surface compounds are more stable than their endohedral counterparts.

Electronic structure theory is fundamental for the prediction and understanding of molecules and materials. Importantly, the reliability of the approximate electronic structure method lies in its capability to describe all the interaction energy components, such as the electrostatic and dispersion interactions. The methodology used in the previous studies on TM doped (ZnS)12,16 nanoclusters (B3LYP), however, did not account for van der Waals interactions. Notice that the TM–cage interaction in the endohedral isomers tends to be weak, and consequently, the lack of specific consideration of dispersion may lead to the underestimation of the stability of the endohedral compounds.

The main goal of this work is to establish the importance of dispersion interactions for the correct description of such systems and to test whether the dispersion could stabilize the endohedral isomers. With this aim, first different DFT functionals are compared to a reference MP2 calculation. Then the selected DFT functional is used to revisit the stability of endohedral compounds of selected first-row TM(ZnS)12 by means of quantum dynamics along with an exhaustive search of the potential energy surface. Characterizing new potentially stable endohedral TM@(ZnS)12 compounds might lead to the discovery of novel magnetic nanostructures, with very promising implications in technological applications such as spintronics.

2. Methods

All the geometry optimizations and frequency calculations were done using the Gaussian16 package.30 Harmonic vibrational frequencies were obtained by analytical differentiation of gradients, to identify whether the characterized structures were true minima or transition states. Such frequencies were then used to evaluate vibrational corrections to Gibbs free energy, using the standard procedure of Gaussian16 (see the Supporting Information). For sulfur and zinc atoms, the relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch, and Jasien (SKBJ)31 were used, and the fully relativistic pseudopotentials, with 10 electrons in the core, developed by Dolg et al.,32,33 were used for the rest of the TM. The reference method to account for the dispersion is the second-order Møller–Plesset theory (MP2).34−38 We must highlight that the MP2 method is not the most accurate wave function based method, but for the systems studied here it is affordable, unlike other post Hartree–Fock methods such as Coupled Cluster. Several DFT functionals were compared to MP2: B3LYP,39 CAM-B3LYP,40 M06,41 M06-2X,41 wB97X-D,42 PBE43,44 combined with the D3 version of Grimme’s dispersion with Becke–Johnson damping,45 denoted hereafter as PBE-D3BJ, and a set of double-hybrid methods, including exact HF exchange with an MP2-like correlation to DFT calculations. Concretely, the following double-hybrid functionals have been used: B2PLYP46 and mPW2PLYP47 methods, developed by Grimme, and their corresponding empirical dispersion corrected48 counterparts B2PLYPD and mPW2PLYPD. In addition, B2PLYPD3 which combines the B2PLYP method with Grimme’s D3BJ dispersion,45,49 DSDPBEP86,50,51 a dispersion-corrected double-hybrid functional with Grimme’s D3BJ dispersion, and the PBE0DH52 and PBEQIDH53 double-hybrid functionals.

B3LYP was chosen because it is the functional used in previous works, and as CAM-B3LYP, it does not include dispersion corrections.11,28,29 Both M06 and M06-2X are supposed to describe van der Waals interactions by construction, and wB97X-D includes an empirical atom–atom dispersion potential. Double-hybrid functionals will help in the assessment of the quality of the MP2 reference. Finally, to analyze the noncovalent interactions, we have used the NCIplot4 software.54−56

Ab Initio Born–Oppenheimer molecular dynamics (BO-MD) simulations were performed to additionally explore the thermal stability of selected TM(ZnS)12. The PBE-D3BJ functional was used as described above, combined with a DZP quality basis set and the RI formalism with the corresponding auxiliary basis sets.57−59 The temperature was set to 300 K using the Nosé–Hoover thermostat. The simulation was run for 10000 steps, with a time step of 300 au (7.26 fs) resulting in simulation times as long as 300000 au (7.26 ps). The TURBOMOLE package60 was used to carry out all these simulations.

3. Results and Discussion

3.1. Benchmark of the Density Functional (Method Calibration)

Second-order Møller–Plesset perturbation theory, MP2, is the computationally cheapest post-Hartree–Fock method that accurately describes the van der Waals interactions, with limitations, and is free of electron self-interaction error. This method, however, is still computationally very demanding, especially for geometry optimizations and frequency calculations. For this reason, we have tested several DFT functionals (B3LYP, CAM-B3LYP, M06, M06-2X, wB97XD, PBE-D3BJ, B2PLYP, mPW2PLYP, B2PLYPD, mPW2PLYPD, B2PLYPD3, DSDPBEP86, PBE0DH, and PBEQIDH) against this method, in order to assess the quality of the MP2 value as reference and to identify the level of theory that provides a balance between accuracy and computational cost, in order to use this functional for the rest of the calculations.

In our previous work, the (ZnS) nanoclusters with a first-row TM located inside the cavity (ENDO) and at the surface of the cavity (SURFACE), along with the transition states connecting both isomers, were characterized using the B3LYP functional29 (see Figure 1). Now single-point calculations were performed on these TM(ZnS)12 structures with MP2 and several DFT functionals. In Table 1 the electronic energy difference between SURFACE and ENDO isomers (ΔES-E = ESurf – EEndo) as well as the energy difference between ENDO and transition-state structures (ΔETS = ETS – EEndo) is shown for 5Ti, 7Cr, 3Ni, and 1Zn doped (ZnS)12. These spin states and transition metals have been chosen as representative for early, middle, and late first-row TMs with high and low spins.

Table 1. Free Energy Differences between ENDO and SURFACE Structures (ΔGS-E) and ENDO and Transition State Structures (ΔGTS), in kcal/mol, for 5Ti, 7Cr, 3Ni, and 1Zn Doped (ZnS)1 Nanoclustersa.

  5Ti
 7Cr
 3Ni
 1Zn
  ΔES-E ΔETS ΔES-E ΔETS ΔES-E ΔETS ΔES-E ΔETS
MP2 5.58 5.38 19.80 16.57 8.74 –2.10 27.14 37.18
B3LYPa –18.08 3.93 –2.89 11.73 –15.38 –0.89 –1.66 27.48
CAM-B3LYP –16.60 5.00 –2.95 11.56 –13.00 –0.80 –0.51 31.33
M06-2X 8.20 5.72 12.72 11.85 5.62 5.21 8.20 35.41
M06 6.53 2.64 31.24 16.56 17.94 1.44 19.73 33.87
wB97XD –6.87 –5.19 8.18 14.80 –0.46 1.55 10.80 35.74
PBE-D3BJ 5.78 4.13 22.80 16.66 9.65 –1.84 19.69 32.07
B2PLYP –7.86 4.17 5.74 12.94 0.56 –1.92 8.63 31.20
B2PLYPD –1.77 6.31 16.80 20.03 9.08 2.34 20.57 37.53
B2PLYPD3 3.15 6.12 18.02 17.84 11.32 2.18 19.31 35.38
wPW2PLYP –8.64 4.53 5.05 13.29 –1.13 –1.20 7.69 31.72
wPW2PLYPD –4.21 6.08 13.09 18.45 5.07 1.87 16.37 36.32
DSDPBEP86 6.82 4.95 21.30 17.53 18.52 0.71 22.65 36.56
PBE0DH 2.32 5.45 15.97 16.78 3.05 0.09 14.23 35.30
PBEQIDH 5.09 5.39 18.22 16.96 12.06 –0.47 18.75 36.71
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a

Data taken from ref (29).

According to the results obtained with the B3LYP functional29 in Table 1, all SURFACE structures are more stable than the corresponding ENDO ones. Similar results are obtained with CAM-B3YP, and according to wB97XD for 5Ti and 3Ni, the ENDO compounds are the most stable. On the contrary, MP2 data given in Table 1 shows that in all the cases ENDO compounds are more stable than the corresponding SURFACE structures. Remarkable are the calculated differences of ca. 20 and 27 kcal/mol for 7Cr and 1Zn, respectively. Hence, the consideration of dispersion interactions appears to be crucial in stabilizing the ENDO structures, where the TM is located inside the (ZnS)12 cavity. The results obtained with the remaining DFT functionals support qualitatively the conclusion obtained with MP2 and show the importance of dispersion. Note that in some cases negative values are calculated for ΔETS. These energetic values are obtained by means of single-point calculations using geometries optimized in ref (29) and not at geometries optimized at each level of theory. In addition, thermal and entropic corrections are not considered at this stage. These two facts may explain the negative values calculated for ΔETS.

Table 2 contains the ΔΔE values calculated as the differences between the computed ΔE values with DFT functionals and with MP2 and the calculated difference averages and standard deviations. The average difference of wB97XD with respect to MP2 is similar to those calculated for M06 and M06-2X (around 5 kcal/mol), but unlike the first one, the last two correctly predict the endohedral structures as the most stable ones for all the cases studied. Double-hybrid functionals including empirical dispersion terms are slightly closer to MP2, with average differences around 2–3 kcal/mol, predicting the same isomer as the most stable one. PBE-D3BJ is the method that provides the closest results to MP2. In general, compared to DFT functionals, MP2 energetics favor the endohedral structure by approximately an extra 3–5 kcal/mol, which can be attributed to the known overestimation of dispersion interactions. Considering these results, and because the computational cost of double-hybrid functionals is that of MP2 and not DFT, and the RI formalism in TURBOMOLE is supported only for pure functionals, the PBE-D3BJ method is the chosen one to be used hereafter. In this way, Born–Oppenheimer molecular dynamics calculations will be affordable.

Table 2. ΔΔG Values Calculated as Differences between the Calculated ΔG with DFT Functionals and MP2 ΔG Values, in kcal/mol. Average Values of Calculated Differences and Standard Deviations Are Also Given in kcal/mola.

  5Ti
 7Cr
 3Ni
 1Zn
  
  ΔΔES-E ΔΔETS ΔΔES-E ΔΔETS ΔΔES-E ΔΔETS ΔΔES-E ΔΔETS Ave ± σ
B3LYPa –23.66 –1.45 –22.69 –4.84 –24.12 1.12 –28.80 –9.70 14.56 ± 10.67
CAM-B3LYP –22.19 –0.39 –22.75 –5.01 –21.74 1.31 –27.65 –5.85 13.36 ± 10.49
M06-2X 2.62 0.34 –7.08 –4.72 –3.12 7.32 –18.84 –1.77 5.74 ± 5.80
M06 0.95 –2.74 11.44 1.99 9.19 3.54 –7.41 –3.30 5.07 ± 3.54
wB97XD –12.45 –0.19 –11.62 –1.77 –9.20 3.65 –16.34 –1.44 5.08 ± 5.49
PBE-D3BJ 0.20 –1.25 3.00 0.09 0.91 0.26 –7.45 –5.11 1.17 ± 3.20
B2PLYP –13.44 –1.21 –14.06 –3.63 –8.18 0.18 –18.51 –5.98 8.15 ± 6.20
B2PLYPD –7.35 0.93 –3.00 3.46 0.33 4.44 –6.57 0.35 3.30 ± 2.54
B2PLYPD3 –2.43 0.74 –1.78 1.27 2.58 4.28 –7.83 –1.80 2.84 ± 2.13
wPW2PLYP –14.22 –0.85 –14.75 –3.28 –9.87 0.90 –19.45 –5.46 8.60 ± 6.58
wPW2PLYPD –9.79 0.70 –6.71 1.88 –3.67 3.97 –10.77 –0.86 4.79 ± 3.66
DSDPBEP86 1.24 –0.43 1.50 0.96 9.78 2.81 –4.49 –0.62 2.73 ± 2.95
PBE0DH –3.26 0.07 –3.83 0.21 –5.69 2.19 –12.91 –1.88 3.76 ± 3.87
PBEQIDH –0.49 0.01 –1.58 0.39 3.32 1.63 –8.39 –0.47 2.04 ± 2.60
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a

Data taken from ref (29).

3.2. Full Characterization of (5Ti, 7Cr, 3Ni, 1Zn)@(ZnS)12 Structures

Previously first-row TM doped ZnS nanoclusters were studied, and it was concluded that only Zn would remain enclosed inside the cluster, whereas for the rest of the TMs the preferred position would be at the surface.29 Nevertheless, as shown in the previous section, dispersion interactions could change this in favor of endohedral doping. To unveil this question ENDO and SURFACE compounds, along with the transition states connecting both structures, have been fully optimized with the PBE-D3BJ functional for (5Ti, 7Cr, 3Ni, 1Zn)@(ZnS)12. Since frequency calculations are carried out in these characterizations, hereafter Gibbs free energies will be considered.

In Table 3 the geometrical and energetic data of such structures are shown. For the ENDO compounds, Zn and Cr atoms are located at the center of the cavity, while Ti and Ni are moved from the center, breaking the symmetry of the system.

Table 3. Distance of the TM with the Geometrical Center of the (ZnS)12 Cage, R, in Å and the Symmetry Group of the Calculated Structures and ΔGS-E and ΔGTS in kcal/mol.

  ENDO
 SURFACE    
Metal R Symm Symm ΔGS-E ΔGTS
5Ti 0.91 C1 C1 –5.12 –1.78
7Cr 0.00 D2h C1 16.28 18.61
3Ni 1.01 C1 C1 –0.58 3.73
1Zn 0.00 D2h C1 19.83 35.34
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Our results predict that the ENDO structures are thermodynamically more stable than the corresponding SURFACE ones for 7Cr and 1Zn doped clusters. Similarly, these two metals are the ones that exhibit the largest energy barriers for the ENDO-to-SURFACE isomerization reaction. We would like to point out that according to the B3LYP functional, the SURFACE structures are more stable than the corresponding ENDO.26 These results suggest that the van der Waals forces are responsible for the stabilization of the TM at the center of the (ZnS)12 and they are indeed fundamental for the correct description of these systems. In fact, 7Cr and 1Zn atoms are located at the center of the cluster, with no covalent bonds between the guest and the host but only second-order weak interactions. In the case of 5Ti and 3Ni doped clusters, the SURFACE and ENDO structures are now closer in energy, with energy differences within 5 kcal/mol. For 5Ti doped (ZnS)12, the computed energy barrier for the ENDO-to-SURFACE isomerization is −1.78 kcal/mol. Notice that this negative number suggests that this is a barrierless process, and hence only the surface structure would be obtained experimentally.

With the aim of verifying the relevance of dispersion forces in ENDO compounds, Zn, Cr, Ni, and Ti doped ENDO and SURFACE structures are analyzed using the noncovalent interaction index (NCI), that is a visualization tool based on the density and the reduced density gradient (RDG). The NCI allows identifying noncovalent interactions in real space, characterized by regions with low RDG and density values. The NCI can detect both attractive and repulsive interactions. The first are represented by a negative sign of the Hessian’s second eigenvalue (λ2), while positive values indicate a repulsive interaction. van der Waals or dispersion interactions correspond to regions where λ2 ≈ 0.

Figure 2 represents the regions of space where these interactions are relevant. Blue areas correspond to strong, attractive interactions, green to dispersion interactions, and red to strong repulsive interactions. As shown in Figure 2, dispersion interactions are more relevant in the ENDO conformation than in the SURFACE one. That indicates the relevancy of these interactions to account for energy differences between the two conformers properly. For Cr and Zn, the ENDO conformers are symmetric with the metal located at the center of the cage in both cases. Inspection of Figure 2 indicates that in these cases, the van der Waals region is fully symmetric around the metal, stabilizing the position of the metals at the center of the cage. On the other hand, Ti and Ni in the ENDO conformers are not symmetric, and the metals are located closer to the surface of the cage. Those displacements break the symmetry of the van der Waals areas, being in these cases less relevant in regions with closer TM–ZnS distances. This qualitative analysis reveals the importance of dispersions interactions to calculate conformer stabilization energies for different TMs.

Figure 2.

Figure 2

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NCI analysis of TM doped (ZnS)12 nanoclusters. RDG isosurface with an isovalue of 0.3 au.

It is important to note that those transition metals that prefer to be located at the center of the cage, 7Cr and 1Zn, have half-full or full 4s3d shells. Specifically 7Cr has 4s13d5 electronic configuration and 1Zn 4s23d10. Hence, the spherical shape of the electronic density in these atoms may be determinant for enhancing the stability of the ENDO compounds. Having all this in mind, quantum molecular dynamics (QMD) simulations have been carried out for the ENDO and SURFACE compounds of the four metals (7Cr, 1Zn, 5Ti, and 3Ni), along with selected cases of isoelectronic anionic and cationic TMs that possess spherical electronic structures (see the Supporting Information for details). In addition to the thermal stability, these simulations may also provide the existence of other isomers different from the ENDO and SURFACE considered until now, yielding a deeper knowledge of the configurational space of these compounds. The obtained results are detailed below.

3.3. Molecular Dynamics Simulations at 300 K

According to PBE-D3BJ geometry optimizations, 7Cr prefers to be at the center of the cavity and 5Ti at its surface. Born–Oppenheimer MD simulations were performed for both the ENDO and the SURFACE7Cr(ZnS)12 and 5Ti(ZnS)12 structures, as shown in Figure 3. For the Cr doped ENDO structure it was found that the structure remains intact after 7.26 ps. Conversely, for the SURFACE conformer, it was found that after around 500 time steps (0.36 ps), the dopant atom moves from the surface of the cluster to the center of the cavity. This reconstruction from the SURFACE to the ENDO isomers is accompanied by a sudden energy decrease. Therefore, not only is the SURFACE compound thermodynamically less stable than the ENDO isomer, but it is not thermally stable and it will spontaneously rearrange into the ENDO structure at room temperature. This fact is especially relevant for the synthesis of this kind of compound, where the TM would be very likely incorporated into the cluster afterward. For 5Ti(ZnS)12, however, the SURFACE structure is predicted to be more stable than the corresponding ENDO. MD simulations show that the latter is indeed not thermally stable, since Ti would move from the center to the surface, accompanied by an energy decrease, as observed in Figure S1 of the Supporting Information.

Figure 3.

Figure 3

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Quantum molecular dynamics results for 7Cr(ZnS)12 structures. Total energies and the trajectory of the 7Cr along the simulation time (top) for the ENDO structure and (bottom) for the SURFACE structure. On the left, total energies are depicted vs simulation steps. Each step is 300 au.

In addition to these simulations, Born–Oppenheimer molecular dynamics of selected isoelectronic TM-Zn12S12ENDO and SURFACE structures were carried out, namely: 4s13d5 (Cr, V–), 4s23d5 (Mn, Cr–), 4s13d10 (Cu, Ni–), and 4s23d10 (Zn). The most relevant finding in these cases was that the ENDO structure is stable for 7Cr, 2Cu, and 1Zn, while in other cases the TM(ZnS)12 clusters visited several local minima during the simulation time. Such isomers might be classified into families: ENDO structures with different atoms inside the cavity (TM, Zn, or S), EXO structures with different atoms outside the cage structure (TM, Zn or S), and the SURFACE structure. As it can be observed, from the representative structures of such families depicted in Figure 4, the potential energy surface of TM(ZnS)12 is rich in low-lying isomers that might be reachable at room temperature.

Figure 4.

Figure 4

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Examples of the seven structure family isomers detected in the MD simulations.

3.4. Isomer Stability

According to MD and the geometry optimizations in previous sections, metals with more spherical electronic densities, namely those with half-full or full 4s3d electronic structure, are the best candidates to form stable endohedrally doped ZnS clusters. For this reason, we decided to perform an exhaustive search of the potential energy surface of these systems, by characterizing (geometrical optimization) each of the local minima found in the MD simulations, with the following TMs doped (ZnS)12 clusters: 4s13d5 (Cr, Mn+, V–), 4s23d5 (Mn, Fe+, Cr–), 4s13d10 (Cu, Zn+, Ni–), and 4s23d10 (Zn, Cu–). To have an even broader view of all the electronic and structural possibilities of such compounds, we considered the low- and high-spin states of the TMs.

3.4.1. 4s13d5 and 4s23d5 Nanoclusters

In this case, all the valence electrons in the 3d atomic orbitals, AOs, are unpaired, with a multiplicity 2S + 1= 7 or 6. The corresponding low-lying spin state, with two of the 3d electrons paired and 2S + 1= 5 or 4, was explored too. The energy profiles in Figure 5 show that low-spin structures are in general thermodynamically more stable in 4s13d5 than in 4s23d5. Indeed in the former, going from high-spin to low-spin leads to only one pair of 3d paired electrons, but in the latter, it leads to two pairs of 3d paired electrons. The most stable isomers for each case are depicted in Figure 6. The ENDO isomer is the global minima for 7Cr and 7V–. This result correlates well with the MD simulations shown above and holds them promising for functionalized materials with well-defined magnetic properties. In both 7Cr@(ZnS)12 and 7V–@(ZnS)12 all the valence orbitals are singly occupied and symmetrically distributed in the space, so the interaction between the metal and the cluster is equivalent in all directions confining the TM in the cavity center. Thus, dispersion is key for the stabilization of these structures. However, when two electrons are paired in 5Cr and 5V–, the symmetry is broken and the system is destabilized.

Figure 5.

Figure 5

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Energy profiles of all the TM doped (ZnS)12, in which the TM has either 4s1d5 (above) or 4s2d5 (below) electronic structure.

Figure 6.

Figure 6

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Most stable high- and low-spin structures for all the TM doped (ZnS)12, in which the TMs have either 4s1d5 or 4s2d5 electronic structure.

When the TM is not at the center of the cage, it forms covalent bonds with the closest Zn and S and, as a result, other conformers are thermodynamically stabilized. Particularly interesting is the case of Zn-ENDO, where the TM and one of the Zn atoms of the cluster switched positions, leading to the encapsulation of that Zn. We found that this is the most thermodynamically stable isomer in most cases. For 5Cr, 4 Mn, and 6 Mn, the dopant atom substitutes one Zn atom (while that Zn atom sits at the center of the cluster) retaining the original shape of the cluster. Considering that Zn has a full 3d shell, this scenario agrees with the hypothesis that the endohedral structures are stable when the atom inside the cavity has half-full or full 4s3d shells, stabilized through van der Waals forces.

For the anionic 5V–, 4Cr–, and 6Cr– doped clusters, the most stable structure is Zn-ENDO too. Nevertheless, the resulting structures are significantly distorted, due to the displacement of the anion from the surface toward the encapsulated Zn atom. Because Zn has a partial positive charge, such distortion can be seen as a consequence of the electrostatic attractive interaction between the anionic metal and the Zn atom lying inside the cluster.

In the cationic clusters, conversely, the most thermodynamically stable structures are the ones in which the bonding between the dopant and the S atoms holding partial negative charges is maximized. Regarding the high-spin state, Mn+ and Fe+ are stabilized the most in the S-ENDO structure. Here, one S atom is encapsulated inside the cluster, and the dopants move inward, in order to bond it, resulting in a very distorted and shrunk geometry. For low-spin states, the SURFACE structure is the most thermodynamically stable. In this case, the cationic metal bonds to several S atoms in the surface of the cage, leading to a more expanded shape. Therefore, the electrostatic interactions appear to be the reason for the preference of those isomers. Indeed, the structures that are stabilized with Mn+ and Fe+ are the ones in which the interaction between the TM+ and Zn (with a partial positive charge) is minimized and that between the TM+ and S (with a partial negative charge) is maximized. For this same reason, Zn-EXO and S-EXO structures are unstable or very high in energy for Mn+ and Fe+ cationic metals. Finally, for Mn+, we found for the first time that ENDO is more thermodynamically stable for 5 Mn+ than for 7 Mn+, although the energy difference between them is small. This energy difference is larger in the case of Fe+.

3.4.2. 4s13d10 and 4s23d10 Nanoclusters

The group 4s13d10 has its 3d AOs fully occupied. We would like to point out that the higher multiplicity is achieved by exciting one 3d electron to the 4p AO, and we anticipate that the high-spin-state compounds are not energetically competitive in any case. Therefore, we only considered here the low spin states. Note also that for Zn doped (ZnS)12 there exist fewer isomers, since the ENDO and Zn-ENDO, as well as the TM-EXO and Zn-EXO conformers, are equivalent.

The energy profiles for this group of TM doped (ZnS)12 are shown in Figure 7. The most stable isomers for each case are depicted in Figure 8. For 2Cu the most thermodynamically stable isomer is the endohedral compound, ENDO, stabilized by van der Waals interactions. Although it is very close in energy to several isomers, such as the SURFACE one, the most stable position for 1Cu+ and 1Zn dopants is the center of the cage as well. Unfortunately, these metals have no unpaired electrons (4s13d10), and thus they will not lead to materials with magnetic properties.

Figure 7.

Figure 7

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Energy profiles of all the TM doped (ZnS)12, in which the TMs have either 4s1d10 (top) or 4s2d10 (bottom) electronic structure.

Figure 8.

Figure 8

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Most stable high- and low-spin structures for all the considered TM doped (ZnS)12, in which the TMs have either 4s1d10 or 4s2d10 electronic structure.

The most thermodynamically stable conformer for 2Ni– is Zn-ENDO, similar to most of the anionic compounds shown previously. Led by electrostatic forces, Ni– moves into the cage to bond the encapsulated Zn atom, distorting the cluster. Note that this structure is very close in energy to ENDO. For Zn+, as was found for the other cationic species considered above, the most stable structure is S-ENDO, where the cation is able to maximize the number of bonds with the electronegative S atoms.

4. Conclusions

The endohedrally doped II–VI semiconductor nanomaterials with TMs present a very important feature in dealing with the magnetic properties of 2D or 3D of such cluster-assembled materials, as the TM–TM distance is fixed. In fact, the magnetic properties of these compounds have been found to be connected with the TM–TM distances in related materials. Previously, first- and second-row TM doped ZnS nanoclusters were studied. Two different structures were considered for each case, i.e., endohedral (where the TM is located at the center of the cluster) and exohedral structures (where the TM is at the surface of the cluster). The main conclusion of the work was that generally the TM atoms prefer to be located at the surface of the ZnS clusters and the lifetimes of the endohedral structures were very small. In these studies, however, dispersion interactions were not considered. Here, after carefully choosing the adequate level of theory, we show that the dispersion interactions between the dopant TM and the ZnS nanocluster play a key role in stabilizing some of the endohedral compounds. Additionally, a complete family of TM doped ZnS nanoclusters is explored using ab initio molecular dynamics simulations and local minima optimizations. This study could guide the experimental synthesis of such compounds and help obtain a holistic picture of the interaction between TM and II–VI nanomaterials.

When the dopant atom is charged, the electrostatic forces will be dominant over the dispersion forces. Consequently, for positively charged dopants, the endohedral compounds are thermodynamically less stable than other isomers, due to the electrostatic repulsion between the dopant and the Zn atoms of the cage that are pointing inward the cavity. However, we found that Cr, V–, and Cu are the perfect candidates to obtain endohedrally doped ZnS compounds and hold them promising for functionalized materials with well-defined magnetic properties. First, the endohedral structures are the most stable ones for these candidates; second, they are capable of giving magnetic properties to the semiconducting clusters due to their unpaired electrons.

Acknowledgments

Financial support comes from Eusko Jaurlaritza through project IT1254-19. The authors are thankful for technical and human support provided by SGIker (UPV/EHU, ERDF, EU). E.J.I. acknowledges the support of the Ikerbasque Fellowship. E.R.C. acknowledges funding from the Juan de la Cierva program IJCI-2017-34658.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c02016.

  • Ab initio molecular dynamics simulations, Gibbs free energies of optimized structures, relative Gibbs free energies with respect to the most stable isomer, and cartesian coordinates of optimized structures (PDF)

The authors declare no competing financial interest.

Notes

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Supplementary Material

ao1c02016_si_001.pdf (2.6MB, pdf)

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