Alkali Ion Incorporation into V2O5: a Noncovalent ... - ACS Publications

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Alkali Ion Incorporation into V2O5: a Noncovalent Interactions Analysis V. Riffet,†,‡ J. Contreras-Garcıa,́ †,‡ J. Carrasco,§ and M. Calatayud*,†,‡,∥ †

Laboratoire de Chimie Théorique, Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, F-75005 Paris, France Laboratoire de Chimie Théorique, CNRS, UMR 7616, F-75005 Paris, France § CIC Energigune, Albert Einstein 48, 01510 Miñano, Á lava, Spain ∥ Institut Universitaire de France, France ‡

S Supporting Information *

ABSTRACT: Understanding the interaction of alkali metals with layered materials like vanadia is important for a range of technological applications such as energy storage and heterogeneous catalysis. Here we used the NCI (noncovalent interactions) index to analyze the nature of the chemical bonding between inserted alkali atoms (Li, Na, and K) and vanadia. We found that alkali atoms ionize in bulk vanadia making directional ionic bonds with neighboring oxygen atoms, whereas the dispersive interactions between vanadia layers remain unmodified by the presence of alkali ions. Interestingly, we show how the NCI analysis discriminates among the different vanadium−oxygen types of bond, capturing even finer interactions involving reduced vanadium sites or ring stabilization. In addition, we explored dynamic effects, concluding that the directionality of all interactions is preserved at 500 K.

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INTRODUCTION The interaction of vanadia (V2O5) with alkali ions is important for many technological applications. For instance, alkali ions strongly modify the acid/base and redox behavior of vanadiasupported catalysts for selective oxidation reactions.1−3 Vanadia can also readily intercalate alkali and alkaline-earth ions, making it an appealing cathode material for rechargeable batteries.4−10 Understanding the nature of the interaction between the alkali ions and vanadia is therefore a timely issue, necessary to unravel the mechanisms controlling the stability of these systems. Bulk vanadia structure is composed of layers stacked in the [001] direction, where the cohesion of the crystal is ensured by van der Waals (vdW) forces.11 The addition of alkali atoms in the bulk material takes place in the interlayer region thus altering the forces balance. Recently, the effect of vdW forces in the thermodynamics and kinetics of alkali and alkaline-earth doped α-vanadia was addressed by some of us12 and other authors.5,6 A general conclusion from these studies was that vdW interactions help to stabilize inserted ions and contribute to hinder ion diffusion. However, besides geometric and energetic characterizations, the topology, directionality, and interplay of the different interactions have not been thoroughly investigated yet. Toward this end, the use of reactivity indices in the frame of conceptual DFT methods is helpful for the characterization of chemically active sites in a series of vanadia-based materials.13 In the present work we precisely aim at describing and analyzing the interactions between various alkali metals (Li, Na, and K) and αvanadia using the so-called noncovalent interactions index © 2016 American Chemical Society

(NCI), which is based on the reduced electron density gradient. The NCI approach has shown great success for visualizing weak interactions and enabling the characterization of both stabilizing (hydrogen bonds, vdW) and destabilizing (steric clashes) interactions in different materials.14−16 α-Vanadia is a relatively simple layered transition metal oxide, but yet it presents different chemical bonds and orientations, with the presence of edge and corner sharing VO5 pyramidal units to form two-dimensional periodic stacked layers and terminally bound oxygen atoms (vanadyl groups). This offers the the possibility of exploring the capabilities of the NCI analysis in a rich variety of structural motifs. The remainder of the paper involves a description of the computational methods employed. Following this, we show how the NCI approach captures both weak (dispersive vdW forces in between layers) and strong (V−O and alkali-O ionic bonding) interactions in the alkali metal−vanadia system. We then present and discuss our analysis, revealing the fine bonding structure associated with the presence of V4+ sites formed when alkali atoms ionize, as well as unexpected stabilizing cycle interactions. A dynamic study is carried out and we close with some conclusions. Received: November 27, 2015 Revised: January 26, 2016 Published: January 26, 2016 4259

DOI: 10.1021/acs.jpcc.5b11600 J. Phys. Chem. C 2016, 120, 4259−4265

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The Journal of Physical Chemistry C

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optimal application of the NCI analysis a fine grid is needed, so the option Prec = Accurate has been set to generate grids with twice as many points in each direction as the grids for the orbitals. Since we are interested in noncovalent interactions, only the valence charge density has been used for the analysis. After the static analysis and in order to take the dynamic behavior of the system into account we performed molecular dynamics (MD) simulations. The total free energy (i.e., free electronic energy + Madelung energy of ions + kinetic energy of ions) was kept constant, corresponding to a microcanonical ensemble. The temperature was set to 500 K rescaling every 10 steps, with a time step of 1 fs. Low precision was used (cutoff 250 eV, electronic loop convergence 10 −4 eV, Li and Na pseudopotentials with only one valence electron). A first run of 0.5 ps was done for the equilibration, then a run of 1.2 ps was done to extract the geometry every 10 steps. A static calculation was done afterward for each selected geometry as described above (Prec = Accurate, cutoff 500 eV). NCI Topological Analysis. NCI is a topological tool to visualize noncovalent interactions, providing rich representations of a range of attractive (vdW, hydrogen, and ionic bonding) and repulsive (steric clashes) interactions. The NCI scheme is based on the so-called s(ρ) function, which is defined using the electron density, ρ, and its first derivatives as follows:

COMPUTATIONAL DETAILS Spin-polarized DFT calculations were performed using a supercell approach and the optPBE-vdW functional17 as

Figure 1. Noncovalent interactions in phenol dimer. Left: s(ρ) with the three peaks for hydrogen bond, vdW, and steric repulsion. Right: 3D image with coloring (blue-green-red) as explained in the text.

implemented in the VASP 5.3 code.18,19 Of the various vdWinclusive methodologies available, the nonlocal optPBE-vdW density functional has shown to perform well for a broad range of systems, in particular when applied to layered materials12,20,21 The projector augmented wave pseudopotentials PAW22,23 replace the core electrons, whereas the valence electrons (V:3p6 3d4 4s1, O:2s22p4, Li:1s22s1, Na:2p63s1, K:3p6 4s1) are explicitly treated by a plane wave basis set with cutoff 500 eV. The DFT+U scheme24 was used for properly describing the localized nature of V 3d states. Here, we set the value of U to 4.0, as the one previously proposed for studying ion insertion into V2O5.12,25,26 The distance between two k-points in the Brillouin zone was set to ∼0.04 Å−1 (2 × 2 × 2 sampling). The electronic convergence was achieved for a threshold of 10−6 eV. The structures used are those optimized with the same computational scheme in ref 12, i.e., 1 × 3 × 3 supercells V36O90 of dimensions 11.689 × 10.883 × 13.267 Å3, containing one alkali atom of Li, Na, or K. Static single-point calculations have been performed to obtain the charge density, which is contained in a grid type file. For an

s(ρ) =

|∇ρ| 1 2(3π 2)1/3 ρ 4/3

(1)

It can be shown27 that noninteracting systems give rise to a ρ−1/3 baseline when s is plotted against ρ. Interactions give rise to deviations from this baseline in the shape of peaks (Figure 1 left). Most commonly, s is plotted in terms of sign(λ2)ρ, which gives rise to a classification of interactions: • attractive weak interactions (such as hydrogen bonds or ionic interactions) appear far to the left (negative sign)

Figure 2. NCI analysis of the bulk vanadia structure. (a) Plot of s(ρ); (b) plot of s(sign(λ2)ρ). The meaning of regions A, B, and C is described in the text. (c) Labeling of atoms in the structure (d) NCI isosurfaces with s = 0.3 au and the color scale −0.05 < sign(λ2)ρ < 0.05 au. 4260


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The Journal of Physical Chemistry C • vdW interactions are revealed around zero (very small densities) • repulsive steric clashes give rise to peaks to the far right, since λ2 is positive due to charge depletion (see ref 16 for more details). These interactions can be highlighted within the molecular frame by means of s isosurfaces. In order to visually identify the interaction type, a color code is used:16 blue for attractive, green for vdW, and red for clashes. Figure 1 exemplifies this by considering a phenol dimer: a blue surface highlights the hydrogen bond between the alcohols, red cigars appear for the steric repulsion inside the phenol rings, and green surfaces are shown for the van der Waals interaction between the two units. The NCI analysis has been carried out with the CRITIC2 code28 with a step size along each axis of 0.05 au. The NCI regions are then visualized using Visual Molecular Dynamics software version 1.9.1.29 In the case of MD simulations, the charge density is obtained for each geometry in a static single point calculation as described above, and then the averaged charge density, ρ̅, of all the structures is used to perform the NCI analysis. Although not stated in the original publication,30 this choice stems from the fact that ρ̅ is a well-defined ensemble density, enabling the use of its derivatives to perform the averaged NCI analysis as follows: |∇ρ ̅ | 1 2 1/3 2(3π ) ρ ̅ 4/3 (2) Note that while ρ̅ is well-defined, an average of s, i.e., s ̅ = ∑ si /ni, where ni represents the number of averaged snapshots would not be so since s, by its definition (eq 1), cannot be separated into the ensemble contributions, i.e., s is not directly averageable. s(ρ ̅ ) =

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RESULTS AND DISCUSSION Bulk Vanadia. The reduced density gradient (s) vs density (ρ) diagrams and NCI isosurfaces for bulk vanadia are shown in

Figure 4. a) Model cluster and bond lengths in Å, b) NCI isosurfaces generated for s = 0.3 au and colored over the range −0.05 < sign(λ2)ρ < 0.05 au and c) HOMO and LUMO for the clusters V2O5,cut and V2O5,gaz.

Figure 3. Detail of NCI isosurfaces in the bulk vanadia structure (a) ionic interactions and (b) dispersion interactions generated for s = 0.3 au and colored over the range −0.05 < sign(λ2)ρ < 0.05 au. The ring interactions are indicated with an asterisk.

Figure 2. Essentially, bulk vanadia shows three interaction types: ionic interactions (region A), strong noncovalent interactions (region B), and weak noncovalent interactions (region C) whose absolute electron density ranges are of [0.070, 0.260], [0.020, 0.050], and [0.0, 0.020] au respectively. Region A is associated with ionic bonding between each V atom and its five nearest O neighbors (Figure 3a). Interestingly, one can easily distinguish one peak at −0.25 au associated with V−Omono interactions (also called VO or vanadyl groups), and

Figure 5. NCI isosurfaces using (a) s = 0.3 au and colored over the scale −0.05 < sign(λ2)ρ < 0.05 for the supercell and (b) s = 0.3 au and colored over the range −0.025 < sign(λ2)ρ < 0.025 au for the local environment of M = Li, Na, K.

a group of three peaks between −0.07 and −0.15 au, assigned to three different V−O environments. We provide a detailed 4261


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Table 1. Nature, Number of Interactions, and Electron Density Range (au) of New Interactions Due to Alkali Incorporationa Li interactions

a

nature

#1 #2 (#2′)

M···OV M···Odi

#3 (#3′)

M···Otri

#4 V4+O···V5f

M···Vneighbor V4+O···V5f

5+

Na

K

sign(λ2)ρ

counting

sign(λ2)ρ

counting

sign(λ2)ρ

counting

[−0.016,−0.003] −0.020 −0.011 −0.0175

3 2

4 2

2 1

[−0.020,−0.018] [−0.020,−0.018] ([0.005, 0.007]) [−0.015,−0.014] ([0.005, 0.007]) ∼0.008 −0.030

4 2 (2)

∼0.011 −0.029

[−0.014,−0.012] −0.017 −0.016 −0.011 −0.009 ∼0.008 −0.029

1

2 4 1

2 (2) 4 1

Labelling as in Figures 3b and 5.

interaction, identified in the NCI analysis, is due to a polarization effect within the V2O5 unit (ΔEHOMO→LUMO(V2O5,cut) = 146 kJ mol−1). We have analyzed independently the cluster geometrical parameters in order to understand what the differential structural parameter is. An in-depth analysis of lengths and angles (see the Supporting Information) has shown that the distance V2···O3 (and V2···O4) is crucial to understand the different behavior of the solid and the gas clusters. Thus, the NCI analysis also reveals here polarization effects in the solid as well as their absence in the fully optimized gas-phase cluster (see the Supporting Information), which is consistent with it being absent in other optimized structures. All in all, the constrained solid framework gives rise to different electronic structures, exhibiting different reactivity than the molecular realm. The interactions of the third type (C) are found in the electron density range [−0.012, 0.012] au, where a set of peaks can be observed in the 2D plot of Figure 2a,b. They are mainly associated with dispersion interactions and most of them are located in the region between the layers and also connect the vanadyl VO sites of one layer to the 5-fold vanadium sites (V5f) of the next layer as shown in the Figure 3b. For this last interaction, note that all the distances VO···V5f are of 2.804 Å and the NCI peak is at −0.012 au. These interactions (C) are responsible for the cohesion of the crystal in the [001] direction. Alkali-Doped Vanadia. The alkali-doped systems are represented in Figure 5. They correspond to the energetically most favorable intercalation sites found in our previous work.12 Upon insertion of a neutral alkali atom, an electron is transferred from the alkali to a neighboring vanadium V5+ site, the alkali ionizes and one vanadium is thus reduced to V4+. For the sake of simplicity we will use M (M = Li, Na, and K) instead of M+ in the text. The NCI analysis reveals the existence of new attractive interactions between the alkali sites and the neighboring oxygen sites from the layers in contact. Indeed, new isosurfaces (peaks) appear in the 3D representations (2D plots) as shown in Figure 5 (Figure S3). The nature, the number, and the electron density range of these new interactions are summarized in Table 1. The interaction #1 (Figure 5b) is of type M···OV5+, and we counted 3, 4, and 4 of such contacts within bulk vanadia doped with Li, Na, and K, respectively. Note that in the Li case, the three NCI peaks are localized around −0.150, −0.008, and −0.005 au, the last two peaks being associated with Li···OV5+ dispersion interactions. Indeed, the values are very low and the shape of the isosurface supports a dispersive interaction rather than an ionic interaction. Isosurfaces #2 correspond to attractive interactions between the alkali cation and the dicoordinated oxygen, noted M···Odi. These interactions are the strongest attractive interactions around Li and Na. Isosurfaces #3 involve the tricoordinated oxygens and the alkaline cation, and the resulting interactions are noted M···Otri. Indeed, Li interacts with its

Figure 6. NCI isosurfaces highlighting the ionization of alkaline metals (Li, Na, and K) using s = 0.3 au and colored over the range −0.05 < sign(λ2)ρ < 0.05 au.

analysis of each peak assignment in the Supporting Information. The blue thin disc-shape isosurfaces (Figures 2c,d) revealed by the NCI analysis in the V−O bonds can be characterized as ionic interactions31 indicating thus an ionic character for the different V−O bonds. Such picture is fully coherent with previous studies based on electron localization function ELF pointing toward an unshared electron interaction between the O atoms in the bulk32,33 and gas-phase clusters.34−36 In particular, the bulk vanadyl VO bond is classified as mainly dative, whereas the other V−O bonds are ionic according to an atoms in molecules analysis.32,33 In summary, each type of oxygen possesses different reactivity and plays different roles in chemical reactions.37 The peaks at +0.038 and −0.038 au correspond to the second type of interaction (region B). They are associated with ring interactions of the V2O2 cycles present in the structure. It is interesting to note that the 3D representation displays, in the center of the ring, a region which is both red (steric clashes) and blue (attractive interactions), see Figure 3. Most commonly, NCI analysis of cyclic structures finds only red regions in the rings.15,16,27 The stabilizing character found in bulk vanadia was only observed up to now in transition states, but disappears in stable structures.38 We carried out a deeper investigation in a simplified model taking V2O5 clusters. We have performed an analysis of two gas-phase clusters with stoichiometry V2O5: a bulk-cut cluster fixed to the bulk positions, hereafter named V2O5,cut and an optimized gas-phase structure, hereafter named V2O5,gaz (see Figure 4). The O3···O4 stabilizing interaction is still identified within V2O5,cut , indicating that this interaction is present in the V2O5 solid. On the contrary, only steric clashes are present within the ring of V2O5,gaz. From the orbital point of view the differences are found in the LUMO (see Figure 4c). Whereas the LUMO of V2O5,cut includes a bonding combination of two lobes from the 2p atomic orbital of O3 and O4 within the ring (blue node in the ring), it does not appear in those of V2O5,gaz. So, the stabilizing 4262


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Figure 7. (a,b) s vs sign(λ2)ρ (left and middle) for static (green) and averaged (red) electron densities from undoped and K-doped vanadia systems, respectively. For the sake of clarity, the y axis for the static systems is shifted +0.1 au NCI isosurfaces (right) using s = 0.3 au and the color scale −0.05 < sign(λ2)ρ < 0.05 for the supercell. (c) NCI isosurfaces using s = 0.3 au and colored over the range −0.025 < sign(λ2)ρ < 0.025 au for the local environment of K.

ions,15,31 it is also found for Na and Li at s = 0.8 and 1.5 au, respectively. The ions are accommodated maximizing the number of these interactions. Li, which is smaller, goes close to one of the layers to ensure complexation with two oxygen sites, Na is able to establish two strong interactions with one of the layers, while it weakly interacts with the other neighboring layer. Finally, K is able to establish six strong interactions with the layer above and below. The dispersive interactions between layers are only slightly affected by the presence of the alkali atom: the green isosurfaces are modified in the region of the alkali ion but are present in the interlayer region as for the undoped system, see Figure 5a. The distances between the vanadyl VO sites of one layer to the 5fold vanadium sites (V5f) of the next layer are overall situated within the [2.679, 2.891], [2.656, 2.861] and [2.626, 2.951] Å interval for Li, Na and K, respectively (vs 2.804 Å in the bulk vanadia). The associated NCI peaks are in the [−0.017, 0.008], [−0,017, 0.008], and [−0.020, 0.008] au range, respectively. Those directly around M (×4) are longer and thus these

nearest neighbor Otri while Na and K interact with their two nearest neighbors Otri. Compared to Li and Na, K is a bigger ion. Thus, it can interact, but more weakly, with more distant oxygens as those involved in interactions #2′ and #3′ (see Table 1 and Figure 5b); they correspond to dispersion interactions. The multiple oxygen coordination in vanadia is related to the rich reactivity of vanadia-based compounds.13,37 There exist weaker repulsive interactions between alkaline cations and the neighboring V sites (interactions type #4). These interactions, noted M···Vneighbor, are identified in the three cases of doping. The analysis of the NCI isosurfaces in Figure 5b shows the distribution of interactions around each alkali atom. Going from Li to K involves increasing both the number and type of isosurfaces, and their symmetry around the alkali site. This is explained by the size of the ion: Li is small and stays closer to one layer, and K is bigger and occupies the center of the cavity formed by two vanadia layers; Na shows an intermediate situation. The blue isosurface around K is a typical feature of complexation of 4263


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molecular model (V2O5) allows us to understand that the polarization effects stabilize the V2O2 rings. In case (ii), alkali atoms ionize in bulk vanadia making directional ionic bonds with neighboring oxygen atoms. Furthermore, we found that the dispersive interactions between vanadia layers remain unmodified by the presence of alkali ions. We explored also dynamic effects at 500 K by considering an averaged charge density. We concluded that the directionality of all interactions is preserved at this temperature. The NCI analysis is therefore a very useful tool in the analysis of bonding in layered materials.

interactions are weaker than the other ones: [2.942, 2.979, 3.002, 3.231] Å for Li, [3.028, 3.030, 3.084, 3.230] Å for Na, and [3.061, 3.063, 3.127, 3.261] Å for K. The associated NCI peaks are within the [−0.008, −0.005] au interval, which are features of the dispersive interactions. However, an evident strengthening of the interlayer interaction is observed between a VO neighboring the alkali atom and the V site from the layer below (see Figure 6 cyan blue isosurface), the associated distance VO···V5f being equal to 2.439, 2.439, and 2.422 Å for Li, Na, and K, respectively. This corresponds to the NCI peak at −0.029, −0.029, and −0.030 au in Figure S3, for Li, Na, and K, respectively, and is therefore a strong attractive interaction. The evident strengthening of this isolated interaction can be explained by the reduction of one of the vanadium sites in V4+ due to the ionization of Li, Na and K alkaline metals and is not observed for the other vanadium sites which are V5+ sites. The binding of vanadium to the layer below has been reported for oxygen defective bulk vanadia39 and is fully consistent with our observation. The NCI method is thus able to capture this fine interaction in the absence of an oxygen vacancy. Dynamic Behavior. The NCI regions that appear in the bulk and alkali-doped system appear generally as spots and irregular surfaces, since they correspond to single static structures. However, in a real system the ions move around an equilibrium position and the interactions evolve accordingly. In order to account for the dynamic behavior in the material and its impact on bonding we have carried out molecular dynamics runs. In the equilibrated runs we extract selected structures and calculate the corresponding electron density. Then we obtain an averaged electron density which should capture the dynamics of the system, in a similar way as in fluctuating systems.30 The details on the MD runs analysis are given as Supporting Information. Figure 7 displays the NCI plots and isosurfaces obtained for MD averaged electron density in the case of bulk and K (see Figure S15 for Li and Na). It can be observed that some isosurfaces are smoothed compared to the static calculations, but the overall picture is similar to the static case. The regions of the VO bonds are the most affected, mainly broadening the range of s values. In the studied time frame, and since the Li ions only interact with one layer, they are more mobile. The Li ions visit during the run the cavity between layers interacting with 2−3 oxygen sites at the same time. Na and K ions are less mobile than Li and move in a restricted region between the two layers, see Figure S14. Compared to the static cases, no additional interactions appear other than the ones already described for the three alkali atoms studied, see for instance the case of K in Figures 5 (static) and Figure 7 (dynamic). However, the non symmetric placement of Li (interactions only with one layer) gives rise to a dynamic behavior between layers. We conclude that it is likely that the directionality of the alkali-vanadia interactions is preserved at the temperature studied. The VO bond is the most affected one by temperature.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b11600. Supplements for NCI results (3D representations, 2D plots, detailed assignments). Complete study + Cartesian coordinates of the molecular models V2O5. Details of the molecular dynamics. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +33 1 44 27 25 05. Fax: +33 1 44 27 41 17. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed using HPC resources from GENCICINES/IDRI S (Grants 2014-x2014082131, 2015x2015082131) and the CCRE-DSI of Université P. M. Curie. M.C. thanks Dr. B. Diawara for the visualization program Modelview. J.C. is supported by the MINECO through a Ramón y Cajal Fellowship and acknowledges support by the Marie Curie Career Integration Grant FP7-PEOPLE-2011-CIG: Project NanoWGS and The Royal Society through the Newton Alumnus scheme. COST CM1104 action is acknowledged.

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REFERENCES

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CONCLUSION Using the NCI topology tool, we first studied the nature of the chemical bonding within bulk vanadia and then the changes due to incorporation of alkali atoms (Li, Na, and K). The presence of weak (dispersive interlayer) and strong (ionic V−O and alkaliO) interactions are especially highlighted. Interestingly, the NCI analysis allows discriminating the different vanadium−oxygen types of bond, capturing even finer interactions as (i) the ring stabilization or (ii) those involving reduced vanadium sites formed when alkali atoms ionize. For case (i), the study of a 4264


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