# Synthesis Target Structures for Alkaline Earth Oxide Clusters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Data Mining and Interatomic Potentials

#### 2.2. Predicted Structures—Density Functional Theory

## 3. Results and Discussion

#### 3.1. Structures of (MO)${}_{n}$ Clusters ($n\le 18$ and 24)

#### 3.2. Second-Order Energies and Structural Motifs

#### 3.3. Coordination Numbers and Deformation

#### 3.4. Dipole Moments

#### 3.5. Selecting Targets for Nanofabrication

#### 3.5.1. Magnesium Oxide Clusters

#### 3.5.2. Clusters of Calcium, Strontium and Barium Oxide

#### 3.6. Nanoclusters of Size $n=12$

#### 3.7. Comparison with Previous Results

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Second-order energy differences, $\Delta E$, of (MgO)${}_{n}$ clusters for $n=2$ to 17. Ball and stick models (blue and red representing Mg and O atoms) of GM clusters with relatively high stability with respect to neighbouring sizes (i.e., those with negative second-order energy) are also shown.

**Figure 2.**Second-order energy differences, $\Delta E$, of (MO)${}_{n}$ (M = Ca, Sr, Ba) clusters for $n=2$ to 17. Ball and stick models (purple and red representing M and O atoms) of (SrO)${}_{n}$ GM clusters with relatively high stability with respect to neighbouring sizes (i.e., those with negative second-order energy) are also shown.

**Figure 3.**Average coordination numbers for GM nanoclusters of (MO)${}_{n}$ as a function of size n for each binary oxide (cutoffs vary by compound and are set to avoid physically meaningless diagonal “bonds” between two nearest neighbour like charged ions.

**Figure 4.**Deviation from ideal angle for $n=2$ to 4 GM around O atoms based on DFT-optimised geometries and perfectly symmetric squares, hexagons and cubes.

**Figure 5.**Density of structures for (MgO)${}_{n}$. Blue impulses indicate local minima energies (per formula unit), green curves are thermally smeared energies indicating overlap of different structures, vertical red lines indicate the $n-1$ local minimum.

**Figure 6.**Summary of all density of structures plots—here, black indicates sizes that are unfavourable (higher energy than the next lower size), yellow indicates sizes where only one structure is thermally accessible at 100 K, and red shows sizes where multiple structures are likely to be observed experimentally.

**Figure 7.**Energies relative to the GM for all reported geometries of the $n=12$ cluster. The high symmetry geometries of bulk cut, barrel and bubble are highlighted. Where no line is drawn, corresponding minima were not found for all compounds.

**Table 1.**Lowest energy local minima (LM) for (MO)${}_{n}$, $n=4$ to 12. The first, second, third and fourth character in the labels indicate the rank found for when M = Mg, Ca, Sr, and Ba, respectively, where A implies the global minimum, B the 2nd lowest LM, C the 3rd and X implies that the LM is outside of the top three. For each LM, only one representative configuration is shown for all compounds, with colour representations Mg, Ca, Sr, Ba and . A stick is shown if an oxygen anion is within the first coordination shell of a cation (typically less than 2.5 Å for Mg and 2.85 Å for Ba).

n | Structures/Labels | |||||
---|---|---|---|---|---|---|

$\mathbf{4}$ | ||||||

AAAA | ||||||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | |||||

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | |||||

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | |||||

BaO ${E}_{\mathrm{rel}}$ / meV/BaO | 0.0 | |||||

$\mathbf{5}$ | ||||||

AAXX | BCBX | CBAC | XXCB | XXXA | ||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 121.3 | 132.9 | N/A | N/A | |

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | 19.4 | 2.1 | N/A | N/A | |

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | N/A | 11.5 | 0.0 | 13 | N/A | |

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | N/A | N/A | 10.4 | 2.1 | 0.0 | |

$\mathbf{6}$ | ||||||

ABBB | BAAA | CCXX | XXCX | XXXC | ||

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 44.5 | 400.5 | N/A | 527.4 | |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 62.9 | 0.0 | 338.8 | N/A | 443.7 | |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 58.1 | 0.0 | N/A | 410.2 | N/A | |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 22.4 | 0.0 | N/A | N/A | 111.1 | |

$\mathbf{7}$ | ||||||

AAAB | BXXX | CXXX | XBCC | XCXX | XXBA | |

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 72.1 | 73.6 | 161.0 | N/A | N/A |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | N/A | 147.5 | 48.7 | 51.1 | N/A |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | N/A | 149.8 | 25.0 | N/A | 9.2 |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 1.1 | N/A | 117.3 | 16.1 | N/A | N/A |

$\mathbf{8}$ | ||||||

AXXC | BAAA | CXXX | XBBB | XCCX | ||

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 6.0 | 60.2 | N/A | 313.1 | |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 113.7 | 0.0 | 216.8 | 71.2 | 78.1 | |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 111.7 | 0.0 | 221.2 | 64.9 | 72.9 | |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 73.5 | 0.0 | 169.9 | 35.5 | 206.1 | |

$\mathbf{9}$ | ||||||

ABBX | BCXX | CXXX | XAAA | XXCB | XXXC | |

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 91.4 | 241.5 | N/A | 342.2 | 303.5 |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 49.3 | 161.3 | 259.2 | 0.0 | 430.5 | 284.4 |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 47.7 | N/A | 223.8 | 0.0 | 127.0 | 137.3 |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 22.4 | 54.9 | 128.1 | 0.0 | 8.5 | 18.4 |

$\mathbf{10}$ | ||||||

AAAA | BBXX | CXXX | XCBB | XXCX | XXXC | |

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 18.8 | 34.5 | 90.8 | 67.9 | 43.9 |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | 53.1 | 172.9 | 56.6 | 82.2 | 127.7 |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | 102.9 | 173.3 | 50.2 | 96.5 | 113.9 |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 0.0 | 69.9 | 127.8 | 39.3 | 103.9 | 58.5 |

$\mathbf{11}$ | ||||||

AXXX | BBBA | CXXX | XAAC | XCCX | XXXB | |

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 1.1 | 2.4 | N/A | 106.8 | 7.9 |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | N/A | 6.7 | 128.9 | 0.0 | 28.5 | 45.7 |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | N/A | 3.2 | 127.0 | 0.0 | 22.9 | 35.2 |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | N/A | 0.0 | 92.1 | 13.7 | N/A | 12.0 |

$\mathbf{12}$ | ||||||

ABBC | BAAA | CXXX | DCCX | XXXB | ||

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 30.5 | 49.8 | 56.1 | N/A | |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 54.7 | 0.0 | 203.2 | 70.3 | N/A | |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 52.2 | 0.0 | 189.5 | 64.1 | N/A | |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 29.0 | 0.0 | 109.9 | N/A | 3.94 |

**Table 2.**Lowest energy local minima (LM) for (MO)${}_{n}$, $n=13$ to 18 and 24. The first, second, third and fourth character in the labels indicate the rank found for when M = Mg, Ca, Sr, and Ba, respectively, where A implies the global minimum, B the 2nd lowest LM, C the 3rd and X implies that the LM is outside of the top three. For each LM, only one representative configuration is shown for all compounds, with colour representations Mg, Ca, Sr, Ba and . A stick is shown if an oxygen anion is within the first coordination shell of a cation (typically less than 2.5 Å for Mg and 2.85 Å for Ba). In the case of $n=24$, the letters in brackets denote PBESol0 results for (BaO)${}_{24}$.

n | Structures/Labels | |||||||
---|---|---|---|---|---|---|---|---|

13 | ||||||||

ABXX | BAAX | CCXX | XXBX | XXXA | XXXB | XXXC | ||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 26.3 | 57.9 | 245.4 | 190.8 | 8.8 | 13.3 | |

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 47.4 | 0.0 | 98.0 | 153.2 | 203.2 | N/A | N/A | |

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 58.4 | 0.0 | 76.1 | 52.6 | 101.8 | N/A | N/A | |

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | 73.1 | N/A | 56.3 | N/A | 0.0 | N/A | N/A | |

14 | ||||||||

ABCX | BXXX | CXXX | XAAA | XCXB | XXBX | XXXC | ||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 4.0 | 9.8 | 25.5 | 60.5 | 32.0 | N/A | |

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 13.2 | 58.6 | N/A | 0.0 | 42.7 | N/A | 45.0 | |

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 11.1 | 57.3 | N/A | 0.0 | 29.8 | 8.0 | 33.7 | |

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | 27.5 | 34.0 | 9.1 | 0.0 | 4.4 | N/A | 8.9 | |

15 | ||||||||

AXXX | BAAA | CCCX | XBBX | XXXB | XXXC | |||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 21.5 | 38.4 | 82.4 | N/A | N/A | ||

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 137.7 | 0.0 | 48.3 | 39.0 | N/A | N/A | ||

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 120.1 | 0.0 | 45.8 | 26.3 | N/A | N/A | ||

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | 73.5 | 0.0 | N/A | N/A | 3.8 | 14.7 | ||

16 | ||||||||

AAAA | BCBC | CXXX | XBXX | XXCB | ||||

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 24.1 | 114.3 | N/A | N/A | N/A | ||

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | 65.1 | N/A | 62.9 | N/A | N/A | ||

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | 62.3 | N/A | N/A | 78.1 | N/A | ||

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | 0.0 | N/A | N/A | N/A | 34.3 | 47.1 | ||

17 | ||||||||

ACXX | BAAX | CXXX | XBXX | XXBX | XXCA | XXXB | XXXC | |

(MgO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 40.2 | 43.7 | 95.6 | N/A | 110.5 | N/A | 74.5 |

(CaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/CaO | 18.6 | 0.0 | 47.1 | 12.4 | 56.3 | 49.1 | N/A | 117.0 |

(SrO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/SrO | 52.6 | 0.0 | 46.5 | 31.3 | 24.0 | 24.9 | N/A | 113.8 |

(BaO)${}_{n}$ ${E}_{\mathrm{rel}}$ / meV/BaO | 128.8 | 100.0 | 52.0 | 57.7 | N/A | 0.0 | 12.0 | 23.4 |

18 | ||||||||

AAAX | BXXX | CBBA | XCCX | XXXB | XXXC | |||

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 46.3 | 61.0 | 76.0 | 218.2 | N/A | ||

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | 112.5 | 56.4 | 97.8 | 221.4 | N/A | ||

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | 83.3 | 29.7 | 68.4 | 141.7 | N/A | ||

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 31.4 | 33.1 | 0.0 | 50.3 | 6.0 | 20.8 | ||

24 | ||||||||

AAAX(A) | BBBX | CXXX | XCXX | XXCX | XXXA(B) | XXXB(C) | XXXC | |

(MgO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/MgO | 0.0 | 93.4 | 105.4 | N/A | N/A | N/A | N/A | N/A |

(CaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/CaO | 0.0 | 107.6 | 145.5 | 137.3 | N/A | N/A | N/A | N/A |

(SrO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/SrO | 0.0 | 80.0 | 117.1 | N/A | 111.9 | N/A | N/A | N/A |

(BaO)${}_{n}$${E}_{\mathrm{rel}}$ / meV/BaO | 13.9 | 25.8 | 55.4 | N/A | N/A | 0.0 | 1.0 | 7.9 |

**Table 3.**Second-order energy differences ($\Delta E$/meV) for tentative global minima (MO)${}_{n}$ cluster energies of sizes n = 5–17.

$\mathit{n}$ | M = Mg | M = Ca | M = Sr | M = Ba |
---|---|---|---|---|

5 | 196.2 | 242.1 | 220.2 | 178.1 |

6 | −246.0 | −227.3 | −198.1 | −139.0 |

7 | 105.9 | 131.1 | 116.9 | 73.9 |

8 | −10.6 | −58.3 | −63.0 | −61.0 |

9 | −122.1 | −51.5 | −24.4 | 21.7 |

10 | 60.9 | 12.7 | −2.3 | −22.0 |

11 | 47.7 | 52.4 | 45.0 | 18.7 |

12 | −113.4 | −94.6 | −86.8 | −13.7 |

13 | 49.8 | 59.3 | 73.7 | −6.5 |

14 | 42.1 | 13.4 | −6.0 | 12.8 |

15 | −45.4 | −17.3 | −8.2 | 6.8 |

16 | −30.1 | −62.8 | −55.2 | −29.1 |

17 | 63.9 | 104.1 | 75.3 | 10.3 |

**Table 4.**Dipole moments of $4\times 3\times 3$ ($n=18$) cuboid clusters of magnesium, calcium, strontium and barium oxides as calculated using the PBEsol functional in FHI-aims.

Cluster | (MgO)${}_{18}$ | (CaO)${}_{18}$ | (SrO)${}_{18}$ | (BaO)${}_{18}$ |
---|---|---|---|---|

Dipole moment/D | 16.2 | 14.9 | 13.7 | 6.0 |

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**MDPI and ACS Style**

Escher, S.G.E.T.; Lazauskas, T.; Zwijnenburg, M.A.; Woodley, S.M. Synthesis Target Structures for Alkaline Earth Oxide Clusters. *Inorganics* **2018**, *6*, 29.
https://doi.org/10.3390/inorganics6010029

**AMA Style**

Escher SGET, Lazauskas T, Zwijnenburg MA, Woodley SM. Synthesis Target Structures for Alkaline Earth Oxide Clusters. *Inorganics*. 2018; 6(1):29.
https://doi.org/10.3390/inorganics6010029

**Chicago/Turabian Style**

Escher, Susanne G. E. T., Tomas Lazauskas, Martijn A. Zwijnenburg, and Scott M. Woodley. 2018. "Synthesis Target Structures for Alkaline Earth Oxide Clusters" *Inorganics* 6, no. 1: 29.
https://doi.org/10.3390/inorganics6010029