# Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Magnetic States of MoMo in the Gas-Phase

#### 2.1.1. Generalized-Gradient Approximation (GGA-PBE) Results

#### 2.1.2. Results from Hubbard-Corrected Functionals

#### 2.2. Magnetic States of MoMo Adsorbed on the Calcite (10.4) Surface

#### 2.3. Magnetic Anisotropy Energy

## 3. Materials and Methods

- (1)
- For each angle $\theta $, perform a non-collinear calculation on an isolated Mo-Mo dimer (the auxiliary system) without SOC, imposing (from input) the desired direction to M. Use the same Hubbard U and Mo-Mo distance as in the molecule.
- (2)
- Save the d states occupations of the two Mo atoms.
- (3)
- Perform a preliminary DFT + U + SOC calculation on the molecule, starting from the saved d states occupations, which are kept fixed for ≈10 electronic iterations.
- (4)
- From the potential achieved at the previous step, proceed with the DFT + U + SOC calculation, this time letting the occupations free to evolve and the molecule reach its self-consistent GS, at the given $\theta $.

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AFiM | antiferrimagnetic |

AFM | antiferromagnetic |

CASSCF | Complete-active-space self-consistent field |

DFPT | Density Functional Perturbation Theory |

DFT | Density Functional Theory |

EMA | easy magnetization axis |

EVM | even-valued magnetization |

FiM | ferrimagnetic |

FM | ferromagnetic |

GGA | Generalized-Gradient Approximation |

KS | Kohn-Sham |

MAE | Magnetic anisotropy energy |

MoMo | dymolybdenum tetraacetate |

${\mathsf{\mu}}_{\mathrm{B}}$ | Bohr magneton |

OVM | odd-valued magnetization |

PBE | Perdew-Burke-Ernzerhof |

SMM | single molecule magnet |

SOC | spin-orbit coupling |

TM | Transition Metal |

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**Figure 1.**The structure of the dimolybdenum tetraacetate (MoMo) (

**a**) in the gas phase and (

**b**) as adsorbed on the three-layers slab model of the calcite (10.4) surface. The chemical species are indicated at the center of each atomic ball in (

**a**).

**Figure 2.**The magnetization of Mo atoms for some of the considered polar angles: $\theta ={0}^{\circ}$ (

**a**); $\theta ={30}^{\circ}$ (

**b**); $\theta ={60}^{\circ}$ (

**c**); $\theta ={90}^{\circ}$ (

**d**). The Mo-Mo EMA is defined by the direction of magnetizaion in (

**a**).

**Figure 3.**The total energy of the system as a function of the polar angle $\theta $ between the total magnetic moment and the molecular Mo-Mo axis (the axis of easy magnetization—EMA). The energy is referred to the ground state with the magnetization aligned along the EAM. The two sets of data refer to two values of the azimuthal angle $\varphi $: 0${}^{\circ}$ (direction of one acetate arm–black diamonds), and 45° (bisecting direction between neighboring arms–blue solid line).

**Table 1.**GGA-PBE results for the MoMo molecule in the gas-phase. For each state, we report the total energy E (relative to the nonmagnetic ground state energy), the total magnetization M, the Mo-Mo distance d${}_{Mo-Mo}$ and the magnetization on the d states of each Mo, n${}^{\uparrow}$- n${}^{\downarrow}$. Double entries in n${}^{\uparrow}$- n${}^{\downarrow}$ refer to the Mo atoms, when they present different magnetizations. In the first row, the numbering at the end of the label refers to the corresponding value of M.

NM | FM1 | FM2 | FM4 | FM6 | FM8 | |
---|---|---|---|---|---|---|

E (eV) | 0 | 0.90 | 1.43 | 3.57 | 4.08 | 5.34 |

M (${\mathsf{\mu}}_{\mathrm{B}}$) | 0 | 1 | 2 | 4 | 6 | 8 |

d${}_{Mo-Mo}$ (Å) | 2.09 | 2.12 | 2.15 | 2.42 | 2.67 | 2.98 |

n${}^{\uparrow}$- n${}^{\downarrow}$ | 0.0 | 0.45, 0.44 | 0.88, 0.87 | 1.82, 1.81 | 2.74 | 3.51 |

NM | AFM | FM2 | AFiM2 | FM4 | FiM4 | FM6 | FM8 | ||
---|---|---|---|---|---|---|---|---|---|

DFT + U | ${U}_{Mo1}$ | 3.84 | 3.58 | 3.54 | 4.09 | 3.61 | 3.58 | 3.60 | 3.23 |

${U}_{Mo2}$ | 3.85 | 3.58 | 3.55 | 4.06 | 3.58 | 3.62 | 3.61 | 3.24 | |

DFT + U + V | ${U}_{Mo1}$ | 4.53 | 4.20 | 4.06 | 4.09 | 4.20 | 4.34 | 4.16 | 3.80 |

${U}_{Mo2}$ | 4.54 | 4.20 | 4.07 | 4.17 | 4.24 | 4.23 | 4.17 | 3.81 | |

${V}_{Mo1-Mo2}$ | 0.40 | 0.07 | 0.14 | 0.01 | 0.01 | 0.07 | −0.18 | 0.18 | |

${V}_{Mo1-O}$ | 1.31 | 1.20 | 1.16 | 1.16 | 1.19 | 1.27 | 1.16 | 1.08 | |

${V}_{Mo2-O}$ | 1.31 | 1.20 | 1.16 | 1.19 | 1.21 | 1.22 | 1.17 | 1.08 |

**Table 3.**DFT+Hubbard results for the MoMo molecule in the gas-phase and as adsorbed on calcite (10.4). DFT + U + ${V}_{ads}$ indicates calculations for MoMo adsorbed on calcite, performed only on lowest-energy magnetic configurations.

NM | AFM | FM2 | AFiM2 | FM4 | FiM4 | FM6 | FM8 | ||
---|---|---|---|---|---|---|---|---|---|

DFT + U | E (eV) | 2.43 | 0.0 | 1.72 | 1.51 | 1.59 | 1.78 | 1.22 | 0.99 |

M (${\mathsf{\mu}}_{\mathrm{B}}$) | 0 | 0 | 2 | 2 | 4 | 4 | 6 | 8 | |

d${}_{Mo-Mo}$ (Å) | 2.09 | 2.54 | 2.14 | 2.57 | 2.70 | 2.70 | 2.66 | 2.99 | |

n${}^{\uparrow}$- n${}^{\downarrow}$ | 0.0 | 3.28, −3.28 | 0.94 | 3.38, −1.5 | 0.53, 3.36 | 3.36, 0.53 | 2.88 | 3.72 | |

DFT + U + V | E (eV) | 2.45 | 0.0 | 2.05 | 1.02 | 2.65 | 1.54 | 1.26 | 0.99 |

M (${\mathsf{\mu}}_{\mathrm{B}}$) | 0 | 0 | 2 | 2 | 4 | 4 | 6 | 8 | |

d${}_{Mo-Mo}$ (Å) | 2.10 | 2.58 | 2.15 | 2.57 | 2.42 | 2.72 | 2.66 | 2.98 | |

n${}^{\uparrow}$- n${}^{\downarrow}$ | 0.0 | 3.32, −3.32 | 0.93 | 3.32, −1.47 | 1.87, 1.93 | 3.36, 0.49 | 2.86 | 3.69 | |

DFT + U + ${V}_{ads}$ | E (eV) | 3.48 | 0.0 | 0.94 | 1.29 | ||||

M (${\mathsf{\mu}}_{\mathrm{B}}$) | 0 | 0 | 2 | 8 | |||||

d${}_{Mo-Mo}$ (Å) | 2.12 | 2.53 | 2.51 | 2.93 | |||||

n${}^{\uparrow}$- n${}^{\downarrow}$ | 0.0 | 3.18, −3.20 | 3.10, −1.27 | 3.67, 3.71 |

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**MDPI and ACS Style**

Cococcioni, M.; Floris, A.
Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface. *Appl. Sci.* **2021**, *11*, 3806.
https://doi.org/10.3390/app11093806

**AMA Style**

Cococcioni M, Floris A.
Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface. *Applied Sciences*. 2021; 11(9):3806.
https://doi.org/10.3390/app11093806

**Chicago/Turabian Style**

Cococcioni, Matteo, and Andrea Floris.
2021. "Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface" *Applied Sciences* 11, no. 9: 3806.
https://doi.org/10.3390/app11093806