#### Abstract

Through unbiased global optimization and density functional theory method, a series
of stable icosahedral magnetic TMLi_{12 (TM=Sc-Fe) clusters are identified, where the
3d transition-metal element is embedded at the center of Li12 cage. Energy calculations
and the moderate HOMO-LUMO gaps confirm their stability. Molecular orbitals analysis
reveals the superatomic properties.}

**Keywords:** Superatoms; Stability; Magnetic Moment; Electronic Shell; Binding energy;
Eb

#### Introduction

In recent years, the field of cluster science have been
increasingly investigated [1-3]. Among them, superatoms, which
can be used to mimic the chemical behaviour of atoms in the
periodic table, are the ‘magic’ atomic clusters [4]. The valance
electron of superatoms are accommodated in a series of quantized
orbitals labeled as 1S, 1P, 1D, 2S, 1F, 2P, etc. Their stability can be
understood by the jellium model, where the motions of electrons
are assumed in a uniform positive spherical background composed
by ionic charge of the cluster’s atomic nuclei and the innermost
electrons [5,6]. The corresponding electronic levels in superatoms
are 1S^{2}1P^{6}1D^{10}2S^{2}1F^{14}2P^{6}, etc., where 2, 8, 18, 20, 34 and 40, etc, are
associated with magic clusters. Such superatoms are non-magnetic
due to all the electrons paired. Khanna and coworkers proposed
the concept of magnetic superatoms and took an isolated VCs_{8} and
a ligated protected MnAu_{24}(SH)_{18} as examples in 2009, where the
magnetic moments were acquired by the orbitals localized at the
atomic sites and the stability was imparted by the diffuse states [7].
Since then, many reports about magnetic superatoms are emerged
[8-12]. In this work, we use Li_{13} as a prototype to design a new
type superatom, which is formed by replacing the central atom
of Li_{13} with a 3d transition-metal element. Then, the stability and
electronic properties of TMLi_{12} are discussed.

### Computational Methods

The structure of TMLi_{12} (TM=Sc, Ti, V, Cr, Mn, Fe, Co and Ni)
are located by unbiased global optimization method and density
functional theory (DFT) of Gaussian16 package [13]. Frequency
calculations prove that the icosahedron is a true energy minimum.
The spin multiplicities (SMs) of each isomer are determined by
comparison their energy of the same structure with different SMs,
where the SM of the lowest energy structure is that of ground states.
All the calculations are completed by adopting pure functional
PW91 and SDD the basis set [14,15].

#### Results and Discussion

The geometric of pure Li13 cluster is a centred icosahedron
with I_{h} symmetry as shown in Figure 1 and [16]. With the central
lithium atom is substituted by 3d transition-metal elements (Sc, Ti,
V, Cr, Mn, Fe, Co and Ni), and the structure retain still except CoLi_{12}
and NiLi_{12} by unbiased global optimization method. To identify the
stability of TMLi_{12} (TM=Sc, Ti, V, Cr, Mn, and Fe), we examine

a) The average binding energy (Eb) per atom of the transition metal atom to the cluster,

b) The energy gaps of the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps).

The E_{b} is defined as the following equation:

Where TM represents the 3d transition-metal atoms Sc, Ti,
V, Cr, Mn, and Fe. E(TMLi_{12}) is the total energy of the I_{h} symmetry
icosahedron. E(Li) and E(TM) are the total energy of the Li and TM
atoms in the free state, respectively. From (Figure 2), it can be seen
that the Eb of TMLi_{12} (TM=Sc, Ti, V, Cr, Mn, Fe) clusters is higher than
that of the corresponding pure Li_{13}. This indicate that embedding 3d
transition-metal elements (Sc, Ti, V, Cr, Mn, and Fe) into Li_{12} cage can
enhance its stability. However, the results of energy gaps give small
values, where large HOMO–LUMO gaps can enhance their stability
and reduce their reactivity. Taking the gaps of typical magnetic
superatoms as reference, the gaps are moderate, for example, V@
Na_{8} (0.69 eV) [7] and MnSr_{9} (0.35 eV) [8]. In addition, the gaps are
underestimated by the standard GGA functionals, and an accurate
gap need apply the hybrid functionals, for instance, the gap of FeLi_{12}
is 0.65 eV at the calculations of TPSSH/SDD. To examine the cause of their stability, we analyze the associated molecular orbitals,
and take MnLi_{12} as representative cluster, which has 19 effective
valence electrons offered by lithium atom (2s^{1) and manganese
atom (4s23d5), respectively. As shown in Figure 3, the lowest state
over the whole cluster has 1S character. The next five states are 1D
states while the degeneracy is broken into three groups of 1, 2 and
2 orbitals due to the oblate shape. The same occurs in the next 1P
states, which is split into Px, Py, Pz and the degeneracy is completely
removed. The next state is 2S, and the last occupied state has 2D
character. Therefore, the electronic filling order of 19e MnLi12 is
1S21Dα51P61Dβ42Sα12Dα1, where the HOMO-LUMO gap (0.07 eV) is from the energy difference of 2Dα1 and 1Dβ1. With three unpaired
electrons, the total spin magnetic moment of MnLi12 is 3.0 μB. Based
on above discussion, the centred icosahedral MnLi12 is a magnatic
superatom, where its stability is acquired by having a spin magnetic
moment of 3.0 μB. All the other clusters are magnatic superatoms
except CrLi12, which is a non-magnatic superatom due to all
the electrons paired. The analysis is similar, and their magnetic
moments also are display in Figure 2.}

#### Conclusion

In the work, we have demonstrated that cluster Li_{12}
endohedrally doped with a 3d transition-metal element (Sc, Ti, V,
Cr, Mn, and Fe) can form stable clusters with I_{h} symmetry. These
high symmetric clusters are identified as magnetic superatoms
except CrLi_{12}, which is non-magnetic. Such a combination could be
extended, where the transition-metal element in the same main
element is embedded and superatoms also exist due to the same
effective valence electrons.

#### Acknowledgement

This work is supported by the PhD Starting Fund of Guangdong Ocean University (120702/R17077).

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