## 3.1 Optimized structures and some parameters of the monomer, dimer and trimer of [email protected]6H6

Figure 1 shows the optimized geometries of [email protected]6H6 and the dimer ([email protected]6)2H10 and the trimer ([email protected]6)3H12. The bond lengths and the charges of monomer, dimer and trimer are listed in Table 1 and Table 2, respectively. The monomer [email protected]6H6 forms the perfect regular hexagon with the planar hexacoordinate Fe atom, possessing the highest *D**6h* symmetry. And the bond lengths and charges agree well with those obtained at BP86/6-311 + G(3df,3pd) level16. For the dimer ([email protected]6)2H10,

it has the highest *D**2d* symmetry and the dihedral angle between the two monomer is 90◦ and the distance between them is 1.660 Å which is in good agreement with the experimental value of B-B bond length (1.691 Å)25, suggesting the interaction between the monomers are very strong. While comparing with the monomer [email protected]6H6, the bond lengths and charges the dimer ([email protected]6)2H10 do not change significantly in each monomer except the B atom that links the other monomer. For the dimer ([email protected]6)2H10, all atoms in each monomer are coplanar, which indicates that the character of monomer [email protected]6H6 is well maintained during the dimerization. The dimer ([email protected]6)2H10 with *D**2h* symmetry is a transition state for the conversion to the *D**2d* conformation. For the trimer ([email protected]6)3H12, it has the highest *C**2v* symmetry and the three monomers are perfectly coplanar. The hole in the trimer is not regular hexagon and it is composed of two different types of B–B distances, which are RB1−B5 = 1.671 Å and RB5−B6 = 1.846 Å, respectively.

The ΔH−L, *VIP* and *VEA* of the monomer, dimer and trimer of [email protected]6H6 are also listed in Table 2. It can be seen that the ΔH−L values of monomer, dimer and trimer are 3.58, 3.22 and 2.80 eV, respectively. Although the ΔH−L value of trimer is the smallest among them, it is larger than the ΔH−L value (2.63 eV) of triphenylene26, indicating the monomer, dimer and trimer of [email protected]6H6 are chemically stable. The *VIP* values of monomer, dimer and trimer are 8.06 eV, 7.68 eV and 7.57 eV, respectively, increasing gradually while the *VEA* values of monomer, dimer and trimer are 1.69 eV, 2.15 eV and 2.53 eV, respectively, decreasing gradually.

## 3.2 the molecular orbital and aromaticity of the trimer ([email protected]6)3H12

Since [email protected]6H6 exhibits the similar π molecule orbitals to benzene16, the trimer ([email protected]6)3H12 may be the triphenylene analogue. In order to confirm our conjecture, the π-electron molecular orbitals (MOs) of ([email protected]6)3H12 and triphenylene are plotted in Fig. 2. It can be seen that the shape of these Mos of ([email protected]6)3H12 and triphenylene are similar. For example, the HOMO-5 of ([email protected]6)3H12 is bond MO which is similar to the bond MO of HOMO-9 in triphenylene. In addition, both ([email protected]6)3H12 and triphenylene have three degenerate MOs (HOMO, HOMO-6 and HOMO-8 in ([email protected]6)3H12 and HOMO, HOMO-2 and HOMO-6 in triphenylene). As a result, their nine π-electron MOs accommodate 18 π electrons that satisfy the (4n + 2) Huckel rule. Thus, the trimer ([email protected]6)3H12 exhibits the aromaticity and can be considered to be the triphenylene analogue.

*NICS* is a simple and efficient criterion to characterize aromatic nature. To better understand the aromaticity, the calculated *NICS*(d) (d = 0 and 1 for inside and above the hole, respectively.) of ([email protected]6)3H12 and triphenylene are also shown in Fig. 2. The *NIC*S(0) = -0.53 ppm and *NICS*(1) = -0.28 ppm of the hole in the trimer ([email protected]6)3H12 are less

negative than the *NICS*(0) = -1.72 ppm and *NICS*(1) = -5.09 ppm of the hole in triphenylene, which indicats that the hole of trimer ([email protected]6)3H12 is less aromatic than that of triphenylene. While the monomer in the trimer ([email protected]6)3H12 has very strong aromatic character since its *NICS*(1) = -15.2 ppm is more negative than − 9.8 ppm for the monomer in triphenylene, which can compensate the aromaticity of the hole in trimer ([email protected]6)3H12.

## 3.3 The structure and stability of graphene analogue FeB6

Before building the graphene analogue FeB6, we examined the bigger stable aggregates. Two kinds of different dimerization of the trimer are shown in Fig. 3. The six monomers reveal perfect coplanarity in each of them, indicating the trimer possesses very good ability of plane expansion. Thus, assembling the stable trimers ([email protected]6)3H12 can provide the possibility of building graphene analogue FeB6 as the triphenylene in graphene27,28.

And then, we optimized the graphene analogue FeB6, as shown in Fig. 4. The FeB6 with *P6/mmm* symmetry is completely planar structure. The boron-ring with Fe atom in the FeB6 has the B-B bond length of 1.860 Å and B-Fe bond length of 1.860 Å, which are slight longer than those (1.824 Å) of [email protected]6H6 monomer. And the bond lengths of two different B-B in the boron-ring without Fe atom are 1.860 Å and 1.661 Å, which are similar to those of boron-ring in [email protected]6H6 trimer. Therefore, the graphene analogue FeB6 preserves the structural features of monomer and trimer of [email protected]6H6.

We also studied the hexagon hole density of the FeB6. The hexagon hole density (*η*) is defined as26 29a:

According to the formula, the triangular boron sheet has *η *= 0, the hexagonal boron sheet *η *= 1/329. For the FeB6, it represents a hexagonal hole density of *η *= 2/7, which is bigger than those in pure boron α and β29 and very close to the hexagonal boron sheet *η* = 1/3.

Besides, we also investigated the dynamical stability of the FeB6. The phonon dispersion is shown in Fig. 5. The unit cell of FeB6 monolayer has seven atoms, suggesting that the phonon band structures should have 21 phonon branches. The highest frequency reaches up to 1204 cm− 1, and is higher than the highest frequency of 1036 cm− 1 in BSi30 and 924 cm− 1 in Ti2B231, indicative of robust Fe-B and B-B interactions in FeB6 monolayer. Furthermore, the absence of virtual frequencies at any high-symmetry direction also confirms the dynamic stability of the FeB6.