Can CF(3)-functionalized La@C(60) be isolated experimentally and become superconducting?

TL;DR

This study uses ab initio calculations to explore the stability and electronic properties of CF(3)-functionalized La@C(60), suggesting potential for superconductivity under ambient conditions due to stabilization and electronic effects.

Contribution

It provides the first theoretical analysis of CF(3) functionalization on La@C(60), identifying stable isomers and implications for superconductivity enhancement.

Findings

CF(3) radicals favor binding to La@C(60) and C(60)

Stable isomers depend on the number of radicals and charge state

CF(3) functionalization may increase superconducting critical temperature

Abstract

Superconducting behavior even under harsh ambient conditions is expected to occur in La@C(60) if it could be isolated from the primary metallofullerene soot when functionalized by CF(3) radicals. We use ab initio density functional theory calculations to compare the stability and electronic structure of C(60) and the La@C(60) endohedral metallofullerene to their counterparts functionalized by CF(3). We found that CF(3) radicals favor binding to C(60) and La@C(60), and have identified the most stable isomers. Structures with an even number m of radicals are energetically preferred for C(60) and structures with odd m for La@C(60) due to the extra charge on the fullerene. This is consistent with a wide HOMO-LUMO gap in La@C(60)(CF(3))(m) with odd m, causing extra stabilization in the closed-shell electronic configuration. CF(3) radicals are both stabilizing agents and molecular separators in a metallic crystal, which could increase the critical temperature for superconductivity.

Equations

$$\Delta E^t(m)=E_{tot}(m)-E_{tot}^{min}(m-1)-\frac{1}{2}{E}_{tot}({\mathrm{C}}_2{\mathrm{F}}_6).$$

$$\Delta E^H=E_{tot}(H/R)-E_{tot}(\mathrm{R})-\frac{1}{2}{E}_{tot}{(\mathrm{H}}_2).$$

Full text

\abbreviations

DFT, PBE, PAW, HOMO, LUMO, HPLC

The discovery of the C60 fullerene 1 with a hollow cage structure immediately triggered the question, whether the space inside could be filled by other atoms. This question has been answered affirmatively shortly afterwards by successfully encapsulating metal atoms including Li, Na, K, Rb, Sr, Ba, Sc, La, Tc and U inside M@C2n endohedral fullerenes, also called metallofullerenes. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

A major reason for the current interest in metallofullerenes such as La@C60 is the possibility to observe superconductivity in solid C60 that is doped endohedrally rather than exohedrally by 3 electrons 14. A molecular crystal formed of isolated and recrystallized La@C60 molecules would be electronically related to M3C60 with M representing alkali atoms. In M3C60 crystals, superconductivity with $T_{c}{\lesssim}40$ K has been observed and explained by electron-phonon coupling that is modulated by the lattice constant 15, 16. The same behavior is expected to occur in the isoelectronic La@C60 crystal. Unlike alkali-based C60 superconductors, La@C60 crystals will be stable under ambient or even harsh conditions.

In spite of the fact that fullerene cages of different size favor encapsulation of metal atoms energetically 3, 5, 13, 17, 18, most of the resulting complexes are highly reactive due to their open-shell configuration and form insoluble polymerized solids 19. Only M@C2n metallofullerenes with large cages 5 ($2n{\gtrsim}74$) have been successfully isolated from the raw soot, with M@C82 dominating. It has been difficult to extract the most abundant M@C60 and M@C70 metallofullerenes due to their insolubility in regular fullerene solvents 13, 20, 21 such as toluene and CS2. Even though several metallofullerenes with cages as small as C60 have been extracted by solvents such as pyridine and aniline 22, 23, 24, 21, it has become a large challenge to separate the M@C60 fraction, since pyridine and aniline solvents are not suitable for high-performance liquid chromatography (HPLC) 20. Only recently, La@C70 and Y@C2n with $2n{\geq}60$, functionalized by CF3 radicals, have been separated using toluene and CS2 as solvents 19, 25. In this new strategy, the function of trifluoromethyl radicals was to further separate the metallofullerene cages and to chemically stabilize their unstable open-shell electronic configuration 26. Isolation and crystallization of the more interesting La@C60 molecules is currently being attempted 14.

In view of the possibility to obtain superconducting behavior in crystalline La@C60 even under harsh ambient conditions, we provide theoretical support for the experimental effort to solubilize the La@C60 endohedral metallofullerene from the primary soot. We made use of ab initio density functional theory calculations to compare the stability and electronic structure of the bare C60 fullerene and La@C60 to their counterparts functionalized by $m$ CF3 radicals. We found that several CF3 radicals can form stable bonds to C60 and La@C60, and have identified the most stable structural isomers for $m{\leq}5$. Generally, structures with an even $m$ are energetically preferred for C60 and structures with an odd $m$ for La@C60 due to the extra 3 electrons donated by the encapsulated La. This is consistent with our finding that a wide HOMO-LUMO gap opens in La@C60(CF3)m molecules with an odd $m$ value, causing extra stabilization in the closed-shell electronic configuration. The two-fold function of CF3 radicals as stabilizing agents and molecular separators may help in isolating specific molecules from the primary soot. If La@C60(CF3)m could be solubilized and recrystallized, endohedral instead of exohedral doping by three electrons per C60 and use of stabilizing CF3 radicals as spacers may lead to superconductivity with a relatively high $T_{c}$ achieved by increasing the lattice constant of the molecular crystal 15, 16. We should note that the range of favorable lattice constants is limited, since their increase beyond a critical value changes doped C60 from a metal to a Mott-Hubbard insulator 27, 28. Even more appealing than changing the lattice constant appears the possibility to remove CF3 radicals after obtaining La@C60(CF3)m in solution and subsequently recrystallize La@C60. Stability even under harsh ambient conditions is expected due to the absence of alkali atoms filling interstitial sites in known M3C60 superconductors. Moreover, the possibility to encapsulate different elemental species provides an additional handle on tuning $T_{c}$ of M@C60 superconductors. 29

1 Results

We have used density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) 30 exchange-correlation functional to determine the equilibrium geometry of La@C60 and La@C60(CF3)m molecules for $m{\leq}5$. For a given number $m$ of attached CF3 radicals, we optimized many different regioisomers, as specified in the Supporting Information, and displayed the most stable structures in Figure 1. Figure 1(a) displays the bare C60 molecule containing a La atom in its equilibrium off-center configuration. As seen in Figure 1(b), CF3 radicals prefer to attach on-top of C atoms in the C60 cage. Whereas the adsorption of a single CF3 radical on the bare C60 cage in a metastable geometry is an endothermic process requiring $0.43$ eV, presence of La in the La@C60 metallofullerene turns this adsorption process exothermic with an energy gain of $0.31$ eV. We considered 10 regioisomers for $m=2$ and display their optimum geometry, the corresponding Schlegel diagram and relative energy in Figure S1 of the Supporting Information, with the most stable geometry given in Figure 1(c). These results indicate that CF3 radicals in the most stable $m=2$ regioisomer are in para (third neighbor) positions on a single hexagon on the C60 surface, and that this structure has a C2v symmetry. Other arrangements of the radicals are penalized energetically up to ${\lesssim}1$ eV. Comparing the relative energies of other regioisomers, we found that CF3 radicals prefer to be close, but not too close on the C60 surface.

A very similar picture emerges for $m=3$ CF3 radicals adsorbed on La@C60. Six different regioisomers, their relative energies and the corresponding Schlegel diagrams are presented in Figure S2 of the Supporting Information. As for $m=2$, the optimum arrangement of CF3 radicals in the most stable isomer, shown in Figure 1(d), is in para position on adjacent hexagonal rings on the C60 surface and results in a mirror symmetry for the molecule. The second most stable isomer contains CF3 radicals separated by 5 neighbor distances, is only ${\approx}0.1$ eV less stable than the most stable structure, and has a C3 symmetry. Even though nearest-neighbor arrangements of CF3 radicals were not considered, other structural candidates incurred an energy penalty of up to ${\lesssim}1.3$ eV with respect to the most stable isomer.

The structural paradigm changes when increasing the number of CF3 radicals attached to La@C60 to $m=4$. Among the 10 regioisomers presented in Figure S3 of the Supporting Information, the most stable structure, shown in Figure 1(e), contains two pairs of CF3 radicals in para-arrangement on hexagonal rings that are separated by half the circumference of the C60 molecule. Another arrangement, with all CF3 radicals in para arrangement on adjacent hexagonal rings, is energetically the second-best isomer, with its energy only $0.051$ eV higher than the most stable structure. The most stable isomer has a C2v symmetry and the second-best isomer only a mirror symmetry.

The structural paradigm for La@C60(CF3)m regioisomers with $m=5$ CF3 radicals is similar to the $m=4$ case. The most stable of ten regioisomers, presented in Figure S4 of the Supporting Information and displayed in Figure 1(f), contains 4 CF3 radicals in para arrangement on three adjacent hexagonal rings. The last radical is separated by 4 neighbor distances from the closest CF3 radical. It is also possible to arrange all five CF3 radicals in para positions on four adjacent hexagonal rings, but this highly symmetric regioisomer is less stable by ${\lesssim}0.9$ eV than the most stable structure.

To find out the preferential number of CF3 radicals attached to the La@C60 molecule, we calculated the energy change ${\Delta}E^{t}(m)$ associated with attaching an extra trifluoromethyl radical to the most stable La@C60(CF3)m-1 isomer and display our results in Figure 2. We defined ${\Delta}E^{t}(m)$ by

[TABLE]

$E_{tot}^{min}(m)$ denotes the total energy of the most stable La@C60(CF3)m isomer. A negative value of ${\Delta}E^{t}(m)$ indicates an exothermic reaction for adsorbing an extra CF3 radical that had been initially formed by dissociating a hexafluoroethane molecule. ${\Delta}E^{t}(0)$ for the bare metallofullerene has been set to zero.

According to our results in Figure 2, it is always possible to find a structural arrangement of CF3 radicals that would further stabilize the La@C60 structure. We find structures with odd number of radicals to be relatively more stable, with $m=3$ providing the optimum stabilization with ${\Delta}E^{t}(3)=-0.44$ eV. In comparison, the stability gain ${\Delta}E^{t}(4)=-0.11$ eV upon adsorbing four radicals is much smaller. Equally interesting as the optimum regioisomer is the range of ${\Delta}E^{t}(m)$ values for a given $m$, which is as wide as $3$ eV. We should not neglect the fact that functionalization by CF3 radicals within the raw soot may not always yield the most stable isomers.

The even-odd alternation in the ${\Delta}E^{t}(m)$ values for the most stable isomers, with odd values referring to higher stability, has been found previously for CF3-functionalized La@C70 and Y@C70 molecules 19, 25. The even-odd alternation is also found in CF3-functionalized fullerenes, which, however, display an energetic preference for an even number of CF3 radicals 31, 32. The preference of fullerenes for an even number of CF3 radicals can be explained easily. Attaching an even number of radicals to nominal double-bonds in the fullerene cage converts the C atoms in the double-bond from an $sp^{2}$ to an $sp^{3}$ configuration, leaving no radical behind. Consequently, an odd number of CF3 radicals will leave at least one C radical behind, lowering the stability of the structure.

As we will discuss next, an La atom – upon its encapsulation – transfers 3 electrons to the C60 shell, whereas the charge transfer caused by attached CF3 radicals is significantly smaller. The odd number of electrons added to the shell modifies its electronic structure, resulting in an energetic preference for an odd instead of an even number $m$ of CF3 radicals attached to C60.

Electronically, there is no difference if the negative charge of the C${}_{60}^{3-}$ shell stems from encapsulated La in a hypothetical La@C60 or from 3 alkali atoms that are interstitial in the M3C60 crystal. The electronic structure of the corresponding molecular crystal will be determined by the narrow band formed of the partly occupied LUMO of the C60 molecules. Except for a dynamical Jahn-Teller effect, the system should be metallic and superconducting, with $T_{c}$ depending in the same way on the lattice constant as in the equivalent M3C60 molecular crystal 16. The present understanding of the origin of superconductivity in alkali-based M3C60 solids is discussed in the Supporting Information.

Plausibilizing the difference between the functionalization of a bare C60 fullerene and the La@C60 metallofullerene requires understanding the charge redistribution introduced by the encapsulated La atom in C60. We discuss this charge redistribution in detail in the Supporting Information, in particular in Figure S1. The essence of our findings is consistent with the Bader charge analysis 33, 34, 35, 36 of the bare C60 molecule and all metallofullerenes depicted in Figure 1. Independent of the presence and number $m$ of attached CF3 radicals, we found a net transfer of ${\approx}1.8$ electrons from the encapsulated La atom to the C60 cage. Restating this finding in a different way, the net charge of the La atom was not affected by the presence of CF3 radicals carrying a net Bader charge $Q{\approx}-0.1e$, which was transferred locally from the C60 cage alone. In view of the ambiguity to assign a delocalized charge to particular atoms, we may assume that the charge transfer from the La atom to the cage is likely underestimated by the Bader analysis. Comparing to similar systems, where a Bader analysis has been performed 37, 38, we found the enclosed La to be most likely in the $3+$ oxidation state, with the C60 cage carrying extra 3 electrons.

The net electron transfer from the encapsulated atom to the surrounding cage is also the cause of the off-center displacement of La by ${\approx}1.2$ Å. In DFT-PBE, this symmetry-lowering displacement is associated with an energy gain of ${\approx}3.3$ eV. This stabilization energy can be simply explained by the electrostatic polarization energy gain caused by a point charge moving off-center inside a spherical metallic shell, as discussed previously for other metallofullerenes 39, 40. Using $+3e$ as the net charge of the enclosed La and $3.5$ Å as the radius of the C60 shell, we estimated in this way an energy gain of $1.7$ eV, the same order of magnitude as the value obtained in the DFT calculation.

If the reason for altering the energetic preference from an even to an odd number of attached CF3 radicals is leaving or not leaving a C radical behind, then a single chemisorbed H atom chemisorbed on the same double-bond as a lone CF3 radical may reverse this preference. To investigate this possibility, we studied the structural and energetic changes associated with the chemisorption of a hydrogen atom on bare and CF3-functionalized fullerenes and metallofullerenes and present our results in Figure 3.

We defined the energy change ${\Delta}E^{H}$ associated with attaching a single H atom to a bare of CF3-functionalized fullerene C60 or metallofullerene La@C60, denoted by R, by

[TABLE]

A negative value of ${\Delta}E^{H}$ indicates that the adsorption of an H atom, which had initially been formed by dissociating an H2 molecule, is exothermic.

The top row in Figure 3 describes different ways of chemically functionalizing a C60 cage. The positive value of ${\Delta}E^{H}$ in the top panel of Figure 3(a) indicates that hydrogen prefers not to adsorb on the bare C60 cage, as discussed previously for carbon nanotubes and fullerenes 41, 42. This behavior changes in presence of an adsorbed CF3 radical, which modifies the electronic structure of the cage. Noting that adsorption of an isolated H atom or an isolated CF3 radical on the cage are both endothermic processes, it is remarkable that the co-adsorption of CF3 and H turns strongly exothermic, as seen in the top panels of Figs. 3(b) and 3(c). As anticipated above and seen in the top panel of Figure 3(c), the largest energy gain occurs when the adsorbates attach to the same double-bond on the cage, in ortho arrangement on the same hexagonal ring, changing the configuration of the adjacent C atoms from $sp^{2}$ to $sp^{3}$ and leaving no C radical behind. Somewhat less favorable is co-adsorption in a para arrangement on the same hexagon, shown in the top panel of Figure 3(b). The adsorption sites and the differences in local bonding mentioned above are best discussed using the Schlegel diagrams in the bottom panels of Figure 3.

The energetics of chemical functionalization changes completely when a La atom becomes enclosed in the C60 cage. Since the adsorption of an isolated H atom or an isolated CF3 radical become exothermic processes on La@C60, it is not surprising that all values of ${\Delta}E^{H}$ are negative, as seen in the second row of Figure 3. This means, in other words, that hydrogenation of La@C60(CF3)m is always exothermic, irrespective of the presence of CF3 radicals on the surface. Unlike in the top row, the three values of ${\Delta}E^{H}$ in the second row are much more similar: adsorbing an extra CF3 radical next to a pre-adsorbed H atom lowers the energy by ${\approx}0.1$ eV in the para configuration and raises it by ${\approx}0.2$ eV in the ortho configuration. We note the small energetic preference for the para configuration in this case, which is reminiscent of the most stable regioisomer of La@C60(CF3)2 shown in Figure 1(c).

The change in behavior can be attributed to the 3 electrons donated to the C60 cage from the encapsulated La atom. Each of these extra electrons can be partly transferred to the electronegative CF3 radical and participate in bonding, leaving no C radical behind. This is the reason behind our finding in Figure 2 that La@C60(CF3)m is most stable for $m=3$.

As suggested by the above results, electronic structure plays the key role in determining both the stability and reactivity of fullerenes and (functionalized) metallofullerenes. The electronic eigenstates of the optimized bare C60 molecule and of the La@C60(CF3)m molecules with $0{\leq}m{\leq}5$, depicted in Figure 1, are presented in Figure 4. The energy eigenvalues are the Kohn-Sham energies of our DFT-PBE calculations, which are known to underestimate the HOMO-LUMO gap.

As seen in Figure 4(a), the calculated gap between the fivefold degenerate $h_{u}$ HOMO and the threefold degenerate $t_{1u}$ LUMO of the highly symmetric C60 molecule is ${\approx}1.6$ eV wide, slightly lower than the observed value 43 of $1.9$ eV. The calculated electronic spectrum of La@C60 is shown in Figure 4(b). As expected, the off-center displacement of the La atom reduces the symmetry and the degeneracy of electronic states. For the sake of simple comparison, we highlighted the occupied $h_{u}$ state of C60 and the corresponding occupied eigenstates in La@C60 by the orange-bounded rectangle. As seen in Figure 4(b), the symmetry lowering due to the off-center displacement of La splits the $h_{u}$ state of C60 into three closely-spaced states, two of which are doubly degenerate. More interesting is the behavior of the initially unfilled $t_{1u}$ state in the C60 molecule, which splits into two states, as highlighted by the red-bounded rectangle in Figs. 4(a) and 4(b). The lower of these states in La@C60 is doubly degenerate and acquires 3 extra electrons from the enclosed La atom. Consequently, this partly occupied state defines the Fermi level and provides a metallic character for the La@C60 molecule. The significant fundamental band gap is responsible for the high stability and low reactivity of the C60 molecule, whereas a vanishing band gap renders La@C60 highly reactive. To better understand the effect of the encapsuled La atom on the electronic structure of the La@C60 molecule, we discuss the frontier states near the Fermi level of C60 and La@C60 molecules in the Supporting Information.

For La@C60(CF3)m metallofullerenes functionalized with $m{\geq}1$ CF3 radicals, the eigenstates undergo a complex change and can no longer be simply compared to those of the bare C60 molecule. Comparing our results in Figs. 4(b-g), we find zero fundamental band gap in molecules with an even number $m$ of CF3 radicals and a nonzero band gap if $m$ is odd. This finding suggests that La@C60 molecules with an odd number of CF3 radicals should be more stable, in accord with our previous findings based on total energy calculations. Among La@C60(CF3)m molecules, we found the largest HOMO-LUMO gap $E_{g}{\approx}1.0$ eV for $m=5$, followed by $E_{g}{\approx}0.7$ eV for $m=3$ and a very small value $E_{g}{\approx}0.1$ eV for $m=1$. Consequently, we expect metallofullerenes with $m=3$ and $m=5$ CF3 radicals to be most abundant and easiest to separate from the primary soot, as also suggested by preliminary experimental data 14. Metallofullerenes with an even number of CF3 radicals have unpaired electrons at the Fermi level, which makes these molecules more reactive and less stable.

All molecules discussed above will be further stabilized when crystallizing in a lattice. We performed corresponding calculations and found that, same as C60 molecules, the metallofullerenes prefer the close-packed fcc lattice, and also found no indication of dimerization in the lattice. One issue that is typically neglected when judging the stability of crystalline lattices using single-molecule description is the effect of the long-range dipole-dipole interaction. To judge the importance of this effect, we performed DFT-PBE calculations for selected fullerene and metallofullerene lattices. Even though the PBE exchange-correlation functional does not describe the van der Waals interaction accurately, such calculations still provide an adequate description of the charge redistribution and dipole-dipole interaction. C60 molecules, carrying no dipole moment, crystallize preferably in an fcc lattice with a nearest-neighbor distance of 10.83 Å, gaining energetically ${\approx}0.06$ eV per molecule. According to our Bader charge analysis, La@C60 metallofullerenes carry a dipole moment $p=3.3$ D and crystallize in an fcc lattice with a slightly reduced nearest-neighbor distance of 10.72 Å, gaining ${\approx}0.10$ eV per molecule. The stabilization of the La@C60 lattice with respect to crystalline C60 lattice, however small, benefits to a large degree from the long-range dipole-dipole interaction, since an fcc lattice of $p=3.3$ D point dipoles should be stabilized by a comparable energy of ${\approx}0.06$ eV/molecule. We have furthermore found that functionalization of the La@C60 metallofullerene by CF3 radicals increases the molecular dipole moment, but also increases the nearest-neighbor distance. In the fcc lattice of La@C60CF3 molecules with a dipole moment $p{\approx}12.4$ D, the nearest-neighbor distance increases to $11.72$ Å and the stabilization in the lattice changes to ${\approx}0.09$ eV/molecule. Similarly, in the fcc lattice of the most stable La@C60(CF3)2 molecules with a dipole moment $p{\approx}18.9$ D, the nearest-neighbor distance changes to $11.68$ Å and the stabilization in the lattice changes to ${\approx}0.10$ eV/molecule. The above DFT-PBE values of the lattice stabilization energy in CF3-functionalized metallofullerenes are one order of magnitude smaller than estimates based on the interaction of point dipoles. Our overall finding is that long-range dipole-dipole interaction is of secondary importance for these lattices.

2 Conclusions

In summary, exploring the possibility to obtain superconducting behavior in crystalline La@C60 even under harsh ambient conditions, we provided theoretical support for the experimental effort to solubilize the La@C60 endohedral metallofullerene from the primary soot. We used ab initio density functional theory calculations to compare the stability and electronic structure of the bare C60 fullerene and La@C60 to their counterparts functionalized by $m$ CF3 radicals. We found that several CF3 radicals can form stable bonds to C60 and La@C60, and have identified the most stable structural isomers for $m{\leq}5$. Generally, structures with an even $m$ are energetically preferred for C60 and structures with an odd $m$ for La@C60 due to the extra 3 electrons donated by the encapsulated La. This is consistent with our finding that a wide HOMO-LUMO gap opens in La@C60(CF3)m molecules with an odd $m$ value, causing extra stabilization in the closed-shell electronic configuration. We also addressed the possibility of a single hydrogen atom adsorbing at a C radical site in La@C60(CF3)m, which would further stabilize the open-shell configuration for odd $m$ values and reduce the even/odd alternation in stability. We found that the two-fold function of CF3 radicals as stabilizing agents and molecular separators may help in isolating specific molecules from the primary soot. If La@C60(CF3)m could be solubilized and recrystallized, endohedral instead of exohedral doping by three electrons per C60 and use of stabilizing CF3 radicals as spacers may lead to superconductivity with a relatively high $T_{c}$ achieved by optimizing the lattice constant of the molecular crystal. Stability even under harsh ambient conditions should then be expected due to the absence of alkali atoms filling the interstitial sites in known M3C60 superconductors.

3 Computational Techniques

We utilized ab initio density functional theory (DFT) as implemented in the VASP code 44, 45, 46 to optimize the structure of C60 and La@C60(CF3)m functionalized with $0{\leq}m{\leq}5$ CF3 radicals and obtained the total energy as well as the electronic structure for these systems. We used projector-augmented-wave (PAW) pseudopotentials 47 and the Perdew-Burke-Ernzerhof (PBE) 30 exchange-correlation functional. All isolated structures have been represented using periodic boundary conditions and separated by a $12$ Å thick vacuum region, so that no band dispersion could be detected. We used $500$ eV as the electronic kinetic energy cutoff for the plane-wave basis and a total energy difference between subsequent iterations below $10^{-5}$ eV as the criterion for reaching self-consistency. All geometries have been optimized using the conjugate-gradient method 48 until none of the residual Hellmann-Feynman forces exceeded $10^{-2}$ eV/Å.

{suppinfo}

Additional information is provided regarding the origin of superconductivity in alkali-based M3C60 solids, charge distribution in the frontier states of pristine C60 and La@C60 molecules, and the equilibrium structure and stability of different La@C60(CF3)m regioisomers.

**Author Information

**

**Corresponding Author

∗**E-mail: tomanek@pa.msu.edu

**Notes

**The authors declare no competing financial interest.

{acknowledgement}

We would like to acknowledge useful discussions with Hisanori Shinohara, who inspired this study and advised us of experimental progress in his group, and with Zhongqi Jin. This study was supported by the NSF/AFOSR EFRI 2-DARE grant number #EFMA-1433459. Computational resources have been provided by the Michigan State University High Performance Computing Center.