Modification of boron nitride nanocages by titanium doping results unexpectedly in exohedral complexes

Despite their early experimental production and observation, the unambiguous molecular structures of metal-containing boron nitride (BN) nanocages still remain mysterious. It has been commonly assumed that this family of compounds has the metal atom confined inside the cage, just like their isoelectronic cousins, carbon metallofullerenes do. Here, we demonstrate that Ti(BN)n (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}n = 12–24) complexes have, unexpectedly, an exohedral structure instead of an endohedral one, which could be verified by collision-induced dissociation experiments. The predicted global minimum structures exhibit some common bonding features accounting for their high stability, and could be readily synthesized under typical conditions for generating BN nanoclusters. The Ti doping dramatically changes not only the cage topology, but the arrangement of B and N atoms, endowing the resultant compounds with potential for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2 capture and nitrogen fixation. These findings may expand or alter the understanding of BN nanostructures functionalized with other transition metals.


Supplementary Method 1: Identification of cage isomers and regioisomers of (BN) n fullerenes
Given a (BN) n fullerene molecule, there are two types of isomerism. First, the topology of the cage framework (i.e., the connectivity between atoms) gives a unique trivalent molecular graph, provided that all vertices (atoms) are indistinguishable. Hence, (BN) n and C 2n fullerenes have the same cage isomerism. To rigorously enumerate all possible cage isomers (trivalent molecular graphs), we have used the plantri program. 1 On the other hand, on top of a fixed cage topology, there are many possible ways to place n B and n N atoms, leading to the regioisomerism. For this reason, we use the letter i to denote an isomeric form of the cage connectivity and the letter j to denote a regioisomer of the BN arrangement.
Unlike classical fullerene cages, which consist of only pentagons and hexagons and can thus be readily identified using Fowler-Manolopoulos ring spiral algorithm, 2 the (BN) n cages considered in this work generally contain squares, pentagons, hexagons, and some may contain heptagons or octagons as well. Here, we have employed an algorithm 3 based on the connectivity list using the canonical labeling of vertices that follows the breadth-first-search (BFS) numbering scheme. 4,5 Using this technique, both the cage isomer and the regioisomer of BN distribution can be uniquely and readily identified.  3 we first choose a starting B atom at position iAt (running from 1 to 2n) to generate an initial arrangement of B, N atoms. This initial guess of B, N positions, corresponding to regioisomer j 0 , are deduced by placing B and N, as alternately as possible, on the cage vertices, following the connectivity list. Apparently, such a procedure does not necessarily give the optimal B, N arrangement with a minimum number of B-B (N-N) bonds. Nevertheless, it is reasonable enough for the subsequent optimization, which is to be detailed below. As shown in Supplementary Figure 1, after one step of optimization of B, N positions, usually a number of better regioisomers {j} are generated, which have fewer B-B (N-N) bonds than the initial regioisomer j 0 . Then, this better set of regioisomers {j} will be used as new initial guess configurations and be subject to a second round of optimization, which will generate more new regioisomers possibly with fewer B-B (N-N) bonds. By repeating the same procedure for maxIter iterations, we will arrive at a converged set of regioisomers with a minimum possible number of B-B (N-N) bonds. In the present work, we took a sufficiently large value of 1000 for maxIter to ensure the convergence. On top of this, by running the starting B atom at all possible positions on the cage (i.e., iAt varying from 1 to 2n), it is almost guaranteed that all regioisomers with the minimum possible number of B-B and N-N bonds are found. Now, we describe the algorithm of minimizing the number of B-B and N-N bonds, starting from a given initial arrangement of B and N atoms. As shown in Supplementary  2, given a cage topology i with a regioisomer j 0 , we count the initial number of B-B (N-N) bonds, denoted by N 0 . By running over all possible (B, N) pairs (no matter they are bonded or not), an interchange between each pair of B, N atoms, say at positions iB and iN , respectively, is rejected if the resultant number of B-B (N-N) bonds increases; otherwise, the swap is accepted, and the corresponding B, N arrangement is kept as a new regioisomer j(iB, iN ). In the end, among all generated new regioisomers, topologically identical ones are removed, by using the canonical numbering technique. 3 To check the efficacy of the algorithm, we optimized the B, N arrangement for some cages composed of squares, hexagons and/or octagons, with a random distribution of B, N atoms so that the initial number of B-B (N-N) bonds are nonzero. In all cases, the optimizations arrived at a correct arrangement with alternate B and N atoms on the cage, as expected. Similarly, we also tried some cages containing pentagons, and the optimizations succeeded to reduce the number of B-B (N-N) bonds to a reasonably small number, and sometimes being one, the minimum possible number of B-B (N-N) bonds that a pentagon-containing cage could possess. Moreover, we have tested the optimization starting from a worst scenario: the B, N atoms were initially placed in such a way that one half side of the cage was filled with all B atoms and the other half with all N atoms. The optimizations led to consistent results with those starting from a more reasonable initial guess of B, N positions. The most extensive search was conducted in the case of Ti(BN) 19 . First, we considered doping the two lowest-energy cage isomers made of squares and hexagons. For each isomer, both endohedral and exohedral doping were systematically considered, by placing initially a Ti atom above all nonequivalent vertices, bond centers and face centers, followed by full geometry optimization. In the endohedral case, an additional initial guess was also taken into account by putting the Ti atom at the geometric center of the cage. In addition, we explored adding the Ti atom to the lowest-energy isomer of pristine cages of (BN) 19 (namely, 1, consisting of an octagon, squares and hexagons), to the third lowest-energy cage isomers consisting of squares and hexagons, the five lowest-energy cage isomers consisting of squares, pentagons and hexagons, as well as the lowest energy cage isomer consisting of only pentagons and hexagons. In these cases, only doping at faces were taken into account. Second, we enumerated all possible (BN) 19 cage isomers that are made of squares, pentagons, hexagons, or made of squares, pentagons, hexagons and a heptagon, or made of squares, pentagons, hexagons and an octagon, and meanwhile contain a key hexagon and have two B-B bonds in the cage.
For each cage candidate, we took each of the hexagonal faces to make the key hexagon, by placing four N atoms on a pair of parallel sides and two B atoms on the rest two corners. For each hexagon, there are at most three possibilities of making the key hexagon (symmetrical equivalent regioisomers are discarded). After the initial assignation of a given key hexagon, there are (2n−6) vertices left on the cage for arranging the rest (n−2) B and (n−4) N atoms. We then applied the optimization described in the preceding subsection to find the optimal B, N arrangements with a minimized number of B-B bonds. All generated regioisomers with more than two B-B bonds were discarded. Note that there was no constraint about the neighboring rings surrounding the key hexagon (namely, not following the rules given in Figure 2b in the text). We did not apply the isolated square rule (ISR) 6 to all these candidates except for those containing a heptagon or an octagon. Subsequently, for all generated BN cage candidates, we placed a single Ti atom above the center of the key hexagon and performed full geometry optimization for prescreening.
Lastly, we explored all possible isomers where the Ti atom is bound to a heptagon or an octagon forming four Ti-N bonds (as specified in Figure 4e,f in the text). In these cases, we only considered the ISR-obeying structures.
Note that we have also taken into account the reversed arrangement of B and N atoms if it gives a different regioisomer from the original one. Thus, we have considered about 2,500 isomers in total for Ti(BN) 19 (see Supplementary Table 1). A prescreening procedure was performed for all candidates at the B3LYP-D3/6-31G(d) level. Subsequently, all obtained isomers lying below 20 kcal mol −1 relative to the lowest energy were re-optimized at the B3LYP-D3/6-31+G(d) level, considering both singlet and triplet states. We also performed the B3LYP-D3/6-31+G(d) calculations for many other higher energy isomers. In total, we had 535 isomers of Ti(BN) 19 in the final refinement calculations, as shown in Supplementary  Table 1.
Supplementary Table 1. The total number (N ) of isomers considered in the prescreening and refinement calculations for the search of low-lying structures of Ti(BN) n (n = 12, 13, 14, 16, 19 and 24). All geometries were fully optimized at the B3LYP-D3 level of theory. For other cage sizes considered in the present work (i.e., n = 12, 13, 14, 16, 24), we searched among all possible cage isomers built of squares, pentagons, hexagons, and a maximum number of one heptagon (or octagon) that contain a key hexagon and have two B-B bonds. Note that due to the relatively small size of the BN cages considered here (12 n 24), isomers with more than one heptagonal or octagonal ring would be rather high in energy. Also, we considered the doping at all possible faces of the lowest-energy pristine cage (i.e., denoted by 1, following the notations throughout this work). Additionally, for n = 16 and 24, we considered binding the Ti atom on a heptagon or an octagon (as illustrated in Figure 4e,f in the text) for all possible isomers made of squares, pentagons, hexagons, and one heptagon (or one octagon) and containing two B-B bonds. All these cage candidates include both ISR and non-ISR isomers except that for n = 24 only ISR isomers were taken into account due to its much larger cage size with a huge number of possible isomers and high computational cost. We imposed no constraint on the neighboring rings surrounding the key hexagon (namely, as given by the rules described in Figure 2b in the text), except that for n = 24 the R 3 -R 6 rings are assumed to be all hexagons.
All candidates were first prescreened at the B3LYP-D3/6-31G(d) level of theory, except that the 3-21G basis set was employed for n = 24 due to the high computational cost. All resulting structures lying below the lowest-energy one by 20 kcal mol −1 were re-optimized at the B3LYP-D3/6-31+G(d) level. To sum up, the total numbers of Ti(BN) n isomers considered in the prescreening and refinement calculations are listed in Supplementary Table  1.

Supplementary Note 1: Basis set convergence tests
To validate the 6-31+G(d) basis set employed in the present work, we did some convergence tests by comparing the results with those obtained from B3LYP-D3 calculations with larger Def2-TZVP and Def2-TZVPP basis sets. Supplementary Table 2 presents such a comparison for relative energies of pristine cages (BN) 19 and of complexes Ti(BN) 19 . The numbering of cage isomers 1-4 is explained in the text. For their detailed molecular structures, see Figure 1 and Figure 2a in the text as well as Supplementary Figure 12. Similar comparison is made for Gibbs free energies of complexation of Ti(BN) 19 (see equation (1) in the text for definition), as shown in Supplementary Table 3. As we can see, for both relative energies and complexation free energies, the three basis sets give very similar results. To justify the 6-31G(d) basis set we used in the prescreening procedures for search of low-lying Ti(BN) n isomers, we compared the relative energies calculated at the B3LYP-D3 level with 6-31G(d) and 6-31+G(d) basis sets. As shown in Supplementary Figures 3 and  4 for systems Ti⊂(BN) 19 and Ti⊂(BN) 24 , respectively, the results obtained by using the 6-31G(d) basis set are in very good agreement with those by the 6-31+G(d).

Supplementary Note 2: Comparison with double-hybrid DFT calculations
Here, we compare the results obtained from the B3LYP-D3/Def2-TZVPP calculations (with full geometry optimization) with those obtained using the B2PLYP-D3/Def2-TZVP 7 method. The B2PLYP-D3 is among the double-hybrid functionals with best performance for energetics of transition metal complexes. 8,9 Due to very large computational cost, for the latter method, we only performed single-point calculations based on the B3LYP-D3/Def2-TZVPP optimized geometries. The tested systems are the same as those used in the assessment in Supplementary Table 6 summarizes the relative energies and structural characteristics for low-lying isomers (within 20 kcal mol −1 with respect to the global minimum) of Ti⊂(BN) 19 containing a key hexagon. R 1 -R 6 are the number of the corresponding neighboring rings surrounding the key hexagon in each isomer (see Figure 2b in the text for detailed description).
As we can see, all these isomers satisfy the structural rules proposed in the text, that is, the neighboring rings R 1 and R 2 are either a square or a pentagon; R 3 -R 6 are either a pentagon, or a hexagon, or a heptagon. Meanwhile, it is worth mentioning that all these isomers also obey the other two stability rules: There are only two B-B bonds present in the cage; and the cage topology follows the isolated square rule. 6 Supplementary Table 6. Relative energies (RE, in kcal mol −1 , without zero-point energy correction) for low-lying isomers of Ti⊂(BN) 19 (within 20 kcal mol −1 ), calculated at the B3LYP-D3/6-31+G(d) level. R 1 -R 6 are the neighboring rings surrounding the key hexagon in each isomer (see Figure 2b in the text for detailed description). The values 4, 5, 6 and 7 represent, respectively, square, pentagon, hexagon and heptagon. The cage isomers in Ti⊂2-Ti⊂66 are labeled in ascending order of the relative energy of the complexes. Key-hexagon-containing isomers that violate the isolated square rule Supplementary Table 7 lists some Ti⊂(BN) 19 isomers that contain a key hexagon and violate the isolated square rule (ISR). 6 We can see that these ISR-violating isomers are at least 41.4 kcal mol −1 in energy above the global minimum. Therefore, we can rule out non-ISR structures when searching for stable Ti⊂(BN) 19 complexes. Table 7. B3LYP-D3/6-31G(d) calculated relative energies (RE, in kcal mol −1 , without zero-point energy correction) for Ti⊂(BN) 19 isomers that contain a key hexagon and violate the isolated square rule. R 1 -R 6 are the neighboring rings surrounding the key hexagon in each isomer (see Figure 2b in the text for detailed description). The values 4, 5 and 6 represent, respectively, square, pentagon and hexagon. NASP is the number of adjacent square pairs in the cage framework. The numbering of isomer Ti⊂n means that it is the n-th lowest-energy isomer in the prescreening set. Key-hexagon-containing isomers that have more than two B-B bonds Supplementary Table 8 shows some Ti⊂(BN) 19 isomers that contain a key hexagon and with four B-B bonds present in the cage. Note that all these isomers obey the isolated square rule. As can be seen, they are at least 113.2 kcal mol −1 higher in energy than the global minimum isomers, and can thus be ruled out.

Supplementary
Supplementary Table 8. B3LYP-D3/6-31G(d) calculated relative energies (RE, in kcal mol −1 , without zero-point energy correction) for Ti⊂(BN) 19 isomers that contain a key hexagon and four B-B bonds. R 1 -R 6 are the neighboring rings surrounding the key hexagon in each isomer (see Figure 2b in the text for detailed description). The values 4, 5 and 6 represent, respectively, square, pentagon and hexagon. N B-B is the number of B-B bonds present in the cage. The numbering of isomer Ti⊂n means that it is the n-th lowest-energy isomer in the prescreening set.

Supplementary Note 6: Lowest-energy isomers of Ti(BN) n
Here we present the 3D molecular structures and Schlegel diagrams of low-lying isomers of Ti(BN) n (n = 12, 13, 14, 16, 19 and 24). To be consistent with the notations used in the text, we denote cage 1 as the lowest-energy isomer of pristine cages (BN) n , whereas cages 2-11 are the cage forms of the ten lowest-energy complexes Ti⊂(BN) n and are consecutively labeled according to the increasing energy of these complexes. For comparison, we also show the complex Ti⊂1 and the endohedral complexes Ti@1 and Ti@2. The relative energies for all these isomers are summarized in Table 2 of the main text. The top view of 3D molecular structures and Schlegel diagrams of them are presented in Supplementary Figures 8-13.
Supplementary Note 8: Temperature-dependent mole fractions of major products of Ti(BN) n Assuming that the system has reached a thermodynamic equilibrium, temperature-dependent mole fractions are calculated on the basis of Maxwell-Boltzmann distribution. 10 Accordingly, the mole fraction of each species of m isomers is calculated as: where G i is the Gibbs free energy of isomer i at temperature T , and σ i is its symmetry number. 10 In the specific case of Ti⊂(BN) n clusters, σ i is the number of symmetrically equivalent faces in the cage where the Ti atom is bound to. For instance, for an isomer containing a key hexagon, it is the number of equivalent hexagonal faces in the cage, multiplied by the number of equivalent ways of making a given hexagonal face a key hexagon. Moreover, if the isomer has an enantiomer, then σ i is doubled. We have also combined the mole fractions of singlet and triplet states together, provided that the equilibrium structures of both states do not differ significantly and can be practically regarded as the same species. Supplementary Figures 15-19 depict the temperature-dependent mole fractions for the major products of Ti(BN) n (n = 12, 13, 14, 16 and 24, respectively), at temperature range of 0-4000 K and a pressure of 1 atm. For comparison, relative concentration of isomer Ti⊂1 is also shown, where 1 is the lowest-energy isomer of pristine cages. The distribution for n = 19 is already presented in Figure 5a in the text.