The Boron Teetotum: Metallic [Ti(B6CxNy)]q and Bimetallic [Ti2

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry 6

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The Boron Teetotum: Metallic [Ti(BCN)] and Bimetallic [Ti(BCN)] Nine-Membered Heterocycles with x + y = 3 and -1 # q # 3 My Phuong Pham-Ho, Hung Tan Pham, and Minh Tho Nguyen

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02713 • Publication Date (Web): 02 Jul 2018 Downloaded from http://pubs.acs.org on July 2, 2018

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The Journal of Physical Chemistry

The Boron Teetotum: Metallic [Ti(B6CxNy)]q and Bimetallic [Ti2(B6CxNy)]q Nine-Membered Heterocycles with x + y = 3 and -1 ≤ q ≤ 3

My Phuong Pham-Ho,≠ Hung Tan Pham& and Minh Tho Nguyen#,%,ǂ,* #

Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City,

700000 Vietnam %

Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 700000

Vietnam &

≠

Institute for Computational Science and Technology, Ho Chi Minh City, 700000 Vietnam Faculty of Chemical Engineering, Ho Chi Minh City University of Technology, 700000

Vietnam ǂ

Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium

Abstract. We investigated the geometry, stability and aromaticity of a series of singly and doubly titaniumdoped boron clusters. Ti dopants bring in planar cyclic form with a nine-membered boron ring B9and B93-, and C, N isoelectronic derivatives where perfectly planar B6N3, B6CN2, B6C2N and B6C3 hetero-rings are coordinated with one and two Ti atoms. The presence of both C and N atoms induces bimetallic heterocycles while Ti2B9q clusters are not stable in cyclic form. Doubly Ti doped clusters have the shape of a teetotum toy. High thermodynamic stability of these bimetallic boron heterocycles, that are global equilibrium structures of corresponding systems, can be understood as the result of a stabilizing overlap between bonding and anti-bonding MOs of Ti2 with different eigenstates of B6CxNy cycles. Both C and N elements, which are more electronegative than the B atom, also enjoy formation of planar nine-membered ring via classical 2c-2e bonding, rather than 1 ACS Paragon Plus Environment

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occupancy of high coordination position. A double aromaticity feature which comprises both σ and π aromaticity, is supported by magnetic responses of electron density within a planar cycle. Such an aromatic character is also in line with the classical electron count for both sets of delocalized σ and π electron systems.

1. Introduction Studies on geometry, stability, electronic structure and bonding phenomena of novel and nonclassical compounds are of crucial importance in the development of modern molecular science. Of the emerging compounds, boron-based clusters are regarded as a seminal class due to their unusual geometric and electronic properties, and potential industrial applications.1 Previous investigations indicated that sp hybridization and multiple aromaticity tend to govern the planar shape for small boron clusters.2,3 The π aromaticity of planar pure boron ring obeys the classical electron counting rule 4N + 2, whereas polycyclic structures such as the B182-, B19- and B202- and related clusters are classified as disk aromatic species.4,5,6 The bowl-shaped boron B30 cluster is identified as a typical non-conventional structure which has a pentagonal hole and satisfies a motif of Bn@B2n@B3n with n = 5.7 Subsequent studies demonstrated that the B32, B35, B36 and, more recently, B50 clusters are also considered as members of bowl-shaped clusters which contain hexagonal and heptagonal hole.8,9,10,11,12 The tubular motif of structure in which Bm strings are connected together in anti-prism fashion, was observed for boron clusters such as B20 (double ring), B27+ and B42 (both being triple ring).10,13,14 The tubular shape emphasizes the rich perspective of electron distribution of boron clusters as it presents a tubular aromaticity which can be rationalized by the models of electron in cylinder and hollow cylinder.12,15 Interestingly, fullerene-like

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structures are also identified for boron clusters including the B40, B42+, B44 and B46 that contain large heptagonal, octagonal and nonagonal holes.16,17,18,19,20,21,22 The doping of transition metal atoms into boron clusters have been known to provide many fundamental changes in the resulting doped derivatives, particularly in their coordination mode. A planar hyper-coordinated structure has thus been identified for the singly doped MB8-, MB9- and MB10- clusters in which the metal dopant is located at the central position of the B7, B8 B9 and B10 ring, named as metallic boron cycles.23 A design principle with emphasis on a double aromaticity has been established for this kind of planar hyper-coordinated molecules. For metallic boron cycles, geometric requirements have carefully been analyzed upon consideration of various combinations of metal dopants and Bn moieties.24 Geometrical features of transition metal doped MBn-/0 clusters, with n = 14-24 and M being a 3d, 4d and 5d metal atom, illustrate the existence of M dopants in a very high coordination number, in either tubular or fullerene form. Although B14 is found to be more stable in a fullerene shape,25 a double ring structure comprising two B7 strings connected together in an anti-prism fashion appears when it is doped by one Fe atom.26 A similar structural motif was found for FeB16, MnB16-, CoB16- and RhB18- in which metal dopant is located inside (2x8) B16 and (2x9) B18 double rings.25,27,28,29 A Ta metal doping induces or reinforces a double ring structure with B16, B18 and B20.30,31 When the dopant is a 3d, 4d and 5d metal atom, an endohedral fullerene-like structure is dominant for boron clusters as predicted by DFT calculations.32 Electron distribution analysis for MBn-/0/+ indicated that transition metal favors strong delocalized bonds with Bn moieties and thereby stabilizes the resulting cyclic clusters.25-32 Doping of two transition metal atoms to boron clusters reveals a novel type of hypercoordinated structure, named as bimetallic boron cycles.33,34 With Fe and Co dopants, bimetallic boron cycles were indeed identified as the global energy structures of B7Co2, B7Fe2 and B7CoFe



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clusters. Each cycle contains a perfectly planar B7 cycle which is decorated by two metallic atoms vertically placed along the C7 axis. The high thermodynamic stability of these bimetallic boron cycles arises from a combination of two stabilizing effects: on the one hand, each dimeric metal M2 delivers its electrons to fill the empty levels of the B7 string, and on the other hand, both antibonding and bonding MOs of M2 are significantly stabilized through orbital interactions with the cyclic B7 counterpart. Recently, a systematic investigation on geometries of two metal doped B7M20/- and B8M20/2pointed out that the bimetallic cycle appears as a general structural motif for B7M20/-, while some metals favor a cyclic structure with a B8 string.35 Previous studies on mixed BxCy-/0 indicated that the C atom tends to avoid a central position and prefers to connect with two B atoms.36 On the basis of such design principle for M2B70/-, much effort has been devoted to a search for metals that stabilize an eight-membered boron ring, and subsequently stable bimetallic boron heterocycles were firmly established for neutral [M2(B6C2)] and [M2(B7N)] with M = Sc and Ti.37 Within such a structure, both metal atoms are again vertically and oppositely coordinated to B6C2 and B7N heterocycles. Hence, another design principle is that a substitution of B- or B2- unit by C or N atom, respectively, can stabilize doped boron cluster in a cyclic form. With the aim of finding metallic boron cycles containing larger nine-membered rings, we set out to carry out a theoretical investigation on the TiB9 and Ti2B9 systems at various charge states, as well as the mixed [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q series with x + y = 3 and q = -1, 0, 1 and 2. As previous studies pointed out that boron cluster tends to favor a planar shape for anions,38 both TiB9 and Ti2B9 are considered in negative charge states. The efficiency of both C and N substitutions is illustrated by exploring geometries of [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q that allow us to understand more deeply the behavior of this isoelectronic series. An electronic structure


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analysis, including a detailed view on bonding and aromaticity, is carried out to rationalize the stability of the clusters considered, and to help implementing further the design principle for bimetallic boron cycles. 2. Computational Methods Intensive structural searches are carried out using stochastic genetic algorithms developed by us.38 In this study, in order to get an efficient approach for generating initial structures for [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q, we modify our algorithm by adding a permutation subroutine in which each atom exchanges its position with all others. In addition, the guess structures for [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q are manually generated on the basis of the previously known B8M2q geometries by substitution of a single B atom by either a N, or two B atoms by two C. Moreover, to ensure that the global minimum isomer of each size is found, several series of geometries having non-conventional shapes are also considered with the aim not to miss unexpectedly stable structures. Based on our previous geometrical predictions for boron clusters, the TPSSh, B3LYP and B3P86 functionals39 are used for geometry optimizations. Initial structures are first optimized using the small 3-21G basis set.40,41 This aims to rapidly eliminate high energy structures, and many guess structures converge to the same minimum. The optimized isomers whose relative energies are lying within a range of 50 kcal/mol with respect to the lowest-lying one, are subsequently re-optimized using the same functionals, but in conjunction with the larger correlation consistent cc-pVTZ basis set.42,43 The cyclic structures are actually found using the 321G basis set. Calculations using the larger cc-pVTZ basis set on the smaller set of geometries confirm this result. Results obtained using three different functionals are consistent with each other pointing toward the same lowest-lying isomer for each size (cf. Table S1, ESI). Similarly, the results concerning the spin states using three functionals are also consistent. All standard electronic



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structure theory computations are performed using the Gaussian 09 suite of program.44 The magnetic response of the electron density is calculated using the CTOCD-DZ method49 implemented in the SYSMO program,45,46 which is connected to the GAMESS-UK package.47 The ring current maps48,49 are constructed using the B3LYP functional with the 6-311G(d) basis set. In each current density map, the contour and shading show the modulus of induced current density, and the arrows display its projection on the plotting plane. As for a convention, anticlockwise or clockwise circulations of electrons correspond to diatropic or paratropic currents, respectively. A diatropic current flow is correlated with an aromatic character, whereas a paratropic current flow suggests an anti-aromatic character. 3 Results and Discussion 3.1 Geometries Several types of equilibrium structures are found from our extensive genetic search, but we describe in the following sections only the ones containing nine-membered cycles that turn out to be the energy global minima. As for a convention, each cyclic structure is labeled as Ti.k.n Ti2.k.n, Ti.CxNy.k.n and Ti2.CxNy.k.n in which x and y are the numbers of C and N atoms, k = 5a (5-, pentanion), 3a (3-, trianion), a (1-, anion), n (0, neutral), c (1, cation), dc (2+, dication) and tc (3+, trication) stand for the charge states, and finally n = A, B, C... denotes the isomers with increasing energy ordering. Accordingly, TiB9q and Ti2B9q clusters are labeled as Ti.k.n, Ti2.k.n, respectively. When a relative energy is mentioned, this value is consistently referred to the corresponding most stable isomer n = A. TiB9- and TiB93- Metallic Boron Cycles. Results on geometric identification for the singly Ti doped TiB9- and TiB93- clusters are shown in Figures 1 and S1 (the letter S standing for a figure in the Supporting Information file, ESI). Accordingly, the ground state of TiB9- anion Ti.a.A (D9h


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3

A2g) possesses a high symmetry cyclic form where Ti is located at the central position of a B9

nonagonal string, giving a perfectly planar metallic boron cycle, with a triplet state. The next isomer Ti.a.B (Cs 3A”) which is in fact established by attaching Ti atom to the ground state of B9 cluster with a slight distortion, is only ~2 kcal/mol less stable. Consequently, both triplet Ti.a.A and Ti.a.B emerge as competitive for the ground state of TiB9- anion cluster.

[Ti(B9)]- A

[Ti(B9)]- B

[Ti(B9)]3-

a)

C1 Ti2B9-

C1 Ti2B93-

Cs Ti2B95-

b) Figure 1. Geometries of a) TiB9- and TiB93- and b) Ti2B9k with k = -1, -3 and -5.



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As for a prediction, attachment of two additional electrons to the triplet Ti9B- releases a singlet metallic boron cycle for TiB93- tri-anion. Some lower-lying isomers of TiB93- are reported in Figure S1 (ESI). As a matter of fact, the singlet TiB93- cycle is computed as most stable isomer (Figure 1). Trianion Ti.3a.A actually has the same shape as that of anion Ti.a.A, and in both cases the Ti dopant is placed at the centre of a B9 string. This geometric identification emphasizes that anion TiB9- as well as trianion TiB93- are new members of metallic boron cycle family. Ti2B9-, Ti2B93- and Ti2B95-. In searching for new bimetallic boron cycles with nine B atoms, the doubly Ti doped Ti2B9q at various charge states (q) including Ti2B9- , Ti2B93- and Ti2B95- are carefully explored and their geometry are now reported in Figures 1b and S2 (ESI). Accordingly, a bimetallic form is not recorded even after adding 5 electrons to the neutral Ti2B9. The most stable isomer of anion Ti2B9- Ti2.a.A is actually formed by adding two B atoms to a [Ti2(B7)]- bimetallic cycle with a distortion, rather than by doping a second Ti atom to TiB9- structure. Regarding trianion B9Ti23-, Ti2.3a.A has a similar shape as Ti2.a.A and is identified as the global minimum structure. Pentanion Ti2B95- remarkably dominates the corresponding structural landscape with a high spin state. Structural characterization for Ti2.5a.A clearly shows that this isomer is formed upon addition of the second Ti dopant to the TiB9 planar cycle. The quintet-triplet energy gap for Ti2.5a.A amounts however to < 1 kcal/mol, and as consequence they are competing for the ground state. Geometric features of doubly Ti doped boron clusters emphasize that bimetallic boron cyclic motif is not predominant when doping two Ti atoms to a B9 moiety. On the other hand, the negative charge effect is not efficiently exerted in stabilizing this doubly transition metal doped boron cluster in a cyclic form. [Ti(B6CxNy)]q. Let us now consider the effect of both C and N substitutions on the singlet TiB93structure. Results of extensive search for isoelectronic systems of [B6CxNyTi]q are displayed in


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Figures 2a and S3 (ESI). Accordingly, metallic heterocyclic structures are now found as global equilibrium structures for the series of B6CxNyTiq with x + y = 3 and q = 0, +1, +2 and +3. The high symmetry and low spin state Ti.3C.n.A (C3v 1A1) is identified for B6C3Ti (Figure 2a). In the latter structure, Ti is attached to a B6C3 nonagonal face yielding subsequently a metallic boron heterocycle [Ti(B6C3)]. Actually, many cyclic structures, which differ from Ti.3C.n.A by the position of C, are found for B6C3Ti but they are significantly less stable. The structural character of [Ti(B6C3)] clearly shows that C atoms tend to avoid each other and do not form C-C bonds.

Ti(B6C3) C3v

[Ti(B6C2N)]+ Cs

[Ti(B6CN2)]2+ Cs

[Ti(B6N3)]3+ C3v

a)



[Ti2(B6C3)]2D3h 1A1g

[Ti2(B6C2N)]C2v 1A1

[Ti2(B6CN2)] C2v 1A1

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[Ti2(B6N3)]+ D3h 1A1g

b) Figure 2. Global minimum structures of a) [Ti(B6CxNy)]q and b) [Ti2(B6CxNy)]q clusters with x + y = 3, q = -2, -1, 0, +1, +2 and +3. Geometry optimizations are carried out using TPSSh/cc-pVTZ computations.

Similar to the neutral carbon [Ti(B6C3)], its isoelectronic nitrogen [Ti(B6N3)]3+ cluster is equally stable as a metallic boron heterocycle where Ti dopant is centrally coordinated to B6N3 hetero-ring. A high symmetry and low spin state isomer Ti.3N.tc.A (C3v 1A1) is in fact calculated to be the ground state for B6N3Ti3+ clusters (Figures 2a and S3 (ESI)). Interestingly, three N atoms of Ti.3N.tc.A prefer a B-N connectivity over a N-N bond. Compared to [Ti(B6C3)], the trication [Ti(B6N3)]3+ is released by substituting three C atoms on the B6C3 ring by three N+ cations. 10 ACS Paragon Plus Environment

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For the mixed [Ti(B6C2N) ]+ clusters, a metallic boron heterocycle is again observed. DFT calculations predict that the singlet state cycle Ti.2CN.c.A (Cs 1A’) is the lowest energy isomer. Geometric characterization for this structure show that it results from replacement of a C atom of [Ti(B6C3)] by one N+ ion. The next isomers, including Ti.2CN.c.B and Ti.2CN.c.C displayed in Figure S3 (ESI), are also in metallic cyclic form but located at ~5 and ~8 kcal/mol above the Ti.2CN.c.A, respectively. For the mixed dication [Ti(B6CN2)]2+, some metallic boron heterocycles are again found, and the singlet cycle Ti.C2N.dc.A (Cs 1A’) serves as the global minimum structure. The main geometric feature of Ti.C2N.dc.A is invariably an attachment of Ti dopant to a nonagonal B6CN2 planar face, and more interestingly, both N atoms of C2N.dc.A do not form N-N or C-N bonds. Actually, the nine-membered ring B6CN2 of Ti.C2N.dc.A can be generated by replacing two C sites of the neutral [Ti(B6C3)] Ti.3C.n.A by two N+ ions. It can be concluded that the [Ti(B6CxNy)]q series, with x + y = 3 and q = 0, +1, +2 and +3, present new members of the metallic boron heterocycle family for the first time where the Ti dopant is centrally attached to nonagonal face of B6CxNy rings. [Ti2(B6CxNy)]q. Bimetallic heterocyclic structures are found for [Ti2(B6CxNy)]q although the pure boron pentanion B9Ti25-, trianion B9Ti23- and anion B9Ti2- are not favored in a cyclic form. In fact, singlet cyclic structures are observed for dianion [Ti2(B6C3)]2-. Many bimetallic boron heterocycles (cf. Figure S4) are equally found for [Ti2(B6C3)]2- clusters, and among them, the highest symmetry isomer Ti2.3C.da.A in which both Ti atoms are capped vertically to the D3h B6C3 nonagonal face in both opposite sides of the plane, is identified as the lowest energy isomer. Note that three C atoms of Ti2.3C.da.A connect with three B-B bonds rather than form C-C connectivity. On the other hand, the neutral heterocycle Ti2.3C.n.A is released by adding the



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second Ti dopant to the neutral Ti.3C.n.A. Geometries of the next less stable isomers are reported in Figure S4 (ESI). This result emphasizes that substitution of a B- ion by a C atom is a simple but efficient approach to establish a bimetallic boron cycle. Regarding the [Ti2(B6N3)]+ cation which is isoelectronic with the [Ti2(B6C3)]2- dianion, DFT calculations predict again that the singlet Ti2.3N.c.A in which two Ti atoms are vertically and oppositely coordinated to a D3h B6N3 heterocycle, is the lowest energy isomer. Similar to its isoelectronic dianion Ti2.3C.da.A, three N atoms of Ti2.3N.c.A also prefer direct interaction with three B-B bonds over formation of N-N bonds. A substitution of C- ion of [Ti2(B6C3)]2- by N atom also releases a cyclic geometry for anion [Ti2(B6C2N)]-. The singlet anion Ti2.2CN.a.A is characterized as the ground state of [Ti2(B6C2N)]anion (Figures 2b and S4 (ESI)). Within the latter, both C and N atoms tend to connect with B atoms rather to form C-N connections. For the neutral [Ti2(B6CN2)], being isoelectronic with [Ti2(B6C2N)]- anion, the singlet Ti2.C2N.n.A emerges as the ground state. The singlet and low symmetry Ti2.C2N.n.B is however only at ~2 kcal/mol higher than Ti2.C2N.n.A in energy, whereas the planar structure Ti2.C2N.n.C is extremely unstable. This structures also comes from a substitution of two C sites of the D3h B6C3 ring in Ti2.C3.n.A by two N ions. Overall, the doubly Ti doped boron clusters have the shape of a teetotum toy, and for the sake of inspiration they can be named after it.

Molecular Dynamic Simulations.

Recently, the dynamic behaviour of various boron clusters has been investigated and it is regarded as a criterion to illustrate the stability of a cluster, in particular when the species is highly fluxional. In the present study, we perform molecular dynamic (MD) simulations for both bimetallic boron 12 ACS Paragon Plus Environment

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cycles [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q at 600 K during 60 ps using the CP2K package.50 As for an example, Figure 3 displays the root main squared deviation (RMSD) of for [Ti2(B6C3)]2,[Ti2(B6N3)]+, [Ti(B6C3)] and [Ti(B6N3)]3+.

b)

a)

c)

d)

Figure 3. RMSD in molecular dynamic simulations of a): [Ti(B6C3)]2-, b): [Ti(B6N3)]3+, c): [Ti2(B6C3)]2- and d): [Ti2(B6N3)]+.



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Table 1. NBO atomic charges (electron), bond length (Å) and Wiberg bond index (WBI) of different connections in [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q with x + y = 3 and q = -1,0,1,2,3 (TPSSh/cc-pVTZ).

qNBO

Ti-Ti

Ti

C

[Ti(B6C3)]

0.34

-0.67

[Ti(B6C2N)]+

0.51

-0.64

-0.90

[Ti(B6CN2)]2+

0.69

-0.62

-0.90

[Ti(B6N3)]3+

0.91

[Ti2(B6C3)]2-

0.26

-0.7

[Ti2B6C2N)]-

0.37

-0.66

-0.85

[Ti2(B6CN2)]

0.46

-0.60

-0.80

[Ti2(B6N3)]+

0.55

Ti-B

Ti-C

Ti-N

B-C

B-N

B-B

2.28

2.1

1.41

1.56

0.46

0.66

1.46

1.24

2.31

2.21

2.15

1.40

1.34

1.55

0.44

0.64

0.50

1.50

1.23

1.21

2.35

2.23

2.19

1.40

1.33

1.57

0.45

0.65

0.47

1.45

1.21

1.16

N

-0.92

-0.80

2.42

2.22

1.33

1.59

0.39

0.44

1.25

1.11

2.18

2.41

2.34

1.42

1.53

1.35

0.41

0.41

1.31

1.31

2.20

2.40

2.38

2.30

1.41

1.36

1.53

1.33

0.40

0.40

0.32

1.41

1.17

1.33

2.21

2.40

2.34

2.29

1.41

1.36

1.51

1.32

0.40

0.37

0.32

1.44

1.21

1.28

2.25

2.36

2.29

1.35

1.51

1.31

0.38

0.31

1.22

1.26


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The RMSD’s of the remainders are given in Figure S5 (ESI). The RMSD values vary in the range of 0.05 - 0.25 Å, whereas the smallest bond length is 1.75 Å. Additionally, the connectivity between atoms in both systems [Ti(B6CxNy)]q and [Ti2(B6CxNy)]q remains unchanged during simulation time, indicating these structures are dynamically stable and not fluxional. Taken together, the above results confirm that the appearance of C and N heteroatoms (with respect to boron) invariably leads to a common structural motif of the bimetallic boron heterocycle for [Ti2(B6CxNy] in which both Ti dopant atoms are coordinated to a B6CxNy nonagonal planar face along the symmetry axis. This result suggests a design principle that substitution of a Bq unit either by a C and/or a N atom provides us another convenient approach to stabilize a bimetallic boron cycle. 3.2 Geometry Factor and Charge Distribution Geometry factor is often regarded as an important condition for formation of metallic boron cycle. To obtain a understanding on the effect of C and N heteroatoms, typical geometric parameters of [Ti2(B6CxNy)]q and [Ti(B6CxNy)]q clusters are collected and given in Table 1. A B-B connection is significantly longer than the B-C and B-N bonds. As consequence, the perimeter of a pure B9 ring is larger than that of B6CxNy counterparts. This explains the fact that Ti atom of a [Ti(B6CxNy)]q cycle is moving out of the B6CxNy plane, whereas the TiB93- exhibits a perfectly planar shape. From a geometric regard, the smaller B6CxNy rings are even more ideal to produce cyclic structures and become more suitable for establishing bimetallic boron heterocycles. 3.3 Partition of Electron Density The chemical bonding phenomena of both mono- and bimetallic boron heterocycles are now explored from a partition of their electron densities making use of the electron localization indicator (ELI-D).51 Figure 4 displays the ELI_D maps of some structures considered which are



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plotted at the bifurcation value of 1.4. Atoms of each nonagonal ring are connected to each other making classical 2e-2c bonds. In both [Ti(B6CxNy)] and [Ti2(B6CxNy)] clusters, a disynaptic basin V(B,B) is found for each pair of B atoms, clearly confirming the B-B connection forming a 2e-2c bond.

[Ti(B6C3)]

[Ti(B6C2N)]+

[Ti(B6CN2)]2+

[Ti(B6N3)]3+

[Ti2(B6C3)]2-

[Ti2(B6C2N)]-

[Ti2(B6CN2)]

[Ti2(B6N3)]+

Figure 4. ELI_D maps of metallic and bimetallic boron heterocycles. Isocontours are plotted at a bifurcation value of 1.4.


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A localization domain is observed in a region between a B and a hetero-atom C and N. As consequence, the B-C and B-N links also constitute 2e-2c bonds in nature. It is notable that localization domains of B-C and B-N bonds are closer to C and N atoms than to B center, presumably due to the difference in electronegativity giving rise to the polarized bonds in B-N and B-C connections. Overall, each B6CxNy planar ring emerges upon formation of classical 2e-2c bonds. For the bonding between both Ti atoms with a B6CxNy planar ring, no localization domain can be located in the regions between the metal and a B6CxNy planar ring, indicating a certain ionic character of the Ti-X bonds with X = B, C and N. An electron localization domain centered on a Ti-Ti bond is observed only at lower bifurcation values, due to their large radii. However, this does not imply that a direct M-M bonding can be ruled out. 3.4 MO Interaction and Bimetallic Configuration The high thermodynamic stability of two metal doped clusters including cyclic and tubular forms has previously been rationalized by a bimetallic configuration. For boron cycles, this approach shows the importance of delocalized bonding between M-M moiety and boron string in stabilizing the boron cycles.35,

37,52

As for a representative example, Figure 5 displays the

qualitative orbital interactions of the Ti2 dimer with the B6C32- planar hetero-ring giving rise to the bimetallic boron heterocycle [Ti2(B6C3)]2-. Obviously, a generalization of the results obtained for B6C32- ring for other heterocycles is straightforward.



B6C32-

Page 18 of 36

[Ti2(B6C3)]2-

Ti2 a1’

σ* π*

e’’

e'

LUMO-LUMO’

(δ)4

e’

e'

e'

HOMO-HOMO’

(σ3d)2

π

e’’ a1’

HOMO-1,1’

δ

e’

a 1’

e'’

δ*

σ3d

(δ*)4

e'’

e’

HOMO-2,2’

σ4s a1’

(π*)4

e’’ HOMO-3 a1’

e’’ (π)4

a1’

(σ4s)2


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Figure 5. Qualitative presentation of orbital interaction between Ti2 and B6C32- resulting [Ti2(B6C3)]2-.

Figure 5 shows orbital interaction diagram of the (D3h 3A1’) B6C32- cycle and the Ti2 dimeric bond which inherently enhances the stability of the resulting boron heterocycles. From there, the

σ4s-MOs (a1’ symmetry) of the Ti2 dimer is enhanced in stability upon overlapping with HOMO3 (a1’ symmetry) of B6C32- and yielding the σ4s level (a1’ symmetry) for the entire system. The π levels of the bimetallic cycle are established from a stabilizing overlap of π-MOs (Ti2) with HOMO-1,1’ of B6C32- having e’’ representation. The stability of δ bond of Ti2, which is a weak bond, is further enhanced by interaction with the degenerate LUMO (e’ representation) of B6C32- and generating a degenerate δ level (HOMO), occupied by 4 electrons, for [Ti2(B6C3)]2-. The σ3d MO of dimeric Ti2 does not significantly interact with B6C32- ring, but it brings in the σ3d level for bimetallic structure. In agreement with the design principle of M2B7-/0, the anti-bonding MOs of Ti2 also enjoy orbital interactions with eigenstates of B6C32- cycle and subsequently it gives rise to an enhanced stability for [Ti2(B6C3)]2- boron heterocycle. The δ*-MOs (e’ representation) and π* MOs (e’’) are significantly stabilized by overlap with HOMO - HOMO’ (e’) and HOMO-2,2’ (e”) of cyclic B6C32-. These stabilizing interactions release the δ* and π* levels and thereby contribute to the stability of [Ti2(B6C3)]2- heterocycle. Regarding the B6C32- cycle, it is clear that both LUMO-LUMO’ and HOMO-HOMO’ are now fully occupied following interaction with Ti2. In other words, the [Ti2(B6C3)]2- bimetallic boron heterocycle contains a bimetallic configuration depicted as [(σ4s)2 (π)4 (π*)4 (δ*)4 (σ3d)2 19 ACS Paragon Plus Environment


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(δ)4] which is now fully occupied by 20 valence electrons. The electron configurations of other bimetallic boron heterocycles are displayed in Figures S6 and S7 (ESI). The π* and δ* levels of the cycles isoelectronic to [Ti2(B6C3)]2- including [Ti2(B6C2N)]-, [Ti2(B6CN2)] and [Ti2(B6N3)]+ are fully occupied, and as a result, they tend to enhance their stability. The σ4s, σ3d, π and δ levels are fully occupied and they obviously play as significant contributors to the stability of these Ti containing boron heterocycles. It is notable that the appearance of N atoms, that are more electronegative than both C and B atoms, leads to a substantial change in the MO energy levels with an expected splitting of doubly degenerate MOs. Overall, the orbital interaction analysis confirms the two factors that enhance thermodynamic stability of bimetallic boron heterocycles. In the first, the empty levels of (B6CxNy) involving LUMO-LUMO’ and HOMO-HOMO’ are occupied. The second factor is that the bonding and anti-bonding MOs of Ti2 are involved in stabilizing interactions with the eigenstates of the (B6CxNy). 3.5 Aromaticity We now probe further the aromatic features of the Ti-doped boron cycles considered using the ring current indicator which is a magnetic response derived from the whole molecular system. The current density maps of separated π and σ systems of electron are also produced on the (B6CxNy) nonagonal planes. Orbital contributions to the total ring current are calculated orbital by orbital, and thereby the participation of each MO to the aromatic character of the whole cluster can clearly be established.


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π electrons HOMO-2,2’

HOMO-3

a)

σ electrons HOMOHOMO’

HOMO-1,1’

HOMO-4

b) Figure 6. π and σ ring current maps of [Ti(B9)]3- metallic boron cycles. 21 ACS Paragon Plus Environment


(π+σ) electrons

Page 22 of 36

π electrons σ electrons

[Ti(B6C3)]

[Ti(B6C2N)]+

[Ti(B6CN2)]2+

[Ti(B6N3)]3+


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Figure 7. Total (π + σ), π and σ ring current maps of some typical [Ti(B6CxNy)]q metallic boron heterocycles.

Figure 6 shows the ring current maps computed for both sets of π and σ electrons of [Ti(B9)]3-. The strongly diatropic current maps are observed for π electrons as well as for σ electrons of [Ti(B9)]3- cycle, thus indicating that this compound can be regarded as having a double π and σ aromaticity. A similar result is also found for metallic boron cycles containing both C and N atoms (the [Ti(B6CxNy)]q series) which is isoelectronic to [Ti(B9)]3-. As shown in Figures 7 and 8, the ring current flows generated by both sets of σ and π electrons of [Ti(B6CxNy)]q metallic cycles are clearly of diatropic nature of magnetic response, and this confers them a doubly σ and π aromatic character. These results equally demonstrate that the appearance of C and N atoms, which are more electronegative than B, maintains the aromatic feature for metallic boron cycles. The ring current density maps of bimetallic boron heterocycles including [Ti2(B6C3)]2-, [Ti2(B6C2N)]-, [Ti2(B6CN2)] and [Ti2(B6N3)]+ structures are displayed in Figure 9. Diatropic current flows are consistently observed for both π and σ electron systems of [Ti2(B6C3)]2- bimetallic heterocycle. A comparable character is identified for [Ti2(B6N3)]+ cycle whose π and σ electrons produce the strongly diatropic current maps (Figure 9). For the mixed boron cycles containing both C and N atoms ([Ti2(B6C2N)]- and [Ti2(B6CN2)] structures), the magnetic ring current of π and σelectrons remains diatropic. All these structures can therefore be regarded as doubly π and σ aromatic.



HOMO-HOMO’

Page 24 of 36

HOMO-2,2’ a)

HOMO-4

HOMO-1,1’ b)

HOMO-3

Figure 8. a) σ and b) π orbital contributions to total ring current maps of [Ti(B6N3)]3+. 24 ACS Paragon Plus Environment

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(π+σ) electrons

π electrons

σ electrons

[Ti2(B6N3)]+

[Ti2 (B6CN2)]

[Ti2(B6C2N)]-



Page 26 of 36

[Ti2(B6C3)]2-

Figure 9. Total (π + σ), π and σ ring current maps.

Let us now more deeply analyze the aromatic feature by considering the orbital contributions to the total ring current (Figure 10). Each cycle of the [Ti2(B6CxNy)]q series contains 10 π electrons; it can thus be classified as an aromatic species according to the classical 4N + 2 Hückel rule. As for a typical example, the magnetic ring current maps calculated for π-MOs of [Ti2(B6N3)]+ cycles are displayed in Figure 10b. For other bimetallic heterocycles, the ring current maps are given in Figures S8, S9 and S10 of ESI file. The doubly degenerate δ* and π* MOs emerge as the main contributor to the diatropic π magnetic current density. Similarly, the π ring current flows of [Ti2(B6C2N)]- and [Ti2(B6CN2) heterocycles are significantly contributed by δ* and π* MOs. Overall, combination of anti-bonding δ* and π* MOs of dimeric Ti2 with the eigenstates of the B6CxNy cycles establishes an orbital stabilization achieving a π aromaticity for the resulting bimetallic boron heterocycles.


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δ-MOs (e’)

π-MOs (e’’)

σ4s (a1’)

a)

δ*-MOs (e’)

π*-MOs (e’’)

HOMO-4

b) Figure 10. a) σ and b) π orbital contributions to total ring current maps of [Ti2(B6N3)]+. Denotations of δ, δ*, π, π* and σ are labeled according to bimetallic configuration which are produced from orbital interaction. 27 ACS Paragon Plus Environment


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With 10 σ electrons, each [Ti2(B6CxNy)]q cycle can also be considered as a σ aromatic species, according to the (4N + 2) electron count. The doubly degenerate δ MOs, among the five MOs involved of [Ti2(B6N3)]+ cycle (Figure 10a), behave as a main contributor to its σ diatropic magnetic current density. The current maps of other MOs show that they are inactive in magnetic response. Similarly, the σ current density of bimetallic cycles containing both C and N atoms are dominated by δ-MOs, which is demonstrated by orbital overlap between δ-MOs(Ti) and B6CxNyq cycle. In summary, the stabilizing orbital overlap of anti-bonding MOs (Ti2) with a B6CxNyq cycle establishes its π aromaticity. The σ aromaticity comes from an overlap of bonding MOs (Ti2) with eigenstates of B6CxNy disk. 4 Concluding Remarks In the present theoretical study, we investigated the geometry, stability, bonding and aromaticity of a series of singly and doubly Ti-doped boron clusters. The doping of Ti atoms establishes a planar cyclic form with nine-membered boron ring, as well as their isoelectronic mixed derivatives B6N3, B6CN2, B6C2N and B6C3. Each of the perfectly planar pure B9-, B93- and mixed B6N3, B6CN2, B6C2N or B6C3 rings is coordinated with either one Ti atom placed at the ring center, or two Ti atoms vertically placed along the symmetry axis. The doubly Ti doped clusters have the shape of a teetotum toy. In all the cases considered, the C and N elements enjoy formation of planar nine-membered ring, via the alternant classical 2c-2e bonding with B atoms, rather than occupancy of a high coordination position. For bimetallic boron cycles, the two Ti dopants bring in delocalized bonding with electrons of the nine-membered rings and thereby induce a double aromaticity. The latter


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feature was identified for both pure [Ti(B9)]3- and mixed isoelectronic [Ti(B6CxNy)]q clusters, and it constitutes a main factor, if not the driving force, for the high thermodynamic stability of these metallic boron cycles.

Acknowledgements. This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 104.06-2015.71.

Supporting Information Figures displaying the lower-lying isomers of TiB9-, TiB93-, Ti2B9k, [Ti(B6CxNy)]k and [Ti2(B6CxNy)]k, RMSD of MD simulations for [Ti(B6C2N)]-, [Ti(B6CN2)], [Ti2(B6C2N)]- and [Ti2(B6CN2)], the bimetallic-configuration of [Ti2(B6C2N)]- and [Ti2(B6CN2)] and [Ti2(B6N3)]+. Figures also show σ and π orbital contributions to total ring current maps of [Ti2(B6CN2)]+, [Ti2(B6C2N)]+ and [Ti2(B6C3)]2-. This material is available free of charge via the Internet at http://pubs.acs.org.

Authors Information Emails: [email protected], [email protected]. ORCID: Minh Tho Nguyen: 0000-0002-3803-0569; Hung Tan Pham: 0000-0001-6356-3167 Note The authors declare no competing financial interest. References



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Boron 9-membered teetotum

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The Boron Teetotum: Metallic [Ti(B6CxNy)]q and Bimetallic [Ti2

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