Theoretical Investigation on Structure-Property Relationship of Asymmetric Clusters (CH 3 FBN 3 ) n ( n = 1– 6)

The structural, relative stability, electronic, IR vibrational, and thermodynamic properties of asymmetric clusters (CH 3 FBN 3 ) n ( n � 1–6) are systematically investigated using density functional theory (DFT) method. Results show that clusters (CH 3 FBN 3 ) n ( n � 2–6) form a cyclic structure with a B atom and a N α atom binding together. Five main characteristic regions are observed and assigned for the calculated IR spectra. The size-dependent second-order energy diﬀerence shows that clusters (CH 3 FBN 3 ) 3 and (CH 3 FBN 3 ) 5 have relatively higher stability and enhanced chemical inertness compared with the neighboring clusters. These two clusters may serve as the cluster-assembled materials. The variations of thermodynamic properties with temperature T or cluster size n are analyzed, respectively. Based on enthalpies in the range of 200–800K, the formations of the most stable clusters (CH 3 FBN 3 ) n ( n � 2–6) from monomer are thermodynamically favorable. These data are helpful to design and synthesize other


Introduction
e extensive studies on boron azides are developed as these molecules have been shown to be good precursors for boron nitride (BN) film deposition [1]. e chemistry of boron azides commenced in 1954 with the synthesis of boron triazide B(N 3 ) 3 [2]; since then, it developed slowly. In 1963, Paetzold produced trimeric (Cl 2 BN 3 ) 3 from the reaction of LiN 3 and BCl 3 in CH 2 Cl 2 solution [3]. e molecular structure of dichloroboron azide containing six-membered boron nitrogen heterocycle with diazo groups bounded to nitrogen atoms was determined by Müller in 1971 [4]. Boron dihalide azides (BX 2 N 3 ) 3 (X � F, Cl, or Br) from the reaction of BCl 3 with trimethylsilyl azide in CH 2 Cl 2 solution were also recorded by Wiberg et al. in 1972 [5]. Dehnicke reported the infrared spectra of the monoazide products, I 2 MN 3 (M � B, Al, Ga), and observed the formation of oligomers of these species in 1978 [6]. Several alkyl and arylboron azides have been synthesized using similar methods. Oligomerization for Me 2 BN 3 was established by 11 B NMR spectroscopy in 1966 [7]. e chemistry of alkylboron azides was further investigated, and the development of this field has been reviewed by Paetzold, Fraenk, and coworkers [8][9][10][11][12][13][14][15][16].
Although the chemistry of boron azides in the condensed phase has been extensively discussed in the literature, research studies of these species in the gas phase are rather limited. With the goal to use boron azides as the singlesource precursors (SSP), knowledge of their gas phase stability and thermodynamic properties becomes essential. e structure of monomers Cl 2 BN 3 and (CH 3 ) 2 BN 3 has been explored using ab initio calculation, and the thermodynamic stabilities of X 2 BN 3 with respect to its dimerization and trimerization have been gained and discussed [17][18][19][20] from the theoretical view. Previous theoretical studies of the boron azides mostly focused on the symmetric boron azides. e effect for the break of the symmetry of substituted boron azides is hardly considered. Here, in accordance with previous theoretical studies on the asymmetric clusters of inorganic boron azides [21,22], and experimental studies on the asymmetric clusters of organic gallane azides and aluminum azides (RR'MN 3 ) n (M � Al, Ga; R � CH 3 ; R' � H, Cl, Br; n � 3−4) [23,24], the structure, stability, IR spectra, and thermodynamic characteristics of the asymmetric clusters of organic boron azides (CH 3 FBN 3 ) n (n � 1 -6) were theoretically discussed in detail. ese discussions will provide fundamental data and references for experimentalist to design and synthesize the novel boron azides in the future.

Computational Methods
As is well known, it is important to choose an appropriate basis set to give the accurate description of clusters' structures and energies. Usually, a substantial size of basis set is required. However, the size of clusters studied in this work excluded the use of a very large basis set, and hence, all calculations were performed using the DFT-B3LYP method with the 6-31G * basis set [25,26] via the Gaussian 09 program package with the default convergence thresholds [27]. To ensure the adequacy of this basis set, we also optimized the clusters with the 6-311 + G * basis set. As shown later on, results obtained from these two basis sets were similar except for slightly numerical differences. e energies of all clusters were also evaluated using the 6-311 + G * basis set. e initial configurations are searched by two ways: (1) by considering the numbers of known clusters (HClBN 3 ) n (n � 1-6) in previous works [21] and (2) by placing -CH 3 groups and F atoms at various substitutional sites (H or Cl) on the basis of optimized (HClBN 3 ) geometries. No symmetry constraints were applied. Lots of rationally initial one-, two-, and three-dimensional configurations were built to seek the most stable structures. In this way, a large number of optimized isomers for the asymmetric clusters (CH 3 FBN 3 ) n (n � 1-6) were obtained. Frequencies as well as their respective IR intensities were then calculated, and the lack of imaginary frequencies confirmed that the true minimum was obtained in each case. According to the previous study, the calculated frequencies were scaled uniformly by 0.96 to approximately correct the systematic overestimation [28].

Structures and Charge Distribution.
A number of isomers are calculated at each size. Here, structures of clusters (CH 3 FBN 3 ) n (n � 1 − 6) having the lowest energy were focused because all properties of clusters (CH 3 FBN 3 ) n (n � 1-6) were calculated based on the lowest energy. Two stable structures of the monomer CH 3 FBN 3 were obtained (connectivity: CH 3 FB−N α −N β −N c ) with a slight difference in geometrical parameters. e clusters (CH 3 FBN 3 ) n (n � 2 -6) are produced by the head-to-tail oligomerization of the CH 3 FBN 3 monomers, which is a starting point for the oligomerizations. Two dimers, seventeen trimers, sixty-four tetramers, two hundred and fifty-six pentamers, and five hundred and thirty-six hexamers are obtained in this manner. Judged by the total energies, the most stable isomers at each size are labeled as 1, 2, 3, 4, 5, and 6 and shown in Figure 1. Obviously, B and N α atoms easily bond together, and B-B and N α -N α bonds are not formed in the clusters (CH 3 FBN 3 ) n (n � 2 − 6). In other words, the clusters (CH 3 FBN 3 ) n (n � 2 − 6) contain cyclic (BN α ) 2n structures with alternating boron and α-nitrogen atoms. e corresponding geometrical parameters are collected in Table 1, and the data in parentheses are calculated results from the 6-311 + G * basis set. e results obtained from different basis sets are generally consistent. In detail, bond lengths (except for B−F bonds) from the 6-311 + G * basis set are slightly shorter than those from the 6-31G * basis set. is whole agreement shows that it is appropriate to choose the 6-31G * basis set to compute the titled systems. erefore, in this work, we only report the geometrical parameters obtained with the 6-31G * basis set. For n � 1, the azide group in the monomer CH 3 FBN 3 is slightly bent with a N α -N β -N c angle of 173.1°. e calculated B-N bond length of 1.447Å is between B-N single (1.58Å) and double bonds (1.37Å). e N β −N c bond length at 1.135Å is shorter than the N α −N β bond length at 1.240Å. e N β −N c bond length is between N-N double (1.25Å) and N-N triple bonds (1.10Å). For n � 2 -6, the computed B-N bond length of 1.601-1.638Å possesses typical character of B-N single bond, which is similar to the B-N length of other covalent boron azides previously determined, such as (F 2 BN 3 ) 3 (1.616Å) [19] and (C 6 F 5 B(N 3 ) 2 ) 3 (1.60Å) [12]. e B−C and B−F bond lengths are in the range of 1.585-1.596Å and 1.363-1.381Å, respectively. e computed structural parameters of the azide units in the clusters (CH 3 FBN 3 ) n (n � 2 -6) are 1.240-1.255Å for N α −N β bonds, 1.128-1.133Å for N β −N c bonds, and 177.1-179.4°for N α −N β −N c bond angle. It is obvious that the azide group is nearly linear. ese results are perfectly consistent with those found in (Cl 2 BN 3 ) 3 (1.25Å, 1.09Å, 178°) [4], (F 2 BN 3 ) 3 (1.249Å, 1.129Å, 179.8°) [19], and (C 6 F 5 B(N 3 ) 2 ) 3 (1.27Å, 1.11Å, 179°) [12]. erefore, the calculation method in this work is reliable, and it gives credence to our computed structural parameters of clusters (CH 3 FBN 3 ) n (n � 2 -6).
rough the above discussions, it is obvious that N β −N c bond is shorter than N α −N β bond in the clusters (CH 3 FBN 3 ) n (n � 1 -6). is can be interpreted as a higher bond order for the terminal N−N bond, showing a preformation of the N 2 molecule. Moreover, the cluster size n has an important effect on the geometries. An obvious increase is shown for the length of B-N α bond with cluster size n increasing from 1 to 2∼6 owing to the tension of the ring. However, B−N α bond length shows little change with cluster size in the range of 2∼6, which fluctuates in the range of 1.601-1.638Å. e N α −N β bond lengths increase as the cluster size n increases from 1 to 5 and show little change from n � 5 to n � 6. Similarly, when cluster size n increases from 1 to 3, the B−C and B−F bond lengths increase. However, the change of B−C and B−F bond lengths is not obvious from n � 4 to n � 6. e N β −N c bond length shortens from 1.135Å in cluster size with 1 to 1.129Å in cluster size with 6 and tends to be constant around 1.130Å with n � 3 -6. Compared with monomer 1, the increasing bond lengths of N α −N β , B−C and B−F bonds that are outside of rings show that N 2 (N β −N c ), -CH 3 , and Fgroups can be easily removed to yield BN material.
To give a deeper understanding on these structures, we calculate the charge distribution of the clusters (CH 3 FBN 3 ) n (n � 1 -6) as shown in Table 2. It can be seen that the charge distribution of CH 3 FBN 3 molecule exhibits zwitterionic characteristics with the charge centers of N and B atoms, respectively. As for (CH 3 FBN 3 ) n (n � 2 -6), charge distributions are similar to those of CH 3 FBN 3. However, because B atoms in these molecules all reach the high coordination, the characteristic of zwitterionic ion for these clusters is a problem needing more studies. Table 3, and the data in parentheses are from the 6-311 + G * basis set. Obviously, the energies obtained at the B3LYP/6-31G * levels are similar to those obtained with the 6-311 + G * basis set. e use of larger basis sets has no significant influence on the binding energies, which again shows that the 6-31G * basis  set is suitable for the clusters studied here. us, in this work, we only report the relative stability of the clusters (CH 3 FBN 3 ) n with the 6-31G * basis set. e uncorrected binding energies (E b ), corrected binding energies (E b-c ), average corrected binding energy (E b-c-ave ), and the second-order energy difference (Δ 2 E) are calculated using the following equations:  Table 3: Total energies (E), zero point energy (ZPE), uncorrected binding energies (E b ), corrected binding energies (E b-c ), average corrected binding energy (E b-c-ave ), and second-order energy difference (Δ 2 E) (unit: kJ · mol −1 ) a .

Relative Stabilities. All energies are displayed in
Clusters   Journal of Chemistry where E (CH 3 FBN 3 ) n and E (CH 3 FBN 3 ) are the total energies of the clusters (CH 3 FBN 3 ) n (n � 2 -6) and CH 3 FBN 3 , respectively; ZPE (CH 3 FBN 3 ) n and ZPE (CH 3 FBN 3 ) represent the zero point energies of the most stable clusters (CH 3 FBN 3 ) n (n � 2 -6) and CH 3 FBN 3 , respectively; and the 0.96 is a scaling factor [28]. From Table 3, the ratios of ZPE corrections to their binding energies E b are large for the clusters (CH 3 FBN 3 ) n (n � 2 − 6). us, it is necessary to carry out the ZPE corrections for the binding energies. For intuitive presentation, the calculated energy is also plotted as a function of cluster size n as shown in Figure 2. e curves of E b (Figure 2(a)) and E b-c (Figure 2(b)) are seen to increase monotonically with the augment of cluster size n, which means that clusters can continue to gain energy during the clusters' growth process. e E b-c-ave values increase sharply with the clusters size n from 2 to 3; then, it approaches to be stable around 13-14 kJ·mol −1 when cluster size n ≥ 3. erefore, the geometrical structures of clusters (CH 3 FBN 3 ) n (n � 1 − 6) tend to be stable when cluster size n ≥ 3. e relative stability of clusters can be also estimated through the Δ 2 E (n). According to the definition, clusters with positive Δ 2 E are more stable than those with negative Δ 2 E. A clear odd-even oscillation behavior is presented in Figure 2(d). e clusters (CH 3 FBN 3 ) n (n � 1 − 6) at n � 3, 5 correspond to local maximal on the curve of Δ 2 E, indicating that they are relatively more stable than other clusters. is trend is in excellent agreement with that of the asymmetric clusters of the inorganic boron azides (HClBN 3 ) n (n � 1 -6) [21]. In particular, the trimer (CH 3 FBN 3 ) 3 possesses the highest stability among all clusters in terms of the largest value of Δ 2 E. e stable structure of six-member ring of trimer plays a vital role.

IR Spectrum.
e IR spectrum is not only the basic property of compounds and effective method to analyze or identify substances, but also has a direct relationship with thermodynamic properties. However, there are no experimental data for the title compounds. us, it is necessary to use the theoretical method to calculate and predict IR spectra for both theoretical and practical reasons. Figure 3 provides the calculated IR spectra of the clusters (CH 3 FBN 3 ) n (n � 1 − 6) at the B3LYP/6-31G * level. Due to intrinsic complexity, it is difficult to assign all vibrational modes.
us, we only analyze and discuss some typical vibrational modes.
Furthermore, compared with monomer, the N 3 asymmetric stretching vibration presents the blue-shifted phenomenon for clusters with n � 2 − 6. However, the N 3 symmetric stretching vibration and the -CH 3 stretching vibration show red-shifted trend. Meanwhile, in three characteristic regions of N 3 asymmetric, N 3 symmetric, and -CH 3 stretching vibration, the number of vibration mode equals to that of azido groups and C-H bonds, respectively. For example, the monomer 1 has three bands at 2923, 2972, and 3022 cm −1 with C-H stretching vibration, and the trimer 3 has three bands at 2213, 2225, and 2240 cm −1 with N 3 asymmetric stretching vibration, and the hexamer 6 has six bands at 1237, 1237, 1245, 1245, 1247, and 1255 cm −1 with N 3 symmetric stretching vibration.

ermodynamic Properties.
ermodynamic functions are important parameters for clusters to predict reactive Journal of Chemistry property in a chemical reaction. According to vibrational analysis and statistical thermodynamic method, the standard molar heat capacity (C θ p,m ), standard molar thermal entropy (S θ m ), and standard molar thermal enthalpy (H θ m ) of the asymmetric clusters (CH 3 FBN 3 ) n (n � 1 -6) in the range of 200-800 K are evaluated and tabulated in Table 4. It is obvious that the calculated thermodynamic functions increase with the temperature T raising. For more clear intuitive, taking monomer 1 as an example, the temperature-dependent relationships for C θ p,m , S θ m , and H θ m are expressed in formulas (2)-(4) and all are plotted in Figure 4(a). ese correlations approximate to linear equations due to the small coefficients of T 2 ; namely, the C θ p,m , S θ m , and H θ m increase linearly with the increase of temperature T. is can be understood from the fact that these three thermodynamic functions are dominated by the weak translational and rotational motions of the clusters at lower temperature, whereas the vibrational motion is intensified and makes more contributions to C θ p,m , S θ m , and H θ m at higher temperature. e same linear relationships are found for clusters (CH 3 FBN 3 ) n with n � 2 -6: S θ m � 231.0291 + 0.4049 T − 1.4317 × 10 − 4 T 2 , R 2 � 0.9998, where R 2 represents the square of correlation coefficient and SD represents standard deviation. Moreover, the cluster size-dependent relationships for C θ p,m , S θ m , and H θ m are expressed in formulas (5)-(7) and all are shown in Figure 4(b). All thermodynamic functions increase monotonically with the enlarged cluster size n; in other words, when one more CH 3 FBN 3 is bound, the C θ p,m , S θ m , and H θ m increase with the average of 108 J·mol −1 K −1 , 133 J·mol −1 K −1 , and 18 kJ·mol −1 , separately.
is means that the contribution of monomer CH 3 FBN 3 to the thermodynamic properties of cluster matches the cluster additivity: C θ p,m � −12.0847 + 108.4637 n, R 2 � 1.0000, S θ m � 211.0987 + 133.2237 n, R 2 � 0.9996, H θ m � 1.0620 + 18.3966 n, R 2 � 0.9999, SD � 0.5260. In addition, the theoretical enthalpies (ΔH) and Gibbs free energies (ΔG) of various oligomerizations from monomer CH 3 FBN 3 in the range of 200-800 K are compiled in Table 5. e values of ΔH in the processes are negative except for the process 1 ⟶ 2 beyond 700 K, indicating that these oligomerization processes are exothermic. e ΔG at a given temperature is evaluated by the equation e values of ΔG are all positive, which reveals the oligomerizations cannot occur spontaneously in the range of 200-800 K. ere are no experimentally thermodynamic data available for the asymmetric clusters (CH 3 FBN 3 ) n (n � 1 − 6), so the calculated thermodynamic functions and the obtained relationships of them with the temperature and cluster size n may help the experiment to further study the physical, chemical, and energetic properties of the asymmetric clusters (CH 3 FBN 3 ) n (n � 1 − 6) or other asymmetric boron azides.

Aromatic Properties.
Here, the aromaticity of the studied systems will be discussed. Because our systems are nonplanar, it is not suitable to use the criterion of nucleusindependent chemical shift (NICS) [30]. In order to find out whether a large π bond exists in our studied system, we use the newly proposed localized orbital locator (LOL)-π method [31] that can be used for studying nonplanar system to study the π bonds of our systems. e LOL-π is analyzed and visualized with the Multiwfn [32]. From Figure 5, there     Journal of Chemistry is π bond of NNNB in 1 and similar π bonds in 2-6. However, the π conjugation of 2-6 is not as good as that of 1.
Meanwhile, Figure 5 also shows no large π bonds in all systems.

Conclusions
We have systematically studied the structure, relative stability, IR, and thermodynamic properties of the asymmetric clusters (CH 3 FBN 3 ) n (n � 1 -6) at the DFT-B3LYP/6-31G * . e B and N α atoms tend to bond together in clusters (CH 3 FBN 3 ) n (n � 2 − 6). e variation trend of geometrical parameters shows N 2 (N β −N c ), -CH 3 , and Fgroups are easily eliminated and BN material is yielded. e calculated Δ 2 E of the asymmetric clusters (CH 3 FBN3) n (n � 1 − 6) exhibits a pronounced odd-even alternation phenomenon with cluster size n increasing, indicating that the cluster at n � 3 is more stable than other clusters. From monomer (n � 1) to clusters (n � 2 -6), the N 3 asymmetric stretching vibration presents blue-shifted trend while the N 3 symmetric stretching vibration and -CH 3 stretching vibration are red-shifted. e thermodynamic functions (C θ p,m , S θ m , and H θ m ) of clusters (CH 3 FBN 3 ) n (n � 1 -6) show linear increase with the augment of both temperature T and cluster size n of clusters. Judged by the enthalpies in the range of 298.2-600 K, the calculated thermodynamic properties demonstrate that the formation of clusters (CH 3 FBN 3 ) n (n � 2 − 6) from the monomer is thermodynamically favorable; however, the formation cannot occur spontaneously.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.