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Theoretical Investigation on Structure-Property Relationship of Asymmetric Clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6).

1. Introduction

The extensive studies on boron azides are developed as these molecules have been shown to be good precursors for boron nitride (BN) film deposition [1]. The chemistry of boron azides commenced in 1954 with the synthesis of boron triazide [B([N.sub.3]).sub.3] [2]; since then, it developed slowly. In 1963, Paetzold produced trimeric [([Cl.sub.2]B[N.sub.3]).sub.3] from the reaction of Li[N.sub.3] and B[Cl.sub.3] in C[H.sub.2][Cl.sub.2] solution [3]. The molecular structure of dichloroboron azide containing six-membered boron nitrogen heterocycle with diazo groups bounded to nitrogen atoms was determined by Muller in 1971 [4]. Boron dihalide azides [(B[X.sub.2][N.sub.3]).sub.3] (X = F, Cl, or Br) from the reaction of B[Cl.sub.3] with trimethylsilyl azide in C[H.sub.2][Cl.sub.2] solution were also recorded by Wiberg et al. in 1972 [5]. Dehnicke reported the infrared spectra of the monoazide products, [I.sub.2]M[N.sub.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.sub.2]B[N.sub.3] was established by [sup.11]B NMR spectroscopy in 1966 [7]. The chemistry of alkylboron azides was further investigated, and the development of this field has been reviewed by Paetzold, Fraenk, and coworkers [8-16].

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. The structure of monomers [Cl.sub.2]B[N.sub.3] and [(C[H.sub.3]).sub.2]B[N.sub.3] has been explored using ab initio calculation, and the thermodynamic stabilities of [X.sub.2]B[N.sub.3] with respect to its dimerization and trimerization have been gained and discussed [17-20] from the theoretical view. Previous theoretical studies of the boron azides mostly focused on the symmetric boron azides.

The 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'M[N.sub.3]).sub.n] (M = Al, Ga; R = C[H.sub.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 [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6) were theoretically discussed in detail. These discussions will provide fundamental data and references for experimentalist to design and synthesize the novel boron azides in the future.

2. 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 6-31[G.sup.*] 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.sup.*] basis set. As shown later on, results obtained from these two basis sets were similar except for slightly numerical differences. The energies of all clusters were also evaluated using the 6-311 + [G.sup.*] basis set. The initial configurations are searched by two ways: (1) by considering the numbers of known clusters [(HClB[N.sub.3]).sub.n] (n = 1-6) in previous works [21] and (2) by placing -C[H.sub.3] groups and F atoms at various substitutional sites (H or Cl) on the basis of optimized (HClB[N.sub.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 [(C[H.sub.3]FB[N.sub.3]).sub.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].

3. Results and Discussion

3.1. Structures and Charge Distribution. A number of isomers are calculated at each size. Here, structures of clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) having the lowest energy were focused because all properties of clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6) were calculated based on the lowest energy. Two stable structures of the monomer C[H.sub.3]FB[N.sub.3] were obtained (connectivity: C[H.sub.3]FB-[N.sub.[alpha]]-[N.sub.[beta]]-[N.sub.[gamma]]) with a slight difference in geometrical parameters. The clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6) are produced by the head-to-tail oligomerization of the C[H.sub.3]FB[N.sub.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 Na atoms easily bond together, and B-B and Na-Na bonds are not formed in the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6). In other words, the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6) contain cyclic [([BN.sub.[alpha]]).sub.2n] structures with alternating boron and a-nitrogen atoms.

The corresponding geometrical parameters are collected in Table 1, and the data in parentheses are calculated results from the 6-311 + [G.sup.*] basis set. The results obtained from different basis sets are generally consistent. In detail, bond lengths (except for B-F bonds) from the 6-311 + [G.sup.*] basis set are slightly shorter than those from the 6-31[G.sup.*] basis set. This whole agreement shows that it is appropriate to choose the 6-31[G.sup.*] basis set to compute the titled systems. Therefore, in this work, we only report the geometrical parameters obtained with the 6-31[G.sup.*] basis set. For n = 1, the azide group in the monomer C[H.sub.3]FB[N.sub.3] is slightly bent with a [N.sub.[alpha]]-[N.sub.[beta]]-[N.sub.[gamma]] angle of 173.1[degrees]. The calculated B-N bond length of 1.447 [Angstrom] is between B-N single (1.58 A) and double bonds (1.37 A). The [N.sub.[beta]]-[N.sub.[gamma]] bond length at 1.135 A is shorter than the [N.sub.a]-[N.sub.[gamma]] bond length at 1.240 A. The [N.sub.[beta]]-[N.sub.[gamma]] bond length is between N-N double (1.25 A) and N-N triple bonds (1.10 A). For n = 2-6, the computed B-N bond length of 1.601-1.638 A 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.sub.2]B[N.sub.3]).sub.3] (1.616 [Angstrom]) [19] and [([C.sub.6][F.sub.5]B[([N.sub.3]).sub.2]).sub.3] (1.60 [Angstrom]) [12]. The B-C and B-F bond lengths are in the range of 1.585-1.596 [Angstrom] and 1.363-1.381 [Angstrom], respectively. The computed structural parameters of the azide units in the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2-6) are 1.240-1.255 [Angstrom] for [N.sub.[alpha]]-[N.sub.[beta]] bonds, 1.128-1.133 [Angstrom] for [N.sub.[beta]]-[N.sub.[gamma]] bonds, and 177.1-179.4[degrees] for [N.sub.[alpha]]-[N.sub.[beta]]-[N.sub.[gamma]] bond angle. It is obvious that the azide group is nearly linear. These results are perfectly consistent with those found in [([Cl.sub.2]B[N.sub.3]).sub.3] (1.25 [Angstrom], 1.09 [Angstrom], 178[degrees]) [4], [([F.sub.2]B[N.sub.3]).sub.3] (1.249 [Angstrom], 1.129 [Angstrom], 179.8[degrees]) [19], and [([C.sub.6][F.sub.5]B[([N.sub.3]).sub.2]).sub.3] (1.27 [Angstrom], 1.11 [Angstrom], 179[degrees]) [12]. Therefore, the calculation method in this work is reliable, and it gives credence to our computed structural parameters of clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2-6).

Through the above discussions, it is obvious that [N.sub.[beta]]-[N.sub.[gamma]] bond is shorter than [N.sub.[alpha]]-[N.sub.[beta]] bond in the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6). This can be interpreted as a higher bond order for the terminal N-N bond, showing a preformation of the [N.sub.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.sub.[alpha]] bond with cluster size n increasing from 1 to 2~6 owing to the tension of the ring. However, B-[N.sub.[alpha]] bond length shows little change with cluster size in the range of 2~6, which fluctuates in the range of 1.601-1.638 [Angstrom]. The [N.sub.[alpha]]-[N.sub.[beta]] 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. The [N.sub.[beta]]-[N.sub.[gamma]] bond length shortens from 1.135 [Angstrom] in cluster size with 1 to 1.129 [Angstrom] in cluster size with 6 and tends to be constant around 1.130 [Angstrom] with n = 3 - 6. Compared with monomer 1, the increasing bond lengths of [N.sub.[alpha]]-[N.sub.[beta]], B-C and B-F bonds that are outside of rings show that [N.sub.2] ([N.sub.[beta]]-[N.sub.[gamma]]), -C[H.sub.3], and [F.sup.-] groups can be easily removed to yield BN material.

To give a deeper understanding on these structures, we calculate the charge distribution of the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) as shown in Table 2. It can be seen that the charge distribution of C[H.sub.3]FB[N.sub.3] molecule exhibits zwitterionic characteristics with the charge centers of N and B atoms, respectively. As for [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6), charge distributions are similar to those of C[H.sub.3]FB[N.sub.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.

3.2. Relative Stabilities. All energies are displayed in Table 3, and the data in parentheses are from the 6-311 + [G.sup.*] basis set. Obviously, the energies obtained at the B3LYP/6-31 [G.sup.*] levels are similar to those obtained with the 6-311 + [G.sup.*] basis set. The use of larger basis sets has no significant influence on the binding energies, which again shows that the 6-31 [G.sup.*] basis set is suitable for the clusters studied here. Thus, in this work, we only report the relative stability of the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] with the 6-31[G.sup.*] basis set. The uncorrected binding energies ([E.sub.b]), corrected binding energies ([E.sub.b-c]), average corrected binding energy ([E.sub.b-c-ave]), and the second-order energy difference ([[DELTA].sub.2]E) are calculated using the following equations:

[mathematical expression not reproducible]. (1)

where E [(C[H.sub.3]FB[N.sub.3]).sub.n] and E (C[H.sub.3]FB[N.sub.3]) are the total energies of the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2-6) and C[H.sub.3]FB[N.sub.3], respectively; ZPE [(C[H.sub.3]FB[N.sub.3]).sub.n] and ZPE (C[H.sub.3]FB[N.sub.3]) represent the zero point energies of the most stable clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2-6) and C[H.sub.3]FB[N.sub.3], respectively; and the 0.96 is a scaling factor [28].

From Table 3, the ratios of ZPE corrections to their binding energies [E.sub.b] are large for the clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6). Thus, 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. The curves of [E.sub.b] (Figure 2(a)) and [E.sub.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. The [E.sub.b-c-ave] values increase sharply with the clusters size n from 2 to 3; then, it approaches to be stable around 13-14kJ-mol-1 when cluster size n [greater than or equal to] 3. Therefore, the geometrical structures of clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) tend to be stable when cluster size n [greater than or equal to] 3.

The relative stability of clusters can be also estimated through the A2E (n). According to the definition, clusters with positive A2E are more stable than those with negative A2E. A clear odd-even oscillation behavior is presented in Figure 2(d). The clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) at n = 3, 5 correspond to local maximal on the curve of A2E, indicating that they are relatively more stable than other clusters. This trend is in excellent agreement with that of the asymmetric clusters of the inorganic boron azides (HClB[N.sub.3])n (n = 1-6) [21]. In particular, the trimer [(C[H.sub.3]FB[N.sub.3]).sub.3] possesses the highest stability among all clusters in terms of the largest value of [[DELTA].sub.2]E. The stable structure of six-member ring of trimer plays a vital role.

3.3. IR Spectrum. The 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. Thus, 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 [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) at the B3LYP/6-31 [G.sup.*] level. Due to intrinsic complexity, it is difficult to assign all vibrational modes. Thus, we only analyze and discuss some typical vibrational modes.

There are five main characteristic regions for clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6) that correspond to the -[N.sub.3] asymmetric and symmetric stretching, -C[H.sub.3] stretching and inplane bending vibrations, and the fingerprint region. As for monomer C[H.sub.3]FB[N.sub.3], the -[N.sub.3] asymmetric and symmetric stretching vibrations with intense peak lie at 2215 and 1360 [cm.sup.-1], respectively. The modes in the range of 2923-3022 [cm.sup.-1] are classified to the characteristic -C[H.sub.3] stretching vibrations. The peak around 1440 [cm.sup.-1] corresponds to the -C[H.sub.3] in-plane bending vibrations. The peaks at less than 1210 [cm.sup.-1] belong to the fingerprint region, which are mainly composed of wagging and scissoring of -C[H.sub.3] and the stretching of B-F and B-C bonds. As can be seen from Figure 3, similar vibrational modes are observed in clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2-6). The regions of 2917-3019, 2202-2243, 1331-1458, 1217-1308, and 0-1204 [cm.sup.-1] are individually assigned to -C[H.sub.3] stretching vibrations, -[N.sub.3] asymmetric stretching vibrations, -C[H.sub.3] in-plane bending vibrations, -[N.sub.3] symmetric stretching vibrations, and fingerprint region. In previous studies, the N-N asymmetrical stretching vibration for [Cl.sub.2]B[N.sub.3], [Br.sub.2]B[N.sub.3], [Me.sub.2]B[N.sub.3], [([C.sub.6][F.sub.5]).sub.2]B[N.sub.3] polymer, and Na[N.sub.3] crystal were individually located at 2210-2219 [15], 2200-2215 [15], 2128 [7, 14], 2135-2209 [cm.sup.-1] [11, 12], and 2128-2151 [cm.sup.-1] [29] from experiments. Our calculated results are in accordance with those in crystal, which shows that the structures of [N.sub.3] groups in clusters and in crystal are identical. Moreover, the obtained result is similar to that found in the clusters (HClB[N.sub.3])n (n = 1-6) (2217-2250 [cm.sup.-1]) of DFT calculations [21].

Furthermore, compared with monomer, the [N.sub.3] asymmetric stretching vibration presents the blue-shifted phenomenon for clusters with n = 2 - 6. However, the [N.sub.3] symmetric stretching vibration and the -C[H.sub.3] stretching vibration show red-shifted trend. Meanwhile, in three characteristic regions of [N.sub.3] asymmetric, [N.sub.3] symmetric, and -C[H.sub.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.sup.-1] with C-H stretching vibration, and the trimer 3 has three bands at 2213, 2225, and 2240 [cm.sup.-1] with [N.sub.3] asymmetric stretching vibration, and the hexamer 6 has six bands at 1237, 1237, 1245, 1245, 1247, and 1255 [cm.sup.-1] with [N.sub.3] symmetric stretching vibration.

3.4. Thermodynamic Properties. Thermodynamic functions are important parameters for clusters to predict reactive property in a chemical reaction. According to vibrational analysis and statistical thermodynamic method, the standard molar heat capacity ([C.sup.[theta].sub.p,m]), standard molar thermal entropy ([S.sup.[theta].sub.p]), and standard molar thermal enthalpy ([H.sup.[theta].sub.m]) of the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.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.sup.[theta].sub.p,m], [S.sup.[theta].sub.p], and [H.sup.[theta].sub.m] are expressed in formulas (2)-(4) and all are plotted in Figure 4(a). These correlations approximate to linear equations due to the small coefficients of [T.sup.2]; namely, the [C.sup.[theta].sub.p,m], [S.sup.[theta].sub.p], and [H.sup.[theta].sub.m] increase linearly with the increase of temperature T. This 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.sup.[theta].sub.p,m], [S.sup.[theta].sub.m], and [H.sup.[theta].sub.m] at higher temperature. The same linear relationships are found for clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] with n = 2-6:

[mathematical expression not reproducible], (2)

[mathematical expression not reproducible], (3)

[mathematical expression not reproducible], (4)

where [R.sup.2] represents the square of correlation coefficient and SD represents standard deviation.

Moreover, the cluster size-dependent relationships for [C.sup.[theta].sub.p,m], [S.sup.[theta].sub.m], and [H.sup.[theta].sub.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 C[H.sub.3]FB[N.sub.3] is bound, the [C.sup.[theta].sub.p,m], [S.sup.[theta].sub.m], and [H.sup.[theta].sub.m] increase with the average of 108 J * [mol.sup.-1] [K.sup.-1], 133 J * [mol.sup.-1] [K.sup.-1], and 18 kJ * [mol.sup.-1], separately. This means that the contribution of monomer C[H.sub.3]FB[N.sub.3] to the thermodynamic properties of cluster matches the cluster additivity:

[mathematical expression not reproducible], (5)

[mathematical expression not reproducible], (6)

[mathematical expression not reproducible], (7)

In addition, the theoretical enthalpies ([DELTA]H) and Gibbs free energies ([DELTA]G) of various oligomerizations from monomer C[H.sub.3]FB[N.sub.3] in the range of 200-800 K are compiled in Table 5. The values of AH in the processes are negative except for the process 1 [right arrow] 2 beyond 700 K, indicating that these oligomerization processes are exothermic. The AG at a given temperature is evaluated by the equation [DELTA]G = [DELTA]H - T[DELTA]S. The values of [DELTA]G are all positive, which reveals the oligomerizations cannot occur spontaneously in the range of 200-800 K. There are no experimentally thermodynamic data available for the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.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 [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) or other asymmetric boron azides.

3.5. 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 [pi] bond exists in our studied system, we use the newly proposed localized orbital locator (LOL)-[pi] method [31] that can be used for studying nonplanar system to study the [pi] bonds of our systems. The LOL-[pi] is analyzed and visualized with the Multiwfn [32]. From Figure 5, there is n bond of NNNB in 1 and similar n bonds in 2-6. However, the n conjugation of 2-6 is not as good as that of 1. Meanwhile, Figure 5 also shows no large n bonds in all systems.

4. Conclusions

We have systematically studied the structure, relative stability, IR, and thermodynamic properties of the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6) at the DFTB3LYP/6-31 [G.sup.*]. The B and [N.sub.[alpha]] atoms tend to bond together in clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6). The variation trend of geometrical parameters shows [N.sub.2] ([N.sub.[beta]]-[N.sub.[gamma]]), -C[H.sub.3], and [F.sup.-] groups are easily eliminated and BN material is yielded. The calculated [[DELTA].sup.2]E of the asymmetric clusters (C[H.sub.3]FB[N.sub.3]) 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.sub.3] asymmetric stretching vibration presents blue-shifted trend while the [N.sub.3] symmetric stretching vibration and -C[H.sub.3] stretching vibration are red-shifted. The thermodynamic functions ([C.sup.[theta].sub.p,m], [S.sup.[theta].sub.m], and [H.sup.[theta].sub.m]) of clusters [(C[H.sub.3]FB[N.sub.3]).sub.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 [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 2 - 6) from the monomer is thermodynamically favorable; however, the formation cannot occur spontaneously.

https://doi.org/10.1155/2020/4106562

Data Availability

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

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Authors' Contributions

Qi-Ying Xia conceptualized the study and was responsible for project administration; Deng-Xue Ma, Yao-Yao Wei, and Yun-Zhi Li were involved in data curation; Guo-Kui Liu was involved in resource management; Deng-Xue Ma and Yao-Yao Wei wrote the original draft; and Qi-Ying Xia and Guo-Kui Liu wrote and edited the manuscript. Deng-Xue Ma and Yao-Yao Wei contributed equally to the work.

Acknowledgments

This work was supported by the Natural Science Foundation of Shandong Province (grant no. ZR2017LB011) and the Undergraduate Education Reform Project of Shandong Province (grant no. Z2018S006).

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Deng-Xue Ma, (1) Yao-Yao Wei, (2) Yun-Zhi Li, (2) Guo-Kui Liu [ID], (2) and Qi-Ying Xia [ID] (2)

(1) School of Materials Science and Engineering, Linyi University, Linyi 276005, China

(2) School of Chemistry and Chemical Engineering, Linyi University, Linyi 276005, China

Correspondence should be addressed to Guo-Kui Liu; liuguokuihappy@163.com and Qi-Ying Xia; xiaqiying@163.com

Received 2 April 2020; Revised 15 May 2020; Accepted 11 June 2020; Published 30 June 2020

Academic Editor: Franck Rabilloud

Caption: FIGURE 1: Structures of the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6).

Caption: FIGURE 2: The uncorrected binding energies [E.sub.b] (a), corrected binding energies [E.sub.b-c] (b), average corrected binding energy [E.sub.b-c-ave] (c), and the second-order energy difference [[DELTA].sub.2]E (d) of the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) versus the cluster size n.

Caption: FIGURE 3: IR spectra of the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1 - 6) with full width at half maxima of 20 cm 1.

Caption: FIGURE 4: Variations of the thermodynamic functions ([C.sup.[theta].sub.p,m] [S.sup.[theta].sub.m], and [H.sup.[theta].sub.m]) with the temperature (T) (a) for the monomer C[H.sub.3]FB[N.sub.3] and the cluster size n (b) and for the asymmetric clusters [(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6).

Caption: FIGURE 5: LOL-[pi] isosurface of different systems with the isovalue of 0.4.
TABLE 1: Ranges of the bond lengths ([Angstrom]) and bond angles
(deg) for the most stable structures of the asymmetric clusters
(C[H.sub.3]FB[N.sub.3]) (n) (n = 1-6) optimized at the DFT-B3LYP
level (a).

                                           1               2

[N.sub.[beta]]-[N.sub.[gamma]]           1.135           1.133
                                        (1.126)         (1.125)
[N.sub.[alpha]]-[N.sub.[beta]]           1.240           1.240
                                        (1.236)         (1.235)
[N.sub.[alpha]]-B                        1.447           1.633
                                        (1.442)      (1.641-1.643)
B-C                                      1.563           1.585
                                        (1.555)         (1.579)
B-F                                      1.341           1.363
                                        (1.349)         (1.374)
C-H                                   1.093-1.098     1.096-1.098
                                     (1.091-1.096)   (1.094-1.096)
B-[N.sub.[alpha]]-B                                      94.1
                                                        (95.2)
[N.sub.[alpha]]-B-[N.sub.[alpha]]                        85.9
                                                        (84.8)
[N.sub.[alpha]]-[N.sub.[beta]]-B         121.3       123.3.1-124.6
                                        (121.4)      (125.6-125.8)
[N.sub.[alpha]]-                         173.1           177.1
  [N.sub.[beta]]-[N.sub.[gamma]]        (173.3)         (177.5)

                                           3               4

[N.sub.[beta]]-[N.sub.[gamma]]        1.128-1.133        1.133
                                     (1.120-1.125)      (1.121)
[N.sub.[alpha]]-[N.sub.[beta]]        1.243-1.246        1.248
                                     (1.240-1.249)      (1.246)
[N.sub.[alpha]]-B                     1.614-1.638     1.601-1.602
                                     (1.613-1.632)   (1.598-1.600)
B-C                                   1.589-1.593        1.591
                                     (1.584-1.588)      (1.587)
B-F                                   1.376-1.381        1.385
                                     (1.388-1.393)      (1.397)
C-H                                   1.094-1.098     1.096-1.098
                                     (1.092-1.096)   (1.094-1.096)
B-[N.sub.[alpha]]-B                   124.7-125.2     126.7-126.9
                                     (123.9-125.0)      (127.1)
[N.sub.[alpha]]-B-[N.sub.[alpha]]     100.2-100.7     102.9-103.1
                                     (99.3-100.7)       (103.3)
[N.sub.[alpha]]-[N.sub.[beta]]-B      117.6-119.6     114.9-118.4
                                     (115.6-119.4)   (118.0-118.6)
[N.sub.[alpha]]-                      177.8-178.9     178.3-178.4
  [N.sub.[beta]]-[N.sub.[gamma]]     (178.1-179.1)   (178.3-178.4)

                                           5               6

[N.sub.[beta]]-[N.sub.[gamma]]        1.128-1.133        1.129
                                     (1.119-1.124)      (1.120)
[N.sub.[alpha]]-[N.sub.[beta]]        1.246-1.255        1.251
                                     (1.243-1.253)      (1.250)
[N.sub.[alpha]]-B                     1.608-1.637        1.606
                                     (1.603-1.627)   (1.601-1.604)
B-C                                   1.591-1.596        1.592
                                     (1.587-1.591)      (1.588)
B-F                                   1.380-1.386     1.387-1.388
                                     (1.387-1.398)   (1.398-1.399)
C-H                                   1.093-1.098     1.094-1.098
                                     (1.091-1.096)   (1.093-1.096)
B-[N.sub.[alpha]]-B                   126.3-128.2     125.2-125.3
                                     (125.6-131.2)   (126.0-126.1)
[N.sub.[alpha]]-B-[N.sub.[alpha]]     105.0-107.8     106.2-106.2
                                     (104.1-106.4)   (106.6-106.7)
[N.sub.[alpha]]-[N.sub.[beta]]-B      115.5-118.7     118.2-118.4
                                     (113.3-118.0)   (117.4-117.5)
[N.sub.[alpha]]-                      178.2-179.4     177.6-177.8
  [N.sub.[beta]]-[N.sub.[gamma]]     (178.3-179.4)   (177.6-177.9)

(a) The data in parentheses are from 6-311 + G* basis set.

TABLE 2: Atomic charge (e) of the most stable
structure (CH3FBN3)n (n = 1--6).

                     1         2         3

[N.sub.[alpha]]   -0.5840   -0.5922   -0.5847
[N.sub.[beta]]    0.2447    0.2761    0.2760
[N.sub.[gamma]]   -0.0175   0.0299    0.0512
B                 1.1319    1.0869    1.0721
F                 -0.4760   -0.4973   -0.5100
C                 -1.0830   -1.0571   -1.0545
H                 0.2627    0.2512    0.2499

                     4         5         6

[N.sub.[alpha]]   -0.5885   -0.5854   -0.5918
[N.sub.[beta]]    0.2753    0.2704    0.2686
[N.sub.[gamma]]   0.0602    0.0608    0.0673
B                 1.0745    1.0773    1.0809
F                 -0.5174   -0.5171   -0.5227
C                 -1.0551   -1.0568   -1.0561
H                 0.2504    0.2503    0.2503

TABLE 3: Total energies (E), zero point energy (ZPE), uncorrected
binding energies ([E.sub.b]), corrected binding energies
([E.sub.b-c]), average corrected binding energy ([E.sub.b-c-ave]),
and second-order energy difference (A2E) (unit: kJ *
[mol.sup.-1]) (a).

Clusters         E         [E.sub.b]     ZPE      [E.sub.b-c]

1           -863544.11                  150.49
           (-863796.61)                (149.36)
2           -1727098.45      10.23      306.95       4.50
           (-1727602.68)    (9.45)     (304.09)     (4.30)
3           -2590684.89      52.56      466.36       38.27
           (-2591439.62)    (49.78)    (462.16)     (36.26)
4           -3454250.88      74.44      624.01       53.27
           (-3455257.97)    (71.51)    (618.54)     (51.26)
5           -4317819.67      99.12      780.67       72.03
           (-4319078.66)    (95.59)    (772.93)     (70.51)
6           -5181384.41     119.75      937.24       86.82
           (-5182894.97)   (115.28)    (927.98)     (84.74)

Clusters   [E.sub.b-c-ave]    [[DELTA].sub.2]E

1

2                2.25              -29.27
                (2.15)            (-27.67)
3               12.76              18.76
               (12.09)            (16.97)
4               13.32              -3.75
               (12.81)            (-4.25)
5               14.41               3.97
               (14.10)             (5.01)
6               14.47
               (14.12)

TABLE 4: Thermodynamic properties for the most stable clusters
[(C[H.sub.3]FB[N.sub.3]).sub.n] (n = 1-6) at different
temperaturesa.

               T                200      298.2      400       500

1   [C.sup.[theta].sub.p,m]    77.73     96.48    113.47    127.30
     [S.sup.[theta].sub.p]     305.18   339.77    370.57    397.42
     [H.sup.[theta].sub.p]     11.30     19.87     30.58     42.65
2   [C.sup.[theta].sub.p,m]    161.34   206.04    243.12    271.97
     [S.sup.[theta].sub.p]     409.57   482.65    548.58    606.05
     [H.sup.[theta].sub.p]     19.88     38.00     60.94     86.75
3   [C.sup.[theta].sub.p,m]    242.25   312.13    369.54    413.90
     [S.sup.[theta].sub.p]     509.21   619.50    719.58    807.00
     [H.sup.[theta].sub.p]     28.47     55.81     90.64    129.90
4   [C.sup.[theta].sub.p,m]    326.44   420.82    497.89    557.25
     [S.sup.[theta].sub.p]     584.95   733.64    868.53    986.27
     [H.sup.[theta].sub.p]     37.13     74.00    120.94    173.82
5   [C.sup.[theta].sub.p,m]    411.59   530.37    627.05    701.33
     [S.sup.[theta].sub.p]     686.62   874.08    1044.02   1192.26
     [H.sup.[theta].sub.p]     46.56     93.03    152.18    218.74
6   [C.sup.[theta].sub.p,m]    496.46   639.39    755.59    844.78
     [S.sup.[theta].sub.p]     788.60   1014.65   1219.48   1398.06
     [H.sup.[theta].sub.p]     55.96    111.99    183.27    263.47

               T                 600       700       800

1   [C.sup.[theta].sub.p,m]    138.62    147.95    155.71
     [S.sup.[theta].sub.p]     421.66    443.75    464.03
     [H.sup.[theta].sub.p]      55.96     70.30     85.50
2   [C.sup.[theta].sub.p,m]    295.00    313.71    329.19
     [S.sup.[theta].sub.p]     657.75    704.68    747.61
     [H.sup.[theta].sub.p]     115.14    145.61    177.78
3   [C.sup.[theta].sub.p,m]    449.12    477.62    501.12
     [S.sup.[theta].sub.p]     885.70    957.14    1022.50
     [H.sup.[theta].sub.p]     173.12    219.50    268.47
4   [C.sup.[theta].sub.p,m]    604.30    642.35    673.70
     [S.sup.[theta].sub.p]     1092.19   1188.30   1276.18
     [H.sup.[theta].sub.p]     231.98    294.38    360.23
5   [C.sup.[theta].sub.p,m]    760.11    807.59    846.71
     [S.sup.[theta].sub.p]     1325.52   1446.38   1556.85
     [H.sup.[theta].sub.p]     291.93    370.39    453.17
6   [C.sup.[theta].sub.p,m]    915.34    972.33    1019.26
     [S.sup.[theta].sub.p]     1558.56   1704.09   1837.08
     [H.sup.[theta].sub.p]     351.61    446.09    545.74

(a) Units: T(K), [C.sup.[theta].sub.p,m] (J * [mol.sup.-1]
* [K.sup.-1]), [S.sup.[theta].sub.m] (J * [mol.sup.-1]
[K.sup.-1]), and [H.sup.[theta].sub.m] (kJ * [mol.sup.-1]).

TABLE 5: Enthalpy change and Gibbs free energy change of
oligomerization at different temperatures3.

                            T        200     298.2     400      500

2(1) [right arrow] (2)   [DELTA]H   -7.22    -6.24    -4.72    -3.05
                         [DELTA]G   32.94    52.45    72.30    91.35
3(1) [right arrow] (3)   [DELTA]H   -43.70   -42.07   -39.37   -36.32
                         [DELTA]G   37.57    77.11    117.48   156.31
4(1) [right arrow] (4)   [DELTA]H   -61.34   -58.75   -54.65   -50.05
                         [DELTA]G   65.81    127.69   190.85   251.66
5(1) [right arrow] (5)   [DELTA]H   -81.97   -78.35   -72.75   -66.54
                         [DELTA]G   85.89    167.51   250.78   330.88
6(1) [right arrow] (6)   [DELTA]H   -98.66   -94.05   -87.03   -79.25
                         [DELTA]G   109.84   211.20   314.55   413.98

                            T        600      700      800

2(1) [right arrow] (2)   [DELTA]H   -1.28     0.51     2.28
                         [DELTA]G   110.06   128.48   146.64
3(1) [right arrow] (3)   [DELTA]H   -33.03   -29.67   -26.30
                         [DELTA]G   194.54   232.21   269.37
4(1) [right arrow] (4)   [DELTA]H   -45.13   -40.09   -35.04
                         [DELTA]G   311.54   370.60   428.91
5(1) [right arrow] (5)   [DELTA]H   -59.90   -53.14   -46.36
                         [DELTA]G   409.77   487.52   564.28
6(1) [right arrow] (6)   [DELTA]H   -70.97   -62.53   -54.08
                         [DELTA]G   511.87   608.36   703.60

(a) Units: T (K), [DELTA]H (kJ * [mol.sup.-1]), and [DELTA]G
(kJ*[mol.sup.-1]).
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Title Annotation:Research Article
Author:Ma, Deng-Xue; Wei, Yao-Yao; Li, Yun-Zhi; Liu, Guo-Kui; Xia, Qi-Ying
Publication:Journal of Chemistry
Date:Jul 31, 2020
Words:7273
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