Ab initio study of hydrocarbon prismanes and their substituted derivatives

Accepted Manuscript Ab initio study of hydrocarbon prismanes and their substituted derivatives Mahmoud A. Salem PII: DOI: Reference:

S0301-0104(18)30671-2 https://doi.org/10.1016/j.chemphys.2018.11.008 CHEMPH 10240

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Chemical Physics

Received Date: Revised Date: Accepted Date:

18 June 2018 21 October 2018 11 November 2018

Please cite this article as: M.A. Salem, Ab initio study of hydrocarbon prismanes and their substituted derivatives, Chemical Physics (2018), doi: https://doi.org/10.1016/j.chemphys.2018.11.008

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Ab initio study of hydrocarbon prismanes and their substituted derivatives Mahmoud A. Salem a,b a

Department of Condensed Matter Physics, National Research Nuclear University ‘‘MEPhI”, Kashirskoe Sh. 31, Moscow 115409, Russia. b Department of Physics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt. E-mail address: [email protected], [email protected]

KEYWORDS: Cubane Pentaprismane Binding energy HOMO-LUMO gap Density functional theory

ABSTRACT Density functional calculations of hydrocarbon prismanes C2nH2n (where n=3-10) and their substituted derivatives are carried out to analyze their structures, binding energies and electronic properties. Five substituting radicals (F, Cl, CH3, OH, NO2) are considered. The results indicate the different behavior of the prismanes by substitutions of hydrogen atoms with different radicals. Effective repulsion of substituting radicals on the pentaprismane cage is detected. The dependences of binding energies on number of substituted radicals demonstrate increasing or decreasing trends for different radicals. HOMO-LUMO gaps are slightly changed by substituting doping. All substituting reactions are found to be endothermal. Fluorination is more energetically feasible than other considered reactions.

[1]

1.

INTRODUCTION

Recently, continuous strong efforts have been made to develop new materials having good thermal stability, impact and shock insensitivity, better performance, economic and environmentally friendly syntheses in order to meet the requirements of future military and space applications. Energetic materials (explosives, propellants and pyrotechnics) are used extensively both for civil and military applications [1]. Prismanes are High-energy density materials (HEDMs) and have attracted considerable attention owing to their superior explosive [2]. Prismanes C2nH2n are the high-strained hydrocarbons, consisting of two joint polygonal carbon rings (see Fig. 1). Prismanes always have high values of strain energies due to large deviations of their bond angles from the tetrahedral one and high symmetries in the absence of possibilities for confirmation optimization. It is difficult to select favorable conditions for their synthesis [3]. Despite numerous attempts at the synthesis of the above-mentioned compounds, by now, an only limited set of prismanes is experimentally obtained. Triprismane [4] has been synthesized by combining benzvalene with 4-phenyltriazolinedione. Philip E. Eaton and Thomas W. Cole have synthesized cubane for the first time by using of Nbromosuccinimide with 2-cyclopentenone as a radical-initiated reaction [5]. Regards to the role of the cyclobutadiene transfer reaction, it is convenient to synthesize the cubane system [6]. The pentaprismane [7] can be synthesized by contracting homopentaprismane into a pentaprismane using the Favorskii contraction. The synthesis of higher [n]prismanes with n = 6–10 continues to challenge experimentalists. However, in many recent studies, prismanes were investigated theoretically via quantum-chemical approaches. Structures and stabilities of triprismane C6H6 [8], cubane C8H8 [9, 10], pentaprismane C10H10 [11], hexaprismane C12H12 [11, 12], heptaprismane C14H14 and octaprismane C16H16 [12] in the ideal-gas state have been studied. It was found that prismanes have high importance due to higher energetic properties over conventional energetic compounds [2, 13]. Despite their high straining, prismanes demonstrate remarkable kinetic stabilities, which decreases with n [14]. Moreover, they can take part in the chemical reaction resulting in various derivatives like nitrocubanes [15, 16], nitroxycubanes [17], and chlorinecubanes [18]. Molecular dynamics simulations and investigations of potential energy profiles confirm moderate stabilities of more complicated [2]

prismanes derivatives, like cyclotetracubyl (C8H6)4 [19], hexa-bi-prismane C18H12 [20], and hypercubane C40H24 [21]. So, prismanes may be used as a basis for novel stable molecules and materials. In this paper, we study a set of substituted prismanes, in which one or more hydrogen atoms are replaced by different radicals (F, Cl, OH, NO2, CH3). The effect of hydrogen replacement on geometrical structures, binding energies and HOMOLUMO gaps of carbon prismanes are investigated. One of the motivating factors for these studies has been the recent theoretical result on the stability and unique structural and electronic properties of prismanes C2nH2n (with n=3-10) in virtue of theoretical calculation methods. The synthesis paths for prismanes often contain their substitutional derivatives [22]. So, the present investigation can be useful for designing of synthesis of stable prismanes and their derivatives in future and tuning of their properties via substitution.

2.

COMPUTATIONAL DETAILS

Optimization of the geometries and obtaining of the structural and energy characteristics of the prismanes were made using density functional theory with Becke's three-parameter hybrid method and the Lee-Yang-Parr exchange-correlation energy functional (B3LYP) [23]. This method ensured good agreement with experimental data and for analysis of factors governing the structural and energy characteristics of the prismanes. To ensure the validity of adopted functional, some data are also recalculated with the Perdew–Burke–Ernzerhof (PBE) type of generalized gradient approximation (GGA) for exchange and correlation functional [24]. The same electron basis set 6-311G*[25] are used for both functionals. The geometries of all prismanes were optimized using the GAMESS program package [26]. However, the quiet agreement of the general trends of HOMO-LUMO gaps calculated by the PBE functional with the more popular functional B3LYP [27] for different polymers. In addition, for some systems, the PBE functional reproduces well the experimental HOMO-LUMO gaps [28]. Therefore, the PBE functional is still reasonable for just comparing the different tendencies of HOMO-LUMO gaps.

[3]

Besides, the obtained molecular orbitals by the PBE functional and the B3LYP have essentially the same characters [29]. We apply the method of structural relaxation to obtain the equilibrium structures of the prismanes and the decomposition products. So, the corresponding initial configuration relax to a state with the local or global energy minimum under the influence of intramolecular forces only. The criteria for stopping relaxation was the residual forces become lower than 0.0001 eV/A.

The binding energies Eb of prismanes ClHk are calculated by the equation [14]: Eb[eV/atom] =(1/Nat) (KE(H)+lE(C)-E(total)),

(1)

where Nat = k + l is the total number of atoms in the prismane, E(C) and E(H) are the energies of isolated carbon and hydrogen atoms, respectively, and Etotal is the total energy of the corresponding prismane. To evaluate stability of the functionalized prismanes C2nH2n-1R (R = Cl, F, OH, NO2 and CH3), we regard the reactions in the form: C2nH2n+R2→ C2nH2n-1R+HR

(2)

The energy difference ΔE between products and reactants are calculated as ΔE=E(C2nH2n-1R) +E(HR)-E(C2nH2n)-E(R2)

(3)

3. RESULTS AND DISCUSSION 3.1. GEOMETRIC STRUCTURES OF PRISMANES It is possible to distinguish the different types of carbon-carbon covalent bonds for the all prismanes (see Figure 1): parallel (l‖) to main axis interlayer C–C bonds, perpendicular (l⊥) to main axis intralayer C–C bonds and lCH represents the C–H bond length. The critical geometrical parameters of various C2nH2n prismanes (n=3 to 10) obtained by the B3LYP/6-311G(d) method are shown in Table 1. a

b

[4]

c

d

e

g

f

h

Fig. 1: Optimized geometries of prismanes (triprismane (a), cubane (b), pentaprismane (c), hexaprismane (d), heptaprismane (e), octaprismane (f), nonaprismane (g), decaprismane (h).

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Optimized bond lengths indicate that l⊥ bond length increases with n. This may be caused by the nonequivalence of p-orbitals spatial distribution of neighboring carbon atoms along and across the main axis of prismane. Thus, it leads to redistribution of electronic density, which defines the formation of two types of covalent bonds in prismane. It is interesting to notice that in small prismanes (n ≤ 8) l‖ bond lengths are quite longer than l⊥. For higher prismanes (n > 8), the reverse trend is observed. Due to the effect of rehybridization of the carbon centers produced by steric strain, the prismane series are distinguished by shortened C–H bonds caused by the high degree of the σ-character of the C–H bond [30]. Table 1 Optimized binding energies (eV/atom) (see formula (1)), bond lengths (Å), bond angle CCH (degrees) and HOMO-LUMO gaps (eV) of various prismanes isomers at the B3LYP/6-311G(d) level. n

Eb

lǁ

l⊥

lCH

CCH

HOMO-LUMO

3 4 5 6 7 8 9 10

4.43 4.52 4.65 4.64 4.59 4.55 4.49 4.45

1.559 1.571 1.571 1.567 1.569 1.566 1.564 1.564

1.523 1.571 1.561 1.560 1.562 1.566 1.571 1.577

1.083 1.090 1.091 1.092 1.093 1.093 1.094 1.094

132.70 125.23 123.26 121.49 119.61 118.71 117.78 117.07

7.73 8.34 7.83 7.03 6.91 6.47 6.55 6.32

Form table 1, it is noted the decrease of outward bowing of the CCH bonds with increasing of n. The present calculation yields a geometric CCH bond angle. These values are acceptable to those of previous ab initio calculations [11, 31].

3.2. BINDING ENERGIES AND HOMO-LUMO GAPS OF PRISMANES We calculate binding energies and HOMO-LUMO gaps at the same level of theory (see Table 1). The values of binding energies are in good agreement with the previously obtained results [8, 30]. Form our calculations, it is obvious that [6]

pentaprismane represents the maximum binding energy and therefore the higher thermodynamic stability compared to all other prismanes with n=3 to 10. A HOMO-LUMO gap is defined as energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. The obtained binding energies Eb and the HOMO-LUMO gaps for prismanes are summarized in Table 1. It should be noted that the values of the HOMO-LUMO gaps behave a decreased trend except the that of cubane. Decreasing of the HOMO-LUMO gap with increasing the size of the molecule is typical and expected fact. The exception of cubane from this trend is concerning with its additional symmetry. From the values presented in Table 1, one can see that the accuracy of the resulting data is in good agreement with the previously published data [30] for the calculation of HOMOLUMO gap.

3.3. PRISMANES WITH A SINGLE SUBSTITUTIONAL GROUP The terminating groups replacing a hydrogen atom in carbon prismanes were investigated in some detail. Prismanes contained single F, Cl, OH, NO2 or CH3 radical are optimized and characterized as proper energy minima. Some examples of such substituted derivatives of triprismane are depicted in Fig. 2. Energies ΔE of corresponding substituting reactions calculated with formula (2) are presented in Fig. 3. In these calculations, two different functionals B3LYP and PBE are applied. One can see that both functionals demonstrate the same trends despite minor mismatches in values. The positive values of ΔE indicate that substitution of a hydrogen atom by any radical is energetically unfavorable. One can see from Fig. 3, that the behavior of ΔE as a function of n strongly dependents of radical type. According to our calculations, fluorination of higher prismanes is the most favorable process among all considered reactions of substituting. a

b

c

[7]

Fig. 2: Triprismane doped with CH3 (a), NO2 (b), OH (c).

(a)

(b)

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Fig. 3: Energy of substituting reactions ΔE (eV) vs. n for all regarded radicals calculated with B3LYP (a) and PBE methods(b). The chemical stabilities against electronic excitations are relevant to the HOMOLUMO energy gaps. The HOMO-LUMO energy gap of various molecules is shown in Fig. 4 (a, b). For the C20H19R isomers, it is obvious to see that the C20H19(NO2) has the lowest HOMO-LUMO gap (5.3 eV), while the C8H7F has the highest one (8.3 eV). According to Fig.4, It is noted that with increasing n, HOMO-LUMO energy gap of the prismane isomers are matching to each other in addition to the small value at large value of n due to higher HOMO energy and lower LUMO energy. The obtained results from Table 1 and Fig. 4 suggest that increasing, even more, the number of carbon atoms in the prismanes, does not lead to significantly decrease of this energy gap. Only by increasing the number of substituted atoms the energy gap could be decreased, and even then, only slightly. (a)

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(b)

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Fig. 4: HOMO-LUMO gaps vs. n for all radicals using B3LYP (a) and PBE methods(b).

3.4. MULTIPLE SUBSTITUTION OF POLYPENTAPRISMANE Table 1 proves that the pentaprismane possesses the highest value of binding energy and thus, it is the most stable prismane. Therefore, its derivatives are more promising for synthesis and applications, and we investigate them in more detail. So, we regard different isomers of substituted prismane C10H10-qRq (q=1-10, R=Cl, F, OH, NO2 and CH3). The C-C bonds for pentaprismane in the five-membered rings are calculated to be 1.561 Å (Table 1) that completely agrees with the previously reported value of 1.565Å [7]. The HCC angle is 123.26 that agrees with the previously reported values 123.24 [11] and 123.3 [32]. Calculated lengths of C-H bonds (1.091 Å) are also in the agreement with the value of 1.083 Å [11, 31]. In this study, we consider all possible isomers of the multi-substituted pentaprismane. Their binding energies are available in Supplementary Materials. For all considered radicals, isomers with the maximal distance between the substituted groups possess the lowest energy. This fact indicates the effective repulsion of substituted groups. The similar effect was previously reported for methylcubanes [33] and nitrocubanes [9]. The energy differences between isomers with adjacent and separated groups have a scale of 20 meV. According to our calculations of the binding energies of the most feasible pentaprismane isomers with q-substituted hydrogens, we have fitted the dependence Eb as a function of q as shown in Fig.5. This dependence is substantially non-linear and, therefore, it is fitted with the quadratic polynomial fit. Thus, Eb = K0 + K1*q + K2 *q2

(4)

Here K0, K1, and K2 are fitted parameters, presented in Table 2. Table 2. Fitting coefficients for the quadratic dependence of binding energy of pentaprismane as a function of the number of substituted hydrogens q (see formula (4)). [11]

Radical F Cl OH NO2 CH3

K0 (eV) 4.645 4.651 4.648 4.634 4.630

K1 (eV) 0.031 - 0.046 - 0.025 - 0.044 - 0.039

K2(eV) *10-3 -1.9 -1.2 0.96 0 1.6

Fig. 5: Binding energies of the most feasible isomers of pentaprismane C10H10–qRq as a function of the number of substituted hydrogen atoms q (R = F, Cl, OH, NO2, CH3).

It is a notable fact that for fluorinated prismanes Eb decreases with q, whereas for all other substituting radicals the reverse trend takes place. We also calculate HOMO-LUMO gaps of substituted pentaprismane as is shown in Fig. 6. According to our calculations, there is a decrease of the HOMO-LUMO gap by increasing the number of substituted atoms. It is noted that the decrease in HOMO-LUMO gaps is associated with the increase in the kinetic stabilities of the

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prismanes [34]. On the other hand, the values of gaps remain inside the region of 5-8 eV, and substituting is not the efficient way to transfer prismanes to semiconductors.

Fig. 6: HOMO-LUMO gaps of the most feasible isomers of pentaprismane C10H10– qRq as a function of the number of substituted hydrogen atoms q (R = F, Cl, OH, NO2, CH3).

4. CONCLUSIONS In this study, we presented systematic ab initio calculations of the structural and energetic characteristics of substituted hydrocarbon [n]prismanes with n = 3 to 10. According to our calculations, substituting of hydrogen atom by any radical in energetically unfavorable. However, the additional energy needed for substitution is sufficiently low and depends in a complex manner on prismane size and concrete radical. So, one can choose different radicals which are suitable to functionalize different prismanes. Despite substituting, prismanes possess very high HOMOLUMO gaps, typical for small strained molecules, and therefore their usages in electronics are limited. We believe that functionalized higher prismanes can be as useful as cubane for energetics and medical applications. [13]

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Highlights  We apply DFT to study functionalized carbon prismanes  Energies, HOMO-LUMO gaps, dipole moments and polarizabilities are calculated [16]

 Cl, F, OH, NO2 and CH3 functional groups are considered  Isomers with adjacent radicals are less favorable

Graphical abstract We present density functional study of hydrocarbon [n]prismanes (n=3-10) doped with Cl, F, OH, NO2 and CH3 radicals. Attaching of NO2 radical results in the lowest values of HOMO-LUMO gaps.

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