Diazomethane addition to sumanene as a subfullerene structure: A theoretical mechanistic study

Computational and Theoretical Chemistry 1093 (2016) 40–47

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Diazomethane addition to sumanene as a subfullerene structure: A theoretical mechanistic study Adel Reisi-Vanani ⇑, Somayeh Bahramian Department of Physical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, Iran

a r t i c l e

i n f o

Article history: Received 22 July 2016 Received in revised form 14 August 2016 Accepted 14 August 2016 Available online 16 August 2016 Keywords: Density functional theory (DFT) 1,3-Dipolar cycloaddition Transition state Intrinsic reaction coordinate Sumanene Diazomethane

a b s t r a c t In present study, kinetics and reaction mechanism of diazomethane and sumanene in gas phase were studied using quantum calculations at B3LYP/6-311+G(d,p) level of theory. Functionalization of the sumanene by this reaction was investigated in proposed fourteen pathways for different kinds of CAC bond. Vibrational frequencies analysis and intrinsic reaction coordinate (IRC) calculations were carried out and the rate constants for all paths were calculated by using canonical transition state theory (CTST). The best and the worst paths and dominant products for this reaction were determined. Stability of the intermediates, transition sates and products was discussed. Results showed that in the first step of CH2N2 addition to sumanene and formation of corresponding transition state, hub position has the least and rim position has the most barrier energy. Also, for all types of CAC bond, sumanene with a ACH2A group as a bridge was formed and conversion of a sumanene hexagon to heptagon happened for all positions except spoke. Generally, diazomethane can add a ACH2A group in the carbon chain, insert ACH2A group as a bridge or add a ACH3 group to the structure. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Functionalization of the carbon structures to improve physical and chemical properties for increasing their applications is an interesting and progressive research areas. One of the most important reactions that uses for this objective is 1,3-dipolar cycloaddition reaction. A chemical reaction between a 1,3-dipole and a dipolarophile to form a five-membered ring is called the 1,3dipolar cycloaddition reaction. For the first time, these reactions were described in the end of 19th century, following the discovery of 1,3-dipoles. Rolf Huisgen established in the 1960s, mechanistic investigation and synthetic application of these reactions [1]. Therefore, they are sometimes nominated to Huisgen cycloadditions. German chemist, Hans von Pechmann in 1894 discovered diazomethane (CH2N2) that is the simplest diazo compound [2]. Sumanene and corannulene are from subfullerene structures and as bowl-shaped p-conjugated aromatic compounds and carbon nanostructures that can play significant role in nanotechnology such as carbon nanotubes and other buckybowls for gas storage, drug delivery, and optical materials. Sumanene is a C3v symmetric buckybowl and a bowl-shaped p-conjugated aromatic compound with possessing interesting structural and physical

⇑ Corresponding author. E-mail address: [email protected] (A. Reisi-Vanani). http://dx.doi.org/10.1016/j.comptc.2016.08.016 2210-271X/Ó 2016 Elsevier B.V. All rights reserved.

properties [3]. Three sp3 hybridized carbon atoms at the benzylic positions is a special structural feature of the sumanene. These benzylic positions of sumanene are ready to undergo further functionalization via the corresponding species such as radicals, cations, anions, and carbenes. For synthesis of new bowl-shaped compounds, it is an attractive key structure that was investigated by researcher [4–10]. Research about sumanene started with its first synthesis in 2003 [3] besides some earlier theoretical studies [11,12]. Reaction of diazomethane with other carbon structures has been done, previously. A systematic study of the reaction of C60 with substituted diazomethane has done by Suzuki et al. [13]. They showed that C60 is a reactive dipolarophile and pyrazolinofullerene forms from the reaction of fullerene C60 with diazomethane (the yield of
44% in 5 min). If, it refluxes in toluene, it quantitatively convertes to [5,6]-open adduct. If, pyrazolinofullerene irradiates, it converts to [5,6]-open and [6,6]-closed adducts in the 3:4 ratio in the overall yield of 21% [14,15]. Perhaps, a biradical intermediate in the singlet or triplet states creates them. The reaction of fullerene C70 with diazomethane was considered and three regioisomeric pyrazolinofullerene were formed [15]. In another work, Kavita et al. showed that reactions of C60 with diazomethane, nitrile oxide, and nitrone lead to formation of fullerene fused heterocycles; theoretically, these reactions can take up four types of additions, closed and open [6,6] and [5,6] additions, and all of them

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A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47

have been investigated [16]. Tuktarov and co-workers studied selective cyclopropanation of C60-fullerene with diazomethane under the catalysis with Pd(acac)2, and individual [5,6]-open and [6,6]-closed cycloadducts were obtained [17]. In two other works, catalytic cycloaddition of diazo compounds to [60] fullerene were investigated by Tuktarov et al. [18,19]. Dipolarophility of C60 was first reported in 1992 [20]. Electronic structure and chemical properties of mono and multiplyfunctionalized fullerene derivatives that are produced through [2 +3] cycloaddition reactions of 1,3-dipoles such as nitriloxide, azide and azomethine with C60 fullerene were studied by Anafcheh and Ghafouri [21]. For corannulene derivatives, the relationship between the inversion energy barrier and the bowl depth was considered by Seiders et al. [22]. The 1,3-dipolar reaction of corannulene with some dipoles, such as diazomethane, nitrile oxide, and nitrone through its rim and spoke p-bonds was done by Kavita et al. [23]. They showed that the rim addition yields one possible adduct but spoke addition yields two regioselective adducts. Also, the energy profiles were revealed that rim addition is more favorable kinetically and thermodynamically than spoke addition and rim addition has lower activation energy and higher exothermicity than spoke addition [23]. This study is a continuation of our colleagues cycle works devoted to quantum-chemical modeling of the reactions of polycyclic hydrocarbons with dipole molecules: hydrogen azide and corannulene [24], ozone and corannulene [25], phenyl azide and carbon nanotube [26] and nitrous oxide and sumanene [27]. Addition of hydrogen azide to corannulene showed that rim position and after that hub position are the best for functionalization of corannulene, energetically and the major products are corannulene with an aziridine group in rim and hub positions, respectively [24]. Addition of ozone to corannulene showed that rim position is the best and corannulene epoxide with a triangle cycle in the rim position is major product [25]. Addition of N2O to sumanene showed that flank position is more favorable than other positions, energetically and sumanene with an epoxide group in flank, spoke and hub6 positions are formed; also products with an enol in rim position and oxepin group in hub5 position are major products. Products related to rim and flank positions are more stable than corresponding products related to hub and spoke positions [27]. Sumanene unlike C60, has two accessible different faces: concave (inside) and convex (outside). This molecule has five various CAC bonds including rim, flank, spoke, hub5 and hub6 (Fig. 1). In this study, the functionalization of sumanene in five positions and fourteen ways were evaluated by diazomethane. For each position, different paths were proposed and investigated. Barrier energies, rate constants, structures of transition states, intermediates and products for all paths were determined and results were discussed.

2. Computational details In this study, addition of diazomethane to different CAC bonds of the sumanene were evaluated. Geometries of all reactants, intermediates, products and transition states have been full optimized at the B3LYP/6-311+G(d,p) level of theory. Calculating of the harmonic vibrational frequencies were carried out for all stationary points at the same level of theory to determine minima and transition states respect to number of imaginary frequency (Nimage). Nimage must be zero and one for minima and transition states, respectively. All transition states were located with synchronous transit-guided quasi-Newton (STQN) method at the same level of theory [28–30]. The IRC calculations were done to verify each transition state connects the expected reactants and products. All calculations were done using Gaussian 03 package [31] and all

concave

convex

a

b Fig. 1. (a) Concave and convex sides and (b) various kind of CAC bonds and benzylic carbons of the sumanene (C21H12).

structures were created or visualized by GaussView 5 software [32]. Calculation of the rate constants were done by CTST using the following equation [33–35]:

KðTÞ ¼ CðTÞ

E kB T Q – TS RTa e h QR

ð1Þ

In this equation C (T) is the tunneling factor, kB, T and h are the Boltzmann constant, temperature in Kelvin and Plank constant, respectively. Q – TS and Q R are partition functions of the transition states and reactants, respectively. Ea is the barrier energy (including zero-point energy), and R is the universal gas constant. Here, calculation of tunneling factor was done by Wigner’s method which uses the following equation [36]:

CðTÞ ¼ 1 þ

 2 1 hm– 24 K B T

ð2Þ

that m– is the imaginary frequency of the related transition state and is lone variable of Wigner’s method for calculation of tunneling factor. At high temperature, small m– and for reactions without elec-

42

A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47 H2C

6

-N2

N

H2C

6

Path 1-1

TS3

TS2

N

1

H3C

1

2

1

P1

Int2

N

N

H2C

2

1

N

1

Path 1-2

2

P2

TS5

TS4

H2 C

1

Int3

-N2 2

C H2

Int5 2

P4

N

H2C

TS10

Path 1-3

TS9

TS8

TS7

TS11

N CH2

3

-N2

3

4

2 CH3

2

1

2

Int4

H2 C

N

2

TS6

N

N

H2C

Int1

N C H2

TS1

P3

Int6

Path 2-1

N

3

Path 2-2

TS14 N

2

2

N

Int7

3

N

CH2

N CH2

P5

3

TS13

TS12

2

2 CH2 3

CH2

Int9

Int8

3

-N2

TS16

TS15

Int10 H2C N

2

3

-N2

TS17

+

C H2

Int2

Path 2-3 P1

Path 2-4

TS9

TS18

Int11

TS3

2 CH3

2

1

N

CH3

Int6

P3

CH2N2

-N2

H2 C

5

TS20

Path 3-1

4

N H2C

N

P6

3 4

TS19

N

3

Int12

N

CH2

4

TS21

N

3

-N2

TS25

Path 3-2

TS23

P4

Int14 H3C

2 CH2 3

CH2

3 4

4

TS22

Int13

N

4

TS24

-N2

H2 C

3

H2C

6

Path 3-3

TS3

P1

Int2

Int15

H2 C

-N2

N

5

TS26

4

Path 4-1

3

TS27

N CH2

P4

4

5

N

N

Int16

N

H2C

5

N C H2

TS29

Path 4-2

4

P7 4

TS28

Int17

-N2

TS30

5

H2 C

4

5

H

-N2

TS32

H

1

+ CH2 (triplet) Int19

1

TS33

+CH3 (doublet)

Int20

4

Path 4-3

CH3

Path 5-1

P6

Int18

H

H2 C

TS31

H

TS34

1

P8

Fig. 2. Five investigated reactions of sumanene with diazomethane in ‘‘rim”, ‘‘flank”, ‘‘spoke”, ‘‘hub6” and ‘‘rim benzylic” positions in fourteen pathways.

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A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47

tron and hydrogen transfer, the quantum tunneling effect has a small deviation from classical behavior. Therefore, tunneling correction factor can be correctly calculated by Eq. (2). In present work, because of its values are almost equal to unit, we ignored from them in calculation of the rate constants. 3. Results and discussion 3.1. The 1,3-dipolar cycloaddition reaction of CH2N2 and sumanene Sumanene has five various CAC bonds including rim, flank, spoke, hub5 and hub6 (presented in Fig. 1). We evaluated reaction of these CAC bonds as dipolarophile with diazomethane molecule as a 1,3-dipole and labeled them reactions (1)–(5) and for each them, various pathways were proposed and examined. Then, energy barriers for all reaction pathways were determined. Sumanene similar to corannulene and unlike fullerene has two faces for attacking of diazomethane molecule: concave and convex. In this work, attacking diazomethane to different CAC bonds of the sumanene was studied only from convex face, because of the less spatial prohibition of convex face and negative curvature of the concave face [27,37]. First, diazomethane attacks as a 1,3-dipolar to one of the CAC bonds of the sumanene as a dipolarophile and a five membered heterocycle contain CANAN is produced which has three carbon atoms, two nitrogen atoms and a double bond between two nitrogen atoms. Afterward, an NAC bond cleavage happens and either N2 extrusion or rearrangement can be done in the next steps. As shown in Fig. 2, these intermediates related to rim, flank, spoke and hub6 positions labeled to Int1, Int7, Int11, Int12, Int15 and Int16, respectively. Then, we tracked these reactions to eliminate N2 or other rearrangement that presented in Fig. 2. We tried to add diazomethane to hub5 position frequently, but all calculations

failed and no transition state, intermediate or product corresponding to hub5 was found. All transition states which were studied on the potential energy surface of reactions (1)–(5) were labeled as TS1–TS34. ZPE-corrected energy, barrier energy and imaginary vibrational frequency of all species in Fig. 2 have been collected in Table 1. For a distinct comparison of relative energy of all involved species in considered paths, we exposed energy profile diagrams prepared by ZPE-corrected energy in Fig. 3. For the first step of CH2N2 addition to all positions of the sumanene, optimized structure of transition states have been depicted in Fig. 4. Because of regioselectivity, there are two different transition states for flank (TS10 and TS17) and spoke (TS19 and TS24) positions. Comparison of corresponding bond lengths in these structures shows that they are very similar together but aren’t equal, exactly. These structures show that there is almost equal linkage between CH2N2 and sumanene in all positions. A general comparison between TS10 and TS17 or between TS19 and TS24 reveals that corresponding bond lengths are almost the same, so regioselectivity hasn’t large effect on bonding of CH2N2 to sumanene. This problem is further confirmed by comparison of energy barriers of corresponding transition states in Table 1 that are very close together. 3.1.1. Reaction 1: The 1,3-dipolar cycloaddition reaction of CH2N2 to rim position We obtained three pathways for diazomethane addition to rim position of the sumanene which labeled (1–1), (1–2) and (1–3) (Fig. 2). There are nine transition states (TS1–TS9), six intermediates (Int1–Int6) and three products (P1–P3) related to these paths. The energy profile diagram (in kcal mol1) for reaction (1) has been shown in Fig. 3(a). In the first step, CH2N2 attacks to rim position of sumanene and Int1 via TS1 with energy barrier equal to 30.09 kcal mol1 is produced. Then, two NAC bonds cleave, simul-

Table 1 ZPE-corrected energy (Hartree) of all species and imaginary vibrational frequency (cm1) of transition states (brought in Fig. 2). Structure

ZPE-corrected energy

Ea

Imaginary frequency

Structure

ZPE-corrected energy

Ea

Imaginary frequency

C21H12 CH2N2 TS1 Int1 TS2 Int2 N2 TS3 P1 TS4 Int3 TS5 Int4 TS6 P2 TS7 Int5 TS8 Int6 TS9 P3 TS10 Int7 TS11 P4 TS12 Int8 TS13 Int9 TS14 P5 TS15 Int10

807.3542 148.7541 956.0603 956.0933 956.0699 846.6127 109.5541 846.5060 846.5254 956.0587 956.0932 956.0722 956.1010 956.0653 956.1097 956.0639 846.6416 846.5681 846.5858 846.4873 846.5267 956.0628 956.1054 956.0699 846.5993 956.0589 956.0854 956.0493 956.1073 956.0656 956.1219 956.0616 846.6283

– – 30.09 – 14.73 – – 66.92 – 21.71 – 13.15 – 22.42 – 23.33 – 46.11 – 61.82 – 28.51 – 22.27 – 29.14 – 22.67 – 26.23 – 28.68 –

– – 497.10 – 458.66 – – 868.01 – 314.13 – 369.39 – 498.39 – 583.28 – 486.57 – 1074.53 – 489.89 – 500.44 – 243.83 – 168.99 – 530.39 – 566.83 –

TS16 TS17 Int11 TS18 TS19 Int12 TS20 P6 TS21 Int13 TS22 Int14 TS23 TS24 Int15 TS25 TS26 Int16 TS27 TS28 Int17 TS29 P7 TS30 Int18 TS31 TS32 CH2 (Triplet) TS33 CH3 (Doublet) C21H11 TS34 P8

846.6113 956.0638 956.1075 956.0571 956.0645 956.1021 956.0699 846.6033 956.0290 956.0391 956.0241 846.5985 846.5979 956.0625 956.0989 956.0771 956.0669 956.1001 956.0713 956.0159 956.0163 955.7827 955.8156 955.9937 846.6039 846.6031 148.6813 39.1489 846.5009 39.8255 806.7270 846.5115 846.6508

10.75 27.89 – 31.62 27.47 – 20.24

347.05 508.18 – 280.99 492.70 – 498.67 – 460.60 – 452.17 – 236.15 496.30 – 465.59 483.99 – 490.96 227.00 – 480.50 – 290.38 – 183.23 499.14 – 618.83 – – 945.34 –

45.87 – 9.43 – 0.40 28.70 – 13.69 25.91 – 18.08 52.85 – 146.57 – 14.16 – 0.47 45.67 – 1.39 – – 25.71 –

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A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47

Fig. 3. Energy profile (in kcal mol1) for the reaction of sumanene with diazomethane in (a) rim, (b) flank, (c) spoke, (d) hub6 and (e) benzylic positions.

A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47

45

Fig. 4. Optimized structures of the TS1, TS10, TS17, TS19, TS24 and TS26; bond lengths are in Å; gray, blue and white colors show carbon, nitrogen and hydrogen atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

taneously and Int1 transforms to Int2 via TS2 with energy barrier equal to 14.73 kcal mol1. Int2 with a triangle cycle in flank position is very stable, thermodynamically (about 36.74 kcal mol1 more stable than primitive materials). In the following, in path (1–1), Int2 can rearrange to P1 via TS3 with a high energy barrier equal to 66.92 kcal mol1. Because of high energy barrier, this step don’t proceed in usual condition. Also, in another path, Int2 can rearrange to Int3 and then Int4 that can proceed from (12) and (1–3) pathways and forms P2 and P3 after passing from several steps (Fig. 3(a)). As shown in Fig. 3(a), P1 and P2 aren’t very stable, thermodynamically. It should be noted that in path (1–3), Int5 is the most stable product for CH2N2 addition to rim position. It is similar to sumanene; only, there is a heptagon instead of a hexagon. Also, Int6 with a triangle cycle in rim position is more unstable than Int2 that has a triangle cycle in flank position. Because of a very high barrier energy for TS9, this step don’t proceed in usual condition and P3 isn’t produced. Comparison of the barrier energies in Table 1 and relative energies in Fig. 3(a) confirms that Int2 and Int5 are dominant products, kinetically and thermodynamically. A slick transition from reactants to products on the potential energy surface of the rim position paths was shown and IRC plots for all transition states have been shown in Fig. 5(a).

3.1.2. Reaction 2: The 1,3-dipolar cycloaddition reaction of CH2N2 to flank position According to Fig. 2, for addition of CH2N2 to flank position, four pathways labeled (2–1), (2–2), (2–3) and (2–4) were investigated. There are eleven transition states (TS3, TS9, TS10–TS18), seven intermediates (Int2, Int6, Int7–Int11) and four products (P1, P3– P5) for these paths. For reaction 2, because of regioselectivity, diazomethane can be added to sumanene in two different directions with different intermediates (Int7 and Int11). The energy profile

diagram (in kcal mol1) for this position has been shown in Fig. 3 (b). For this position, Int7 and Int11 are the first intermediates. Comparison of the barrier energies equal to 28.51 and 27.89 kcal mol1 for transition states related to Int7 and Int11 and relative energies of them (1.79 and 0.47 kcal mol1), respectively, shows that these intermediates aren’t very difference (see Fig. 4, also). As shown in Fig. 3(b), P4 with a triangle cycle in spoke position which creates in path (2–1) and Int10 with a heptagon cycle instead of hexagon cycle which creates in path (2–3) are the most stable products which produces in reaction 2. The IRC plots for all transition states of the reaction (2) clearly show a slick transition from reactants to products on the potential energy surface (Fig. 5(b)).

3.1.3. Reaction 3: The 1,3-dipolar cycloaddition reaction of CH2N2 to spoke position As shown in Fig. 2, for diazomethane addition to spoke position, we studied three pathways labeled (3–1), (3–2) and (3–3). There are five intermediates (Int2, Int12–Int15), eight transition states (TS3, TS19–TS25) and three products (P1, P4 and P6) related to it (Fig. 2). For reaction (3) similar to reaction (2), diazomethane can be added to sumanene in two different directions with different intermediates (Int12 and Int15). Energy profile diagram (in kcal mol1) for these pathways has been shown in Fig. 3(c). Int12 and Int15 are the first intermediates for reaction (3) that form via TS19 and TS24 from addition of CH2N2 in two various directions with energy barriers equal to 27.47 and 28.70 kcal mol1, respectively; also, relative energies of them are 3.80 and 5.86 kcal mol1. These results show that these intermediates aren’t very different (see Fig. 4, also). A brief glance to Fig. 3(c) shows that P6 with a triangle cycle in hub position (produced in path (3–1)), Int2 with a triangle cycle in flank position (produced in path (3–3)), Int14 with a ACH2A bridge in spoke position (produced in path (3–2)) and P4

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A. Reisi-Vanani, S. Bahramian / Computational and Theoretical Chemistry 1093 (2016) 40–47

a

-956.3

TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9

Energy (Hartree)

-956.32 -956.34 -956.36 -956.38 -956.4 -956.42 -956.44 -4

-2

0

2

4

Reaction Coordinate

b

-956.32

TS10 TS11 TS12 TS13 TS14 TS15 TS16 TS17 TS18

-956.34

Energy (Hartree)

-956.36 -956.38 -956.4 -956.42 -956.44 -956.46 -956.48 -4

-3

-2

-1

0

1

2

3

4

3.1.4. Reaction 4: The 1,3-dipolar cycloaddition reaction of CH2N2 to hub6 position For hub position, there are two various CAC bonds (hub6 and hub5 presented in Fig. 1). Previously, it is said that we tried to add diazomethane to hub5 position frequently, but all calculations failed. Diazomethane addition to hub6 position was considered in three pathways that labeled: (4–1), (4–2) and (4–3). There are six transition states (TS26–TS31), three intermediates (Int16–Int18) and three products (P4, P6 and P7) related to them (Fig. 2). The energy profile diagram (in kcal mol1) for these pathways has been shown in Fig. 3(d). In the first step, Int16 forms via TS26 with energy barrier equal to 25.91 kcal mol1. Int16 can release N2 and transform to P4 via TS27 with energy barrier equal to 18.08 kcal mol1 in path (4–1). This path is very suitable and effectual, kinetically and thermodynamically. In another path, Int16 can rearrange to Int17 that from two different paths transform to P7 and Int18. From the point of view of kinetics and thermodynamics, P7 is very unstable so path (4–2) will not proceed in usual condition and P7 will not create; but Int18 that in the following rearranges to P6, is very stable and it is predicted that path (4–3) proceeds well. The IRC plots for transition states related to reaction 4 clearly show a slick transition from reactants to products on the potential energy surface and their plots have been prought in Fig. 5(d).

Reaction Coordinate Energy (Hartree)

c

TS19

-956.3 -956.32 -956.34 -956.36 -956.38 -956.4 -956.42 -956.44 -956.46

TS20 TS21 TS22 TS23 TS24 TS25

-4

-3

-2

-1

0

1

2

3

4

Reaction Coordinate

Energy (Hartree)

d

-956

TS26

-956.1

TS27 TS28

-956.2

TS29 TS30

-956.3

TS31

-956.4 -956.5 -4

-3

-2

-1

0

1

2

3

4

Reaction Coordinate

Energy (Hartree)

e

TS32

-956.05 -956.1 -956.15 -956.2 -956.25 -956.3 -956.35 -956.4 -956.45

TS33 TS34

-4

-2

0

2

4

Reaction Coordinate Fig. 5. IRC plots for transition states related to reaction paths of sumanene and diazomethane in (a) rim, (b) flank, (c) spoke, (d) hub6 and (e) benzylic positions.

with a triangle cycle in spoke position (produced in path (3–2)) are the most dominant products which produce in reaction (3). For confirmation of the link between the appointed transition states and the reactants or products on the potential energy surface, we did IRC calculations that results have been depicted in Fig. 5(c).

3.1.5. Reaction 5: Decomposition of CH2N2 and free radical addition of CH2 to benzylic position With respect to significant of benzylic position of the sumanene, we tried to functionalize it. In pathway (5–1), we surveyed the free radical attacking of the triplet CH2 to benzylic hydrogen. In the first step, with elimination of N2 from diazomethane molecule, triplet and singlet CH2 is formed. Calculations for addition of singlet CH2 to benzylic hydrogen failed, frequently, but not for triplet CH2. N2 elimination proceeds via TS32 with energy barrier equal to 45.67 kcal mol1. Then, triplet CH2 attacks to benzylic hydrogen and CH3 radical and Int20 form via TS33 with energy barrier 1.39 kcal mol1; then CH3 radical reacts with Int20 and very stable P8 product creates. P8 is the most stable product among of all products. Comparison of some products such as P1 and P3 with relative energy equal to 17.99 and 60.68 kcal mol1, respectively, shows that substitution of benzylic hydrogen with methyl group is very favorable than substitution of rim hydrogen, thermodynamically. The IRC plots for transition states were brought to confirm the smooth transition from reactants to products in Fig. 5(e). 3.2. Rate constants We tried to calculate the rate constants using CTST theory with respect to obtained energy barriers of the rate determining step of the reactions (1)–(5). Eqs. (1) and (2) were applied to calculate the rate constants. Tunneling factor is almost equal to unit for all considered paths, therefore we neglected from it in these calculations. Lowest barrier energies of transition states related to the rate determining step of the considered paths of reactions (1)–(5) are belong to TS1, TS10, TS19, TS26 and TS32, respectively (Figs. 2 and 3 and Table 1). These values are equal to 30.09, 28.51, 27.47, 25.91 and 45.67 kcal mol1 and calculated rate constants are equal to 1.15  101, 9.53  102, 9.81  102, 1.95  101 and 8.18  105 S1, respectively. It is possible that trend of the calculated values of the rate constants won’t be in agreement with energy barriers, because in calculation of the rate constants, one must apply more factors such as symmetry number and transmission coefficient and must use more parameters. With respect to barrier energy of the rate determining step, one can concluded that the rate of the reactions (1)–(4) are almost close together, but for reaction (5), it is different.

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4. Conclusions In this study, kinetics and reaction mechanism of diazomethane with sumanene in fourteen pathways for various kinds of CAC bond were investigated at B3LYP/6-311+G(d,p) level of theory. Vibrational frequencies analysis and IRC calculations were done to confirm existence and reality of the transition states. For the rate determining steps, rate constants for all paths were calculated using CTST. Results showed that a sumanene in which a benzylic hydrogen substituted with a methyl group (P8) is the most stable product and after that a product in which seven-member ring substituted with a hexagon (Int5) has the highest stability. In the first step of CH2N2 addition to sumanene and formation of corresponding transition state, hub position has the least and rim position has the most barrier energy. Conversion of a hexagon of sumanene to heptagon happened for all positions except spoke. For all types of CAC bond, sumanene with a ACH2A group as a bridge (product with a triangle cycle) was formed. In general, diazomethane adds a ACH2A group in the carbon chain (Int5, Int10, Int18), inserts ACH2A group as a bridge (Int2, Int6, P4, P6) or adds a ACH3 group to the structure (P1, P3, P8). Acknowledgment The authors are grateful to University of Kashan for supporting this work by Grant No. 463577/6. References [1] R. Huisgen, 1.3-Dipolare cycloadditionen rückschau und ausblick, Angew. Chem. 75 (1963) 604–637. [2] A. Lévai, Synthesis of pyrazolines by the reactions of a,b-enones with diazomethane and hydrazines (review), Chem. Heterocycl. Compd. 33 (1997) 647–659. [3] H. Sakurai, T. Daiko, T. Hirao, A synthesis of sumanene, a fullerene fragment, Science 301 (2003). 1878–1878. [4] S. Armakovic´, S.J. Armakovic´, J.P. Šetrajcˇic´, Hydrogen storage properties of sumanene, Int. J. Hydrogen Energy 38 (2013) 12190–12198. [5] T. Amaya, T. Hirao, A molecular bowl sumanene, Chem. Commun. (Camb) 47 (2011) 10524–10535. [6] H. Sakurai, T. Daiko, H. Sakane, T. Amaya, T. Hirao, Structural elucidation of sumanene and generation of its benzylic anions, J. Am. Chem. Soc. 127 (2005) 11580–11581. [7] D. Vijay, H. Sakurai, V. Subramanian, G.N. Sastry, Where to bind in buckybowls? The dilemma of a metal ion, Phys. Chem. Chem. Phys. 14 (2012) 3057–3065. [8] U.D. Priyakumar, G.N. Sastry, Cation-p interactions of curved polycyclic systems: M+ (M = Li and Na) ion complexation with buckybowls, Tetrahedron Lett. 44 (2003) 6043–6046. [9] S. Armakovic, S.J. Armakovic, J.P. Setrajcic, L.D. Dzambas, Specificities of boron disubstituted sumanenes, J. Mol. Model. 19 (2013) 1153–1166. [10] S. Armakovic´, S.J. Armakovic´, J.P. Šetrajcˇic´, I.J. Šetrajcˇic´, Optical and bowl-tobowl inversion properties of sumanene substituted on its benzylic positions; a DFT/TD-DFT study, Chem. Phys. Lett. 578 (2013) 156–161. [11] G. NarahariáSastry, Synthetic strategies towards C60. Molecular mechanics and MNDO study on sumanene and related structures, J. Chem. Soc., Perkin Trans. 2 (1993) 1867–1871. [12] U.D. Priyakumar, G.N. Sastry, First ab initio and density functional study on the structure, bowl-to-bowl inversion barrier, and vibrational spectra of the elusive C3v-Symmetric Buckybowl: sumanene, C21H12, J. Phys. Chem. A 105 (2001) 4488–4494. [13] T. Suzuki, Q. Li, K. Khemani, F. Wudl, Dihydrofulleroid H3C61: synthesis and properties of the parent fulleroid, J. Am. Chem. Soc. 114 (1992) 7301–7302.

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