Ab initio studies on topological analysis and substituent effects of reactions between ketenimine and olefin

Journal of Molecular Structure (Theochem) 528 (2000) 111–119 www.elsevier.nl/locate/theochem

Ab initio studies on topological analysis and substituent effects of reactions between ketenimine and olefin De-Cai Fang*, Hui-Ming Li Department of Chemistry, Beijing Normal University, Beijing 100875, People’s Republic of China Received 12 October 1999; accepted 11 November 1999

Abstract The cycloaddition reactions between ketenimine and olefin have been studied theoretically. For the model reaction …H2 CyCyNH ⫹ H2 CyCH2 †; the stationary points are located by HF/6-31G, MP2/6-31G ⴱ and B3LYP/6-31⫹⫹G ⴱⴱ. The topological analysis shows that both transition states are open-ring structures, i.e. only one bond to be formed has bond critical point. For the reaction of H2 CyCyNH with …CF2 †3 CyCF2 ; the activation barriers for different approaching modes have been lowered. While for the reaction of …CF3 †2 CyCyNH with …CF3 †2 CyCF2 ; the reaction across the CyN double bond in ketenimine becomes more feasible than that across the CyC one. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Cycloaddition reactions; Ketenimine; Olefin; Topological analysis; Substituent effects

1. Introduction Heterocumulenes have found widespread applications in organic synthesis and reviews on all aspects of their reactivity have appeared [1–4]. Only a few

examples of [2 ⫹ 2] cycloaddition of ketenimines with some double bonded compounds have been reported [1,4–10]. Theoretical studies on such reactions mainly focus on the reaction with imine [11–13] * Corresponding author. E-mail address: [email protected] (D.-C. Fang).

or aldehyde [14]. In general, such type of reactions take place at the CyC bond of ketenimine, but in special cases, the cycloaddition reaction could take place at the CyN bond of the ketenimine, as shown by the following reaction [1,15]:

where R ˆ Ph; Et, Bu or substituted Ph, which represent one of the few additions known to occur across the CyN double bond of the ketenimine. In this paper, ab initio studies of the mechanisms for these types of reactions are presented. The studied reactions are shown in Scheme 1. where …A† R1 ˆ R2 ˆ R3 ˆ H;

0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00481-9

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Scheme 1.

…B†R1 ˆ H; R2 ˆ F; R3 ˆ CF3 ; …C†R1 ˆ R3 ˆ CF3 ; R2 ˆ F: In addition, we have a continuing interest in the study of the mechanism for the cycloaddition reactions between cumulenes and double-bonded compounds to form four-membered rings [14,16– 19].

2. The methods of calculations Ab initio molecular orbital SCF calculations are carried out within the restricted Hartree–Fock formalism (RHF) for the titled reactions. The geometries of reactants, products and transition states have been fully optimized. For the model

Fig. 1. The numbering systems for the model reaction.

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Table 1 ˚ ; angle in degree; HF: HF/6-31G; MP2: MP2/6-31G ⴱ; B3LYP: The obtained geometric parameters for TSA(1) and PA(1) (bond length in A B3LYP/6-31⫹⫹G ⴱⴱ) TSA(1)

PA(1)

HF

MP2

B3LYP

HF

MP2

B3LYP

C2 –C1 C3 –C2 C4 –C3 C4 –C1 N5 –C1 H6 –N5 H7 –C2 H8 –C2 H9 –C3 H10 –C3 H11 –C4 H12 –C4 C3C2C1 C4C3C2 C4C1C2 N5C1C2 H6N5C1 H7C2C1 H8C2C1 H9C3C4 H10C3C4 H11C4C3 H12C4C3 C4C3C2C1 N5C1C2C3 H6N5C1C2 H7C2C1C4 H8C2C1C4 H9C3C4C1 H10C3C4C1 H11C4C3C2 H12C4C3C2

1.370 2.588 1.396 1.771 1.276 1.005 1.075 1.066 1.072 1.070 1.074 1.072 59.24 72.31 107.25 140.92 116.25 119.56 121.98 120.06 122.92 118.42 119.09 46.36 138.29 ⫺19.65 167.68 4.16 76.61 ⫺105.46 84.21 ⫺127.94

1.384 2.682 1.403 1.765 1.279 1.024 1.089 1.080 1.086 1.085 1.087 1.085 59.62 68.01 105.60 140.68 111.58 119.55 121.05 120.19 122.48 117.77 119.22 46.83 44.89 ⫺33.39 160.65 ⫺2.15 75.04 ⫺103.57 84.53 ⫺131.05

1.380 2.747 1.406 1.764 1.280 1.021 1.088 1.080 1.085 1.084 1.087 1.086 58.03 66.84 107.52 139.79 112.42 119.50 121.70 120.46 122.52 117.33 118.60 46.87 146.23 ⫺31.10 162.36 ⫺3.39 74.55 ⫺102.64 85.60 ⫺131.74

1.528 1.559 1.558 1.516 1.255 1.008 1.084 1.084 1.081 1.081 1.082 1.082 88.26 90.10 92.92 136.55 115.84 114.35 114.35 114.47 114.47 115.47 115.47 0.00 180.00 0.00 117.04 ⫺117.04 116.85 ⫺116.85 116.00 ⫺116.00

1.529 1.555 1.555 1.520 1.275 1.028 1.095 1.095 1.092 1.092 1.094 1.094 88.06 90.60 92.93 137.25 109.69 114.31 114.33 114.36 114.37 115.64 115.62 0.06 179.92 0.01 117.20 ⫺117.22 116.94 ⫺117.08 115.90 ⫺116.00

reaction (H2CyCH2 ⫹ H2CyCyNH), the stationary points have been located at the HF/6-31G, MP2/631G ⴱ and B3LYP/6-31⫹⫹G ⴱⴱ level, respectively, however for substituted reactions, only HF/6-31G was used to save CPU time. In order to get better energetics, a single-point MP2/6-31G has been employed based on the HF/6-31G geometry. The transition states were further confirmed by the computation of force constants analytically and characterized by the only imaginary vibration mode. All ab initio calculations were performed using the Gaussian94W program package [20]. The principal method that has been used to study the electronic density distribution is the Bader’s

1.534 1.562 1.562 1.524 1.267 1.025 1.096 1.096 1.093 1.093 1.095 1.095 88.37 90.17 92.70 136.88 110.97 114.16 114.18 114.40 114.42 115.70 115.67 0.06 179.91 0.02 117.32 ⫺117.35 116.81 ⫺116.96 115.93 116.09

theory of AIM [21–23]. This method has been successfully applied to study the reactivity [24–34]. AIM98PC package [35], a PC version of AIMPAC [36], was employed for the electron density topological analysis using the electron densities obtained from the B3LYP/6-31⫹⫹G ⴱⴱ calculations.

3. Results and discussion 3.1. The model reaction H2 CyCH2 ⫹ H2 CyCyNH For this case, only two possible products could be

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Table 2 ˚ ; angle in degree; HF: HF/6-31G; MP2: MP2/6-31G ⴱ; B3LYP: The optimized geometric parameters for TSA(2) and PA(2) (bond length in A B3LYP/6-31⫹⫹G ⴱⴱ) TSA(2)

PA(2)

HF

MP2

B3LYP

HF

MP2

B3LYP

N2 –C1 C3 –N2 C4 –C3 C4 –C1 C5 –C1 H6 –N2 H7 –C5 H8 –C5 H9 –C3 H10 –C3 H11 –C4 H12 –C4 C3N2C1 C4C3N2 C4C1N2 C5C1N2 H6N2C1 H7C5C1 H8C5C1 H9C3C4 H10C3C4 H11C4C3 H12C4C3 C4C3N2C1 C5C1N2C3 H6N2C1C5 H7C5C1N2 H8C5C1N2 H9C3C4C1 H10C3C4C1 H11C4C3N2 H12C4C3N2

1.309 2.391 1.398 1.781 1.340 1.010 1.074 1.070 1.074 1.067 1.075 1.072 70.08 75.51 103.77 140.79 113.31 119.46 122.48 120.43 122.18 117.47 117.60 35.35 144.94 ⫺20.61 ⫺16.86 163.80 87.00 ⫺91.93 84.63 ⫺131.60

1.321 2.459 1.457 1.561 1.383 1.037 1.086 1.084 1.086 1.081 1.100 1.093 71.01 69.26 110.58 125.31 108.95 120.73 121.44 120.29 120.96 115.60 113.28 16.16 162.06 2.43 ⫺37.72 151.32 114.33 ⫺75.12 103.16 ⫺132.14

1.300 2.641 1.416 1.686 1.374 1.025 1.086 1.084 1.086 1.082 1.099 1.088 69.05 67.48 111.19 136.22 108.91 120.01 121.56 121.22 120.58 115.58 115.06 18.40 161.82 ⫺15.42 ⫺33.74 156.29 115.29 ⫺57.89 92.88 ⫺136.47

1.391 1.465 1.561 1.528 1.324 .988 1.073 1.072 1.082 1.082 1.080 1.080 95.99 86.65 90.58 134.03 131.77 121.88 120.65 115.11 115.11 114.97 114.97 0.00 180.00 0.00 0.00 180.00 115.68 ⫺115.68 115.78 ⫺115.78

1.417 1.482 1.549 1.518 1.337 1.018 1.085 1.083 1.097 1.094 1.093 1.092 91.24 87.93 91.56 132.86 119.57 121.77 120.32 112.18 117.83 113.29 116.92 15.78 160.78 34.64 .06 179.23 100.46 ⫺131.02 98.88 ⫺132.14

Table 3 The total energies (au) and relative energies (kcal/mol) for the model reaction

C2H4 H2 CyCyNH C2 H4 ⫹ H2 CyCyNH TSA(1) PA(1) TSA(2) PA(2)

HF/6-31G

MP2/6-31Gⴱ

B3LYP/6-31⫹⫹G ⴱⴱ

⫺78.004456 ⫺131.811444 ⫺209.81590 ⫺209.718993 (60.81) ⫺209.854579 (⫺24.27) ⫺209.709375 (66.85) ⫺209.844373 (⫺17.87)

⫺78.285028 ⫺132.278416 ⫺210.563444 ⫺210.506325 (35.84) ⫺210.621693 (⫺36.55) ⫺210.493578 (43.84) ⫺210.604290 (⫺25.63)

⫺78.599705 ⫺132.726991 ⫺211.326696 ⫺211.266472 (37.79) ⫺211.367025 (⫺25.31) ⫺211.256991 (43.74) ⫺211.354084 (⫺17.19)

1.409 1.480 1.558 1.526 1.338 1.014 1.086 1.084 1.097 1.094 1.094 1.092 92.90 87.67 91.55 132.99 122.36 121.78 120.26 112.87 117.32 113.95 116.29 11.79 165.52 32.96 .11 179.46 104.30 ⫺126.89 103.50 ⫺127.66

D.-C. Fang, H.-M. Li / Journal of Molecular Structure (Theochem) 528 (2000) 111–119 Table 4 The Topological properties of electron density distributions at the BCPs from B3LYP/6-31⫹⫹G ⴱⴱ calculations

rb C2H4 CyC 0.3456 H2 CyCyNH CyC 0.3375 CyN 0.4139 TSA(1) C2 –C1 0.3186 C4 –C1 0.1382 0.3060 C4 –C3 N5 –C1 0.3875 PA(1) C2 –C1 0.2476 C3 –C2 0.2321 C4 –C1 0.2548 0.2325 C4 –C3 N5 –C1 0.3924 TSA(2) N2 –C1 0.3743 0.1679 C4 –C1 C4 –C3 0.3014 C5 –C1 0.3197 PA(2) N2 –C1 0.2992 C3 –N2 0.2590 C4 –C3 0.2354 C4 –C1 0.2507 0.3400 C5 –C1

7 2r b

e

Hb

⫺1.0151

0.3591

⫺2.6193

⫺0.9955 ⫺0.6776

0.5256 0.1701

⫺3.3206 ⫺4.9508

⫺0.8845 ⫺0.1373 ⫺0.8241 ⫺1.1146

0.2727 0.0502 0.1724 0.1933

⫺2.2379 ⫺0.5173 ⫺2.0437 ⫺4.5298

⫺0.5649 ⫺0.5009 ⫺0.6057 ⫺0.5028 ⫺0.7915

0.0280 0.0065 0.0409 0.0038 0.2129

⫺1.3536 ⫺1.2081 ⫺1.4246 ⫺1.2102 ⫺4.6527

⫺1.1054 ⫺0.2399 ⫺0.8070 ⫺0.8823

0.2178 0.0658 0.1403 0.2775

⫺4.3108 ⫺0.7119 ⫺1.9708 ⫺2.2719

⫺0.9553 ⫺0.6949 ⫺0.5795 ⫺0.5852 ⫺0.9880

0.0815 0.0356 0.0085 0.0040 0.4208

⫺2.7897 ⫺1.9130 ⫺1.2403 ⫺1.3863 ⫺2.6157

found. The atomic numbering systems of the stationary points are given in Fig. 1, along with the displacement of vectors of normal mode of TSA(1) and TSA(2) with an imaginary frequency, which are clearly connected to reactants and product. The optimized geometric parameters are listed in Tables 1 and 2, respectively, which reveal that the geometries obtained at HF/6-31G, MP2/6-31G ⴱ and B3LYP/631⫹⫹G ⴱⴱ are very similar. The largest difference for bond length in TSA(1) is on the loose C3C2 bond, which changes from 2.588(HF/6-31G) to ˚ (B3LYP/62.682(MP2/6-31G ⴱ) and then to 2.747 A ⴱⴱ 31⫹⫹G ). For all other bonds, they are less than ˚ . The main difference for angles in TSA(1) is 0.02 A about 5⬚ for C3C2C1. Table 3 lists the total energies for the stationary points along the reaction path and activation barriers, which shows that the reaction occurring via CyC

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bond of ketenimine is of lower energy barrier than that of CyN bond as shown before [11–14]. MP2/631G ⴱ and B3LYP/6-31⫹⫹G ⴱⴱ give very similar reaction heats and activation barriers. In order to better understand the bonding properties during the reaction process, topological analysis has been done for reactants, transition states and products based on B3LYP/6-31⫹⫹G ⴱⴱ wavefunctions. Table 4 lists the electron density (r ), Laplacian of electron densities (7 2r ), ellipticity (e ) and local energy density (Hb) at bond critical point (BCP). As we know, e ˆ …l 1 =l2 † ⫺ 1: For a single bond l1 艑 l2 and therefore e 艑 0; while for a double bond l1 ⬎ l2 and therefore e ⬎ 0: Table 4 reveals that in both products, the ring is composed of single bonds, while in TSA(1), C2 –C1 and C4 –C3 are of partially double bond character. All of Hb is less than zero, which means there are mostly covalent bonds in these systems. From the change of r b, we realize that in TSA(1), the magnitude r b for C4 –C1 is quite small, which means only a partial single bond has been formed in TSA(1), for another bond C3 –C2, no bond critical point could be found. In TSA(2), we could find the bond critical point for C4 –C1 bond, but not for C3 – N2. Therefore, such transition states are very asynchronous, but the reaction is concerted because no intermediates could be found during the reaction process. The same conclusion can be drawn from the molecular graphs and Laplacian distributions of the transition states and products depicted in Fig. 2(a)–(d). In these figures, the dashed lines denote the positive values of 7 2r and solid lines denote their negative values. In addition, bond paths (heavy solid lines), BCP (solid circle), ring critical point (open triangle) are shown for r (r). In both transition states, only one bond to be formed has a bond critical point, so no ring critical point could be found, i.e. the ring is formed after the transition state. Each product has one ring critical point. 3.2. The cycloaddition reactions between H 2 CyCyNH and …CF3 †2 CyCF2 There are four possible addition modes as shown in Scheme 1. The main optimized geometries of the possible four transition states are depicted in Fig. 3, which shows that in all the four transition states, the distances between C (or N) and C of the two

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Fig. 2. The molecular graphs and Laplacian of electron density distributions (7 2r ): (a) the 7 2r (r) and the molecular graph of TSA(1), the plane illustrated contains C1, C2 and C4; (b) those for PA(1), the plane illustrated contains C1, C2 and C4; (c) those for TSA(2) plotted for C1, N2 and C4; and (d) the same as (c), but for PA(2).

CF3 groups are always longer than those of another forming bond (without CF3 substituents). This is due to the two CF3 on C having much larger steric repulsion. The obtained total energies and relative energies are listed in Table 5, which reveals that the reaction B(1) is the easiest one, but reaction B(2) has an energy barrier higher 11 kcal/mol than reaction B(1). Why do reactions B(3) and B(4) have much higher energy barriers? The reason is very simple, because the approaching mode of reaction B(3) or B(4) is not favorable for the interaction of reactants (see Fig. 3). In TSB(3), the charges of C1 and C4, or C2 and C3 have the same sign, the same as for the TSB(4) case. In addition, both the reactions B(1) and B(2) have lower energy barriers than the corresponding unsubstituted reactions.

3.3. The cycloaddition reactions between …CF3 †2 CyCF2 and …CF3 †2 CyCyNH For this case, there are four possible approaching modes between two reactants as stated before. The presence of the two larger CF3 groups on the terminal carbon of ketenimine makes it difficult for the approaching one between olefin CyC double bond and ketenimine CyC double bond. In fact, the geometries of transition states are also different from the previous ones. Comparing Fig. 3 with Fig. 4, one can realize that the bonds C4 –C1 and C3 –C2 in TSC(1) and TSC(2) are very different from those of TSB(1) and TSB(2), respectively, because of two CF3 groups on C3. However, for the reactions at the CyN in ketenimine, the geometries of transition states are similar.

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˚ and angle is in degree) for TSB(1)–TSB(4), along with the Fig. 3. The main geometric parameters obtained at HF/6-31G (bond length is in A atomic charges (in parenthesis).

Table 5 The total energies (au) and relative energies (kcal/mol) for substituted reactions

H2 CyCyNH …CF3 †2 CyCyNH …CF3 †2 CyCF2 H2 CyCyNH ⫹ …CF3 †2 CyCF2 …CF3 †2 CyCyNH ⫹ …CF3 †2 CyCF2 TSB(1) TSB(2) TSB(3) TSB(4) TSC(1) TSC(2) TSC(3) TSC(4) a

HF/6-31G

MP2//HFa

⫺131.811444 ⫺802.822391 ⫺946.632575 ⫺1078.444019 ⫺1749.454966 ⫺1078.422412(13.56) ⫺1078.414404(18.58) ⫺1078.340827(64.75) ⫺1078.341565(64.29) ⫺1749.324230(82.04) ⫺1749.384336(44.32) ⫺1749.293676(101.21) ⫺1749.322114(83.37)

⫺132.276005 ⫺804.777551 ⫺948.820470 ⫺1081.096475 ⫺1753.598021 ⫺1081.075839(12.95) ⫺1081.059430(23.25) ⫺1081.031087(41.03) ⫺1081.031790(40.59) ⫺1753.517350(50.62) ⫺1753.547810(31.51) ⫺1753.502869(59.71) ⫺1753.537105(38.23)

Single point MP2/6-31G calculation based on HF/6-31G geometry.

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˚ and angle is in degree) for TSC(1)–TSC(4), along with the Fig. 4. The main geometric parameters obtained at HF/6-31G (bond length is in A atomic charges (in parenthesis).

The obtained activation barriers are also listed in Table 5. Now the reaction C(3) has the lowest energy barrier because TSC(3) has lowest steric repulsion, which accounts for why the reaction mainly proceeds via the CyN bond in ketenimine rather than the CyC bond for this case.

to proceed than that of CyN bond. And the energy barriers are much lower than the model system. 3. For …CF3 †2 CyCF2 ⫹ …CF3 †2 CyCyNH case, the reaction across CyN in ketenimine becomes more feasible than that across CyC one. Acknowledgements

4. Conclusions Ab initio studies on the cycloaddition reactions between ketenimine and olefin have resulted in the following conclusions: 1. For the model reaction, topological analysis shows that both transition states are open-ringed. The reaction across CyC in ketenimine has lower energy barrier than that across CyN bond in ketenimine. 2. For …CF3 †2 CyCF2 ⫹ H2 CyCyNH system, the reaction across CyC in ketenimine is also easier

This project was supported by National Natural Science Foundation of China (no. 29603002) and the Cross-Century Foundation of Beijing Normal University. The authors express their gratitude to Dr Kelsey M. Forsythe for his careful checking and improvement of the English of the manuscript. References [1] S. Patai, The Chemistry of Ketenes, Allenes and Related Compounds, Wiley, New York, 1980.

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