Quantum-chemical investigation of the nucleophilic opening of the ...

LITERATURE CITED i.

R. M. Aminova, M. B. Zuev, and I. D. Morozova, Izv. Akad. Nauk SSSR, Ser. Khim., 2190 (1979). P. P. Schastnev and A. A. Cheremisin, Zh. Strukt. Khim., 23, 139 (1982). R. M. Aminova, Dokl. Akad. Nauk SSSR, 219, 625 (1974). R. M. Aminova, Mol. Phys., 37, 319 (1979). O. P. Charkin, A. E. Smolyar, A. S. Zyubin, and N. M. Klimenko, Zh. Strukt. Khim., 15, 539 (1974). V. G. Zakzhevskii, N. M. Zlimenko, and O. P. Charkin, Zh. Strukt. Khim., 17, 545 (1976). R. F. Stewart, J. Chem. Phys., 54, 431 (1970). F. Schindler, H. Schmidbaur, and G. Jones, Chem. Ber., 98, 3345 (1965). G. Mavel, in: Progress in Nuclear Magnetic Resonance Spectroscopy, Vol. i, J. Emsley (editor), Pergamon Press, Oxford (1966), p. 251. R. M. Aminova and Yu. Yu. Samitov, Teor. Eksp. Khim., 19, 209 (1983).

2. 3. 4. 5. 6. 7. 8. 9. i0.

QUANTUM-CHEMICAL

INVESTIGATION OF THE NUCLEOPHILIC

OPENING OF THE ETHYLENIMINE RING. i,

CHAIN-GROWTH REACTIONS IN THE SYNTHESIS OF

POLYETHYLENIMINE UDC 530.145:542.91:541.64:547.415.3

L. M. Timofeeva and D. S. Zhuk

The reactions involving the opening of small stressed rings are important from the point of view of their participation in the polymerization processes of. these rings in the growth and chain-termination steps. The acid-catalyzed stepwise cationic polymerization of ethylenimine (EI) was studied experimentally, and a general ~echanism for the synthesis of polyethylenimine (PEI) was established as a result [i, 2]. However, a number of details were not examined. Therefore, it seemed to be of interest to investigate the chain-growth reactions of PEI, which have not previously been studied, with the use of quantum-chemical methods. These reactions may be assigned to two types: opening of the unsubstituted protonated ring in EIH § under the action of various nucleophiles and interaction of an N-substituted ring in EIH* with these nucleophiles. In the present work we restricted outselves to the investigation of reactions of the former type. The nucleophiles in the growth reactions of PEI are the monomer EI, as well as various fragments of the uncharged polymer chain: the substituted EI ring (the head) and the terminal and mid-chain amino groups (the tails). Two methods of interaction are distinguished, according to the type of nucleophile participating in the reaction: "head-to-head" (EIH" reacts with the substituted EI ring of the attacking chain) and "head-to-tail" (EIH + is attached by amino groups in:a~chain). The equal probability of the two mechanisms was postulated on the basis of kinetic data from an investigation of model mixtures in [3]. However, the predominance of the latter method was demonstrated in [4]. We took into account the "head-to-tail" method in the study of the reaction in the gaseous phase for the time being. In [5] it was shown that the quantum-chemical investigation of the mechanism for the growth of a PEI chain in the gaseous phase may be restricted in the first step to the calculation of the dimerization reaction of E1 (i) and:model reactions (2) and (3), which result in the formation of linear and branched PEI chains:

H~ H N / N+\. + ./__~

-~

H2 H~]

(i)

NH~(Co))~N\

H2

A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. i0, pp. 2259-2264, October, 1985. Original article submitted July 27, 1984.

2090

0568-5230/85/3410-2090509.50

9 1986 Plenum Publishing

Corporation

~;z

H

H

I

~t~ H

%~.

Fig. i. Geometric structure of the transition state of reaction (i): a) Trans transition state (approach of the nucleophile toward the C--C bond); b) cis transition state (approach of the nucleophile toward a C--N bond). The bond lengths are given in angstroms, and the bond angles are given in degrees.

/ + N\

T +E + NH2Et --~ NH~(CH~.)2N t H~ (U) H2 N § / + \ + NHEt~ -~ NH,z(CH2)2NEt2 (III) u

(2)

(3)

The potential curve of the model reaction of EIH+ with ethylamine (EA) (2) was calculated in [5] by the SCF--MO--LCAO method in the MINDO/3 approximation [6]. The MINDO/3 method was also previously [7, 8] used to investigate the mechanism of the opening of the aziridine ring. The results of these studies showed that~this method permits the adequate description of the ring-opening reaction of ethylenimine. In the present work we investigated reaction (i) and model process (3) in the framework of the MINDO/3 method. TEe dimerization reaction of EI was studied in greatest detail, since it is a real synthesis process, and the dimer of EI (DEI) is a product, which is of practical interest in itself. Various approaches of EI to the EIH + ring were investigated. As a result, we established two reaction channels, viz., the cis and trans approaches of the nucleophile toward EIH + with the formation of the cis and trans isomers of protonated DEI (I), respectively. The calculation of the trans channel was first performed for various fixed values of the C~--N2 distance with optimization of all the remaining independent variables. More exact values of the geometric parameters and the energy of the transition state were found according to the method of McIver and Komornicki [9]. The search for the transition state in the cis reaction channel was carried out at once according to the method in [9] with optimization of all the independent parameters. Figure 1 shows the geometric structures of the transition states for both channels of reaction (I). Table 1 presents the values of the heats of formation (5Hf ~ of the reactants and products of the reaction, as well as the activation energies. Since the activation energy obtained in the cis channel of reaction (i) is s i g n i f i c a n t l y higher than that in the trans channel, only the statistically more probable trans a p p r o a c h was investigated in reaction (3). Of the four conformers of diethylamin e (DEA) corresponding to rotation of a C--C bond around a C--N bond, we took the most stable conformer, in which the C--C--N--C--C chain of atoms lies in one plane, and each of the C--C bonds is located in a trans position of a C--N bond. Reaction (3) with a trans transition state was first investigated with various fixed C2--N2 distances. Several points on the potential curve were calculated in the region of the proposed transition state with complete optimization of the geometry. The regions of the trans transition state were studied in this manner for three spatial orientations of the reactants: a cis orientation, in which the N2--H bond of DEA is located in the cis position

2091

TABLE I. Keats of Formation of Reactants and Products and Activation Energies of Reactions Calculated by the MINDO/3 Method Molecule

5H~ ~ k c a l / m o l e caldula tioh (ex~eriment~

Reacdon

Ea ,

kcal/mole

+

EI EIH+ DEA

DMA cis-I trans-I tram- Ill tram- IV

2L2 (30,2 [6]) 169,0 (176 [iO]) -18,2 3,6 (t,0 [6]) 169,4 t69,5 ~52,4 t71,0

EIH+ + NH~ ~ NI~I2(CH~% 2NH3- trans EII-I~ + El'-* cis-I EII-V + EI "-* tran~-I EIH + + E A - - trans-II EIH + + D E A ~ trans-III EIH+ + DMA -~ tran~-IV

~5,8 [81

30,5

16,8

20,0 i5] 32,9 29,8

to the CI--C2 bond of the EIH § ring, as well as gauche and trans orientations (with the N2--H bond at 60 and 180 ~ angles to the CI--C2 bond, respectively). The third conformer of the transition state had a lower total energy, and its geometry and energy were refined according to the method in [9], the C--H bond lengths and the dihedral angles of the CH~ group not being varied further. The final geometric structure of the transition state is shown in Fig. 2. As is seen from Table i, the MINDO/3 method satisfactorily evaluates AHf ~ of the amines investigated. The value of E a for the trans channel of the dimerization reaction corresponds to the experimental values of the activation energy for the polymerization of EI i n various solvents (15-25 kcal/mole [2]). From a comparison of the activation energies of the cis and trans channels of interaction (i) it follows that, statistically, the trans approach of the nucleophile (toward the C--C b o n d ) s h o u l d be preferentially realized in the gaseous phase. The result obtained is consistent with the experimental data on polymerization in solution [ii, 12], where a high degree of optical rotstion of the polymer, whose sign was opposite to that of the rotation of the monomer, was observed. An analysis of the reaction products shows that the polymerization takes place according to an SN2 mechanism in solution [I, 2]. In addition, an IR-spectroscopic investigation of crystallin e salts of ethylenimine hydrochloride, EIH+'CI-(HCI)n>2, obtained at 77~ and investigations of this system in an Xe matrix at ~60~ attest to the high stability of the protonated rins which does not open below 243~ even i n the presence of a nucleophile [13]. The large value of Ea (54 kcal/mole) for the opening of the protonated ring: obtained in the MINDO/3 calculation of the gas-phase isomerization of EIH+ to the carbocation confirms the stability of this ring [7]. In our opinion the reason for the high activation energy in the cis channel of the dimerization reaction is the stronger repulsion of the cores of the atoms of the reacting molecules in comparison to that in the trans channel. The energies for the core repulsion Ec are 3422.9325 eV in the cis transition state and 3286.5964 eV in the t r a n s transition state. The increase in Ec is attributed to the decrease in the distance between the reacting molecules in the cis transition state (see Fig. i). A l t h o u g h the energy of the electron--core attraction is increased in this case, a higher total energy was still obtained for the eis transition state. A similar result was obtained in [8] in the MINDO/3 calculation of the interaction of EIH + with ammonia in the gaseous phase. Apparently, the fact that attack i n the direction of the C-C bond is preferential is common to the reactions of EIH § with amines. The calculated activation energies in the trans channels of reactions (i) and (2) are comparable to the real activation energies for the polymerization of El. At the same time, the value of E a for reaction (3) was considerably higher than the values of E a for reactions (I) and (2). This result was unexpected, if we take into account that the gas-phase basicity (GB) of secondary amines is greater than the GB of monosubstituted amines (EI is an exception). Therefore, there is some question as to the possibility of correctly evaluating the interaction in system (3) by the MINDO/3 method. In order to test the method, we calculated the reaction of EIH+ with dimethylamine (DMA) H~ ~N

+

(4)

H

The trans :channel of reaction (4) was investigated according to the method in [9] with complete optimization of all the independent parameters. In this case, only one of the possible conformations of the" trans transition state, in which the N2--H of DMA is found in the trans position to the C~--C2 bond of the EIH + ring, was considered on the b a s i s of the results of the calculation

2092

Ni c5

Nf

I~

I

Fig.

2

Fig. 3

Fig. 2. Geometric structure of the transition state of reaction (3) for the trans reaction channel. Fig. 3. Geometric structure of the transition state of reaction (4) for the trans reaction channel. TABLE 2. Charges q on Atoms in Nucleophiles Calculated by the MINDO/3 and CNDO/2 Methods, Proton Affinity (PA) Calculated by the MINDO/3 Method, and Experimental Values of the PA and GasPhase Basicities (GB) of These Compounds Charges on atoms : 10 3, MINDO/3 CNDO/2 * N

EI

EA

DMA

DEA

-i35 -162

--t76 -200

--162 -168

-i84 -i84

9t 64

200 127

209 115

220 i37

83

53 72

57 73

6i 85

59 80

202,7

2i8,2

218,0

2i0,2

214,7

205 196

215,7 207,2

207,8

220,5 21t,5

216,5

NH3

-250

C bonded to N H bonded to N PA, keal[n2ole MINDO t13 1 ' pA k e a l / m o l e flO] GBIk e a l l m o l e ~14]

*The geometry was optimized in the framework of the MINDO/3 method. #The PA of molecule M was calculated according to the formula: PA(M)-= AHf(H § + s -- 5Hf(MH+), where AHf(H § = 366 kcal/mole. of reaction (3). Figure 3 depicts the optimal geometric structure of the transition state found. The corresponding value of E a is 29.8 kcal/mole (see Table i). The reason for the increase in E a along the series of reactions from (i) to (4) can be found by analyzing the charges on the atoms in the nucleophiles considered. Table 2 presents the charges calculated by the MINDO/3 and CNDO/2 methods [15]. From these data it follows that there is a correlation between the increase in the positive charge on the C and H atoms bonded to an N atom and the increase in the activation energies of the corresponding reactions. The electrostatic repulsion between the atoms with like charges in'the nucleophile and the CH2 group of the protonated ring being attacked clearly increases with incr6asing charge.

2093

From a comparison of the values of the proton affinity (PA) calculated by the M!NDO/3 method and the experimental data on the PA and the gas-phase basicities (GB) for the series of nucleophiles under consideration it is seen (see Table 2) that ~ e method correctly evaluates the values of the PA for EA and EI, but underestimates the proton affinity of DMA, and, according to the data for the GB of DEA, it gives a qualitatively incorrect picture in the series. It may be assumed that the calculated values of E a for nucleophilic addition reactions (3) and (4) are overestimated. Therefore, for the time being, we cannot compare the energetics of model reactions for the formation of linear and branched chains of PEI in the framework of calculations ~ the interactions by the MINDO/3 method. We thank V. I. Faustov for providing the MINDO/3 program. CONCLUSIONS i. The gas-phase dimerization reactions of ethyleneimine and the reactions of protonated ethylenimine with dimethylamine and diethylamine, which simulate the formation of a branched chain of polyethylenimine, have been investigated by the semiempirical quantum-chemical MINDO/3 method, Two channels have been established for the dimerization reaction , viz., the cis (toward a C--N bond) and the trans (toward the C--C bond) approaches of the nucleophile toward the protonated ring, the activation energy in the trans channel being significantly lower. The results obtained are consistent with the experimental data. 2. The high values obtained for the activation energies of the reactions of protonated ethylenimine with disubstituted amines may be attributed, as the calculations of the proton affinity of dimethyl- and diethylamine show, to the errors of the MINDO/3 method. LITERATURE CITED I. 2.

3. 4. 5.

6. 7. 8. .

i0. ii. 12. 13. 14. 15.

2094

P. A. Gembitskii, D. S. Zhuk~ and V. A. Kargin, Polyethylenimine [in Russian], Nauka, Moscow (1971). P. A. Gembitskii, Dissertation, Moscow (1978). G. D. Jones, D. S. MacWilliams, and N. A. Braxtor, J. Org. Chem., 30, 1944 (1965). V. E. Selezneva, A. I. Chmarin, T. L. Golitsyna, and D. S. Zhuk, Izv. Akad. Nauk SSSR, Ser. Khim., ~96 (1975). L. M. Timofeeva and D. S. Zhuk, Izv. Akad. Nauk SSSR, Ser. Khim., 442 (1984). R. Bingham, M. Dewar, and D. J. Lo, J. Am. Chem. S.c., 97, 1285 (1975). L. M. Timofeeva and V. G. Avakyan, Izv. Akad. Nauk SSSR, Ser. Khim., 1557 (1980). S. G. Koldobskii, V. A. Bobylev, G. F. Tereshchenko, and Yu. V. Puzanov, Zh. Obshch. Khim., 3, 2356 (1983). J. W. Mclver and A. Komornicki, J. Am. Chem. S.c., 94, 2625 (1972). B. Solka and M. Russel, J. Phys. Chem., 78, 1268 (19--74). J. Minoura, M. Takebayashi, and C. C. Price, J. Am. Chem. S.c., 81, 4689 (1959). S. Tsuboyama, Bull. Chem. S.c. Jpn., 35, 1004 (1962). T. L. Lebedeva, Dissertation, Moscow (1980). E. M. Arnet, in: Proton Transfer Reactions, E. Galdin and V. L. Gold (eds.), Chapman and Hall, London (1975), Chap. 3. J. A. Pople, D. P.~ Santry, and G. A. Segal, J. Chem. Phys., 43, 129 (1965).