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Importance of charge-transfer effects in regiochemistry of 1,3-dipolar cycloadditions between azides and substituted ethylenes
Journal of Molecular Structure (Theochem) 572 (2001) 193±202
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Importance of charge-transfer effects in regiochemistry of 1,3dipolar cycloadditions between azides and substituted ethylenes Jacek Korchowiec a,*, Asit K. Chandra b, Tadafumi Uchimaru b b
a K. GuminÂski Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Tsukuba 305-8565, Japan
Received 10 April 2001; revised 12 June 2001; accepted 14 June 2001
Abstract The self-consistent charge and con®guration method for subsystems (SCCCMS) is used to study the cycloaddition reactions of 1,3-dipoles such as R±N3 (R H and CH3) azides with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes acting as dipolarophiles. All calculations are performed for reactive systems (1,3-dipole/dipolarophile) in transition-state (TS) geometries. Special emphasis is put on the components of interaction energy and on DFT-based reactivity indices. It is shown that charge-transfer (CT) energy is not responsible for the observed trends in regioselectivity though its stabilizing in¯uence cannot be disregarded. The CT energy is the only term, which is very sensitive to the type of substituent in azide and ethylene molecules. The main factor governing the orientation in 1,3-dipolar cycloaddition is the Heitler±London energy. Present analysis also con®rms adequacy of a simple two-reactant regional softness matching rule, called the maximum complementarity rule, for predicting more stable con®gurations. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Cycloaddition reactions; Energy partitioning schemes; Reactivity indices; Hardness/softness and Fukui function data
1. Introduction The 1,3 dipolar cycloaddition (1,3DC) reaction is a classical tool for the preparation of ®ve-membered heterocycle rings [1,2]. The suf®cient choice of substrates (1,3 dipoles and dipolarophiles) gives the possibility to control the regio, diastereo, and enantioselectivity of 1,3DC reaction. Especially, regioselectivity is a major feature of 1,3DC since it occurs with any unsymmetrical dipolarophiles. Thus, it is not surprising that many experimental [2±4] and theoretical [5±9] works have been carried out for 1,3DC reactions. * Corresponding author. Tel.: 148-12-6336377; fax: 148-126340515. E-mail address: [email protected] (J. Korchowiec).
The mechanism of pericyclic reactions can be understood through the Woodward±Hoffmann rule [10] based on the conservation of the orbital symmetry during the reaction course. The 1,3DC reaction occurs by a concerted mechanism in which two new s-bonds are formed simultaneously. At the same time two p-bonds disappear. Additional insight into cycloaddition reactions can be gained from the perturbational theory [11,12]. However, most of the perturbative treatments of cycloaddition are limited only to charge transfer (CT) (overlap, delocalization) stabilization [6,7]. Such analyses are usually reduced to porbitals, namely frontier orbitals [12]. The highest occupied (HO) and the lowest unoccupied (LU) orbitals of both reactants are especially important due to the inverse dependence of CT stabilization energy on orbital energy difference. According to Sustmann [7]
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00629-7
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and Houk et al. [6], the 1,3DC reactions are classi®ed into three types: (i) HO-controlled processes when interaction of 1,3-dipoles HO with LU of dipolarophile is especially large; (ii) LU-controlled when interaction of dipole LU with dipolarophile HO is signi®cant; (iii) HO/LU-controlled if both reaction channels are equally important. Recently, one can observe the growing interest in density functional based reactivity descriptors. Several matching criteria involving softness or Fukui function (FF) (unity normalized softness) have been proposed [13±17]. Relative success of such approaches in applications to regioselectivity problems can be qualitatively understood since FF generalizes the frontier orbital theory and gives theoretical explanation within density functional theory (DFT) [18]. Among the matching criteria, the most frequently used is a regional analogous of hard±soft-acid-and-bases (HSAB) principle of GaÂzquea and MeÂndez [13]. Atoms of different addends arrange themselves in such a way that soft (hard) atom of one reactant is bonded to soft (hard) atoms of the other reactant. However, one should remember that this principle was derived from the perspective of noninteracting species. In the case of strongly coupled reactants, the picture changes due to mutual interactions: atom of one reactant exhibiting the most weakly bonded electrons is coordinated to atom of the other reactant in which the valence electrons are the most strongly bonded [15,19]. This principle which is contrary to the regional HSAB principle was veri®ed only in semiempirical type of modeling. Both approaches were generalized to multi-site interactions [14±16], as in cycloaddition reactions. The aim of this paper is twofold: ®rst, we have characterized the energetic aspects of the 1,3DC reactions between R±N3 (R H and CH3) azides and H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes. Special emphasis is given on the decomposition of the interaction energy within the self-consistent charge and con®guration method for subsystems (SCCCMS) [20,21]. We would like to examine which energy term is responsible for path selectivity trends. Second, we have numerically veri®ed the maximum complementarity rule [15], which was intuitively introduced, in rationalizing the observed trends in regioselectivity.
2. Computational methodology 2.1. Self-consistent charge and con®guration scheme The SCCCMS calculations have been described elsewhere [20,21]. Here, we concentrate on the facts important for the current analysis. The main assumption of the scheme is based on intra-reactant equilibrium, marked by the chemical potential equalization equations [19]
m AM ; 2EM =2NA NB mM r ; dEM =drA ~r NB A ~ M mM r ; dEM =drB ~r NA ; B ; 2EM =2NB NA mB ~
1
where EM denotes energy of a system M composed of two mutually closed subsystems A (an acid) and B (a base). The ®rst-order derivatives of energy with respect to the number of electrons in subsystem X A; B (NX) and with respect to the electron density (r X) M specify the global mM r chemical X and local mX ~ potentials which are equalized throughout the whole position space ~r for the assumed constraints. Eq. (1) can be proved by the following transformation:
mM r 2EM =2NA dNA =drA ~r 1 2EM =2NB A ~ dNB =drA ~r 2EM =2NA mM A; notice that dNA =drA ~r
Z
drA ~r 0 =drA ~r d~r 0
Z
d ~r 0 2 ~r d~r 0 1
and dNB =drA ~r 0 since perturbation in A does not change NB : In the same way, the equalization in the other subsystem can be shown. By controlling the number of electrons in both subsystems, one can probe the energy surface in populational space. The second-order Taylor expansion of the energy around the reference point (neutral subsystems) gives via Eq. (1) the CT stabilization ECT 2 mCT 2 =2hCT M 2 M M M ; 2 mM A 2 mB =2 hAA 1 hBB 2 2hAB ;
2
where the hardness parameters are de®ned as follows:
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202
hM XY
2
2 EM =2NX 2NY ; X; Y A; B: The CT chemical potential and hardness result from dNA 2dNB ; dNCT . 0 constraint (electrons ¯ow from B to A). Other components of the interaction energy
p max Dbb aa 0 TS ! TS ;
EINT EM 2 EA0 1 EB0 ;
is de®ned by the CT softness parameters ! ! 2NxX 2NxX 2mCT CT sx = 2mCT N 2NCT N 2NCT N
3
namely, electrostatic EES and polarization EP contributions are de®ned as follows: r EES EAr 1 EBr 2 Vqq 2 EA 1 EB
and P r EP EAP 1 EBP 2 Vqq 2 EAr 1 EBr 2 Vqq :
0
TS
195
4
where 0
CT CT 2 CT CT 2 Dbb aa 0 TS sa 2 sb 1 sa 0 2 sb 0
; fxCT =hCT ; X x A a; B b
5
6
The CT FF index fxCT describes how electron population on atom x belonging to subsystem X, NxX ; changes due to CT between subsystems. These FF indices can be easily obtained within the SCCCMS scheme [22] 2NA f CT NA NA0 1 1; NB0 2 1 2 NA NA0 ; NB0 ; A ; 2NCT 7
The upper indices correspond to rigid (r) and relaxed polarized (P) electron densities and pointr charge P P termsP Vqq P Pdistributions. The additional P and Vqq a[A b[B qa a[A b[B qa qb =rab P r qb =rab ± Vqq ; appearing only for interacting species, are introduced in order to eliminate the electrostatic interactions (between the point-charge distributions {qa } and {qb }), which are doubly counted. Energies EA0 and EB0 in Eq. (3) correspond to reactants in the minimum energy structure and are different from these EA EAr ; EAP and EB EBr ; EBP computed for reactants owning the molecular system geometry. The energy difference, EDEF EA 1 EB 2 EA0 1 EB0 ; de®nes deformation (DEF) part of EINT : The exchange energy EEX is a consequence of the balance equation EINT EDEF 1 EES 1 ECT 1 EP 1 EEX since SCCCMS work within the polarization approximation. The ®rst-order classical EES and nonclassical EEX electrostatic energies de®ne the Heitler±London (HL) energy, EHL EES 1 EEX :
Here, vectors NA and NB collect electron populations in A and B, respectively. The overall number of electrons in both interacting subsystems are given in the parentheses. The reference system is speci®ed by 0 0 NP Both FF vectors are unity normalized A and NB : P CT fa 1; fbCT 1: In contrast to the original paper [22], the CT FF of basic reactant is changed in order to keep the same normalization condition in the limit of separated reactants as in the work of Parr and Yang [18].
2.2. Regional softness matching criteria
2.3. Computational details
Cyclization reactions involve two pairs of coordinating atoms: a±b and a 0 ±b 0 , where a and a 0 denote atoms of the acidic (electron accepting) reactant A, while b and b 0 indicate atoms in basic (electron donating) reactant B. It is a question which of the possible arrangements a±b/a 0 ±b 0 or a±b 0 /a 0 ±b is the favored one. In the case of strongly interacting subsystem, the maximum complementarity rule was proposed [15]. According to the rule, the preferred arrangement of reactants in the lowest energy transition state, TS p follows from the maximum principle
All calculations were carried out using the gaussian 98 suite of programs [23]. The geometries of the transition states were taken from Ref. [14]. The same level of theory as in supermolecule calculations, i.e. the hybrid B3LYP functional [24,25] with 6-31G(d,p) basis set, was used for the SCCCMS calculations. The electrostatically derived charges were adopted in the current analysis (the CHelpG option in gaussian package. In comparison to previous analyses [20,21], we have restricted the SCCCMS calculations to the
f CT B ;2
2NB 2NCT
NB NA0 ; NB0 2 NB NA0 1 1; NB0 2 1:
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H H
R
b
b'
C
C
N
N
a
X
H
H
N
X
R
a'
b'
b
C
C
N a
TS1
N
H H
N a'
TS2 (X = F, Cl, OH, CN; R = H, CH3)
Fig. 1. Two possible arrangements of reactants in cycloaddition between azides and mono-substituted ethylenes.
isoelectronic cut of the energy surface in the populational space, dNA 2dNB ; dNCT . 0: This allows us to make the SCCCMS computation time shorter without loosing any important information concerning interacting subsystems. The obtained results differ by 0.1 kcal/mol from those obtained by considering the whole populational space. Such accuracy was used throughout the paper. 3. Results and discussion The results obtained from our theoretical investigations are presented in two sections. In Section 3.1, we concentrate our attention on the energetic aspects of the 1,3DC reactions. Section 3.2 is directed towards DFT based reactivity indices. Except for symmetric ethylene (H2CyCH2) molecule, all its singly substituted derivatives (H2CyCHX, X F; Cl, CH3, OH, and CN) react with N3H or
N3CH3 azide on two different ways. In Fig. 1, we have schematically shown two possible arrangements of reactants for the transition-state (TS) structures. The TS, where the substituted nitrogen atom of azide joins to the unsubstituted carbon atom of ethylene is denoted as TS1. The opposite arrangement is referred to as TS2. The letters a, a 0 and b, b 0 are introduced in order to show how to apply the Criterion (4). The problem of regioselectivity is discussed in both sections. 3.1. Partitioning of the interaction energy Tables 1 and 2 show the results of energy partitioning for both possible arrangements in the transition states. The ®rst table corresponds to N3H, the second one to N3CH3, both acting as 1,3-dipole molecules. The signs of energy terms indicate stabilizing (negative signs) or destabilizing (positive signs) contributions. Both tables clearly indicate that the DEF contribution to INT energy (`electronic' activation energy) is the biggest one. It is the energy term, which can be separated into reactant contributions. The numbers in the fourth column correspond to deformation in azide molecule, so approximately 72±80% of EDEF comes from 1,3-dipole molecule. One should expect such behavior since azide is of propargyl/allenyl anion type. Its p-electron system is almost linear (/NNN 171:68 in N3H and 172.98 in N3CH3). Thus, additional bending of NNN angle (from 33.1 to 38.88) destroys one of 3-center p-orbitals, while the other one is preserved. The remaining part of
Table 1 Decomposition of the interaction energy into DEF, HL, CT, and polarization components at the B3LYP level of theory (all values are in kcal/mol) for the cycloaddition reactions of N3H azide with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes (calculated for the TS structures) Reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
EDEF
A EDEF
EHL
ECT
EP
EINT
30.5 29.4 29.4 29.8 29.2 29.5 33.3 31.9 26.9 30.4 26.9
23.0 22.4 21.9 22.3 22.3 22.3 25.3 24.7 19.7 22.7 21.3
26.7 27.7 26.9 28.6 26.4 27.1 24.3 28.4 27.9 211.5 27.3
22.4 22.5 21.3 21.2 22.8 22.8 24.6 24.6 20.4 20.3 21.7
20.4 20.5 20.5 20.3 20.3 20.5 20.6 20.5 21.0 20.2 20.4
21.0 18.6 20.6 19.8 19.6 19.1 23.8 18.5 17.7 18.5 17.5
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197
Table 2 Decomposition of the interaction energy into DEF, HL, CT, and polarization components at the B3LYP level of theory (all values are in kcal/ mol) for the cycloaddition reactions of N3CH3 azide with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes (calculated for the TS structures) Reaction H3CNNN/C2H3F H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
EDEF
A EDEF
EHL
ECT
EP
EINT
29.0 27.4 28.0 28.4 27.7 28.2 31.8 30.0 25.5 28.9 25.5
21.8 20.9 20.8 21.1 21.2 21.3 24.1 23.3 18.5 21.4 20.3
27.1 28.1 27.4 29.0 26.8 27.3 24.8 28.1 28.3 212.1 27.5
21.6 21.4 20.7 20.6 21.9 21.9 23.4 23.5 20.1 20.0 21.1
20.2 20.4 20.3 20.2 20.2 20.2 20.6 20.2 20.7 20.1 20.2
20.1 17.6 19.6 18.7 18.9 18.7 23.0 18.2 16.4 16.6 16.8
deformation comes from ethylene. The planarity of this molecule is destroyed. The H±C±C±H and X±C±C±H dihedral bonds are no longer 1808 and some degree of rehybridization sp2 ! sp3 is seen on both carbon atoms. It is worthwhile to note that DEF energy is always more destabilizing for N3H/C2H3X system (Table 1) than for N3CH3/C2H3X (Table 2) one. The energy differences EDEF N3 H 2 EDEF N3 CH3 range
Fig. 2. Diagram showing dependence of mCT and hCT on the type of substituent for C2H3X/N3H (squares) and C2H3X/N3CH3 (triangles) reactive systems, X ±OH; ±F, ±CH3, ±H, ±Cl, and ±CN. Open (closed) squares and triangles correspond to TS1 (TS2) structures.
from 1.0 to 1.5 kcal/mol. This can be attributed to the hyper-conjugative stabilization in N3CH3 molecule. The highest stabilizing contribution to EINT comes from H±L energy. Such `electrostatic' stabilization is higher for N3CH3/C2H3X (Table 2) than for N3H/ C2H3X (Table 1). The next general observation is that EHL TS1 . EHL TS2: Thus, formation of TS2 is electrostatically controlled process. One can also notice that the electron-withdrawing substituents (± CN, ±Cl) show greater stabilization than electronreleasing substituents. The CT energy (always stabilizing contribution) strongly depends on the type of substituent attached to ethylene as well as to azide. The CT stabilization is greater for electron donating substituents: ±F, ±CH3 and ±OH than for electron accepting substituents: ± CN and ±Cl. However, the difference in CT energy is insigni®cant between TS1 and TS2. Both TS structures have practically the same CT energy. In Fig. 2, we have plotted CT quantities, i.e. CT chemical potentials and hardnesses, for all reactive systems. The lines connecting points are introduced for the clarity reason. The open squares (triangles) correspond to TS1, while closed squares (triangles) correspond to TS2. The same scale and accuracy (two signi®cant digits) are used for CT chemical potentials and CT hardness data, as well as for N3H/ C2H3X (squares) and N3CH3/C2H3X (triangles) reactive systems. The diagram shows that hCT does not change much with donor/acceptor character of X. In other words, all systems have similar resistance to the
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Fig. 3. Qualitative diagram showing in¯uence of substituents on chemical potentials of basic (B) and acidic (A) reactants.
CT (Eq. (2)). In contrast to hCT ; mCT strongly depends on substituents attached to the ethylene. Thus, the differences in chemical potentials of reactants, i.e. mCT ; are responsible for trends in ECT : The chemical potential of dipolarophile molecule M mM B is higher than that of 1,3-dipole molecule mA for M M all the systems mCT , 0 ) mA , mB : It means that electrons ¯ow from ethylene (B) to azide (A). Dependence of ECT on the substituents can be qualitatively shown on the chemical potential diagram (Fig. 3). The presence of electron-releasing functional groups M increases the chemical potential: mM A 0 . mA and M M mB 0 . mB : The opposite effect is observed for elecM M tron-withdrawing substituents: mM A 00 , mA and mB 00 , M mB : These shifts in the chemical potential of reactants explain why the CT energy decreases when going from electron-releasing to electron-withdrawing M M substituents in dipolarophile umM A 2 mB 00 u , umA 2 M M M M M M mM B u , umA 2 mB 0 u or umA 0 2 mB 00 u , umA 0 2 mB u , M M umA 0 2 mB 0 u; as well as decrease in ECT for N3CH3 Table 2) in comparison to N3H (Table 1) M M M M M umM umM A 0 2 mB u , umA 2 mB u; A 0 2 mB 00 u , umA 2 M M M M mM B 00 u; and umA 0 2 mB 0 u , umA 2 mB 0 u: Such behavior is really re¯ected in Fig. 2 and is consistent with HO, LU and HO/LU mechanism based on frontier orbital energies. Similar to CT stabilization, the polarization energy also does not differ much between two possible
transition states EP TS1 < EP TS2 (except N3CH3/ C2H3CN and N3H/C2H3CN systems). This stabilizing contribution to interaction energy is the smallest one. Such behavior of EP can be easily understood. EP is the second-order contribution while EHL and ECT are the ®rst-order contributions. This explains why EP is one order of magnitude smaller than the other contributions to EINT : In the last column of Tables 1 and 2,we have presented the interaction energies for N3H/C2H3X and N3CH3/C2H3X systems, respectively. One can observe that EINT for the former systems are higher than for the latter systems. It can be attributed to higher EDEF destabilization and lower EHL stabilization for the N3H than for N3CH3 azide. The next general observation is that for all but N3CH3/ C2H3CN and N3H/C2H3CN reactive systems the TS2 has lower energy than TS1. It is usually assumed that for the same pairs of reactants the preexponential factor in the Arrhenius sense is not responsible for trends in regioselectivity [5±9,14]. Thus, the relative amount of the two possible cycloadducts is proportional to the exponential factor exp 2DE0± =RT: In other words, the regioselectivity in the 1,3DCs is determined by the relative energies of two transition states. High regioselectivity can be observed in the case of vinyl alcohol and ¯uoroethylene. For these systems deformation and electronic (H±L energy) effects favor the TS2. In the case of chloroethylene and methylethylene deformation contributions slightly favor the TS1 while electronic contributions underlay the dominant role of TS2. Thus, the formation of TS2 is the electrostatically controlled process. The strong interplay between deformation and electrostatic effects is observed for cyanoethylene. The EHL strongly stabilizes TS2 while EDEF shows the opposite, also very strong, effect. One should observe for N3CH3/C2H3CN and N3H/C2H3CN reactive systems very unusual behavior of polarization energy EP TS1 q EP TS2: Thus, the mechanism of 1,3DC reaction for cyanoethylene is rather complicated process. Nevertheless, we can conclude, like other researchers [2,6,7], that if the steric energy (EDEF and part of exchange-repulsion energy) is insigni®cant, the product distribution will be determined by electronic effects. The CT energy has caused much controversy.
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202 Table 3 The number of electrons transferred from substituted ethylene to N3H molecule obtained from SCCCMS (NCT 2mCT =hCT ; column P I) and supermolecule (NCT i[B qi ; column II) calculations (all values are in atomic units) NCT Reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
I
II
0.14 0.14 0.11 0.10 0.15 0.16 0.20 0.20 0.06 0.05 0.12
0.13 0.13 0.09 0.09 0.16 0.18 0.20 0.17 0.02 0.07 0.12
Different schemes of energy partitioning lead to qualitatively different pictures of the role of the CT effects in the chemical processes [26±31]. The SCCCMS gives correct predictions of the CT between subsystems as compared with supermolecular calculations [21]. In Tables 3 and 4, we compare the SCCCMS estimates for the amount of CT with the estimates obtained from supermolecular calculations. One can observe a good coincidence of both sets. The high deviation is seen for C2H3CN/N3CH3 system in TS1 Table 4 The number of electrons transferred from substituted ethylene to N3CH3 molecule obtained from SCCCMS (NCT 2mCT =hCT ; P column I) and supermolecule (NCT i[B qi ; column II) calculations (all values are in atomic units) NCT Reaction H3CNNN/C2H3F H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
I
II
0.12 0.11 0.08 0.07 0.13 0.13 0.17 0.18 0.03 0.01 0.09
0.08 0.08 0.05 0.06 0.12 0.13 0.13 0.16 2 0.02 0.01 0.08
199
geometry; the SCCCMS scheme and supermolecular calculations give different directions of CT. Electron af®nity (A) and ionization energy (I) can be used to estimate the direction of CT and energy cost for transferring an electron between subsystems. However, one should be careful in such qualitative considerations based on isolated reactant data. For all but cyanoethylene/azide systems, Idipolarophile 2 Adipole , Idipole 2 Adipolarophile [14]. It means that electrons ¯ow from dipolarophile (ethylene) to dipole (azide). The reverse direction is observed for cyanoethylene. The SCCCMS calculations show that even for this system electrons ¯ow from dipolarophile to azide. Supermolecular calculations predict CT from azide to cyanoethylene only for C2H3CN/N3CH3 system in TS1 geometry. For C2H3CN/N3CH3 (TS2) and C2H3CN/N3H (TS1 and TS2) systems, the CT occurs from cyanoethylene to azide. The results in Tables 3 and 4 in general show that the LU controlled process is more important as compared with HO controlled process. When the electron donating character of substituent in the dipolarophile decreases, the contribution of the LU controlled process is reduced. But even in such a case, the contribution of the LU controlled process is greater than the HO controlled process for C2H3X/ N3CH3 and C2H3X/N3H systems. 3.2. Regioselectivity predictions via softness±softness matching rules Data presented in Section 3.1 show that CT energy is not responsible for the observed trends in regioselectivity. In other words, the CT chemical potentials and hardnesses (Eq. (2) and Fig. 2) are practically the same for all pairs of reactants: mCT TS1 < mCT TS2; hCT TS1 < hCT TS2: Thus, 0one can simplify the Criterion (4) by expressing Dbb aa 0 TS via the CT FF of reactants 0
CT CT 2 CT CT 2 Dbb aa 0 TS fa 2 fb 1 fa 0 2 fb 0 :
8
Reaction of azides with substituted ethylenes is the LU-controlled process. It means, that electrons ¯ow from ethylene to azide. The suf®cient selection of substituents in both reactants allows one to increase the participation of HO interaction. This is observed for electron withdrawing substituents in dipolarophile and electron releasing substituents in 1,3-dipole
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Table 5 D-values associated with two transition states for each of the cycloaddition reactions between N3H and H2CyCHX (X H; F, Cl, CH3, OH, and CN) molecules, computed for forward B ! A and backward A ! B donations
D TS reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
B!A
A!B
0.02 0.13 0.05 0.09 0.02 0.07 0.07 0.44 0.05 0.03 0.02
0.01 0.15 0.08 0.14 0.01 0.09 0.05 0.81 0.27 0.11 0.01
molecules, respectively. Thus, CH3N3/C2H3CN system can be described as LU/HO controlled 0 process. For this reason, we have computed Dbb aa 0 TS for forward B ! A; as well as for backward A ! B donations. 0 In Tables 5 and 6, we have listed Dbb aa 0 TS values, computed via Eq. (8) for all reactive systems and both possible donations. Except for the cycloaddition between cyanoethylene and azides, the TS2 is favorable D TS2 . D TS1: This is true for forward, as
well as for backward donations. For cyanoethylene/ azide system, D -criterion favors TS1. These observations are in accord with interaction energies (Tables 1 and 2). One should remember that softness (FF) data are connected with CT stabilization. Thus, it is somewhat surprising that the Criterion (4) works so well even though ECT is practically the same for both transition states. This can be qualitatively explained by taking into account the second-order Taylor expansion of the system energy in reactant resolution E E NA ; NB ; nA ; nB : Notice that NA 1 NB N and nA ~r 1 nB ~r n ~r; where n denotes the external potential (due to nuclei). The only term depending clearly on FFs is the mixed dN dv component (part of ECT )[19]: Z 2 dE dn ~r dNA d~r d2 Emix 2NA dnA ~r A
H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
1
Z 2 dE dn ~r dNA d~r 2NA dnB ~r B
1
Z 2 dE dn ~r dNB d~r 2NB dnB ~r B
2
1
B!A
A!B
0.02 0.06 0.05 0.09 0.02 0.06 0.07 0.39 0.05 0.04 0.02
0.00 0.02 0.07 0.12 0.01 0.07 0.04 0.59 0.25 0.13 0.00
Z
fBA ~r dnA ~r d~r dNCT
Z 2 2 fAB ~r dnB ~r d~r dNCT
D TS
H3CNNN/C2H3F
Z 2 dE dn ~r dNB d~r 2NB dnA ~r A
Z ; fAA ~r dnA ~r d~r dNCT
Table 6 D-values associated with two transition states for each of the cycloaddition reactions between N3CH3 and H2CyCHX (X H; F, Cl, CH3, OH, and CN) molecules, computed for forward B ! A and backward A ! B donations
reaction
1
;
Z
Z
fBB ~r dnA ~r d~r dNCT
fACT ~r dnA ~r d~r dNCT
2
Z
fBCT ~r dnB ~r d~r dNCT ;
9
where fAA ~r and fBB ~r are diagonal FFs while fBA ~r and fAB ~r are off-diagonal FFs. The change of sign in the equation follows from closure relation dNA 2dNB dNCT : Within the polarization approximation, perturbations
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202 Table 7 Comparison between FF indices of isolated and interacting species for N3H/H2CyCHF (acid/base) reactive system in TS1 geometry ia
Reactant
0 fi[X
XX fi[X
CT: A ! B (backward donation) X A; Y B Na 0.40 N 0.09 Na 0 0.40 0.12 Ha X B; Y A Cb 0 0.33 Cb 0.40 0.06 Hb Hb 0.05 Hb 0 0.09 Fb 0 0.07 CT: B ! A (forward donation) X A; Y B Na 0.26 N 0.18 Na 0 0.42 0.14 Ha X B; Y A Cb 0 0.28 Cb 0.54 0.01 Hb Hb 20.01 Hb 0 0.04 Fb 0 0.14 a
YX fi[X
CT fi[X
0.43 0.06 0.41 0.10 0.31 0.45 0.04 0.04 0.09 0.06
20.25 0.23 20.11 0.13 20.22 20.24 0.11 0.12 0.13 0.10
0.68 20.18 0.52 20.02 0.53 0.69 20.06 20.08 20.04 20.04
0.29 0.14 0.45 0.12 0.28 0.56 0.01 20.02 0.04 0.13
20.26 0.24 20.10 0.12 20.26 20.16 0.09 0.11 0.13 0.10
0.55 20.09 0.55 20.00 0.55 0.72 20.08 20.12 20.09 0.03
See Fig. 1.
in the external potentials are approximated by the electrostatic potentials of the reaction partners: dnA ~r < fB ~r ; dnB ~r < fA ~r : In the TS, azide molecule is in the negative basin of electrostatic potential of ethylene and vice versa. In other words, fB ~r , 0 and fA ~r , 0; so the ®rst term in Eq. (9) is stabilizing while the second one is destabilizing. Thus, the highest stabilization is when fACT ~r of azide reaches maximum. The lowest destabilization is observed when fBCT ~r of ethylene reaches minimum. These observations qualitatively explain validity of the maximum complementarity rule for forward donation. In the same way, one can justify the Criterion (8) for the backward donation. The above considerations are even more clear in atoms-in-molecule (AIM) resolution. Eq. (9) can be then written in discrete form ! X CT B X CT A 2 d Emix fi fi 2 fi fi dNCT 10 i[A
i[B
Here, fBi fA i is the electrostatic potential at the position of atom i belonging to B (A) exerted by the
201
whole molecule A (B). This equation can be used to explain (qualitatively) the maximum complementarity rule for multi-site interactions. Nevertheless, one should remember that the mixed term is rather small (few percents of ECT ) and here we discuss this energy contribution in order to qualitatively explain the maximum complementarity rule and to show that it works in line with the electrostatic energy. Such explanation was not given in the original paper [15]. The CT FF indices computed via Eq. (7) include diagonal and off-diagonal effects. In order to decompose these indices, one has to consider a contact of reactant A (B) with its external macroscopic electron reservoir. The suf®cient formulas are then as follows [22]: f AA NA NA0 1 1; NB0 2 NA NA0 ; NB0 ; f BA NA NA0 ; NB0 2 NA NA0 ; NB0 2 1;
11
f AB NB NA0 1 1; NB0 2 NB NA0 ; NB0 ; f BB NB NA0 ; NB0 2 NB NA0 ; NB0 2 1: All variables have the same meaning as in Eq. (7). In the limit of separated reactants the off-diagonal FFs disappear and the diagonal FFs are nothing else but FF of isolated species. Of course, it is a question as to how strong the modi®cation of diagonal FF is due to interactions and how it is additionally corrected due to off-diagonal effects. In Table 7, we have compared the isolated reactant data in AIM resolution with diagonal FF indices for N3H/H2CyCHF system in TS1. The table also includes the off-diagonal and CT FF indices. Practically for all 0 atoms (i), FF indices of isolated reactant fi[X and diagXX onal FF indices fi[X X A; B are very close to each YX other. The magnitute of off-diagonal corrections fi[X is comparable to diagonal one, so the resultant CT FF CT indices fi[X do not resemble the isolated reactant data 0 fi[X : Moreover, the directly interacting atoms are clearly distinguished. For example, CT FF indices for Na, Na 0 , Cb, and Cb 0 are much greater then for the remaining atoms. Thus, the main contribution to d2 Emix comes from pairs of directly interacting atoms (see Eq. (10)). This numerical observation also explains why the matching criteria are limited to the pairs of directly interacting atoms. The above observations are true for
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every system considered in the paper (data available from the authors). It is worth to note that the off-diagonal FFs correctly describe the charge rearrangement due to polarization [32] and thus possess information about mutually polarized reactants (before CT). It can be concluded that the off-diagonal FFs are responsible for the fact that the matching criterion for strongly interacting subsystems (maximum softness rule) is orthogonal to the regional HSAB rule (minimum softness rule). 4. Conclusions In this paper, we have investigated the mechanism of 1,3DC reaction between azides and mono-substituted ethylenes. The regioselectivity in the 1,3DC is found to be electrostatically controlled process. CT energy of the two TSs, TS1 and TS2, do not differ signi®cantly. However, it is the only term of energy partitioning, which is very sensitive to the nature of the substituent. The amount of charge transferred from dipolarophile to dipole molecules, estimated from SCCCMS scheme is very close to independent, supermolecular predictions. Such correlation indicates that CT energy is correctly treated in our approach. Present analysis con®rms adequacy of the maximum softness (FFs) principle in predicting preferable arrangements of reactants in the TS structure for 1,3DC reaction. The criterion strongly depends on electrostatic potentials of both reactants. In other words, it has a full knowledge of interactions due to strong offdiagonal FF corrections. It works independently on the assumed direction of CT. Such behavior allows one to use this principle in regiochemistry considerations. Acknowledgements All calculations have been done in ACK CYFRONET AGH; the computational grant No KBN/SGI_ORIGIN_2000/UJ/067/1999. AKC thanks NEDO, Japan for providing him a researcher position. References
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[20] [21] [22] [23]
[24] [25] [26] [27] [28] [29] [30] [31] [32]
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K.V. Gothelf, A. Jùrgensen, Chem. Rev. 98 (1998) 863. M. Regitz, Chem. Rev. 90 (1990) 191. G. L'abbeÂ, Chem. Rev. 69 (1969) 345. R. Huisgen, Angew. Chem. 75 (1963) 741. K.N. Houk, J. Sims, C.R. Wats, L.J. Luskus, J. Am. Chem. Soc. 95 (1973) 7301. R. Sustmann, Tetrahedron Lett. (1971) 2717. L. NyulaÂszi, P. VaÂrnai, W. Eisfeld, M. Regitz, J. Comput. Chem. 18 (1997) 609. E.C. Magnuson, J. Pranata, J. Comput. Chem. 19 (1998) 1795. R.B. Woodward, R. Hoffmann, J. Am. Chem. Soc. 87 (1965) 395. L. Salem, J. Am. Chem. Soc. 90 (1968) 543±553. K. Fukui, Theory of Orientation and Stereoselection, Springer, Heidelberg, 1982. J.L. GaÂzquea, F. MeÂndez, J. Phys. Chem. 98 (1994) 4591. A.K. Chandra, T. Uchimaru, M.T. Nguyen, J. Chem. Soc., Perkin Trans. 2 (1999) 2117. A.K. Chandra, A. Michalak, M.T. Nguyen, R.F. Nalewajski, J. Phys. Chem. A 102 (1998) 10182. S. Damoun, G. Van de Woude, F. MeÂndez, P. Gerlings, J. Phys. Chem. A 101 (1997) 886. P.K. Chattaraj, P. Fuentealba, B. GoÂmez, R. Contreras, J. Am. Chem. Soc. 122 (2000) 348. R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. R.F. Nalewajski, J. Korchowiec, Charge Sensitivity Approach to Electronic Structure and Chemical Reactivity, Advanced Series in Physical Chemistry, vol. 8, World Scienti®c, Singapore, 1997. J. Korchowiec, T. Uchimaru, J. Phys. Chem. A 102 (1998) 6682. J. Korchowiec, T. Uchimaru, J. Chem. Phys. 112 (2000) 1623. J. Korchowiec, T. Uchimaru, J. Phys. Chem. A 102 (1998) 10167. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Inc.: Pittsburgh PA, 1998. A.D. Becke, J. Chem. Phys. 98 (1993) 5648. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. C. Hayes, J. Stone, Mol. Phys. 53 (1984) 83. K. Kitaura, K. Morokuma, Int. J. Quant. Chem. 10 (1976) 325. W.J. Stevens, W.H. Fink, Chem. Phys. Lett. 139 (1987) 15. A. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899. W. Chen, M.S. Gordon, J. Phys. Chem. 100 (1996) 14316. E.D. Glendening, A. Streitwieser, J. Chem. Phys. 100 (1994) 2900. J. Korchowiec, A.K. Chandra, T. Uchimaru, S. Kawahara, K. Matsumura, S. Tsuzuki, M. Mikami, Chem. Phys. Lett. 308 (1999) 229.
www.elsevier.com/locate/theochem
Importance of charge-transfer effects in regiochemistry of 1,3dipolar cycloadditions between azides and substituted ethylenes Jacek Korchowiec a,*, Asit K. Chandra b, Tadafumi Uchimaru b b
a K. GuminÂski Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Tsukuba 305-8565, Japan
Received 10 April 2001; revised 12 June 2001; accepted 14 June 2001
Abstract The self-consistent charge and con®guration method for subsystems (SCCCMS) is used to study the cycloaddition reactions of 1,3-dipoles such as R±N3 (R H and CH3) azides with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes acting as dipolarophiles. All calculations are performed for reactive systems (1,3-dipole/dipolarophile) in transition-state (TS) geometries. Special emphasis is put on the components of interaction energy and on DFT-based reactivity indices. It is shown that charge-transfer (CT) energy is not responsible for the observed trends in regioselectivity though its stabilizing in¯uence cannot be disregarded. The CT energy is the only term, which is very sensitive to the type of substituent in azide and ethylene molecules. The main factor governing the orientation in 1,3-dipolar cycloaddition is the Heitler±London energy. Present analysis also con®rms adequacy of a simple two-reactant regional softness matching rule, called the maximum complementarity rule, for predicting more stable con®gurations. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Cycloaddition reactions; Energy partitioning schemes; Reactivity indices; Hardness/softness and Fukui function data
1. Introduction The 1,3 dipolar cycloaddition (1,3DC) reaction is a classical tool for the preparation of ®ve-membered heterocycle rings [1,2]. The suf®cient choice of substrates (1,3 dipoles and dipolarophiles) gives the possibility to control the regio, diastereo, and enantioselectivity of 1,3DC reaction. Especially, regioselectivity is a major feature of 1,3DC since it occurs with any unsymmetrical dipolarophiles. Thus, it is not surprising that many experimental [2±4] and theoretical [5±9] works have been carried out for 1,3DC reactions. * Corresponding author. Tel.: 148-12-6336377; fax: 148-126340515. E-mail address: [email protected] (J. Korchowiec).
The mechanism of pericyclic reactions can be understood through the Woodward±Hoffmann rule [10] based on the conservation of the orbital symmetry during the reaction course. The 1,3DC reaction occurs by a concerted mechanism in which two new s-bonds are formed simultaneously. At the same time two p-bonds disappear. Additional insight into cycloaddition reactions can be gained from the perturbational theory [11,12]. However, most of the perturbative treatments of cycloaddition are limited only to charge transfer (CT) (overlap, delocalization) stabilization [6,7]. Such analyses are usually reduced to porbitals, namely frontier orbitals [12]. The highest occupied (HO) and the lowest unoccupied (LU) orbitals of both reactants are especially important due to the inverse dependence of CT stabilization energy on orbital energy difference. According to Sustmann [7]
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00629-7
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and Houk et al. [6], the 1,3DC reactions are classi®ed into three types: (i) HO-controlled processes when interaction of 1,3-dipoles HO with LU of dipolarophile is especially large; (ii) LU-controlled when interaction of dipole LU with dipolarophile HO is signi®cant; (iii) HO/LU-controlled if both reaction channels are equally important. Recently, one can observe the growing interest in density functional based reactivity descriptors. Several matching criteria involving softness or Fukui function (FF) (unity normalized softness) have been proposed [13±17]. Relative success of such approaches in applications to regioselectivity problems can be qualitatively understood since FF generalizes the frontier orbital theory and gives theoretical explanation within density functional theory (DFT) [18]. Among the matching criteria, the most frequently used is a regional analogous of hard±soft-acid-and-bases (HSAB) principle of GaÂzquea and MeÂndez [13]. Atoms of different addends arrange themselves in such a way that soft (hard) atom of one reactant is bonded to soft (hard) atoms of the other reactant. However, one should remember that this principle was derived from the perspective of noninteracting species. In the case of strongly coupled reactants, the picture changes due to mutual interactions: atom of one reactant exhibiting the most weakly bonded electrons is coordinated to atom of the other reactant in which the valence electrons are the most strongly bonded [15,19]. This principle which is contrary to the regional HSAB principle was veri®ed only in semiempirical type of modeling. Both approaches were generalized to multi-site interactions [14±16], as in cycloaddition reactions. The aim of this paper is twofold: ®rst, we have characterized the energetic aspects of the 1,3DC reactions between R±N3 (R H and CH3) azides and H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes. Special emphasis is given on the decomposition of the interaction energy within the self-consistent charge and con®guration method for subsystems (SCCCMS) [20,21]. We would like to examine which energy term is responsible for path selectivity trends. Second, we have numerically veri®ed the maximum complementarity rule [15], which was intuitively introduced, in rationalizing the observed trends in regioselectivity.
2. Computational methodology 2.1. Self-consistent charge and con®guration scheme The SCCCMS calculations have been described elsewhere [20,21]. Here, we concentrate on the facts important for the current analysis. The main assumption of the scheme is based on intra-reactant equilibrium, marked by the chemical potential equalization equations [19]
m AM ; 2EM =2NA NB mM r ; dEM =drA ~r NB A ~ M mM r ; dEM =drB ~r NA ; B ; 2EM =2NB NA mB ~
1
where EM denotes energy of a system M composed of two mutually closed subsystems A (an acid) and B (a base). The ®rst-order derivatives of energy with respect to the number of electrons in subsystem X A; B (NX) and with respect to the electron density (r X) M specify the global mM r chemical X and local mX ~ potentials which are equalized throughout the whole position space ~r for the assumed constraints. Eq. (1) can be proved by the following transformation:
mM r 2EM =2NA dNA =drA ~r 1 2EM =2NB A ~ dNB =drA ~r 2EM =2NA mM A; notice that dNA =drA ~r
Z
drA ~r 0 =drA ~r d~r 0
Z
d ~r 0 2 ~r d~r 0 1
and dNB =drA ~r 0 since perturbation in A does not change NB : In the same way, the equalization in the other subsystem can be shown. By controlling the number of electrons in both subsystems, one can probe the energy surface in populational space. The second-order Taylor expansion of the energy around the reference point (neutral subsystems) gives via Eq. (1) the CT stabilization ECT 2 mCT 2 =2hCT M 2 M M M ; 2 mM A 2 mB =2 hAA 1 hBB 2 2hAB ;
2
where the hardness parameters are de®ned as follows:
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202
hM XY
2
2 EM =2NX 2NY ; X; Y A; B: The CT chemical potential and hardness result from dNA 2dNB ; dNCT . 0 constraint (electrons ¯ow from B to A). Other components of the interaction energy
p max Dbb aa 0 TS ! TS ;
EINT EM 2 EA0 1 EB0 ;
is de®ned by the CT softness parameters ! ! 2NxX 2NxX 2mCT CT sx = 2mCT N 2NCT N 2NCT N
3
namely, electrostatic EES and polarization EP contributions are de®ned as follows: r EES EAr 1 EBr 2 Vqq 2 EA 1 EB
and P r EP EAP 1 EBP 2 Vqq 2 EAr 1 EBr 2 Vqq :
0
TS
195
4
where 0
CT CT 2 CT CT 2 Dbb aa 0 TS sa 2 sb 1 sa 0 2 sb 0
; fxCT =hCT ; X x A a; B b
5
6
The CT FF index fxCT describes how electron population on atom x belonging to subsystem X, NxX ; changes due to CT between subsystems. These FF indices can be easily obtained within the SCCCMS scheme [22] 2NA f CT NA NA0 1 1; NB0 2 1 2 NA NA0 ; NB0 ; A ; 2NCT 7
The upper indices correspond to rigid (r) and relaxed polarized (P) electron densities and pointr charge P P termsP Vqq P Pdistributions. The additional P and Vqq a[A b[B qa a[A b[B qa qb =rab P r qb =rab ± Vqq ; appearing only for interacting species, are introduced in order to eliminate the electrostatic interactions (between the point-charge distributions {qa } and {qb }), which are doubly counted. Energies EA0 and EB0 in Eq. (3) correspond to reactants in the minimum energy structure and are different from these EA EAr ; EAP and EB EBr ; EBP computed for reactants owning the molecular system geometry. The energy difference, EDEF EA 1 EB 2 EA0 1 EB0 ; de®nes deformation (DEF) part of EINT : The exchange energy EEX is a consequence of the balance equation EINT EDEF 1 EES 1 ECT 1 EP 1 EEX since SCCCMS work within the polarization approximation. The ®rst-order classical EES and nonclassical EEX electrostatic energies de®ne the Heitler±London (HL) energy, EHL EES 1 EEX :
Here, vectors NA and NB collect electron populations in A and B, respectively. The overall number of electrons in both interacting subsystems are given in the parentheses. The reference system is speci®ed by 0 0 NP Both FF vectors are unity normalized A and NB : P CT fa 1; fbCT 1: In contrast to the original paper [22], the CT FF of basic reactant is changed in order to keep the same normalization condition in the limit of separated reactants as in the work of Parr and Yang [18].
2.2. Regional softness matching criteria
2.3. Computational details
Cyclization reactions involve two pairs of coordinating atoms: a±b and a 0 ±b 0 , where a and a 0 denote atoms of the acidic (electron accepting) reactant A, while b and b 0 indicate atoms in basic (electron donating) reactant B. It is a question which of the possible arrangements a±b/a 0 ±b 0 or a±b 0 /a 0 ±b is the favored one. In the case of strongly interacting subsystem, the maximum complementarity rule was proposed [15]. According to the rule, the preferred arrangement of reactants in the lowest energy transition state, TS p follows from the maximum principle
All calculations were carried out using the gaussian 98 suite of programs [23]. The geometries of the transition states were taken from Ref. [14]. The same level of theory as in supermolecule calculations, i.e. the hybrid B3LYP functional [24,25] with 6-31G(d,p) basis set, was used for the SCCCMS calculations. The electrostatically derived charges were adopted in the current analysis (the CHelpG option in gaussian package. In comparison to previous analyses [20,21], we have restricted the SCCCMS calculations to the
f CT B ;2
2NB 2NCT
NB NA0 ; NB0 2 NB NA0 1 1; NB0 2 1:
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H H
R
b
b'
C
C
N
N
a
X
H
H
N
X
R
a'
b'
b
C
C
N a
TS1
N
H H
N a'
TS2 (X = F, Cl, OH, CN; R = H, CH3)
Fig. 1. Two possible arrangements of reactants in cycloaddition between azides and mono-substituted ethylenes.
isoelectronic cut of the energy surface in the populational space, dNA 2dNB ; dNCT . 0: This allows us to make the SCCCMS computation time shorter without loosing any important information concerning interacting subsystems. The obtained results differ by 0.1 kcal/mol from those obtained by considering the whole populational space. Such accuracy was used throughout the paper. 3. Results and discussion The results obtained from our theoretical investigations are presented in two sections. In Section 3.1, we concentrate our attention on the energetic aspects of the 1,3DC reactions. Section 3.2 is directed towards DFT based reactivity indices. Except for symmetric ethylene (H2CyCH2) molecule, all its singly substituted derivatives (H2CyCHX, X F; Cl, CH3, OH, and CN) react with N3H or
N3CH3 azide on two different ways. In Fig. 1, we have schematically shown two possible arrangements of reactants for the transition-state (TS) structures. The TS, where the substituted nitrogen atom of azide joins to the unsubstituted carbon atom of ethylene is denoted as TS1. The opposite arrangement is referred to as TS2. The letters a, a 0 and b, b 0 are introduced in order to show how to apply the Criterion (4). The problem of regioselectivity is discussed in both sections. 3.1. Partitioning of the interaction energy Tables 1 and 2 show the results of energy partitioning for both possible arrangements in the transition states. The ®rst table corresponds to N3H, the second one to N3CH3, both acting as 1,3-dipole molecules. The signs of energy terms indicate stabilizing (negative signs) or destabilizing (positive signs) contributions. Both tables clearly indicate that the DEF contribution to INT energy (`electronic' activation energy) is the biggest one. It is the energy term, which can be separated into reactant contributions. The numbers in the fourth column correspond to deformation in azide molecule, so approximately 72±80% of EDEF comes from 1,3-dipole molecule. One should expect such behavior since azide is of propargyl/allenyl anion type. Its p-electron system is almost linear (/NNN 171:68 in N3H and 172.98 in N3CH3). Thus, additional bending of NNN angle (from 33.1 to 38.88) destroys one of 3-center p-orbitals, while the other one is preserved. The remaining part of
Table 1 Decomposition of the interaction energy into DEF, HL, CT, and polarization components at the B3LYP level of theory (all values are in kcal/mol) for the cycloaddition reactions of N3H azide with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes (calculated for the TS structures) Reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
EDEF
A EDEF
EHL
ECT
EP
EINT
30.5 29.4 29.4 29.8 29.2 29.5 33.3 31.9 26.9 30.4 26.9
23.0 22.4 21.9 22.3 22.3 22.3 25.3 24.7 19.7 22.7 21.3
26.7 27.7 26.9 28.6 26.4 27.1 24.3 28.4 27.9 211.5 27.3
22.4 22.5 21.3 21.2 22.8 22.8 24.6 24.6 20.4 20.3 21.7
20.4 20.5 20.5 20.3 20.3 20.5 20.6 20.5 21.0 20.2 20.4
21.0 18.6 20.6 19.8 19.6 19.1 23.8 18.5 17.7 18.5 17.5
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202
197
Table 2 Decomposition of the interaction energy into DEF, HL, CT, and polarization components at the B3LYP level of theory (all values are in kcal/ mol) for the cycloaddition reactions of N3CH3 azide with H2CyCHX (X H; F, Cl, CH3, OH, and CN) ethylenes (calculated for the TS structures) Reaction H3CNNN/C2H3F H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
EDEF
A EDEF
EHL
ECT
EP
EINT
29.0 27.4 28.0 28.4 27.7 28.2 31.8 30.0 25.5 28.9 25.5
21.8 20.9 20.8 21.1 21.2 21.3 24.1 23.3 18.5 21.4 20.3
27.1 28.1 27.4 29.0 26.8 27.3 24.8 28.1 28.3 212.1 27.5
21.6 21.4 20.7 20.6 21.9 21.9 23.4 23.5 20.1 20.0 21.1
20.2 20.4 20.3 20.2 20.2 20.2 20.6 20.2 20.7 20.1 20.2
20.1 17.6 19.6 18.7 18.9 18.7 23.0 18.2 16.4 16.6 16.8
deformation comes from ethylene. The planarity of this molecule is destroyed. The H±C±C±H and X±C±C±H dihedral bonds are no longer 1808 and some degree of rehybridization sp2 ! sp3 is seen on both carbon atoms. It is worthwhile to note that DEF energy is always more destabilizing for N3H/C2H3X system (Table 1) than for N3CH3/C2H3X (Table 2) one. The energy differences EDEF N3 H 2 EDEF N3 CH3 range
Fig. 2. Diagram showing dependence of mCT and hCT on the type of substituent for C2H3X/N3H (squares) and C2H3X/N3CH3 (triangles) reactive systems, X ±OH; ±F, ±CH3, ±H, ±Cl, and ±CN. Open (closed) squares and triangles correspond to TS1 (TS2) structures.
from 1.0 to 1.5 kcal/mol. This can be attributed to the hyper-conjugative stabilization in N3CH3 molecule. The highest stabilizing contribution to EINT comes from H±L energy. Such `electrostatic' stabilization is higher for N3CH3/C2H3X (Table 2) than for N3H/ C2H3X (Table 1). The next general observation is that EHL TS1 . EHL TS2: Thus, formation of TS2 is electrostatically controlled process. One can also notice that the electron-withdrawing substituents (± CN, ±Cl) show greater stabilization than electronreleasing substituents. The CT energy (always stabilizing contribution) strongly depends on the type of substituent attached to ethylene as well as to azide. The CT stabilization is greater for electron donating substituents: ±F, ±CH3 and ±OH than for electron accepting substituents: ± CN and ±Cl. However, the difference in CT energy is insigni®cant between TS1 and TS2. Both TS structures have practically the same CT energy. In Fig. 2, we have plotted CT quantities, i.e. CT chemical potentials and hardnesses, for all reactive systems. The lines connecting points are introduced for the clarity reason. The open squares (triangles) correspond to TS1, while closed squares (triangles) correspond to TS2. The same scale and accuracy (two signi®cant digits) are used for CT chemical potentials and CT hardness data, as well as for N3H/ C2H3X (squares) and N3CH3/C2H3X (triangles) reactive systems. The diagram shows that hCT does not change much with donor/acceptor character of X. In other words, all systems have similar resistance to the
198
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Fig. 3. Qualitative diagram showing in¯uence of substituents on chemical potentials of basic (B) and acidic (A) reactants.
CT (Eq. (2)). In contrast to hCT ; mCT strongly depends on substituents attached to the ethylene. Thus, the differences in chemical potentials of reactants, i.e. mCT ; are responsible for trends in ECT : The chemical potential of dipolarophile molecule M mM B is higher than that of 1,3-dipole molecule mA for M M all the systems mCT , 0 ) mA , mB : It means that electrons ¯ow from ethylene (B) to azide (A). Dependence of ECT on the substituents can be qualitatively shown on the chemical potential diagram (Fig. 3). The presence of electron-releasing functional groups M increases the chemical potential: mM A 0 . mA and M M mB 0 . mB : The opposite effect is observed for elecM M tron-withdrawing substituents: mM A 00 , mA and mB 00 , M mB : These shifts in the chemical potential of reactants explain why the CT energy decreases when going from electron-releasing to electron-withdrawing M M substituents in dipolarophile umM A 2 mB 00 u , umA 2 M M M M M M mM B u , umA 2 mB 0 u or umA 0 2 mB 00 u , umA 0 2 mB u , M M umA 0 2 mB 0 u; as well as decrease in ECT for N3CH3 Table 2) in comparison to N3H (Table 1) M M M M M umM umM A 0 2 mB u , umA 2 mB u; A 0 2 mB 00 u , umA 2 M M M M mM B 00 u; and umA 0 2 mB 0 u , umA 2 mB 0 u: Such behavior is really re¯ected in Fig. 2 and is consistent with HO, LU and HO/LU mechanism based on frontier orbital energies. Similar to CT stabilization, the polarization energy also does not differ much between two possible
transition states EP TS1 < EP TS2 (except N3CH3/ C2H3CN and N3H/C2H3CN systems). This stabilizing contribution to interaction energy is the smallest one. Such behavior of EP can be easily understood. EP is the second-order contribution while EHL and ECT are the ®rst-order contributions. This explains why EP is one order of magnitude smaller than the other contributions to EINT : In the last column of Tables 1 and 2,we have presented the interaction energies for N3H/C2H3X and N3CH3/C2H3X systems, respectively. One can observe that EINT for the former systems are higher than for the latter systems. It can be attributed to higher EDEF destabilization and lower EHL stabilization for the N3H than for N3CH3 azide. The next general observation is that for all but N3CH3/ C2H3CN and N3H/C2H3CN reactive systems the TS2 has lower energy than TS1. It is usually assumed that for the same pairs of reactants the preexponential factor in the Arrhenius sense is not responsible for trends in regioselectivity [5±9,14]. Thus, the relative amount of the two possible cycloadducts is proportional to the exponential factor exp 2DE0± =RT: In other words, the regioselectivity in the 1,3DCs is determined by the relative energies of two transition states. High regioselectivity can be observed in the case of vinyl alcohol and ¯uoroethylene. For these systems deformation and electronic (H±L energy) effects favor the TS2. In the case of chloroethylene and methylethylene deformation contributions slightly favor the TS1 while electronic contributions underlay the dominant role of TS2. Thus, the formation of TS2 is the electrostatically controlled process. The strong interplay between deformation and electrostatic effects is observed for cyanoethylene. The EHL strongly stabilizes TS2 while EDEF shows the opposite, also very strong, effect. One should observe for N3CH3/C2H3CN and N3H/C2H3CN reactive systems very unusual behavior of polarization energy EP TS1 q EP TS2: Thus, the mechanism of 1,3DC reaction for cyanoethylene is rather complicated process. Nevertheless, we can conclude, like other researchers [2,6,7], that if the steric energy (EDEF and part of exchange-repulsion energy) is insigni®cant, the product distribution will be determined by electronic effects. The CT energy has caused much controversy.
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202 Table 3 The number of electrons transferred from substituted ethylene to N3H molecule obtained from SCCCMS (NCT 2mCT =hCT ; column P I) and supermolecule (NCT i[B qi ; column II) calculations (all values are in atomic units) NCT Reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
I
II
0.14 0.14 0.11 0.10 0.15 0.16 0.20 0.20 0.06 0.05 0.12
0.13 0.13 0.09 0.09 0.16 0.18 0.20 0.17 0.02 0.07 0.12
Different schemes of energy partitioning lead to qualitatively different pictures of the role of the CT effects in the chemical processes [26±31]. The SCCCMS gives correct predictions of the CT between subsystems as compared with supermolecular calculations [21]. In Tables 3 and 4, we compare the SCCCMS estimates for the amount of CT with the estimates obtained from supermolecular calculations. One can observe a good coincidence of both sets. The high deviation is seen for C2H3CN/N3CH3 system in TS1 Table 4 The number of electrons transferred from substituted ethylene to N3CH3 molecule obtained from SCCCMS (NCT 2mCT =hCT ; P column I) and supermolecule (NCT i[B qi ; column II) calculations (all values are in atomic units) NCT Reaction H3CNNN/C2H3F H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
I
II
0.12 0.11 0.08 0.07 0.13 0.13 0.17 0.18 0.03 0.01 0.09
0.08 0.08 0.05 0.06 0.12 0.13 0.13 0.16 2 0.02 0.01 0.08
199
geometry; the SCCCMS scheme and supermolecular calculations give different directions of CT. Electron af®nity (A) and ionization energy (I) can be used to estimate the direction of CT and energy cost for transferring an electron between subsystems. However, one should be careful in such qualitative considerations based on isolated reactant data. For all but cyanoethylene/azide systems, Idipolarophile 2 Adipole , Idipole 2 Adipolarophile [14]. It means that electrons ¯ow from dipolarophile (ethylene) to dipole (azide). The reverse direction is observed for cyanoethylene. The SCCCMS calculations show that even for this system electrons ¯ow from dipolarophile to azide. Supermolecular calculations predict CT from azide to cyanoethylene only for C2H3CN/N3CH3 system in TS1 geometry. For C2H3CN/N3CH3 (TS2) and C2H3CN/N3H (TS1 and TS2) systems, the CT occurs from cyanoethylene to azide. The results in Tables 3 and 4 in general show that the LU controlled process is more important as compared with HO controlled process. When the electron donating character of substituent in the dipolarophile decreases, the contribution of the LU controlled process is reduced. But even in such a case, the contribution of the LU controlled process is greater than the HO controlled process for C2H3X/ N3CH3 and C2H3X/N3H systems. 3.2. Regioselectivity predictions via softness±softness matching rules Data presented in Section 3.1 show that CT energy is not responsible for the observed trends in regioselectivity. In other words, the CT chemical potentials and hardnesses (Eq. (2) and Fig. 2) are practically the same for all pairs of reactants: mCT TS1 < mCT TS2; hCT TS1 < hCT TS2: Thus, 0one can simplify the Criterion (4) by expressing Dbb aa 0 TS via the CT FF of reactants 0
CT CT 2 CT CT 2 Dbb aa 0 TS fa 2 fb 1 fa 0 2 fb 0 :
8
Reaction of azides with substituted ethylenes is the LU-controlled process. It means, that electrons ¯ow from ethylene to azide. The suf®cient selection of substituents in both reactants allows one to increase the participation of HO interaction. This is observed for electron withdrawing substituents in dipolarophile and electron releasing substituents in 1,3-dipole
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Table 5 D-values associated with two transition states for each of the cycloaddition reactions between N3H and H2CyCHX (X H; F, Cl, CH3, OH, and CN) molecules, computed for forward B ! A and backward A ! B donations
D TS reaction HNNN/C2H3F HNNN/C2H3Cl HNNN/C2H3CH3 HNNN/C2H3OH HNNN/C2H3CN HNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
B!A
A!B
0.02 0.13 0.05 0.09 0.02 0.07 0.07 0.44 0.05 0.03 0.02
0.01 0.15 0.08 0.14 0.01 0.09 0.05 0.81 0.27 0.11 0.01
molecules, respectively. Thus, CH3N3/C2H3CN system can be described as LU/HO controlled 0 process. For this reason, we have computed Dbb aa 0 TS for forward B ! A; as well as for backward A ! B donations. 0 In Tables 5 and 6, we have listed Dbb aa 0 TS values, computed via Eq. (8) for all reactive systems and both possible donations. Except for the cycloaddition between cyanoethylene and azides, the TS2 is favorable D TS2 . D TS1: This is true for forward, as
well as for backward donations. For cyanoethylene/ azide system, D -criterion favors TS1. These observations are in accord with interaction energies (Tables 1 and 2). One should remember that softness (FF) data are connected with CT stabilization. Thus, it is somewhat surprising that the Criterion (4) works so well even though ECT is practically the same for both transition states. This can be qualitatively explained by taking into account the second-order Taylor expansion of the system energy in reactant resolution E E NA ; NB ; nA ; nB : Notice that NA 1 NB N and nA ~r 1 nB ~r n ~r; where n denotes the external potential (due to nuclei). The only term depending clearly on FFs is the mixed dN dv component (part of ECT )[19]: Z 2 dE dn ~r dNA d~r d2 Emix 2NA dnA ~r A
H3CNNN/C2H3Cl H3CNNN/C2H3CH3 H3CNNN/C2H3OH H3CNNN/C2H3CN H3CNNN/C2H4
TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2 TS1 TS2
1
Z 2 dE dn ~r dNA d~r 2NA dnB ~r B
1
Z 2 dE dn ~r dNB d~r 2NB dnB ~r B
2
1
B!A
A!B
0.02 0.06 0.05 0.09 0.02 0.06 0.07 0.39 0.05 0.04 0.02
0.00 0.02 0.07 0.12 0.01 0.07 0.04 0.59 0.25 0.13 0.00
Z
fBA ~r dnA ~r d~r dNCT
Z 2 2 fAB ~r dnB ~r d~r dNCT
D TS
H3CNNN/C2H3F
Z 2 dE dn ~r dNB d~r 2NB dnA ~r A
Z ; fAA ~r dnA ~r d~r dNCT
Table 6 D-values associated with two transition states for each of the cycloaddition reactions between N3CH3 and H2CyCHX (X H; F, Cl, CH3, OH, and CN) molecules, computed for forward B ! A and backward A ! B donations
reaction
1
;
Z
Z
fBB ~r dnA ~r d~r dNCT
fACT ~r dnA ~r d~r dNCT
2
Z
fBCT ~r dnB ~r d~r dNCT ;
9
where fAA ~r and fBB ~r are diagonal FFs while fBA ~r and fAB ~r are off-diagonal FFs. The change of sign in the equation follows from closure relation dNA 2dNB dNCT : Within the polarization approximation, perturbations
J. Korchowiec et al. / Journal of Molecular Structure (Theochem) 572 (2001) 193±202 Table 7 Comparison between FF indices of isolated and interacting species for N3H/H2CyCHF (acid/base) reactive system in TS1 geometry ia
Reactant
0 fi[X
XX fi[X
CT: A ! B (backward donation) X A; Y B Na 0.40 N 0.09 Na 0 0.40 0.12 Ha X B; Y A Cb 0 0.33 Cb 0.40 0.06 Hb Hb 0.05 Hb 0 0.09 Fb 0 0.07 CT: B ! A (forward donation) X A; Y B Na 0.26 N 0.18 Na 0 0.42 0.14 Ha X B; Y A Cb 0 0.28 Cb 0.54 0.01 Hb Hb 20.01 Hb 0 0.04 Fb 0 0.14 a
YX fi[X
CT fi[X
0.43 0.06 0.41 0.10 0.31 0.45 0.04 0.04 0.09 0.06
20.25 0.23 20.11 0.13 20.22 20.24 0.11 0.12 0.13 0.10
0.68 20.18 0.52 20.02 0.53 0.69 20.06 20.08 20.04 20.04
0.29 0.14 0.45 0.12 0.28 0.56 0.01 20.02 0.04 0.13
20.26 0.24 20.10 0.12 20.26 20.16 0.09 0.11 0.13 0.10
0.55 20.09 0.55 20.00 0.55 0.72 20.08 20.12 20.09 0.03
See Fig. 1.
in the external potentials are approximated by the electrostatic potentials of the reaction partners: dnA ~r < fB ~r ; dnB ~r < fA ~r : In the TS, azide molecule is in the negative basin of electrostatic potential of ethylene and vice versa. In other words, fB ~r , 0 and fA ~r , 0; so the ®rst term in Eq. (9) is stabilizing while the second one is destabilizing. Thus, the highest stabilization is when fACT ~r of azide reaches maximum. The lowest destabilization is observed when fBCT ~r of ethylene reaches minimum. These observations qualitatively explain validity of the maximum complementarity rule for forward donation. In the same way, one can justify the Criterion (8) for the backward donation. The above considerations are even more clear in atoms-in-molecule (AIM) resolution. Eq. (9) can be then written in discrete form ! X CT B X CT A 2 d Emix fi fi 2 fi fi dNCT 10 i[A
i[B
Here, fBi fA i is the electrostatic potential at the position of atom i belonging to B (A) exerted by the
201
whole molecule A (B). This equation can be used to explain (qualitatively) the maximum complementarity rule for multi-site interactions. Nevertheless, one should remember that the mixed term is rather small (few percents of ECT ) and here we discuss this energy contribution in order to qualitatively explain the maximum complementarity rule and to show that it works in line with the electrostatic energy. Such explanation was not given in the original paper [15]. The CT FF indices computed via Eq. (7) include diagonal and off-diagonal effects. In order to decompose these indices, one has to consider a contact of reactant A (B) with its external macroscopic electron reservoir. The suf®cient formulas are then as follows [22]: f AA NA NA0 1 1; NB0 2 NA NA0 ; NB0 ; f BA NA NA0 ; NB0 2 NA NA0 ; NB0 2 1;
11
f AB NB NA0 1 1; NB0 2 NB NA0 ; NB0 ; f BB NB NA0 ; NB0 2 NB NA0 ; NB0 2 1: All variables have the same meaning as in Eq. (7). In the limit of separated reactants the off-diagonal FFs disappear and the diagonal FFs are nothing else but FF of isolated species. Of course, it is a question as to how strong the modi®cation of diagonal FF is due to interactions and how it is additionally corrected due to off-diagonal effects. In Table 7, we have compared the isolated reactant data in AIM resolution with diagonal FF indices for N3H/H2CyCHF system in TS1. The table also includes the off-diagonal and CT FF indices. Practically for all 0 atoms (i), FF indices of isolated reactant fi[X and diagXX onal FF indices fi[X X A; B are very close to each YX other. The magnitute of off-diagonal corrections fi[X is comparable to diagonal one, so the resultant CT FF CT indices fi[X do not resemble the isolated reactant data 0 fi[X : Moreover, the directly interacting atoms are clearly distinguished. For example, CT FF indices for Na, Na 0 , Cb, and Cb 0 are much greater then for the remaining atoms. Thus, the main contribution to d2 Emix comes from pairs of directly interacting atoms (see Eq. (10)). This numerical observation also explains why the matching criteria are limited to the pairs of directly interacting atoms. The above observations are true for
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every system considered in the paper (data available from the authors). It is worth to note that the off-diagonal FFs correctly describe the charge rearrangement due to polarization [32] and thus possess information about mutually polarized reactants (before CT). It can be concluded that the off-diagonal FFs are responsible for the fact that the matching criterion for strongly interacting subsystems (maximum softness rule) is orthogonal to the regional HSAB rule (minimum softness rule). 4. Conclusions In this paper, we have investigated the mechanism of 1,3DC reaction between azides and mono-substituted ethylenes. The regioselectivity in the 1,3DC is found to be electrostatically controlled process. CT energy of the two TSs, TS1 and TS2, do not differ signi®cantly. However, it is the only term of energy partitioning, which is very sensitive to the nature of the substituent. The amount of charge transferred from dipolarophile to dipole molecules, estimated from SCCCMS scheme is very close to independent, supermolecular predictions. Such correlation indicates that CT energy is correctly treated in our approach. Present analysis con®rms adequacy of the maximum softness (FFs) principle in predicting preferable arrangements of reactants in the TS structure for 1,3DC reaction. The criterion strongly depends on electrostatic potentials of both reactants. In other words, it has a full knowledge of interactions due to strong offdiagonal FF corrections. It works independently on the assumed direction of CT. Such behavior allows one to use this principle in regiochemistry considerations. Acknowledgements All calculations have been done in ACK CYFRONET AGH; the computational grant No KBN/SGI_ORIGIN_2000/UJ/067/1999. AKC thanks NEDO, Japan for providing him a researcher position. References
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