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Equilibrium and non-equilibrium solvent effects in electrophilic halogenation of ethylenic compounds
THEO CHEM ELSEVIER
Journal of Molecular
Structure (Theochem)
371 (1996) 107-116
Equilibrium and non-equilibrium solvent effects in electrophilic halogenation of ethylenic compound& X. Assfeld, J. Garapon, D. Rinaldi, M.F. Ruiz-Lhpez, Laboratoire
de Chimie thtorique,
J.L. Rivail”
URA CNRS 510, Institut NancPien de Chimie Molkulaire, Universitt Henri Poincart 54506 Vandoeuvre-l&-Nancy Cedex, France Received 23 January
1996; accepted 20 February
-Nancy
I, BP 239.
1996
Abstract Alkene halogenation belongs to a class of reactions known to be extremely sensitive to the environmental effect. In this article we discuss different aspects of the problem through ab initio calculations. Discrete and continuum models for the solvent are employed to analyse equilibrium and non-equilibrium solvation effects on the reaction of ethylene with molecular bromine. It is shown that there are two mechanisms that lead to transition states of different symmetry. One mechanism is found in gas phase and non-polar solvents. The second one, that leads to the typical CzVtransition state, holds in medium polar to very polar media. In water, the solvent molecules participate actively to the reaction coordinate. In this solvent, non-equilibrium solvation effects are shown to be substantial and larger that those previously reported for the SN2 reaction. Keywords:
Alkene halogenation; Solvent effect; Ab initio calculation; Non-equilibrium solvation; Transition state
1. Introduction Solute-solvent interactions may alter the course of a chemical reaction dramatically, especially if the comparison is made with a process in vacua. This is often the case for reactions in polar media in which large charge transfers are accomplished and more specifically for charge separation processes of the general form: A+BeC-+D+ An illustrative example is the SN2 Menshutkin reaction that have been extensively studied by Bertran and
* Authors for correspondence: M.F. Ruiz-Upez and J.L. Rivail. ’ This paper is dedicated to Professor J. Bertrin on the occasion of his 65th birthday. 0166-1280/96/$15.00
0 1996 Elsevier
PII SO166-1280(96)04530-7
Science
B.V. All
co-workers [l]. The authors have underlined the role played by the solvent molecules which do not limit themselves to merely stabilising the chemical system but participate actively in the reaction. Another interesting reaction belonging to this class is the halogenation of ethylenic compounds. The mechanism of this reaction was postulated in the 1930s [2]. It is generally assumed to be a two-step rruns-addition involving the famous bromonium cation as the key intermediate (see Scheme 1). Since the separation of the two charges in vacua is extremely difficult, it is clear that the driving force for this reaction arises from solvation. The energy required to separate the charges is compensated by the solvation energy as schematised in Fig. 1. The reaction is not possible in gas phase, at least along the CzV reaction mechanism considered in Fig. 1. In solution, the
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X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-116
108
dOI +Br,
-
A
Br
fast
+
+
Br
-
Scheme 1.
structure of the transition state is quite dependent on the nature of the solvent: the more polar the solvent, the earlier the transition state is reached. In halogenated or non-protic solvents, the main contribution to the bromide ion departure can come from assistance of another bromine molecule leading to the very stable tribromide anion. The role of the solvent in bromination has been extensively studied [3]. A recent review on this reaction has been reported by Ruasse [4] including a detailed discussion on open questions such as the nature of
30
10
,lO
\ t
\’ E=80
\’
\ ’
\
Reactants
Products
-50
Fig. 1. Schematic representation of the reaction energy profile for alkene halogenation in gas phase and in solution. Total (solid lines) and solvation (dotted lines) energies. This figure has been obtained by considering the perpendicular approach of a Brr molecule to the ethylene molecule. Calculations are carried out using the NW//B2 level (see text for basis set description). The reaction coordinate is approximated by a LST computation (see Ref. [29]).
bromonium ions (cyclic, open) or the reversibility of the bromonium ion formation. The large solvation effect in these processes is mainly due to the strong solute-solvent interaction at the transition state. It can be estimated by assuming that the solute and the solvent are in equilibrium along the reaction path and by computing the free energy of the whole system at each step. Within this hypothesis the solvent plays the role of a thermal bath, i.e. it has a static effect and the kinetics of the process may be described using Transition State Theory (TST). However, the validity of the TST approach for reactions in solution was questioned in a pioneering work by Kramers [5], who introduced the concept of friction in chemical reactions. This phenomenon is to be related to the finite relaxation time of the solvent and to the coupling of the chemical system with its surrounding. The participation of the solvent in the reaction coordinate involves that the motion of the solvent molecules is an important part of the motion of the whole system along the reaction coordinate. Indeed, if the solvent cannot follow the chemical process, one expects a retarding force (or friction) to be present at the top of the barrier. This dynamics or nonequilibrium solvent effect has been studied by means of stochastic generalised Langevin equation [6] and Molecular Dynamics (MD) simulations [7]. Although it seems natural to treat dynamical effects using either stochastic or MD approaches, continuum models have also been employed for a long time. Examples can be found in Marcus theory [8] for electron transfer reactions, Kurz [9] model for proton transfer reaction mechanisms, also investigated by Timoneda and Hynes [lo], and Kim and Hynes studies on SN1 ionic dissociation processes [ll]. Finally, within a Molecular Orbital model, an ab initio quantummechanical method using the Self-Consistent Reaction Field (SCRF) approach has been adopted to study non-equilibrium solvation [12,13]. The underlying idea in most of these studies is that in fast charge reorganisation processes in polar media, the solvent cannot follow the chemical system so that non-equilibrium solvation is foreseen. The climb to the transition barrier must be preceded by a convenient fluctuation of the solvent so that its inertial polarisation component is suitable to solvate the transition state. The crossing of the barrier is then made with an essentially frozen solvent configuration.
X. Assfeld et al./Journal of Molecular Structure (Theochem) 371 (1996) 107-116
The reaction of halogens with ethylenic compounds has been theoretically studied in the gas phase by a few authors [14-191 but very little has been reported for the process in solution [18,19]. Most of the published articles deal with the reaction of fluorine or chlorine with ethylene. The first ab initio calculations are the result of Hopkinson et al. [14]. The authors analysed the relative stability of cyclic and open reaction intermediates for the reaction of ethylene with fluorine [14a] or chlorine [ 14b]. The cyclic intermediate was predicted to be the most stable in the case of chlorine whereas the opposite stability was obtained for fluorine. The reaction energy was also computed [14b] showing that these are not feasible gas-phase reactions. Kochanski [18] studied the gas phase reaction of ethylene with molecular chlorine and found that there is a CZV minimum corresponding to a Charge Transfer Complex (CTC). The best basis set employed predicted a stabilisation energy of - 3.7 kcal/mol and very small charge transfer. However no transition state could be located in the gas phase after examination of a two-dimensional potential energy surface. It has to be stressed that the existence of CTC complexes of this class was first established by Dubois and Garnier [20] and has been recently revisited [21]. It is accepted that this type of complex is formed before the charge separation that characterises the first step in Scheme 1. Kochanski [18] also discussed qualitatively the possible role of water solvation on the gas phase potential energy surface. Iwaoka et al. [17] have studied the reaction of molecular fluorine with ethylene at the ab initio MP2/6-31 + G level. Their results showed that fluorine and ethylene form a perpendicular prereactive complex with CZV symmetry which then reorientates to a rhombic-type complex as the transition state to give the final product. The reaction of Brz with ethylene has been also studied. A detailed investigation of the relative stability of cyclic and acyclic isomers of isolated C2H4Br+ ions has been reported [El. Besides, Yamabe et al. [16] have reported the gas-phase structure of a transition state (TS) using RHF/3-21G calculations. In this TS, that has C, symmetry (instead of the typical CzV), the Br-Br bond is broken and the bromonium ion is practically formed. The interaction of the forming Brspecies with the hydrogen atoms of the ethylene seems to be an important factor. However, the minima
109
joined by this TS where not identified in that paper. More recently, Cossi et al. [19] have considered the ethylene + bromine reaction in solution. The solvent is represented by a polarizable continuum. Some partial geometry optimisation was carried out for a series of structures and the discussion was focused on the modification by the solvent of the charge distribution of these structures. This work has provided new insights about the nature of bromonium ions and the reversibility of their formation reactions. Nevertheless, an ab initio study of the reaction with full geometry optimisation and transition state location in solution is still lacking. This is the main objective of the present article. Our aim is to describe the structure of the transition state as a function of the solvent nature and to evaluate, at least qualitatively, the solvent effect on the reaction kinetics. We first examine static solvent effects on the reaction of ethylene with bromine as a function of the polarity of the medium. Afterwards, two aspects of dynamic solvent effects are considered: the participation of water in the bromine + ethylene reaction coordinate and the role played by non-equilibrium solvation. The results presented here have been obtained by using continuum and discrete models for the solvent (see below) that allow us to examine the fundamental features of the process. Obtaining more accurate results requires the use of MD simulations [22]. The hybrid Density Functional Theory (DFT)/ MM Molecular Dynamics technique recently implemented in our group [23] is suitable for such a study and work is in progress [24].
2. Models and computational details
2.1. Solvent model We employ a continuum model that has been described in detail in previous articles [25]. The solvation energy is computed through a multipole moment expansion of the reaction field potential. The solvent is characterised by a macroscopic quantity, the relative static dielectric permitivity. Geometry optimisation and transition state location for solvated species are possible within this model. Non-equilibrium solvation may be also accounted for [13] after separating the solvent polarisation into
110
X. Assfeld et alJournal
of Molecular Structure (Theochem) 371 (1996) 107-116
2.2. Basis sets and correlation energy
inertial and non-inertial terms. The non-inertial polarisation is related to the electronic polarisation and is assumed to be in equilibrium with the reactants along the reaction path. The inertial component is associated with atomic (translational + vibrational) and rotational motions of the solvent molecules and with the difference between the static, eo, and the optical (infinite frequency), em, dielectric constants. This allows a global solvent coordinate, to be defined, S, which measures the deviation of the inertial polarisation configuration of the solvent with respect to its equilibrium value. It can be related to the chemical system reaction coordinate R. Hence, the solvent coordinate S will account for a solvent configuration the inertial polarisation of which corresponds to that in equilibrium with the chemical system at Ro so that
Several basis sets have been employed in this work. The first one (hereafter called Bl) is a triple-&plus double polarisation [27]: Br(16s13p7d/lOs8p4d), C(lls6p2d/ %4p2d), H(S2p/3s2p). The second one (hereafter called B2) is the standard LANLlDZ basis set [28] implemented in Gaussian92 [29], augmented with a diffuse function on the bromine atoms. The LANLlDZ basis set is a splitted valence basis set with pseudo-potentials describing the bromine atom cores. The diffuse functions have been obtained in this work by minimising the energy of Br- leading to gaussian exponents of 0.04205. Bl and B2 have been employed for locating stationary points in the gas phase. The simple basis B2 is shown to give reasonable results for the molecular structures and therefore the rest of the computations has been done with this basis set only. Computation of accurate energies would certainly require the use of larger basis sets but this is beyond the scope of the present work. The study of the influence of electronic correlation on geometry parameters is done at the MP2 level. In this case we use an all-electron basis set [[30]a] Br(16sllp5d/5s4p2d), C(lOs6pld/4s3pld), H(Sslp/ 2slp), intermediate between Bl and the simple B2 basis. It will be called hereafter B3. As as result of
S=R-R,,. The parameters
used in this continuum model are the static and the infinite-frequency dielectric permitivity (e. = 78.4 and E, = 1.8 respectively). The latter is used for evaluating non-equilibrium solvent effects only. The cavity shape is chosen to fit as best as possible the solute molecular shape. The solvent accessible surface defined by Richards [26] appears to be a good definition. In this work this surface has been simply fitted by an ellipsoidal cavity.
Table 1 Geometries and energies of the charge transfer complex (CTC) and transition state (TS) for the reaction of molecular bromine with ethylene in the gas phase as computed with the Bl and B2 basis set (see text) Structure Basis set
Geometrical Br-Br Br-C
CTC
parameters
Bl
B2
Bl
B2
2.300 3.536 3.536 1.317 90.0
2.463 3.360 3.360 1.320 90.0
3.115 1.966 2.014 1.451 18.6
3.237 2.121 2.176 1.438 17.5
-0.0517 +0.0340 +0.0177
-0.0995 +0.0329 +0.0666
-0.8898 +0.6148 +0.2750
-0.8990 +0.4802 +0.4188
-5222.792586
-103.438007
-5222.725286 42.23
-103.356460 51.17
(A and degrees)
c-c 8 (a) Mulliken net atomic charges Br :; Cz& Total (a.u.) and relative (kcal mole’) energies E ,DlSl BTS-Ecrc
TS
(a) angle formed by the Br-Br and C-C bond vectors. (b) for the forming bromine anion. (c) for Br in the forming bromonium cation.
X. Assfeld et al.lJournal of Molecular Structure (Theochem) 371 (1996) 107-116
111
relative energy between the pre-reactive complex and the TS is larger when computed at the Bl level, but the estimation made at the B2 level is reasonable. In the CTC, there is a small charge transfer but the TS is practically an ion pair. Note that in the bromonium, the positive charge is shared by the bromine atom and the ethylene group. Therefore, the TS has a late character. No attempt to compute the stabilisation energy of CTC with respect to the reactants has been done. This would require careful evaluation of Basis Set Superposition Error (BSSE) effects. CTC
Fig. 2. Optimised TS.
Ts
geometries
at the RHF/Bl
level for the CTC and
the large computational requirements, only some structures have been studied at this correlated level. Finally, some results have been also obtained with the 6-31G* basis set [3Ob] as indicated below.
3. Results and discussion 3.1. Reaction
mechanism
in gas phase.
We have considered here the reaction of bromine with ethylene and we describe in Table 1 the structure of the stationary points found at the Bl and B2 levels. Both basis sets predict the formation of a CTC complex with CzV symmetry and a transition state with C, symmetry, as shown in Fig. 2. From the comparison of the values obtained with the two basis sets one may note that the simple basis set B2 behaves satisfactorily. The results for the transition state are comparable to those reported before [16]. In particular, all these calculations predict a small value for the angle 8 formed by the Br-Br and C-C bond vectors. The
3.2. Mechanism in solution: dependence relative dielectric permitivity
on the
With the aim of analysing the role of the solutesolvent electrostatic interactions on the structure of the CTC complex and transition state, we have optimised their structures in media with different values of the relative dielectric constant. The results are gathered in Table 2 for the complex and in Table 3 for the transition state. Increasing e. lowers the BrC bondlength in the CTC complex and enlarges the Br-Br and C-C bondlengths. This can be explained by the fact that the solvent stabilises the charge transfer configurations. In the case of the TS, the most striking result is that the symmetry of the system changes with increasing the polarity of the medium. Indeed, in a non-polar solvent with e. = 2, the structure of the TS resembles that obtained in the gas phase except that the angle 8 is much larger and the late character is reinforced: the Br-Br distance increases, the Br-C distance decreases and the charge transfer is enhanced from 0.419 in the gas phase to 0.578 in the non-polar solvent. Conversely, in a low polar solvent with e. = 7 and in more polar solvents, the symmetry of the TS is
Table 2 Geometry of the CTC complex (in A and degrees) as a function of solvent dielectric permitivity
as computed at the RHF level with basis set B2
El) =
2.0
7.0
10.0
20.0
40.0
78.4
Br-Br Br-C
2.472 3.237 3.237 1.322 90.0
2.493 3.045 3.053 1.327 89.5
2.500 3.002 3.012 1.328 89.5
2.513 2.934 2.944 1.330 89.6
2.527 2.879 2.890 1.333 89.5
2.540 2.833 2.843 1.335 89.6
c-c I9
(a) (a) angle formed by the Br-Br
and C-C bond vectors.
112
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-116
Table 3 Geometry of the TS complex (in A and degrees) as a function of solvent dielectric permitivity
as computed at the RHF level with basis set B2
Eg =
2.0
7.0
10.0
20.0
40.0
78.4
Br-Br Br-C
3.763 2.195 2.162 1.430 58.4
2.896 2.378 2.399 1.385 89.1
2.781 2.461 2.481 1.372 89.2
2.676 2.572 2.586 1.357 89.4
2.624 2.647 2.660 1.349 89.5
2.592 2.704 2.715 1.344 89.5
c-c e
(a) (a) angle formed by the Br-Br
and C-C bond vectors.
approximately CzV. Compared with the gas-phase structure, the TS has an earlier character: the Br-Br and C-C bonds are shorter and the Br-C bond lengths are larger. Increasing further the dielectric permitivity does not modify the symmetry of the TS but intensifies its early character, according to Fig. 1. For instance, the charge transfer decreases from 0.525 in EO= 7 to 0.278 in EO= 78.4. The relative energy between the CTC and TS is given in Table 4 for the reaction in different media. It decreases from the gas to the solvent with e. = 2. This is expected since the transition state is rather polar and has a larger solvation energy. However, the relative energy is much smaller for higher dielectric constant solvents because the two structures, the complex and the TS, are now similar. Since the TS has increasing early character and the complex has increasing late character with increasing eo, one may expect that for a sufficiently polar solvent, the TS vanishes and the reaction becomes barrierless. As pointed out above, the energy data obtained with the simple basis set B2 have to be considered as a qualitative trend. Nevertheless, a great electrostatic solvent effect on the barrier is predicted which is in good agreement with experimental measurements. Thus, the relative rate constant varies from 1 in CCL to 1.6 x lo5 in CH30H and 1.1 x lOlo in water [3]. As mentioned, the influence of electronic correlation may be quite important to describe the structure of the reaction species, especially the CTC in which Table 4 Relative energy En - Ecrc (in kcal mol-‘) in different media computed at the RHF level with basis set B2 co =
2.0
7.0
10.0
20.0
40.0
78.4
AE
30.79
3.35
1.76
0.50
0.13
0.02
the dispersion energy is a fundamental contribution [31]. In order to evaluate its effect on the structure of CTC and TS in water, we have carried out MP2 calculations using basis set B3. The optimised structures are given in Table 5. The structure of the CTC computed with this basis set in gas phase is also given. One may first compare the RHF results for the CTC with those given in Table 1 for the gas phase and those given in Table 2 for the complex in water. The effect of the basis set is substantial in particular for the Br-C bond which is predicted to be longer at the RHF/B3 level. The effect of the basis set is however smaller for the TS. As shown, the RHF/B3 geometry is only slightly different from that obtained at the RHF/B2 level (see last column in Table 3). The influence of the correlation energy is very large for the CTC, in whi$h the intermolecular distance changes by about 0.5 A, but only slight for the TS. In the last case, the effect is to shift the TS a little towards the products. Accordingly, the SCF electron density at the forming bromine anion changes from - 0.598 at the RHF geometry to - 0.738 at the MP2 one. The relative energy Ers - Ecrc computed with the B3 basis set is 13.7 kcal mol-’ at the RHF level and 5.7 kcal mol-’ at the MP2 one. Therefore, the effect of correlation on the barrier appears to be substantial too, the balance of TS and CTC correlation energies leading to an activation energy decrease. Note also that these values are quite different from those obtained at the simple RHF/B2 level (see last column of Table 4) which stress the role of polarisation functions in the case of the solvated systems. It has to be pointed out that because of the large magnitude of the reaction field at the TS, a more rigorous treatment of electronic correlation may be necessary although this appears to be too costly in the standard SCRF model. An interesting approach
113
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-I 16
Table 5 Influence of correlation energy on the CTC and TS structures in a medium with ea = 78.4. MP2 calculations tion. Symmetry Czv has been assumed. Gas-phase values in parenthesis. Units are A and degrees TS
CTC
Br-Br Br-C c-c 0
(a)
using the Frozen Core approxima-
RHFlB3
MP2/B3
RHF/‘B3
MP2/B3
2.309 (2.302) 3.450 (3.734) 1.319 (1.318) 90.0 (90.0)
2.368 (2.354) 2.952 (3.021) 1.345 (1.343) 90.0 (90.0)
2.629 2.409 1.360 90.0
2.683 2.300 1.394 90.0
(a) angle formed by the Br-Br
and C-C bond vectors.
can be the SCRF-DFT method [32] in which correlation effects are included self-consistently through a density functional. In contrast, the description of charge transfer complexes at the DFT level is not completely satisfactory [33] and it should be necessary to test the suitability of DFT calculations for transition state structures of this type. 3.3. Solvent participation
in the reaction coordinate
We employ a discrete model to represent the first solvation shell of the bromine + ethylene TS. This is done by adding up to three water molecules interacting with the system and by performing a transition state location taking into account all the geometrical parameters (solute + solvent). The only constraint is that we impose a plane of symmetry. The transition
Fig. 3. Transition vectors for the gas-phase
structures and the transition vectors, i.e. the eigenvectors of the Hessian matrix with negative eigenvalue, obtained using one or three water solvation molecules are plotted in Fig. 3. The geometries are gathered in Table 6. As shown, the geometry of the TS obtained with this model is close to that obtained in the gas phase. The angle 0 increases from the gas phase TS to the TS with one or three water molecules. The solvated structure is earlier as shown by the Br-Br, Br-C and C-C bondlengths. Various attempts to locate a TS with the Br2 molecule perpendicular to the C-C bond were unfruitful. Though the hydrogen bond interactions with the first solvation shell are strong, one may then conclude that the mechanism of ethylene bromination in water is largely dominated by long-range electrostatic interactions.
(a) TS and (b) the TS solvated by one or(c) three water molecules, as computed at the RHF/B2 level.
114
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371
Table 6 Geometry (in A and degrees) of the TS in gas phase and solvated by one or three discrete water molecules
Br-Br Br-C c-c 8
Gas-phase
Mono-solvated
Tri-solvated
3.237 2.121 2.176 1.438 17.5
3.200 2.236 2.308 1.394 41.55
3.139 2.208 2.238 1.404 56.99
The role of the first solvation shell is important from the electronic point of view and modifies significantly the gas-phase charge distribution. This is shown in Table 7. In particular, there is a net electron density transfer from the water molecules to the C2H4Br+ subunit. The electronic density ascribed to the Br- anion is not very sensitive to the presence of water molecules. But the main result of these calculations is the substantial participation of the water molecule coordinates to the transition vector. The participation of the solvent in the reaction coordinate has been analysed in the case of the Menshutkin reaction [l]. As in the case of ethylene bromination, there is a creation of two charges of opposite sign at the TS than separate to form the products. Therefore, some of the conclusions reached in previous works for the Menshutkin reaction are expected to hold in the (first step) bromination of ethylenic compounds. As we discuss below, fluctuations of the solvent play a crucial role when dynamic effects are taken into account. These fluctuations may be stabilised by instantaneous changes in the electronic distribution of the solute [l].
(1996)
3.4. Solvent fluctuations effect
107-116
and non-equilibrium
As pointed out above, in fast reorganisation processes in polar media the climb to the transition state is made in an essentially frozen solvent configuration. A prior solvent fluctuation favouring this climb is required. In fact, certain solvent fluctuations may induce the reaction without any potential barrier [34]. We now analyse this dynamical aspect for alkene halogenation in water. For computational time reasons we decided to do this study for the reaction of ethylene with fluorine instead of bromine. The calculations have been carried out at the RHF/6-31G* level. In the continuum model used here to account for non-equilibrium solvation, the relative free energy of the solute-solvent system may be expressed as AG(R,S) where R is the reaction coordinate and S = R - R. a global solvent coordinate. The reaction coordinate has been chosen here from an Intrinsic Reaction Coordinate [35] calculation in solution using the equilibrium hypothesis. In Fig. 4 we represent the final results for the bidimensional surface AG(R,S). The values are given with respect to the
1.0
0.5
S
0.0
Table 7 Charge distribution of the TS in gas phase and solvated with one or three discrete water molecules
BY (a) CzHdBr’ (b) Hz0 (c) HzG (d)
Gas-phase
Mono-solvated
Tri-solvated
-0.8990 0.8990
-0.8782 0.7409 0.1373
-0.8948 0.7361 0.0049 0.1538
(a) Forming bromine anion. (b) Forming bromonium cation. (c) water molecule with the oxygen on the symmetry plane. (d) sum of charge on water molecules having their oxygen outof-plane.
solvent
-0.5
-1.0 -1.0
-0.5
0.0
0.5
1.0
R Fig. 4. Reaction energy as a function of the Intrinsic Reaction Coordinate R (defined using the hypothesis of equilibrium) and the solvent coordinate S = R - R”. Values are given relative to the equilibrated TS, R = 0, S = 0. Curves correspond to reaction energies of 0, 2 1.2, -+ 2.4, + 3.6, . . . kcalmol~‘.
X. Assfeld et al.iJournal of Molecular Structure (Theochem) 371 (1996) 107-116
free energy for the equilibrated TS. Positive and negative DG regions are distinguished. The x-axis (S = 0) represents the equilibrium reaction path. It may be noted that for a given value of R, the energy for S = 0 (x-axis, equilibrium) is a minimum, as expected. Negative values of S mean that the solvent inertial polarisation is equilibrated with a more advanced point along the reaction coordinate than the considered one. Lines with slope 1, S = R - Ro, represent frozen solvent reactive paths in which the inertial polarisation of the solvent is that in equilibrium with the chemical system at Ro. Therefore, the passage through the TS with a solvent frozen configuration is represented in this scheme by the principal diagonal. One clearly sees in this figure that the derivative of AC at the origin along this line is substantially smaller than that along the x-axis (equilibrium path). For instance, for R = S = 0.1 the variation of AG with respect to the TS is 0.43 kcal mall’ whereas for R = 0.1 and S = 0, it is 0.65 kcal mall’. This augurs a large impact of non-equilibrium solvation on the value of the transmission coefficient K, which measures the departure of the rate constant k from Transition State Theory rate kTST:
4. Conclusions
k K=ps?-
Acknowledgements
Gertner et al. [36] have shown that in the frozen solvent limit K may be approximated by: K=--
%eq
where w eq and w,,~ are the frequencies related to the curvatures at the top of the barrier, assumed to be parabolic in the non-equilibrium region, for the equilibrium and non-adiabatic case respectively. As discussed before [13], the computation of these frequencies is not straightforward since one has to consider an effective solvent mass. Consideration of limiting cases for the solvent mass allows a rough evaluation of K using force constants (see Eq. 24 in Ref. [13]). In our case, we obtain K = 0.64 ? 0.11. This value is smaller than that obtained for the SN2 reaction with the same model [13]: 0.65 Cc K 5 0.92 and indicates a large non-equilibrium solvation effect, especially considering that the continuum model tends to overestimate the transmission coefficient [37].
115
There are two main conclusions in this work that have to be emphasised. Firstly, the dependence of the bromination mechanism on the dielectric permitivity of the medium. From our results, it seems that the typical CZV transition state is only obtained in polar media and that long range interactions are mainly responsible for the stabilisation of this structure. The first solvation shell plays a moderate role which is related to charge delocalization. Secondly, non-equilibrium solvation effects seem to be rather important and larger that in previously studied SN2 reactions. Our study also emphasises the sensitivity of the results to basis set and correlation effects especially in the description of the CTC. Moreover, the continuum model cannot yield quantitative values neither for the solvation energies of the system under study nor for the transmission coefficient. But the main interactions are identified and will substantially simplify the implementation of most accurate hybrid -MD simulations.
This work has been done within the C.N.R.S. project G.D.R. No. 1017. The authors thank the members of the project, in particular Prof. S. Bratos and Dr M.F. Ruasse, for fruitful discussions.
References [l] M. Soll, A.L. Led&, M. D&n, J. Bertran and J.L.M. Abboud, J. Am. Chem. Sot., 113 (1991) 2873; J.L. Abboud, R. Notario, J. Bertran and M. SOB, Prog. Phys. Org. Cbem., 19 (1993) 1; J. Bertran, J.M. Lluch, A. Gonzalez-Lafont. V. Dillet and V. P trez, in Structure and Reactivity in Aqueous Solution: Characterization of Chemical and biological Systems, ed. C.J. Cramer and D.G. Truhlar, ACS Symposium Series 568, ACS, Washington, DC 1994, Chapter 12. [2] P.D. Bartlett and D.S. Tarbell, J. Am. Chem. Sot., 58 (1936) 466. [3] J.E. Dubois, F. Gamier and H. Viellard, Tetrahedron Lett., 17 (1965) 1227; J.E. Dubois and F. Garnier, Tethahedron Lett., 26 (1966) 3047; Chem. Comm., (1968) 241; Bull. Sot. Chim. Fr. (1968) 3797; G.A. Olah and T.R. Hockswender, Jr., J. Am. Chem. Sot., 96 (1974) 3574; M.F. Ruasse and J.E. Dubois, J. Am. Chem. Sot., 97 (1975) 1977; C. Reichardt, Solvent
116
[4] [S] [6]
[7]
[S] [9]
[lo] [ll]
[ 121
[13] [14]
[15] [16] [17] [18]
[19] [20] [21] [22]
_X Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-116 effect in Organic Chemistry, Verlag Chemie, New York 1979, Ch. 5; M.F. Ruasse and S. Montallebi, J. Phys. Org. Chem., 4 (1991) 527. Ruasse M.F., Adv. Phys. Org. Chem., 28 (1993) 207. H.A. Kramers, Physica, 7 (1940) 284. (a) J.T. Hynes, Ann. Rev. Phys. Chem., 36,573 (1985); (b) J.T. Hynes, in Theory of Chemical Reaction Dynamics, edited by M. Baer (CRC, Boca Ratbn, FI, 1985), Vol. 4, p. 171. R.M. Whitnell and K.R. Wilson, Computational molecular dynamics of chemical reactions in solution, Reviews in Computational Chemistry, eds. K.B. Lipkowitz and D.B. Boyd, (UCH Publishers, Inc. New York, 1993). p.67. (a) R.A. Marcus, J. Chem. Phys., 24 (1956) 966; (b) R.A. Marcus, J. Chem. Phys., 24 (1956) 979. (a) J.L. Kurz and L.C. Kurz, J. Am. Chem. Sot., 94, 4451 (1972); (b) J.L. Kurz and J. Lee, J. Am. Chem. Sot., 102 (1980) 5249. J.J. Timoneda and J.T. Hynes, J. Phys. Chem., 95 (1991) 10431. (a) H.J. Kim and J.T. Hynes, J. Am. Chem. Sot., 114 (1992) 10508; (b) H.J. Kim and J.T. Hynes, J. Am. Chem. Sot., 114 (1992) 10528. M.A. Aguilar, F.J. Olivares de1 Valle and J. Tomasi, J. Chem. Phys., 7375 (1993) 98; M. Cossi, M. Persico and J. Tomasi, J. Mol. Liquids, 60 (1994) 87; J. Tomasi, in Structure and Reactivity in Aqueous Solution ACS Symposium Series 568. Eds. C.J. Cramer and D.G. Truhlar, American Chemical Society, Washington, 1994, pg.10. M.F. Ruiz-Lopez, D. Rinaldi and J. Bertran, J. Chem. Phys., 103 (1995) 9249. (a) A.C. Hopkinson, M.H. Lien, K. Yates and LG. Czismadia, Theoret. Chim. Acta, 38 (1975) 21; @) A.C. Hopkinson, M.H. Lien, K. Yates and LG. Czismadia, Theoret. Chim. Acta, 44 (1977) 385. T.P. Hamilton and H.F. Shaefer, III, J. Am. Chem. Sot., 112 (1990) 8260. S. Yamabe, T. Minato and S. Inagaki, J. Chem. Sot., Chem. Comm., (1988) 532. T. Iwaoka, C. Kaneko, A. Shigihara and H. Ichiwaka, J. Phys. Org. Chem., 6 (1993) 195. M. Jaszunski and E. Kochanski, J. Am. Chem. Sot., 99 (1977) 4624; E. Kochanski, in Quantum Theory of Chemical Reactions, VoI.2, Ed. R. Daudel, A. Pullman, L. Salem and A. Veillard, Reidel 1980, pg 177-191. M. Cossi, M. Persico and J. Tomasi, J. Am. Chem. Sot., 116 (1994) 5373. J.E. Dubois and F. Garnier, Spectroschim. Act., 23A (1967) 2279. H.I. Bloemink, K. Hinds, A.C. Legon and J.C. Thorn, Chem. Eur. J., 1 (1995) 17. R.M. Whitnell and K.R. Wilson, in Computational Molecular Dynamics of Chemical Reactions in Solution, Reviews in Computational Chemistry, Lipkowitz, K.B.; Boyd, D.B., Eds.; UCH Publishers, Inc.: New York, 1993; p 67.
[23] I. Tufton, M.T.C. Martins-Costa, C.MiIIot and M.F. RuizLopez, J. Mol. Mod., 1, 196-201 (1995); I. Tur%n, M.T.C. Martins-Costa, C.Millot, M.F. Ruiz-Mpez and J.L. Rivail, J. Comput. Chem., 17 (1996) 19. [24] M. Stmad, M.T.C. Martins-Costa, C. Millet, I. Tufion, M.F. Ruiz-Mpez and J.L. Rivail, submitted. [25] Rivail J.L. Rinaldi D. Ruiz-Lopez M.F. in Theoretical and Computational Models for Organic Chemistry; NATO AS1 Series C, Vol. 339, Ed. S.J. Formosinho, I.G. Csizmadia and L. Amaut, KIuwer Academic Publishers: Dordrecht, 1991; pp. 79-92; D. Rinaldi, J.L. Rivail and N. Rguini, J. Comp. Chem., 13 (1992) 675; V. Dillet, D. Rinaldi, J.G Angyan and J.L. Rivail, Chem. Phys. Len., 202 (1993) 18. [26] F.M. Richards, Ann. Rev. Biophys. Bioeng., 6 (1977) 151. [27] see G.E. Scuseria, M. Duran, R.G.A.R. Maclagan and H.F. Schaefer, III, J. Am. Chem. Sot., 108 (1986) 3248 and references cited therein. [28] P.J. Hay and W.R. Wadt, J. Chem. Phys., 82 (1985) 270; J. Chem. Phys., 82 (1985) 299; W.R Wadt and P.J. Hay, J. Chem. Phys., 82 (1985) 284. [29] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.W. Wong, J.B. Foresman, M.A. Robb, M. HeadGordon, E.S. Replogle, R. Gomperts, J.L. And& K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, Gaussian92/DFI, Revision G.l, Gaussian, Inc., Pittsburgh, PA, 1993. [30] (a) This basis set is taken from program deMon. The contraction is Br(63321/5321/41), C(7111/411/1), H(41/1). See D.R. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. St-Amant and J. Ushio, in Theory and Applications of Density Functional Approaches to Chemistry, J. Labanowski and J. Andzelm Eds., Springer Verlag, Berlin 1991 and H. Godbut, D.R. Salahub, J. Andzelm and E. Wimmer, Can. J. Chem., 70 (1992) 560. DFI calculations with this basis set are being carried out and will be reported in due course; see Ref. 24. (b) W.J. Hehre, R. Ditchfield, J.A. Pople, J. Chem. Phys., 56 (1972) 2257; P.C. Hariharan, J.A. Pople, Theoret. Chim. Acta, 28 (1973) 213. [31] J. Prissette, G. Seger and E. Kochanski, J. Am. Chem. Sot., 100 (1978) 6941. [32] M.F. Ruiz-Lopez, F. Bohr, M.T.C. Martins-Costa and D. Rinaldi, Chem. Phys. Lett., 221 (1994) 109. [33] E. Ruiz, D.R. Salahub and A. Vela, J. Am. Chem. Sot., 117 (1995) 1141. [34] F.R. Tortonda, J.L. Pascual-Ahuir, E. Silla and I. Tufion, J. Phys. Chem., 97 (1993) 11087. [35] K. Fukui, Act. Chem. Res. 14 (1981) 363; C. Gonzalez, H.B. Schlegel, J. Phys. Chem., 90 (1989) 2154; C. Gonzalez, H.B. Schlegel, J. Phys. Chem., 94 (1990) 5523. [36] B.J. Gertner, K.R. Wilson and J.T. Hynes, J. Chem. Phys., 90 (1989) 3537. [37] M.V. Basilevsky, G.E. Chudinov and D.V. Napolov, J. Phys. Chem., 97 (1993) 3270.
Journal of Molecular
Structure (Theochem)
371 (1996) 107-116
Equilibrium and non-equilibrium solvent effects in electrophilic halogenation of ethylenic compound& X. Assfeld, J. Garapon, D. Rinaldi, M.F. Ruiz-Lhpez, Laboratoire
de Chimie thtorique,
J.L. Rivail”
URA CNRS 510, Institut NancPien de Chimie Molkulaire, Universitt Henri Poincart 54506 Vandoeuvre-l&-Nancy Cedex, France Received 23 January
1996; accepted 20 February
-Nancy
I, BP 239.
1996
Abstract Alkene halogenation belongs to a class of reactions known to be extremely sensitive to the environmental effect. In this article we discuss different aspects of the problem through ab initio calculations. Discrete and continuum models for the solvent are employed to analyse equilibrium and non-equilibrium solvation effects on the reaction of ethylene with molecular bromine. It is shown that there are two mechanisms that lead to transition states of different symmetry. One mechanism is found in gas phase and non-polar solvents. The second one, that leads to the typical CzVtransition state, holds in medium polar to very polar media. In water, the solvent molecules participate actively to the reaction coordinate. In this solvent, non-equilibrium solvation effects are shown to be substantial and larger that those previously reported for the SN2 reaction. Keywords:
Alkene halogenation; Solvent effect; Ab initio calculation; Non-equilibrium solvation; Transition state
1. Introduction Solute-solvent interactions may alter the course of a chemical reaction dramatically, especially if the comparison is made with a process in vacua. This is often the case for reactions in polar media in which large charge transfers are accomplished and more specifically for charge separation processes of the general form: A+BeC-+D+ An illustrative example is the SN2 Menshutkin reaction that have been extensively studied by Bertran and
* Authors for correspondence: M.F. Ruiz-Upez and J.L. Rivail. ’ This paper is dedicated to Professor J. Bertrin on the occasion of his 65th birthday. 0166-1280/96/$15.00
0 1996 Elsevier
PII SO166-1280(96)04530-7
Science
B.V. All
co-workers [l]. The authors have underlined the role played by the solvent molecules which do not limit themselves to merely stabilising the chemical system but participate actively in the reaction. Another interesting reaction belonging to this class is the halogenation of ethylenic compounds. The mechanism of this reaction was postulated in the 1930s [2]. It is generally assumed to be a two-step rruns-addition involving the famous bromonium cation as the key intermediate (see Scheme 1). Since the separation of the two charges in vacua is extremely difficult, it is clear that the driving force for this reaction arises from solvation. The energy required to separate the charges is compensated by the solvation energy as schematised in Fig. 1. The reaction is not possible in gas phase, at least along the CzV reaction mechanism considered in Fig. 1. In solution, the
rights reserved
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-116
108
dOI +Br,
-
A
Br
fast
+
+
Br
-
Scheme 1.
structure of the transition state is quite dependent on the nature of the solvent: the more polar the solvent, the earlier the transition state is reached. In halogenated or non-protic solvents, the main contribution to the bromide ion departure can come from assistance of another bromine molecule leading to the very stable tribromide anion. The role of the solvent in bromination has been extensively studied [3]. A recent review on this reaction has been reported by Ruasse [4] including a detailed discussion on open questions such as the nature of
30
10
,lO
\ t
\’ E=80
\’
\ ’
\
Reactants
Products
-50
Fig. 1. Schematic representation of the reaction energy profile for alkene halogenation in gas phase and in solution. Total (solid lines) and solvation (dotted lines) energies. This figure has been obtained by considering the perpendicular approach of a Brr molecule to the ethylene molecule. Calculations are carried out using the NW//B2 level (see text for basis set description). The reaction coordinate is approximated by a LST computation (see Ref. [29]).
bromonium ions (cyclic, open) or the reversibility of the bromonium ion formation. The large solvation effect in these processes is mainly due to the strong solute-solvent interaction at the transition state. It can be estimated by assuming that the solute and the solvent are in equilibrium along the reaction path and by computing the free energy of the whole system at each step. Within this hypothesis the solvent plays the role of a thermal bath, i.e. it has a static effect and the kinetics of the process may be described using Transition State Theory (TST). However, the validity of the TST approach for reactions in solution was questioned in a pioneering work by Kramers [5], who introduced the concept of friction in chemical reactions. This phenomenon is to be related to the finite relaxation time of the solvent and to the coupling of the chemical system with its surrounding. The participation of the solvent in the reaction coordinate involves that the motion of the solvent molecules is an important part of the motion of the whole system along the reaction coordinate. Indeed, if the solvent cannot follow the chemical process, one expects a retarding force (or friction) to be present at the top of the barrier. This dynamics or nonequilibrium solvent effect has been studied by means of stochastic generalised Langevin equation [6] and Molecular Dynamics (MD) simulations [7]. Although it seems natural to treat dynamical effects using either stochastic or MD approaches, continuum models have also been employed for a long time. Examples can be found in Marcus theory [8] for electron transfer reactions, Kurz [9] model for proton transfer reaction mechanisms, also investigated by Timoneda and Hynes [lo], and Kim and Hynes studies on SN1 ionic dissociation processes [ll]. Finally, within a Molecular Orbital model, an ab initio quantummechanical method using the Self-Consistent Reaction Field (SCRF) approach has been adopted to study non-equilibrium solvation [12,13]. The underlying idea in most of these studies is that in fast charge reorganisation processes in polar media, the solvent cannot follow the chemical system so that non-equilibrium solvation is foreseen. The climb to the transition barrier must be preceded by a convenient fluctuation of the solvent so that its inertial polarisation component is suitable to solvate the transition state. The crossing of the barrier is then made with an essentially frozen solvent configuration.
X. Assfeld et al./Journal of Molecular Structure (Theochem) 371 (1996) 107-116
The reaction of halogens with ethylenic compounds has been theoretically studied in the gas phase by a few authors [14-191 but very little has been reported for the process in solution [18,19]. Most of the published articles deal with the reaction of fluorine or chlorine with ethylene. The first ab initio calculations are the result of Hopkinson et al. [14]. The authors analysed the relative stability of cyclic and open reaction intermediates for the reaction of ethylene with fluorine [14a] or chlorine [ 14b]. The cyclic intermediate was predicted to be the most stable in the case of chlorine whereas the opposite stability was obtained for fluorine. The reaction energy was also computed [14b] showing that these are not feasible gas-phase reactions. Kochanski [18] studied the gas phase reaction of ethylene with molecular chlorine and found that there is a CZV minimum corresponding to a Charge Transfer Complex (CTC). The best basis set employed predicted a stabilisation energy of - 3.7 kcal/mol and very small charge transfer. However no transition state could be located in the gas phase after examination of a two-dimensional potential energy surface. It has to be stressed that the existence of CTC complexes of this class was first established by Dubois and Garnier [20] and has been recently revisited [21]. It is accepted that this type of complex is formed before the charge separation that characterises the first step in Scheme 1. Kochanski [18] also discussed qualitatively the possible role of water solvation on the gas phase potential energy surface. Iwaoka et al. [17] have studied the reaction of molecular fluorine with ethylene at the ab initio MP2/6-31 + G level. Their results showed that fluorine and ethylene form a perpendicular prereactive complex with CZV symmetry which then reorientates to a rhombic-type complex as the transition state to give the final product. The reaction of Brz with ethylene has been also studied. A detailed investigation of the relative stability of cyclic and acyclic isomers of isolated C2H4Br+ ions has been reported [El. Besides, Yamabe et al. [16] have reported the gas-phase structure of a transition state (TS) using RHF/3-21G calculations. In this TS, that has C, symmetry (instead of the typical CzV), the Br-Br bond is broken and the bromonium ion is practically formed. The interaction of the forming Brspecies with the hydrogen atoms of the ethylene seems to be an important factor. However, the minima
109
joined by this TS where not identified in that paper. More recently, Cossi et al. [19] have considered the ethylene + bromine reaction in solution. The solvent is represented by a polarizable continuum. Some partial geometry optimisation was carried out for a series of structures and the discussion was focused on the modification by the solvent of the charge distribution of these structures. This work has provided new insights about the nature of bromonium ions and the reversibility of their formation reactions. Nevertheless, an ab initio study of the reaction with full geometry optimisation and transition state location in solution is still lacking. This is the main objective of the present article. Our aim is to describe the structure of the transition state as a function of the solvent nature and to evaluate, at least qualitatively, the solvent effect on the reaction kinetics. We first examine static solvent effects on the reaction of ethylene with bromine as a function of the polarity of the medium. Afterwards, two aspects of dynamic solvent effects are considered: the participation of water in the bromine + ethylene reaction coordinate and the role played by non-equilibrium solvation. The results presented here have been obtained by using continuum and discrete models for the solvent (see below) that allow us to examine the fundamental features of the process. Obtaining more accurate results requires the use of MD simulations [22]. The hybrid Density Functional Theory (DFT)/ MM Molecular Dynamics technique recently implemented in our group [23] is suitable for such a study and work is in progress [24].
2. Models and computational details
2.1. Solvent model We employ a continuum model that has been described in detail in previous articles [25]. The solvation energy is computed through a multipole moment expansion of the reaction field potential. The solvent is characterised by a macroscopic quantity, the relative static dielectric permitivity. Geometry optimisation and transition state location for solvated species are possible within this model. Non-equilibrium solvation may be also accounted for [13] after separating the solvent polarisation into
110
X. Assfeld et alJournal
of Molecular Structure (Theochem) 371 (1996) 107-116
2.2. Basis sets and correlation energy
inertial and non-inertial terms. The non-inertial polarisation is related to the electronic polarisation and is assumed to be in equilibrium with the reactants along the reaction path. The inertial component is associated with atomic (translational + vibrational) and rotational motions of the solvent molecules and with the difference between the static, eo, and the optical (infinite frequency), em, dielectric constants. This allows a global solvent coordinate, to be defined, S, which measures the deviation of the inertial polarisation configuration of the solvent with respect to its equilibrium value. It can be related to the chemical system reaction coordinate R. Hence, the solvent coordinate S will account for a solvent configuration the inertial polarisation of which corresponds to that in equilibrium with the chemical system at Ro so that
Several basis sets have been employed in this work. The first one (hereafter called Bl) is a triple-&plus double polarisation [27]: Br(16s13p7d/lOs8p4d), C(lls6p2d/ %4p2d), H(S2p/3s2p). The second one (hereafter called B2) is the standard LANLlDZ basis set [28] implemented in Gaussian92 [29], augmented with a diffuse function on the bromine atoms. The LANLlDZ basis set is a splitted valence basis set with pseudo-potentials describing the bromine atom cores. The diffuse functions have been obtained in this work by minimising the energy of Br- leading to gaussian exponents of 0.04205. Bl and B2 have been employed for locating stationary points in the gas phase. The simple basis B2 is shown to give reasonable results for the molecular structures and therefore the rest of the computations has been done with this basis set only. Computation of accurate energies would certainly require the use of larger basis sets but this is beyond the scope of the present work. The study of the influence of electronic correlation on geometry parameters is done at the MP2 level. In this case we use an all-electron basis set [[30]a] Br(16sllp5d/5s4p2d), C(lOs6pld/4s3pld), H(Sslp/ 2slp), intermediate between Bl and the simple B2 basis. It will be called hereafter B3. As as result of
S=R-R,,. The parameters
used in this continuum model are the static and the infinite-frequency dielectric permitivity (e. = 78.4 and E, = 1.8 respectively). The latter is used for evaluating non-equilibrium solvent effects only. The cavity shape is chosen to fit as best as possible the solute molecular shape. The solvent accessible surface defined by Richards [26] appears to be a good definition. In this work this surface has been simply fitted by an ellipsoidal cavity.
Table 1 Geometries and energies of the charge transfer complex (CTC) and transition state (TS) for the reaction of molecular bromine with ethylene in the gas phase as computed with the Bl and B2 basis set (see text) Structure Basis set
Geometrical Br-Br Br-C
CTC
parameters
Bl
B2
Bl
B2
2.300 3.536 3.536 1.317 90.0
2.463 3.360 3.360 1.320 90.0
3.115 1.966 2.014 1.451 18.6
3.237 2.121 2.176 1.438 17.5
-0.0517 +0.0340 +0.0177
-0.0995 +0.0329 +0.0666
-0.8898 +0.6148 +0.2750
-0.8990 +0.4802 +0.4188
-5222.792586
-103.438007
-5222.725286 42.23
-103.356460 51.17
(A and degrees)
c-c 8 (a) Mulliken net atomic charges Br :; Cz& Total (a.u.) and relative (kcal mole’) energies E ,DlSl BTS-Ecrc
TS
(a) angle formed by the Br-Br and C-C bond vectors. (b) for the forming bromine anion. (c) for Br in the forming bromonium cation.
X. Assfeld et al.lJournal of Molecular Structure (Theochem) 371 (1996) 107-116
111
relative energy between the pre-reactive complex and the TS is larger when computed at the Bl level, but the estimation made at the B2 level is reasonable. In the CTC, there is a small charge transfer but the TS is practically an ion pair. Note that in the bromonium, the positive charge is shared by the bromine atom and the ethylene group. Therefore, the TS has a late character. No attempt to compute the stabilisation energy of CTC with respect to the reactants has been done. This would require careful evaluation of Basis Set Superposition Error (BSSE) effects. CTC
Fig. 2. Optimised TS.
Ts
geometries
at the RHF/Bl
level for the CTC and
the large computational requirements, only some structures have been studied at this correlated level. Finally, some results have been also obtained with the 6-31G* basis set [3Ob] as indicated below.
3. Results and discussion 3.1. Reaction
mechanism
in gas phase.
We have considered here the reaction of bromine with ethylene and we describe in Table 1 the structure of the stationary points found at the Bl and B2 levels. Both basis sets predict the formation of a CTC complex with CzV symmetry and a transition state with C, symmetry, as shown in Fig. 2. From the comparison of the values obtained with the two basis sets one may note that the simple basis set B2 behaves satisfactorily. The results for the transition state are comparable to those reported before [16]. In particular, all these calculations predict a small value for the angle 8 formed by the Br-Br and C-C bond vectors. The
3.2. Mechanism in solution: dependence relative dielectric permitivity
on the
With the aim of analysing the role of the solutesolvent electrostatic interactions on the structure of the CTC complex and transition state, we have optimised their structures in media with different values of the relative dielectric constant. The results are gathered in Table 2 for the complex and in Table 3 for the transition state. Increasing e. lowers the BrC bondlength in the CTC complex and enlarges the Br-Br and C-C bondlengths. This can be explained by the fact that the solvent stabilises the charge transfer configurations. In the case of the TS, the most striking result is that the symmetry of the system changes with increasing the polarity of the medium. Indeed, in a non-polar solvent with e. = 2, the structure of the TS resembles that obtained in the gas phase except that the angle 8 is much larger and the late character is reinforced: the Br-Br distance increases, the Br-C distance decreases and the charge transfer is enhanced from 0.419 in the gas phase to 0.578 in the non-polar solvent. Conversely, in a low polar solvent with e. = 7 and in more polar solvents, the symmetry of the TS is
Table 2 Geometry of the CTC complex (in A and degrees) as a function of solvent dielectric permitivity
as computed at the RHF level with basis set B2
El) =
2.0
7.0
10.0
20.0
40.0
78.4
Br-Br Br-C
2.472 3.237 3.237 1.322 90.0
2.493 3.045 3.053 1.327 89.5
2.500 3.002 3.012 1.328 89.5
2.513 2.934 2.944 1.330 89.6
2.527 2.879 2.890 1.333 89.5
2.540 2.833 2.843 1.335 89.6
c-c I9
(a) (a) angle formed by the Br-Br
and C-C bond vectors.
112
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-116
Table 3 Geometry of the TS complex (in A and degrees) as a function of solvent dielectric permitivity
as computed at the RHF level with basis set B2
Eg =
2.0
7.0
10.0
20.0
40.0
78.4
Br-Br Br-C
3.763 2.195 2.162 1.430 58.4
2.896 2.378 2.399 1.385 89.1
2.781 2.461 2.481 1.372 89.2
2.676 2.572 2.586 1.357 89.4
2.624 2.647 2.660 1.349 89.5
2.592 2.704 2.715 1.344 89.5
c-c e
(a) (a) angle formed by the Br-Br
and C-C bond vectors.
approximately CzV. Compared with the gas-phase structure, the TS has an earlier character: the Br-Br and C-C bonds are shorter and the Br-C bond lengths are larger. Increasing further the dielectric permitivity does not modify the symmetry of the TS but intensifies its early character, according to Fig. 1. For instance, the charge transfer decreases from 0.525 in EO= 7 to 0.278 in EO= 78.4. The relative energy between the CTC and TS is given in Table 4 for the reaction in different media. It decreases from the gas to the solvent with e. = 2. This is expected since the transition state is rather polar and has a larger solvation energy. However, the relative energy is much smaller for higher dielectric constant solvents because the two structures, the complex and the TS, are now similar. Since the TS has increasing early character and the complex has increasing late character with increasing eo, one may expect that for a sufficiently polar solvent, the TS vanishes and the reaction becomes barrierless. As pointed out above, the energy data obtained with the simple basis set B2 have to be considered as a qualitative trend. Nevertheless, a great electrostatic solvent effect on the barrier is predicted which is in good agreement with experimental measurements. Thus, the relative rate constant varies from 1 in CCL to 1.6 x lo5 in CH30H and 1.1 x lOlo in water [3]. As mentioned, the influence of electronic correlation may be quite important to describe the structure of the reaction species, especially the CTC in which Table 4 Relative energy En - Ecrc (in kcal mol-‘) in different media computed at the RHF level with basis set B2 co =
2.0
7.0
10.0
20.0
40.0
78.4
AE
30.79
3.35
1.76
0.50
0.13
0.02
the dispersion energy is a fundamental contribution [31]. In order to evaluate its effect on the structure of CTC and TS in water, we have carried out MP2 calculations using basis set B3. The optimised structures are given in Table 5. The structure of the CTC computed with this basis set in gas phase is also given. One may first compare the RHF results for the CTC with those given in Table 1 for the gas phase and those given in Table 2 for the complex in water. The effect of the basis set is substantial in particular for the Br-C bond which is predicted to be longer at the RHF/B3 level. The effect of the basis set is however smaller for the TS. As shown, the RHF/B3 geometry is only slightly different from that obtained at the RHF/B2 level (see last column in Table 3). The influence of the correlation energy is very large for the CTC, in whi$h the intermolecular distance changes by about 0.5 A, but only slight for the TS. In the last case, the effect is to shift the TS a little towards the products. Accordingly, the SCF electron density at the forming bromine anion changes from - 0.598 at the RHF geometry to - 0.738 at the MP2 one. The relative energy Ers - Ecrc computed with the B3 basis set is 13.7 kcal mol-’ at the RHF level and 5.7 kcal mol-’ at the MP2 one. Therefore, the effect of correlation on the barrier appears to be substantial too, the balance of TS and CTC correlation energies leading to an activation energy decrease. Note also that these values are quite different from those obtained at the simple RHF/B2 level (see last column of Table 4) which stress the role of polarisation functions in the case of the solvated systems. It has to be pointed out that because of the large magnitude of the reaction field at the TS, a more rigorous treatment of electronic correlation may be necessary although this appears to be too costly in the standard SCRF model. An interesting approach
113
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371 (1996) 107-I 16
Table 5 Influence of correlation energy on the CTC and TS structures in a medium with ea = 78.4. MP2 calculations tion. Symmetry Czv has been assumed. Gas-phase values in parenthesis. Units are A and degrees TS
CTC
Br-Br Br-C c-c 0
(a)
using the Frozen Core approxima-
RHFlB3
MP2/B3
RHF/‘B3
MP2/B3
2.309 (2.302) 3.450 (3.734) 1.319 (1.318) 90.0 (90.0)
2.368 (2.354) 2.952 (3.021) 1.345 (1.343) 90.0 (90.0)
2.629 2.409 1.360 90.0
2.683 2.300 1.394 90.0
(a) angle formed by the Br-Br
and C-C bond vectors.
can be the SCRF-DFT method [32] in which correlation effects are included self-consistently through a density functional. In contrast, the description of charge transfer complexes at the DFT level is not completely satisfactory [33] and it should be necessary to test the suitability of DFT calculations for transition state structures of this type. 3.3. Solvent participation
in the reaction coordinate
We employ a discrete model to represent the first solvation shell of the bromine + ethylene TS. This is done by adding up to three water molecules interacting with the system and by performing a transition state location taking into account all the geometrical parameters (solute + solvent). The only constraint is that we impose a plane of symmetry. The transition
Fig. 3. Transition vectors for the gas-phase
structures and the transition vectors, i.e. the eigenvectors of the Hessian matrix with negative eigenvalue, obtained using one or three water solvation molecules are plotted in Fig. 3. The geometries are gathered in Table 6. As shown, the geometry of the TS obtained with this model is close to that obtained in the gas phase. The angle 0 increases from the gas phase TS to the TS with one or three water molecules. The solvated structure is earlier as shown by the Br-Br, Br-C and C-C bondlengths. Various attempts to locate a TS with the Br2 molecule perpendicular to the C-C bond were unfruitful. Though the hydrogen bond interactions with the first solvation shell are strong, one may then conclude that the mechanism of ethylene bromination in water is largely dominated by long-range electrostatic interactions.
(a) TS and (b) the TS solvated by one or(c) three water molecules, as computed at the RHF/B2 level.
114
X. Assfeld et aLlJournal of Molecular Structure (Theochem) 371
Table 6 Geometry (in A and degrees) of the TS in gas phase and solvated by one or three discrete water molecules
Br-Br Br-C c-c 8
Gas-phase
Mono-solvated
Tri-solvated
3.237 2.121 2.176 1.438 17.5
3.200 2.236 2.308 1.394 41.55
3.139 2.208 2.238 1.404 56.99
The role of the first solvation shell is important from the electronic point of view and modifies significantly the gas-phase charge distribution. This is shown in Table 7. In particular, there is a net electron density transfer from the water molecules to the C2H4Br+ subunit. The electronic density ascribed to the Br- anion is not very sensitive to the presence of water molecules. But the main result of these calculations is the substantial participation of the water molecule coordinates to the transition vector. The participation of the solvent in the reaction coordinate has been analysed in the case of the Menshutkin reaction [l]. As in the case of ethylene bromination, there is a creation of two charges of opposite sign at the TS than separate to form the products. Therefore, some of the conclusions reached in previous works for the Menshutkin reaction are expected to hold in the (first step) bromination of ethylenic compounds. As we discuss below, fluctuations of the solvent play a crucial role when dynamic effects are taken into account. These fluctuations may be stabilised by instantaneous changes in the electronic distribution of the solute [l].
(1996)
3.4. Solvent fluctuations effect
107-116
and non-equilibrium
As pointed out above, in fast reorganisation processes in polar media the climb to the transition state is made in an essentially frozen solvent configuration. A prior solvent fluctuation favouring this climb is required. In fact, certain solvent fluctuations may induce the reaction without any potential barrier [34]. We now analyse this dynamical aspect for alkene halogenation in water. For computational time reasons we decided to do this study for the reaction of ethylene with fluorine instead of bromine. The calculations have been carried out at the RHF/6-31G* level. In the continuum model used here to account for non-equilibrium solvation, the relative free energy of the solute-solvent system may be expressed as AG(R,S) where R is the reaction coordinate and S = R - R. a global solvent coordinate. The reaction coordinate has been chosen here from an Intrinsic Reaction Coordinate [35] calculation in solution using the equilibrium hypothesis. In Fig. 4 we represent the final results for the bidimensional surface AG(R,S). The values are given with respect to the
1.0
0.5
S
0.0
Table 7 Charge distribution of the TS in gas phase and solvated with one or three discrete water molecules
BY (a) CzHdBr’ (b) Hz0 (c) HzG (d)
Gas-phase
Mono-solvated
Tri-solvated
-0.8990 0.8990
-0.8782 0.7409 0.1373
-0.8948 0.7361 0.0049 0.1538
(a) Forming bromine anion. (b) Forming bromonium cation. (c) water molecule with the oxygen on the symmetry plane. (d) sum of charge on water molecules having their oxygen outof-plane.
solvent
-0.5
-1.0 -1.0
-0.5
0.0
0.5
1.0
R Fig. 4. Reaction energy as a function of the Intrinsic Reaction Coordinate R (defined using the hypothesis of equilibrium) and the solvent coordinate S = R - R”. Values are given relative to the equilibrated TS, R = 0, S = 0. Curves correspond to reaction energies of 0, 2 1.2, -+ 2.4, + 3.6, . . . kcalmol~‘.
X. Assfeld et al.iJournal of Molecular Structure (Theochem) 371 (1996) 107-116
free energy for the equilibrated TS. Positive and negative DG regions are distinguished. The x-axis (S = 0) represents the equilibrium reaction path. It may be noted that for a given value of R, the energy for S = 0 (x-axis, equilibrium) is a minimum, as expected. Negative values of S mean that the solvent inertial polarisation is equilibrated with a more advanced point along the reaction coordinate than the considered one. Lines with slope 1, S = R - Ro, represent frozen solvent reactive paths in which the inertial polarisation of the solvent is that in equilibrium with the chemical system at Ro. Therefore, the passage through the TS with a solvent frozen configuration is represented in this scheme by the principal diagonal. One clearly sees in this figure that the derivative of AC at the origin along this line is substantially smaller than that along the x-axis (equilibrium path). For instance, for R = S = 0.1 the variation of AG with respect to the TS is 0.43 kcal mall’ whereas for R = 0.1 and S = 0, it is 0.65 kcal mall’. This augurs a large impact of non-equilibrium solvation on the value of the transmission coefficient K, which measures the departure of the rate constant k from Transition State Theory rate kTST:
4. Conclusions
k K=ps?-
Acknowledgements
Gertner et al. [36] have shown that in the frozen solvent limit K may be approximated by: K=--
%eq
where w eq and w,,~ are the frequencies related to the curvatures at the top of the barrier, assumed to be parabolic in the non-equilibrium region, for the equilibrium and non-adiabatic case respectively. As discussed before [13], the computation of these frequencies is not straightforward since one has to consider an effective solvent mass. Consideration of limiting cases for the solvent mass allows a rough evaluation of K using force constants (see Eq. 24 in Ref. [13]). In our case, we obtain K = 0.64 ? 0.11. This value is smaller than that obtained for the SN2 reaction with the same model [13]: 0.65 Cc K 5 0.92 and indicates a large non-equilibrium solvation effect, especially considering that the continuum model tends to overestimate the transmission coefficient [37].
115
There are two main conclusions in this work that have to be emphasised. Firstly, the dependence of the bromination mechanism on the dielectric permitivity of the medium. From our results, it seems that the typical CZV transition state is only obtained in polar media and that long range interactions are mainly responsible for the stabilisation of this structure. The first solvation shell plays a moderate role which is related to charge delocalization. Secondly, non-equilibrium solvation effects seem to be rather important and larger that in previously studied SN2 reactions. Our study also emphasises the sensitivity of the results to basis set and correlation effects especially in the description of the CTC. Moreover, the continuum model cannot yield quantitative values neither for the solvation energies of the system under study nor for the transmission coefficient. But the main interactions are identified and will substantially simplify the implementation of most accurate hybrid -MD simulations.
This work has been done within the C.N.R.S. project G.D.R. No. 1017. The authors thank the members of the project, in particular Prof. S. Bratos and Dr M.F. Ruasse, for fruitful discussions.
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