Volume 56, number 3 CHEMICAL PHYSICS LETTERS 15June1978

A LOCAL ORBITAL DESCRIPTION OF THE Cl- + CH,CI SN2 REACTION

Gary SIMON!3 and Erach R. TALATY Department of Chemistry, Wichita State University. Wichita, Kansas 67208. US4

Received 1 February 1978

We have studied theoretically the C TV reaction path of the Cl-+ CH3Cl SN~ reaction, using the ab-initio FSGO method. We find that the departure of the leaving group begins at an early stage ir, the reaction. This observation is signiticant in that Cl- is a “good” leaving group; previous theoretical investigations of SN~ mechanisms noted a Late departure of the anion but involved poorer leaving groups. The calculations suggest that the transition state should be viewed as a tight “ion triplet”, Cl-[CG] Cl-, rather than as a carbon with five distorted covalent bonds.

Although there have been several theoretical inves- tigations of SR2 mechanisms reported in the last few years, most of these investigations [ 1,2] have involved poor leaving groups, such as H- and F-. The S,2 reaction between Cl- and CH3C1, on the other hand, may be regarded as a prototype for SN2 reactions in which there is a good leaving group. In this letter we report the results of a theoretical study of the C,, re-

action path of this reaction. The (apparently) only prior study [3] of this system reported a geometry and energy for the D3, intermediate, but did not map out a reaction path and did not compare this reaction to the analogous F- + CH3F process.

As a computational tool we have used the floating spherical gaussian orbital (FSGO) method [4,5], which directly employs core, lone pair, and bonding orbitals. This method does not yield the high energetic accuracy which can now be obtained by some procedures 161, but it is ab-initio, readily interpretable in terms of orbital locations and sizes, and comparatively in- expensive. Thus, it enables one to visualize a reaction in terms of what happens to the various electron pairs and at least partially provides the physical description and insight which has been sought by several inves- tigators [l-3,6-10]. Although the FSGO method has been widely used to study stable molecules [S] , the only prior application [1 l] * to a chemical reaction

* Exchnling calculations on Hg and b.

was largely unsuccessful. In that instance the system studied (proton transfer in hR-@JI$) may have been inappropriate since FSGO wavefunctions poorly de- scribe the lone pair electrons of nitrogen, oxygen, and fluorine [S] . There are no comparable difficulties with the lone pair electrons of second- [ 121 or third- [ 131 row atoms. Hence, the SN2 reaction between Cl- and CHaCl emerges as both an intriguing and practical FSGO study.

Salient features of our calculations are summarized in table I_ For four different innut Cl-(incoming)- C distances, all other geometric and electronic param- eters were optimized. The calculated FSGO geometry of the isolated CH3Cl molecule is rather accurate: the predicted C-H bond length is within 0.015 bohr of the experimental value, the H-C-Cl angle is correctly predicted to be smaller than the H-C-H angle, and the C-Cl bond length is underestimated by 6% or 0.19 bohr. The D3h intermediate state C-Cl distance is underestimated by almost the identical amount, 0.20 bohr, as compared to the bond length calculated by Keil and Al-&i&s [3] . If one examines the variation in the FSGO total energy as the reactants approach, the dominant feature is a large decrease in energy. This is precisely what would have been anticipated from studies [I,21 on the related F- + CH3F reaction. How- ever, we do not fiid the anticipated sharp upturn near the D3h intermediate geometry. Consequently, the D3n structure is predicted to be lower in energy than the

Volume 56, number 3 CHEMICAL PHYSICS LETTERS lSJunei978

Table 1 Features of the a-+ CH3Cl SN2 reactiona)

-___ ___~ ___-~_---_----_ -_---~- --_ _ - ___-- R (Cl---C)

-~-_ --__ co 8 5 4.32

-- ---_ _-__

energy -827.578 (-958.791)e) -827.595 -827.635 -827.641 (-958.776)e) R (C--Cl) 3.180 (3.37)t-J 3.410 4.026 4.32 (452)e) R (C--H) 2.084 (2.098)f) 2.057 2.024 2.019 LHCH 111.18 (1 lOS)fJ 114.74 119.62 120.00 R (imcoming) b) R (outgoing) b) 2.06;

7.974 4.896 4.200 2.690 3.753 4.200

m (incomhtg) c) 1.000 0.997 0.979 0.972 m(outgoing)c) 0.648 0.789 0.932 0.972 cz(incoming)d) 0.323 0.322 0.325 0.325 ar(outgoing)d) 0.363 0.340 0.325 0.325 ~(carbon corc)d) 9.297 9.3 16 9.343 9.345

-- -. ----_

a) Energy in hartrees, distances in bohr, angles in degrees. b) R denotes distance of orbitd center of incoming or outgoing C-CL orbital from carbon. c) m denotes orbital distance from carbon divided bv C-Cl internuclear dtstance. d) Q is the gaussian exponent of the indicated FSGOI e) Theoretical values from ref. [3]. f) Experimental values from ref. [ 15]_

reactants - this is almost certainly an artifact of the limited FSGO basis set. It is not supported by the sophisticated coupled electron pair approximation cal- culations of Keil and Ahlrichs [3] _ As a parallel, we note that conventional molecular orbital calculations [ 1.21 using sp atomic orbital basis sets also erroneously predict [F-CH3-F] - to be more stable than F- + CH3F. The relative energetics along the reaction path are, therefore, highly basis-set dependent, and are probably the least accurate aspect of our caiculatron. It should be emphasized that, as in previous FSGO (and other) calculations [5,12--141, energetic inac- curacies do not preclude the successful prediction of electronic distributions, geometries, and other proper- ties.

One of the key conclusions of Dedieu and Veillard’s study [ 11 of SN2 reactions was that the leaving group departed late in the reaction. In the F- + CH3F reac- tion, they found that when the incoming F-C dis- tance was 10,7,5, and 4 bohr, the outgoing F-C bond was stretched by only 0_02,0.04,0_09, and 0.16 bohr, respectively_ Almost all of the stretching of the outgoing F-C bond occurred when the incoming fluorine was nearly at its Dsh state location. In con- trast, our calculations show that the C-Cl bond stretches much more readily, at much larger incoming

Cl-C distances. When the incoming chloride ion is

8 bohr from the carbon, the carbon-chlorine bond has already stretched 0.23 bohr; by the time the in- coming Ci-C distance is 5 bohr, some 74% of the stretching of the outgoing Cl-C bond has occurred. This difference in behavior between C-F and C-CL correlates with the ease of orbital motion within the bond as the reaction progresses. In CH,Ci, the C-c’r FSGO is centered 65% of the bond length away from the carbon, but when the incoming Cl- is g bohr away, this value has shifted to 79% In comparison, Dedieu and Veillard’s [ 1] “charge center” analysis suggests that for the fluorine analog the respective percentages would be approximately 67% and 68%. Apparently, it is the high polarizability of the C-Cl bond which leads to this major difference in reaction path. We sug- gest that this is closely re!ated to the nature of Cl- as a gocd leaving group, and speculate that good leaving groups will generally show greater bond length dis- tortions at larger incoming nucleophile-carbon dis- tances than do poorer leaving groups.

There are many similarities between the F- + CH3F and Ci- + CH,Cl reactions. From table 1, one observes that the exponent of a Cl- lone pair orbital is 0.322, while the C-Cl orbital in CH3C1 has an ex- ponent of 0.363. In the Dsh intermediate C-Cl ex-

Volume 56, number 3 CHEMICAL PHYSICS LETTERS -1SJune1978

ponents are 0.325, virtually identical to the chloride ion orbital. Moreover, in the intermediate state, the C-Cl orbitals are centered 97% of the bond distance toward their respective chlorines. This degree of ion- icity would probably be reduced somewhat by the addi- tion of more basis functions and the inclusion of correlation effects; nevertheless, it is clear that the FSGO intermediate state should be viewed as an “ion triplet”, Cl- [CH3] +Cl-, rather than as a carbon with five distorted covalent bonds. Presumably, the ionic bonding is sufficiently “tight” to lead to the SN2 in- version stereochemistry_ An FSGO charge decomposi- tion [ 141 shows that each chloride has a charge of -0.944 e, while the central methyl group is +0.888 e. According to this description the carbon atom bears a large positive charge, which rationalizes the steady shrinkage of the C-H bond length and the increasing compactness of the carbon core orbital as the reaction progresses. These results are in agreement with previous calculations on the analogous fluorine reaction.

We suggest that these results constitute a physically attractive and interpretable description of the Cl- + CH3Cl SN2 reaction, and illuminate the role which the FSGO method can play in the study of closed- shell chemical reactions. It should be noted that the FSGO method is quite economical, and that these cai- culations took only a small fraction of the computer time which standard LCAO methods would have re- quired. Calculations on large systems, including third- and even fourth-row atoms, should be practical_

Useful conversations with Dr. Jean R. Simons are gratefully acknowledged.

References .

[ 1 J A. Dedieu and A. Veillard, I. Am. Chem. Sot- 94 (1972) 6730.

[2] A.J. Duke and R.F.W. Bader, Chem. Phys. Letters 10 (1971) 631.

[3] F. KeiLand R. Ahh-ichs, I. Am. Chem. Sot. 98 (1976) 4787.

[4] A. Frost, J. CLtem. Phys. 47 (1967) 3707. [S] A.A. Frost, in: Modem theoreticaL chemistry, Vol. 2, ed.

H.F. Schaefer, to be pbLished.

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