DOI: 10.1002/chem.200903569

Response to the Comment on “The Interplay between Steric and ElectronicEffects in SN2 Reactions”

Israel Fern�ndez,[a] Gernot Frenking,[b] and Einar Uggerud*[c]

We reply to the preceding Correspondence article in thisissue by Zeist and Bickelhaupt,[1] in which the authors chal-lenge the interpretation of the energy decomposition analy-sis (EDA)[2] that was applied by us in a recent study of thereaction course of SN2 reactions.[3] Unlike previous work, inwhich the SN2 reaction often is analyzed in terms of interac-tions between an attacking nucleophile and a substrate, wealso considered the effect of the leaving group on theenergy terms of the EDA along the reaction path. We thinkthis is a particularly reasonable approach for an identity re-action such as X� + R3C�X, where in the transition struc-ture [X···R3C···X]� the nucleophile and the leaving groupare equivalent, and also since this is a heterolytic process.We found that the steric repulsion between the nucleophileand the substrate is overcompensated by the loss of stericrepulsion between the substrate and the leaving group. Thisconclusion was reached by calculating the interactions be-tween [X···X]2� and CR3

+ along the least energy reactionpath and by applying the EDA to the calculated energies.

Zeist and Bickelhaupt used the same approach and ob-tained numerical results for the systems F� + R3C�F (R=

H, Me), which are essentially identical to our data. Thecurves of the EDA values that are shown in Figure 1 b intheir Correspondence[1] support the conclusion that thesteric repulsion, which is identified with the DEPauli term ofthe EDA, decreases along the reaction path and that theDEPauli value for the transition structure is smaller than forthe reactants. The small hump in the curve for F� + Me3C�F, which was already observed by us in our previous study,[3]

is interesting but not relevant for the present topic. Zeistand Bickelhaupt then introduce a new scenario where theyconsider a hypothetical system in which they suppress thegeometric relaxation of the substrate when the nucleophileapproaches. Not surprisingly, they observe a steep rise of thePauli repulsion yielding a curve that exhibits an increase ofthe DEPauli term along the reaction course (Figure 1 c in theCorrespondence by Zeist and Bickelhaupt). The authorsthus conclude that “increased steric congestion around thefive-coordinate central atom causes the barrier in the SN2 re-action”.

We do not consider this statement of Zeist and Bickel-haupt to be valid. The use of a hypothetical system wherethe geometry of the substrate is frozen implies by necessitythat the Pauli repulsion term increases as the nucleophileapproaches. This procedure is also questionable from aformal point of view since only electronic and not nucleardegrees of freedom are optimized. The behavior of this arti-ficially constrained system is exactly opposite of what wasfound in the system for which the positions of the nuclei areallowed to adjust. In addition, the conclusion of Zeist andBickelhaupt is based on a different interpretation of theEDA because energy terms in the EDA, which are not asso-ciated with steric repulsion, are arbitrarily added to theDEPauli term. The statement in the second paragraph of theCorrespondence by Zeist and Bickelhaupt, which states: “It

Keywords: energy decompositionanalysis · molecular modeling · nu-cleophilic substitution · reactionmechanisms · steric hindrance

Abstract: Only by allowing full geometry optimization for all energy points alongthe reaction coordinates does it become possible to perform a meaningful analysisof the variation of the various energy terms during a chemical reaction. Great careshould also be taken in the definitions of the energy terms, and only Pauli repul-sion should be included in the steric interaction term.

[a] Dr. I. Fern�ndezDepartamento de Qu�mica Org�nicaFacultad de Qu�mica, Universidad Complutense28040 Madrid (Spain)

[b] Prof. Dr. G. FrenkingFachbereich Chemie, Philipps-Universit�t MarburgHans-Meerwein-Strasse, 35043 Marburg (Germany)

[c] Prof. E. UggerudMassespektrometrilaboratoriet og Senter for teoretiskog beregningsbasert kjemi (CTCC)Kjemisk institutt, Universitetet i OsloPostboks 1033 Blindern, 0315 Oslo (Norway)E-mail : einar.uggerud@kjemi.uio.no

� 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2010, 16, 5542 – 55435542

is therefore crucial to be aware that the overall effect ofsteric hindrance…is contained not only in the steric or Paulirepulsion but also in the changes in other energy terms..”runs counter not only to our conclusion but also to the phys-ical interpretation of the EDA terms that has been advocat-ed in the past.[4] This is unfortunate since the original EDAprovides precisely defined mathematical terms that make itpossible to identify chemical concepts with numerical datain a consistent manner.[5] The central term of the EDA isthe instantaneous interaction energy DEint between the frag-ments in the geometry of the species that is the subject of theanalysis [Eq. (1)]:

DEint ¼ DEelstat þ DEPauli þ DEorb ð1Þ

The term DEelstat gives the electrostatic interaction energybetween the fragments, DEPauli refers to the steric repulsionbetween the fragments, and DEorb is the orbital interactionterm, which can be identified with covalent bonding. Incases where the investigated species is an equilibrium struc-ture the interaction energy DEint and the bond dissociationenergy De are related by the expression given in Equa-tion (2).:

�De ¼ DEprep þ DEint ð2Þ

The term DEprep gives the relaxation of the fragmentsfrom the geometry in the molecule to the equilibrium struc-ture. This term is named DEstrain by Zeist and Bickelhaupt.Essential to this discussion, is the fact that the unfavorableDEprep term of the R3C moiety within the tetrahedral R3CXspecies is almost fully released in passing from reactants totransition structure, since the R3C unit within [X···R3C···X]�

for all practical reasons has the same planar geometry as inthe reference state. If DEprep (or DEstrain) becomes furtherpartitioned into the energy terms given in Equation (1),which is the approach applied by Zeist and Bickelhaupt inthe preceding Correspondence, it would mean that the EDAresults refer to a geometry that does not represent theactual structure of the investigated species. This positionwas previously expressed in review articles by Bickelhauptet al.[6] and by some of us.[7] We prefer to use the real systemusing the optimized geometries rather than a hypothetical

system with non-equilibrium structures for the bonding anal-ysis that is inherent to the EDA. There is agreement be-tween the work of Zeist and Bickelhaupt and ours that theactual activation barriers for the systems F� + R3C�F (R=

H, Me) come from weaker orbital interactions due to therather long carbon–fluorine distances in the transition statesrather than steric repulsion.

Finally, we would like to comment on the statementsabout steric hindrance by Zeist and Bickelhaupt made inthe last paragraph of their Correspondence. They write:“Indeed, steric hindrance is not an observable in the senseof a “Hermitian operator for steric hindrance”. But sterichindrance is the observable behavior of the eigenvalue of aquantum mechanical operator, namely, the Hamiltonian.” Wefind the two statements contradict each other. Strictlyspeaking, what is observable is the change of the totalenergy of a system that comes from the change in nuclearconfiguration during the course of a reaction. The identifica-tion of an energy change with steric hindrance is subject toan interpretation that may be plausible and useful and yet,which is always arbitrary. Nature does not know steric hin-drance, only energy changes.

[1] W.-J. van Zeist, F. M. Bickelhaupt, Chem. Eur. J. 2010, 16, DOI:10.1002/chem.200902337.

[2] a) K. Morokuma, J. Chem. Phys. 1971, 55 ; b) T. Ziegler, A. Rauk,Theor. Chem. Acc. 1977, 46.

[3] I. Fern�ndez, G. Frenking, E. Uggerud, Chem. Eur. J. 2009, 15, 2166.[4] A. Krapp, F. M. Bickelhaupt, G. Frenking, Chem. Eur. J. 2006, 12,

9196.[5] For a pertinent example see the EDA definitions of hyperconjuga-

tion, conjugation, and aromaticity in: a) D. Cappel, S. T�llmann, A.Krapp, G. Frenking, Angew. Chem. 2005, 117, 3683; Angew. Chem.Int. Ed. 2005, 44, 3617; b) I. Fern�ndez, G. Frenking, Chem. Eur. J.2006, 12, 3617; c) I. Fern�ndez, G. Frenking, Faraday Discuss. 2007,135, 403.

[6] F. M. Bickelhaupt, E. J. Baerends, Rev. Comput. Chem. 2000, 15, 1.[7] a) G. Frenking, K. Wichmann, N. Frçhlich, C. Loschen, M. Lein, J.

Frunzke, V. M. Ray�n, Coord. Chem. Rev. 2003, 238–239, 55; b) M.Lein, G. Frenking, Theory and Applications of ComputationalChemistry: The First 40 Years (Eds.: C. E. Dykstra, G. Frenking, K. S.Kim, G. E. Scuseria), Elsevier, Amsterdam, 2005.

Published online: April 21, 2010

Chem. Eur. J. 2010, 16, 5542 – 5543 � 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 5543

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