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`PAPER
`
`On the origin of the steric effectw
`Balazs Pinter,*a Tim Fievez,a F. Matthias Bickelhaupt,b Paul Geerlingsa and
`Frank De Proft*a
`
`Received 4th April 2012, Accepted 10th May 2012
`DOI: 10.1039/c2cp41090g
`
`A quantitative analysis of the steric effect of aliphatic groups was carried out from first principles.
`An intuitive framework is proposed that allows the separation and straightforward interpretation
`of two contributors to the steric effect: steric strain and steric shielding (hindrance). When a
`sterically demanding group is introduced near a reactive center, deformation of its reactive zone
`will occur. By quantifying this deformation, a convincing correlation was established with
`Taft’s steric parameters for groups of typical size, supporting the intuitive image of steric
`shielding; bulky groups slow down the reaction by limiting the accessibility of the reactive centre.
`On the other hand, the strong initial repulsion between the reactant and the substrate by means
`of the filled–filled orbital interaction results in the deformation of the substrate as well as a less
`stabilizing reaction zone, which are the manifestations of the steric strain. We thus conclude
`that both steric strain and steric hindrance can be derived from the Pauli repulsion evolving
`between the reactants in the course of the reaction.
`
`hydrolysis of substituted esters led Taft to define the total
` 
`steric effect, ES,10 of a substituent relative to a reference11 as
`ES ¼ log
`
`ð1Þ
`
`A
`
`k k
`
`0
`
`Introduction
`
`In spite of the early recognition of the importance of the steric
`effect1 and the spread of the concept throughout the chemical
`literature,2 by the beginning of the 1940s ‘‘steric hindrance. . .
`has become the last refuge of the puzzled organic chemist’’.3
`Reasons for very little progress in describing the steric effect in
`a quantitative manner during this period include scarce knowledge
`of reaction mechanisms, lack of proper experimental methods to
`determine the reaction rate and lack of reactions to separate
`electronic and steric effects and the general attempt to account
`for all chemical behaviours in terms of electronic effects due to
`the success of Stieglitz, Robinson, and Ingold’s electronic
`theory.4 The outstanding work of Ingold5 in the understanding
`of reaction mechanisms and that of Brown6 in developing
`techniques for the determination of kinetic and thermodynamic
`data eventually paved the way for the development of the first
`consistent quantitative scale of the steric effect introduced by
`Robert W. Taft.7
`Following the initial proposal of Ingold,8 the recognition
`that steric effects operate almost alone9 in acid catalysed
`
`a Eenheid Algemene Chemie (ALGC), Member of the QCMM
`VUB-UGent Alliance Research Group, Vrije Universiteit Brussel,
`Pleinlaan 2, Brussel, Belgium. E-mail: pbalazs@vub.ac.be,
`fdeprof@vub.ac.be; Fax: +32 2629 3317; Tel: +32 2629 3520
`b Department of Theoretical Chemistry and Amsterdam Center for
`Multiscale Modeling, Vrije Universiteit Amsterdam, De Boelelaan
`1083, Amsterdam, The Netherlands
`w Electronic supplementary information (ESI) available: Cartesian
`coordinates of the optimized structures,
`interaction potentials for
`1–22, transition state structure of 8-TS, correlation between XSE
`values and Taft constants. See DOI: 10.1039/c2cp41090g
`
`where k and k0 are the rate constants for the hydrolysis of the
`substituted and the reference esters, respectively. The average
`values of log(k/k0)A for five related reactions (vide infra) were
`used to reduce small specific effects and experimental errors in
`evaluating ES.12 Assuming that polar and steric effects dominate
`the reactivity of ester hydrolysis under basic conditions and
`that the steric effect is identical in the acid and base catalysed
`reaction, Taft suggested eqn (2) for evaluating the net polar
`effect of a substituent.7,13
`
`
`
` 
`
` 
`
`
`
`ð2Þ
`
`A
`
`k k
`
`0
`
` log
`
`B
`
`k k
`
`0
`
`s ¼ 1
`2:48
`
`log
`
`In this expression, the prefactor is merely introduced to put s*
`on the same scale as the well-known Hammett s values.14
`Shorter discussed the validity and limitations of Taft’s
`assumptions in detail.15 In spite of some criticisms of Taft’s
`steric parameters at various occasions16,17 and the development
`of modified,17 novel18 as well as corrected19 steric parameters,
`the ES scale nevertheless became and remained the standard
`quantitative measure of the steric effect in physical organic
`chemistry.
`Taft also played a pioneering role in the understanding of
`how the steric effect operates.20 His statements that ‘‘it is
`meaningless and deceptive to say that a molecule is ‘‘sterically
`hindered’’
`from a general reactivity point of view’’ and
`
`9846
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`This journal is c the Owner Societies 2012
`
`Cite this: Phys.Chem.Chem.Phys., 2012, 14, 9846–9854
`
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` / Journal Homepage
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`
`SYNGENTA EXHIBIT 1017
`Syngenta v. FMC, PGR2020-00028
`
`

`

`‘‘changes in steric interactions between reactant and transition
`states are the only factors that affect rates’’ clearly highlight
`his interpretation of the steric effect within the framework of
`transition state theory.20 Accordingly, the steric contributions
`to the activation free energy were analysed and classified into
`potential- and kinetic-energy factors. It is straightforward to
`see how the former, also called steric strain, operates: since the
`coordination number of the carbonyl carbon changes from
`three to four when going from the reactant to the transition
`state during the acid-catalysed ester hydrolysis, the presence of
`substituents of increasing size near the reactive centre results in
`an increasing potential energy or steric strain due to the
`repulsion between non-bonded atoms. The kinetic-energy
`steric effect was associated with the change in steric hindrance
`of internal motions during the activation process.
`This effect is analogous to the entropy contribution to the
`activation free energy described in the principle of Prince and
`Hammett;21 when going from the reactant to the transition
`state, bulkier functional groups will give rise to more entropy
`loss as compared to smaller groups. In-depth investigation of the
`measured kinetic parameters revealed that this steric hindrance of
`internal motions dominates the total steric energy of activation
`for substituents of small (e.g. –CH3, i-butyl) and medium sizes
`(e.g. –CH2(cyclohexyl), –CH(C6H5)2). Introduction of even larger
`groups (i.e. beyond the g position relative to the carbonyl carbon
`atom, such as e.g. –CH(tert-butyl)(CH3), –C(C2H5)3) leads to an
`increasing importance of steric strain, but never without an
`accompanying increased steric hindrance of motions.22 This more
`negative activation entropy due to the introduction of bulkier
`groups DS#
`steric can be also linked to the steric factor P of collision
`theory through the expression P ¼ eDS#
`steric . This provides a
`natural bridge between transition state theory and collision
`theory concerning the steric effect.23
`Numerous attempts have been made to relate the ES constants
`to topological indices and geometrical, structural or physical
`parameters of substituents. From the excellent correlation found
`between ES values and van der Waals radii of groups (r$ as
`depicted in Scheme 1a in the case of a –CX3 group) Charton
`concluded24 that ES values are indeed free of inductive and
`resonance effects and, consequently, are pure measures of steric
`effects. However, this work used different sets, such as –CH2X,
`–CHX2 and –CX3, each with only five to seven substituents and
`with small overall ES ranges, which might be insufficient to
`clearly separate steric and electronic effects.25 Another wide-
`spread principle, Newman’s rule of six,26 which states that the
`number of atoms in the sixth position from the carbonyl oxygen
`(see Scheme 1b) determines the steric effect, was established by
`
`Scheme 1 Charton’s size-related metrics for –CX3 type groups (side
`view and top view) (a), Newman’s rule of six (b) and steric congestion
`as the inverse of accessibility of the carbonyl carbon for the approaching
`reactant R (c).
`
`qualitatively testing several reactions.27 This approach how-
`ever is evidently limited to b substitution of alkyl groups.
`These empirical methods have the important advantage of
`simplicity and are certainly useful for rough estimation of the
`steric effect, however, they do not provide insight into the
`nature of the steric hindrance, which is crucial in developing a
`universal concept of this quantity.
`The conceptually more elaborate but still purely geometrical
`method of Wipke and Gund28 was intended to predict the
`steric effect in the reactant state of the substrate independently
`of the structure of the transition state and reaction partner.
`Their steric congestion (Cxa, Scheme 1c), evaluated by eqn (3)
`and (4), describes the accessibility of the reactive carbonyl
`carbon (C1) for an approaching reactant R. It is clearly an
`approximation for the cross-section in collision theory. As
`such, it covers at least a part of the entropy factor although it
`is not straightforward how to interpret Cxa in Taft’s potential-
`and kinetic-energy steric effect framework (vide supra). The
`calculated congestions gave satisfactory correlation with the
`stereoselectivity of nucleophilic addition to 52 ketones; how-
`ever, they did not correlate as well with the absolute rate of the
`reaction.
`
`Axa(i) = 2pr2(1 cosy)
`
`Cxa = SiCxa(i) = Si(1/Axa(i))
`
`(3)
`
`(4)
`
`In molecular mechanics based methods, steric effects are
`treated as the sum of bond length and angle deformation
`(Baeyer strain), torsional eclipsing energy (Pitzer strain) and
`non-bonded interactions.29 The key idea of these methods is
`that the deviation in steric strain (DSE) when going from the
`reactant to the transition state equals the activation enthalpy
`(DH) and was established for various solvolysis reactions by
`obtaining linear correlation with the corresponding experi-
`mental rates.30 No such relationship, however, could be
`established for SN2 type reactions.31 The linear expression
`log(k/k0) = 0.340 0.789SE found for acid-catalyzed ester
`hydrolysis supports, then again, that ES values do in fact
`provide an exclusive measure of the steric effect.32
`Despite the developments in computational chemistry codes
`and supercomputers, the times where ‘‘. . .qualitative application of
`the theories of steric effects, aided by rapid computer calculations
`of molecular and transition state structures. . .’’ are still yet to
`come.33 Instead, practicing mechanistic computational chemists
`often regard steric effects as a universal redeeming rationale for
`phenomena that cannot be interpreted on electrostatic and orbital
`interaction origins. This is actually not inappropriate concerning
`the more or less obscure concept of the steric effect, which in
`practice embodies the views of strain, hindrance of internal
`motions, kinetic trapping, repulsion between non-bonded atoms,
`etc. In other words, as expressed by Ferna´ ndez, Frenking and
`Uggerud, the operationally defined steric effect lacks ‘‘rigorous
`mathematical accuracy’’.34 Unfortunately, the situation is more
`complicated since the minimal energy difference in activation
`barriers, sometimes as small as 2–3 kcal mol1 (that makes the
`difference between inhibited (slow) and allowed (fast) reaction)
`that we wish to capture and interpret, is far beyond the accuracy of
`most of the applied methods. No new concepts have completely
`resolved the post-Babelian conditions concerning the steric effect;
`
`This journal is c the Owner Societies 2012
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`9847
`
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`

`

`recently Weizsa¨ cker kinetic energy,35 Fisher information,36
`steric energy37 as well as various isodesmic38 reactions were
`proposed as a measure of the steric effect. Moreover, a very
`recent electron density based approach introduced by Yang
`and co-workers allows the visualization of, besides other
`fundamental properties, steric clashes in small molecules,
`molecular complexes and solids.39
`Being the only source of net repulsive interactions between
`molecular fragments, Pauli repulsion has been associated with
`the steric interaction for some time now.40 Very recently its
`quantification within the framework of the activation-strain
`model has shed light on the actions of the steric effect in
`bimolecular SN2 reactions41 and oxidative addition/insertion
`processes.42 Going from hydrogen to methyl substituents the
`larger steric effect was manifested in higher ‘‘activation’’
`strain, the energy associated with deforming the reactants
`from their equilibrium geometry, as well as in stronger Pauli
`repulsion between fragments. It turns out that the excess
`‘‘activation’’ strain originates from and its magnitude depends
`on the Pauli repulsion too: a strong initial Pauli repulsion
`results in an additional reactant deformation that actually
`relieves part of the inducing steric interaction.43 This concept
`provides a rational interpretation of the steric strain, the steric
`effect that is manifested in the potential energy, but however,
`does not account for and cannot describe the contribution of
`steric shielding.
`In this contribution we interpret and quantify the two
`actions of the steric effect: steric shielding and steric strain.
`We demonstrate that for groups of typical size, the steric
`effect, manifested in rate retardation of ester hydrolysis and
`represented by Taft constants, is dominated by shielding rather
`than strain. As a proof of concept we provide quantitative
`justifications for the intuitive image that bulky groups introduced
`near the reactive centre slow down the reaction by limiting the
`accessibility of the reactive centre. Our framework allows for
`straightforward and intuitive distinction of these conceptually
`different actions of the steric effect.
`
`Computational details
`
`In order to scrutinize the steric effect, we focus on one of its
`defining reactions, the acid catalysed hydrolysis of esters. To
`this end, protonated esters 1–19 and 20–22 were optimized at
`B3LYP44/aug-cc-pVTZ45 and B3LYP/aug-cc-pVDZ levels,
`respectively, using Gaussian0346 software.
`Using equilibrium geometries, interaction energy calculations
`for the approach of the model nucleophile were carried out with
`the PBE47 functional in combination with a TZ2P basis set using
`the Amsterdam Density Functional (ADF) program package.48
`To evaluate the two contributions of the steric effect for groups
`1–22, interaction potentials were determined on a 4  4 A˚ square
`grid centred above C1, at 2 A˚
`from the substrate, using 441
`points (ca. 28 points A˚ 2). The distance of 2 A˚ between the
`fragments is chosen to allow the description of the steric effect
`in the initial stages of the bond formation process. Note that
`specifying the electron configuration of the fragments ensures
`the required ionic interaction of the reactants, i.e. the alter-
`native association of the reactants as a radical pair, which
`might be appropriate at larger distances, is thus eliminated
`
`from the description. For details of our protocol of calculating
`interaction energy potentials see ref. 49.
`The narrowing of the reactive area was quantified using
`an exclusion method. We defined that the reference system
`(R = CH3) has a circular reactive area with a radius of 1 A˚ at
`2 A˚
`from the reactive centre. By investigating the same circle
`centred above the reactive carbon for our test series we can
`determine what percentage of this area is available for attack
`for a given substituent. By setting a threshold limit for the
`Pauli repulsion we can easily decide whether a point in the
`circle is a part of the reactive zone or the incoming nucleophile
`would feel too strong repulsion to approach this point. Based
`on the analysis below, we applied a standard limit value of
`100 kcal mol1; if the Pauli repulsion is lower than this value in
`a given point then that point is available for attack whereas for
`higher values it is excluded from the reactive zone.
`Interaction energy contour plots were generated with Mathe-
`1. The distance
`matica and all contour lines are given in kcal mol
`1 for
`between contour lines is consistently fixed to 10 kcal mol
`
`DEPauli, DVelst and DEoi and to 5 kcal mol1 for DEnoi and DEint.
`The color-coding is chosen such that dark regions correspond to
`the most stable zones and the light regions to the least stable areas
`in the plot (e.g. in Fig. 2). Areas where the reactant is too close
`to the substrate are indicated in white.
`
`Results
`
`To quantify the steric effect of aliphatic groups, we selected and
`investigated a set of protonated esters 1–22 (Scheme 2) that are
`the active species of the rate determining step in acid catalyzed
`ester hydrolysis, one of the defining reactions of Taft’s constant.
`For such a reaction, as it was demonstrated (vide supra) groups
`introduced close to the reactive center, i.e. at the carbonyl carbon
`atom, contribute to the increase of the activation barrier through
`the enthalpy as well as the entropy. These contributions change
`proportionally only in a few specific cases50 and hence, any
`model intended to describe the steric effect should properly
`consider and characterize the two contributions separately. It
`implies, as was also noted by others, that single parameter
`models are de facto bogus. Consequently, our model will use
`two parameters; the area of the reactive zone and the average
`Pauli repulsion within this area.
`
`Scheme 2 Investigated protonated methylesters 1–22 and numbering
`of the relevant atoms.
`
`9848
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`This journal is c the Owner Societies 2012
`
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`

`

`The area of the reactive zone, the surface through which the
`reactant can approach the reactive site of the substrate, is
`introduced to measure the accessibility of the reactive centre. It
`resembles the reactive cross-section s* in collision theory, defined
`as s* = Ps, where P is the steric factor ðP ¼ eDS#
`stericÞ and s is
`the collision cross-section.23 Accordingly, we define the steric
`shielding as the process by which sterically demanding groups
`limit the accessibility of the reactive centre.
`Bulky groups do not only limit the accessibility of the
`reactive centre but also exert considerable repulsion against
`the incoming reactant due to the filled–filled orbital interaction.
`Such repulsion induces the deformation of the substrate on the
`one hand and results in a less stabilizing interaction energy on
`the other. Taking into account that resonance and inductive
`effects are minor and do not vary with R in the investigated
`reaction, one can expect that orbital and electrostatic interac-
`tions between the incoming reactant and the reactive centre are
`nearly constant for varying R. Thus, the total interaction energy
`along the reaction coordinate becomes less stabilizing with
`increasing group size solely because of the stronger Pauli
`repulsion between the substrate and reactant. Since both the
`deformation and the change in the interaction energy are
`manifested as an increase of potential energy, their effect is
`considered to be the steric strain and quantified by the average
`Pauli repulsion in the reactive zone.
`Our methodology for evaluating the steric shielding as well
`as the steric strain of alkyl groups is straightforward; as
`illustrated in Fig. 1, a model nucleophile (F) is moved along
`a rectangular grid parallel to the skeleton, defined by the O1,
`C1 and O2 atoms, of the protonated ester [R–C(OH)–OCH3]+
`and the interaction energy between the substrate and the nucleo-
`phile is determined in every point of the grid. The origin of the
`grid, [0, 0], was set to C1 whereas axes x and y were chosen to be
`parallel with and perpendicular to the C1–O2 bond, respectively.
`The fluoride ion was chosen as the model nucleophile to avoid
`complications of directional dependence. Its electrostatic inter-
`action with the protonated substrate is considered to produce a
`linearly scaled background compared to a neutral nucleophile. In
`every scanned point along the grid, the interaction energy DEint
`was decomposed into Pauli, electrostatic and orbital interaction
`terms using the Ziegler–Rauk decomposition scheme.51 Such a
`protocol enables us to visualize in-plane contour plots for
`these fundamental properties (DEPauli, DVelst and DEoi) and
`for
`two derived quantities,
`the non-orbital
`interaction
`
`Fig. 1 Schematic representation of our approach to quantify the
`steric effect of aliphatic groups; scans of the interaction energy
`between the protonated ester and the model nucleophile are performed
`along a rectangular grid at 2 A˚
`from the substrate. The green area is
`used to determine the steric effect of the substituent. Only plane1 is
`shown in the case of R = tert-butyl for simplicity.
`
`(DEnoi = DEPauli + DVelst) and total
`interaction energies
`(DEint = DEPauli + DVelst + DEoi), as functions of the relative
`position of the nucleophile to the ester. (Note: ‘‘non-orbital
`interaction’’ refers to all interactions except for the stabilizing
`orbital interactions.) As we will demonstrate, the interaction
`energy between the nucleophile and the substrate, which we
`will term the ‘‘interaction energy potential’’, contains enough
`information to quantify the steric effect of alkyl substituents in
`the molecule.
`interaction energy potential (DEint) calculated
`The total
`for the methyl substituted protonated ester (Fig. 2) clearly
`identifies the reactive zone, an attractive area around the
`minimal potential at position [0, 0],
`through which the
`nucleophile attacks the target carbon centre. The other attrac-
`tive zone around [(1/2), 2] orients the incoming nucleophile
`to an unreactive site of the substrate probably resulting in a
`non-reactive collision.
`DEpauli shows that the –OCH3 moiety and the group R exert
`considerable Pauli repulsion when the reactant approaches
`from their directions. The effect of the latter substituent is
`‘delocalized’ in the direction of the central carbon meaning
`that the exerted repulsion considerably affects the potential
`above and below the reactive carbon, which is the footprint of
`the steric effect.
`The electrostatic potential (DVelst) closely resembles the
`Pauli repulsion potential, but with opposite sign; due to slight
`electron deficient character of the out-of-plane hydrogens, the
`incoming nucleophile experiences the strongest electrostatic
`attraction in the proximity of the methyl groups. Also, the
`effect of partially localized positive charge is manifested in the
`rather attractive electrostatics above the central carbon atom.
`As shown in the DEoi potential, orbital interaction plays an
`important role in controlling the approach of the incoming
`nucleophile:
`the orbital
`interaction attraction above the
`reactive carbon is dominant enough to modify the appearance
`of DEnoi resulting in a preferred almost perpendicular approach
`to the carbon, in agreement with the calculated transition state
`geometry (Fig. S1, ESIw).52 The large distance of 1.74 A˚
`calculated between the reactive carbon and the oxygen atom
`of the incoming water molecule and the slight pyramidalization
`around C1 indicate an early TS for the hydrolysis. Such small
`geometrical distortion of the substrate when going from the
`reactant to the TS ensures that the steric effect can be described
`during the initial stages of the reaction.
`Scanning the interaction energy in planes at different distances
`from the molecule allows us to construct the three-dimensional
`picture of the ‘reactive channel’, the energetically preferred region
`above the reactive carbon that provides the optimal approach for
`the nucleophile. Such a channel with a typical conical shape is
`illustrated in Fig. 3 with interaction potential isosurface values of
`(a) 40 kcal mol
`1 and (b) 130 kcal mol
`1; the former also
`shows a valley above the central carbon allowing the nucleophile
`to get closer and interact with the carbon atom. Note that the
`reactive channel shown in Fig. 3b closely resembles the
`hypothetical cone in Wipke’s steric congestion method.28
`Changing the substituent on the central carbon (C1,
`Scheme 1) atom has a crucial impact on the shape of reactive
`channels. For instance, bulky groups that bend out of the
`plane in the proximity of C1 exert strong Pauli repulsion in the
`
`This journal is c the Owner Societies 2012
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`9849
`
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`

`

`Fig. 3 Shape of the reactive channel of the methyl substituted protonated
`ester with (a) 40 kcal mol1 and (b) 130 kcal mol1 isosurface values.
`
`Fig. 4 Interaction energy (top) and Pauli repulsion (bottom) potentials
`above the reactive carbon center for methyl (1), axial cyclohexyl
`(110, plane2) and tert-butyl (8, plane2) substituents.
`
`how the area and shape of the reactive zone, the cross-section
`of the reactive channel, change as a function of the substituent.
`The reference system (1: R = CH3) almost has a circular
`reactive zone with radius of about 1 A˚ as can be seen from the
`DEint plot. This circular shape deforms to oval and to a
`semicircle when going from methyl to cyclohexyl (110) and
`to tert-butyl substituents (8).
`Comparison of the corresponding total interaction energy
`and the Pauli repulsion potentials (Fig. 4) clearly shows
`that the deformation of the reactive zone originates from
`the overwhelming Pauli repulsion in the proximity of the
`substituent. As a rule of thumb, we found that when the Pauli
`term reaches a value of about 100 kcal mol1,
`it also
`dominates the overall appearance of the total
`interaction
`energy map. We now conjecture that the two important
`parameters for describing the steric effect provided by these
`calculations are the area of the reactive zone and the inter-
`action energy in this zone. To evaluate the steric effect of the
`functional groups, we propose that the size of the reactive
`area describes the steric shielding, whereas the average Pauli
`repulsion in the reactive area describes the strain energy
`contribution to the steric effect.
`For a set of alkyl substituted protonated esters, Table 1
`summarizes the size of the reactive zone in points (N) through
`which the reactant can approach the reactive carbon. In the
`absence of a mirror plane the two sides of the molecule from
`which the nucleophile can approach are not identical and need
`
`Fig. 2 Contour plot of the Pauli repulsion (DEPauli), electrostatic inter-
`action (DVelst), orbital interaction (DEoi), non-orbital interaction (DEnoi)
`and total interaction energy (DEint) potentials along a 6 A˚  5 A˚ grid for 1
`(R = CH3) in a plane that is 2 A˚ above the molecular plane.
`
`neighbourhood of the reactive carbon resulting in a less
`attractive and deformed reactive channel. Fig. 4 illustrates
`
`9850
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`This journal is c the Owner Societies 2012
`
`Published on 10 May 2012. Downloaded by Reprints Desk on 2/19/2020 9:38:57 PM.
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`
`

`

`Table 1 Taft constant (ES),16 number of reactive zone points in plane1 (N1) and plane2 (N2), average number of reactive zone points (Navg),
`average Pauli repulsion in the reactive zone of plane1 (hDEPaulii(1)) and plane2 (hDEPaulii(2)) in kcal mol1 and logarithm of relative reactive zone
`
`
`size log(Navg(R)/Navg(1)) for the investigated protonated esters
`log NavgðRÞ
`Navgð1Þ
`
`hDEPaulii(1)
`
`hDEPaulii(2)
`
`R
`
`ES
`
`N1
`
`N2
`
`Navg
`
`1
`2
`3
`4
`5
`6
`7
`8
`9
`10
`11
`110
`12
`13
`14
`140
`15
`16
`17
`18
`19
`20
`21
`210
`22
`
`–CH3
`–CH2CH3
`n-Propyl
`n-Butyl
`n-Pentyl
`i-Propyl
`i-Butyl
`tert-Butyl
`Cyclobutyl
`Cyclopentyl
`Cyclohexyleq
`Cyclohexylax
`Cycloheptyl
`–CH2C(CH3)3
`–(CH2)2CH(CH3)2
`–(CH2)2CH(CH3)2(2)
`–CH2Ph
`–C(CH2CH3)3
`–CH(CH3)(CH2CH3)
`–CH(CH3)(Ph)
`–CH(CH2CH3)2
`–(1-CH3–c-hexyl)
`–C(CH3)2(c-hexyl)
`–C(CH3)2(c-hexyl)(2)
`–CHPh2
`
`0.00
`0.07
`0.36
`0.39
`0.40
`0.47
`0.93
`1.54
`0.06
`0.51
`0.79
`0.79
`1.10
`1.74
`0.35
`0.35
`0.37
`3.80
`1.13
`1.19
`1.98
`2.03
`2.49
`2.49
`1.76
`
`79
`77
`60
`72
`72
`72
`9
`29
`81
`78
`43
`67
`67
`6
`77
`4
`73
`30
`24
`27
`19
`11
`48
`26
`2
`
`79
`77
`72
`63
`63
`25
`78
`53
`37
`20
`41
`20
`5
`81
`79
`67
`75
`15
`64
`70
`31
`47
`0
`22
`67
`
`79
`77
`66
`67.5
`67.5
`48.5
`43.5
`41
`59
`49
`42
`43.5
`36
`43.5
`78
`35.5
`74
`22.5
`44
`48.5
`25
`29
`24
`24
`34.5
`
`69.20
`69.64
`72.97
`71.43
`71.05
`71.40
`80.51
`74.41
`65.87
`68.19
`75.33
`71.36
`72.02
`83.19
`70.56
`88.18
`71.98
`73.73
`75.47
`74.35
`77.10
`84.44
`—
`77.32
`93.74
`
`69.20
`69.63
`71.82
`73.61
`73.63
`75.42
`69.13
`75.47
`76.17
`76.28
`76.46
`77.34
`87.16
`69.23
`70.18
`73.72
`71.08
`82.83
`71.41
`72.90
`78.61
`77.77
`76.50
`81.39
`73.03
`
`0.00
`0.01
`0.08
`0.07
`0.07
`0.21
`0.26
`0.28
`0.13
`0.21
`0.27
`0.26
`0.34
`0.26
`0.01
`0.35
`0.03
`0.55
`0.25
`0.21
`0.50
`0.44
`0.52
`0.52
`0.36
`
`to be evaluated separately (plane1 (N1) and plane2 (N2)).
`At the applied resolution of 28 points A˚ 2 the default analysed
`circle consists of 81 points. As expected, the highest average
`number of points occurs for the methyl substituted reference
`system (Navg(1) = 79). The advantageous orientation of
`cyclobutyl and –CH2C(CH3)3 substituents results in one
`completely unhindered side in 9 and 13, respectively, although,
`the overall accessibility of C1 is worse in these systems,
`Navg(9) = 59 and Navg(13) = 43.5, than for 1. In good
`agreement with the experimental measurement the predicted
`most shielded carbon centre appears in system 16 having the
`bulky –C(CH2CH3)3 substituent. Introduction of two phenyl
`rings on C2, as expected, has a prominent influence on the
`shielding; plane1 of the –CHPh2 substituted protonated ester
`(22) is more shielded (N1(22) = 2) than either side of the
`–C(CH2CH3)3 substituted derivative (16).
`The average Pauli repulsion calculated in the reactive zone
`(hDEPaulii(1) and hDEPaulii(2)) varies between 66 kcal mol
`1
`1 (R = CHPh2
`(R = cyclobutyl (9), plane1) and 94 kcal mol
`(22), plane1). No unambiguous direct correlation can be
`recognized between the Taft constants and this average
`hDEPaulii, however, the statement that ‘‘the bigger the reactive
`zone the smaller the repulsion experienced’’ is valid in most of
`the cases. For example, in the plane of 12 and 13, several
`accessible points (B5) are associated with relatively high
`average repulsion of about 85 kcal mol1 whereas the reactive
`zone of 67 points in 110 (plane1) and 12 (plane1) has a
`hDEPaulii(1) of only B72 kcal mol1. The wide range of almost
`1 for the average hDEPaulii, which would result in
`30 kcal mol
`an unrealistic 4.6  1021-fold retardation of the reaction rate
`at 30 1C, shows that the predicted strain effect has to be scaled
`down. For this sole purpose we introduce the parameter a,
`with an expected value of 0.05–0.1, to put the effect of
`
`hDEPaulii on the same scale as for the shielding effect described
`by the change in the reactive zone area.
`We finally propose to estimate the steric effect XSE of
`group R as
`
` 
`XSEðRÞ ¼ log
`
`kX
`R
`kX
`1
`
`ð5aÞ
`
`RT
`
`RT
`
`þ N2ðRÞeahDEPauliðRÞið2Þ
`R ¼ N1ðRÞeahDEPauliðRÞið1Þ
` kR ð5bÞ
`kX
`where N1(1) = N2(1) = 79 and hDEPauli(1)i(1) = hDEPauli(1)i(2) =
`69.2 kcal mol1 are the values corresponding to the methyl
`substituent. To test the reliability of our method and validity of
`our assumptions, XSE values for various a parameters were plotted
`against the Taft constants and their correlation was determined.
`Using an a value of 0.01, a satisfactory agreement (R2 = 0.82) was
`found between calculated XSE and experimental ES parameters
`(Fig. S2, ESIw).
`Importantly, the small a value indicates that the exponential
`term in eqn (5a) and (5b), i.e. the steric strain in our framework,
`affects the correlation insignificantly. Accordingly, we investigated
`the foreshadowed relationship between the relative size of the
`reactive zone (log(Navg(R)/Navg(1))) and Taft constants; as can be
`seen in Fig. 5, an acceptable correlation with R2 of 0.82 indeed
`exists between the relative reactive zone size for protonated esters
`1–22 and steric constants of the corresponding aliphatic groups.
`One can interpret the latter correlation and the predicted small a
`parameter as an indication of negligible steric strain contribution
`to the decrease of the reaction rate for the majority of the
`investigated substrates as an a value of 0.01 results in a predicted
`maximal strain contribution of 0.3 kcal mol1. Such interpretation
`is indeed partially valid; Taft had shown that many of the
`investigated substrates exhibit a considerable entropy contribution
`
`This journal is c the Owner Societies 2012
`
`Phys. Chem. Chem. Phys., 2012, 14, 9846–9854
`
`9851
`
`Published on 10 May 2012. Downloaded by Reprints Desk on 2/19/2020 9:38:57 PM.
`
`View Article Online
`
`