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Nucleophilic Aromatic Substitution Reactions Described by the Local Electron Attachment Energy Joakim Halldin Stenlid, and Tore Brinck J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.7b00059 • Publication Date (Web): 14 Feb 2017 Downloaded from http://pubs.acs.org on February 17, 2017

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The Journal of Organic Chemistry

Nucleophilic Aromatic Substitution Reactions Described by the Local Electron Attachment Energy Joakim H. Stenlid and Tore Brinck* Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden *E-mail: [email protected]

Table of Content (TOC) graphics

Abstract A local multi-orbital electrophilicity descriptor, the local electron attachment energy [E(r)], is used to study the nucleophilic aromatic substitution reactions of SNAr and VNS (vicarious nucleophilic substitution). The E(r) considers all virtual orbitals below the free electron limit and is determined on the molecular isodensity contour of 0.004 a.u. Good (R2=0.83) to excellent (R2=0.98) correlations are found between descriptor values and experimental reactivity data for six series of electron-deficient arenes. These include homo- and heteroarenes, rings of five to six atoms and a variation of fluorine, bromine and hydride leaving groups. The solvent, temperature and nucleophile are in addition varied between the series. The surface E(r) [ES(r)] is shown to provide better reactivity predictions than transition-state calculations for a concerted SNAr

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reaction with a bromine nucleofug, it gives substantially stronger correlations than LUMO energies and is over-all more reliable than the molecular electrostatic potential. With the use of ES(r) one can identify the various electrophilic sites within a molecule and correctly predict isomeric distributions. Since the calculations of ES(r) are computationally inexpensive, the descriptor offers fast but accurate reactivity predictions for the important nucleophilic aromatic substitution class of reactions. Applications in e.g. drug discovery, synthesis and toxicology studies are envisaged.

Introduction Nucleophilic aromatic substitutions (NAS) of electron deficient arenes are versatile and wellestablished synthetic tools, both for general synthesis as well as industrial purposes.1–5 In order to master this class of reactions, numerous methodologies have been derived over the years for a priori estimations of reactivity and regioselectivity. Experimental descriptors, e.g. the Hammett constants6–8 along with various empirical rules,2,9–12 as for instance the ortho/para directing ability of the nitro group, have been employed, as have many quantum chemical descriptors. The latter category includes the frontier molecular orbital approach (LUMO),13,14 Fukui functions, Parr’s electrophilicty index15,16 (and local hardness/softness),17 the so-called Iπ-repulsion model,18,19 relative energies of the σ-adduct intermediate20–23 (explained below) and the molecular surface electrostatic potential,24,25 among others. Quantum chemical approaches are especially useful for compounds with complex substituent patterns where the combined substituent effect is difficult to predict, and when no experimental data is available. This is for instance the case for previously unreported and/or short-lived compounds. However, few if any of the above methods are able to combine computational efficiency, accuracy and ease of


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automation in their predictions, which is often required for large-scale screenings or on-the-fly analysis. The arguable most well-recognized and versatile nucleophilic aromatic substitution reaction is the two-step addition-elimination reaction, known as SNAr. This type of reaction takes place between an electron deficient arene (e.g. nitro-arenes or pyridine derivatives) and a suitable nucleophile.3 The putative mechanism2,3,5 proceeds over a non-aromatic σ-adduct intermediate (also known as the σ-complex or the Meisenheimer complex), before a leaving group (often a halogen) is expulsed to regain the aromaticity as the product is formed. This mechanistic picture has, however, been questioned lately especially for weakly activated or deactivated substances with favorable leaving groups, e.g. bromide or chloride, where there are indications of a concerted reaction mechanism.20,26–28 A closely related, but less recognized, reaction type is the vicarious nucleophilic substitution (VNS).4,29–33 In the VNS reaction the sites occupied by hydrogen atoms are substituted. It has been found that addition to these sites proceed much faster than addition to e.g. halogenated sites. However, reaction via the SNAr mechanism at the hydrogen occupied sites would lead to an hydride anion leaving group, a much less favorable leaving group than those traditionally used in SNAr reactions. To circumvent this, special conditions typically have to be employed in order to facilitate the reaction; in the VNS reaction, for instance, one often uses the chloromethyl phenyl sulfone carbanion nucleophile that is able to directly abstract the hydrogen nucleofug as a proton instead of a hydride upon formation of the σH-adduct via a HCl β-elimination.30 A comparison between the SNAr and VNS mechanisms is given in Figure 1.


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Figure 1. Schematic comparison between the nucleophilic aromatic substitution (SNAr) and the vicarious nucleophilic substitution (VNS) mechanisms 1-halo-4-nitrobenzene. To the left is the ES(r) at the 0.004 a.u. surface of X=F from series 5 displayed. Coloring: red < -1.3 eV < yellow < -0.8 eV < green. ES,min are found at all ring carbons. The ortho (ES,min=-1.72 eV) and meta (-1.22 eV) positions with respect to the nitro group are potentially VNS active while the para (-0.87 eV) position is a SNAr site. ES,min are also found on the over the C-N bond between the ipso carbon and the nitro group (-1.47 eV) and on the oxygen atoms of the nitro group (-1.25 eV). The ES(r) of 1-halo-4-nitrobenzene is discussed in more detail in the Introduction section.

In the present study the computationally inexpensive local electron attachment energy descriptor [E(r)],25 which is based merely on ground-states Kohn-Sham DFT calculations of the studied compounds, is used for estimations of both reactivity trends and regioselectivity for reactions with arenes that are active in the SNAr or VNS reactions. The E(r) descriptor is here compared to experimental data, but also to higher-level quantum chemical methods as well as other ground-state descriptors, e.g. the molecular electrostatic potential [V(r)]. For reactivity estimations, it has previously been shown25,34 that good correlations with experimental and computational data can be obtained by evaluating the E(r) and V(r) at molecular isodensity contours (here 0.004 a.u.) that typically lie close to the van der Waals radii of the atoms that constitutes the molecule. When E(r) and V(r) are analyzed at molecular surfaces they are denoted ES(r) and VS(r), respectively. Surface minima in E(r) [ES,min] and surface maxima in V(r) [VS,max] reflect sites susceptible to nucleophilic attack. The surface map of 1-Fluoro-4-nitrobenzene in Figure 1 serves as an example of the use of ES(r). This compound is active in both the SNAr and VNS reactions and ES,min are found in the


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vicinities of all ring carbons with the lowest surface minimum (ES,min=-1.72 eV) positioned ortho relative to the activating nitro group. The ortho position is also the preferred VNS site in this molecule, and the magnitude of the ES,min reflects the relative reactivity at this position, the ortho position of the less activated nitrobenzene compound is e.g. associated with a higher ES,min (-1.40 eV). The meta carbons of 1-Fluoro-4-nitrobenzene are also potential VNS sites but have a higher ES,min (-1.22 eV) than the ortho carbons, in agreement with the experimentally well-established ortho directing effect of the nitro group. In addition, there is a surface minimum (-0.87 eV ) associated with the para position that reflects the reactivity of SNAr. However, it must be emphasized that the relative reactivity of the ortho versus the para position is this molecule is not directly accessible by ES(r) due to the difference in leaving group. In comparison, we note that ES(r) is capable of ranking the ortho, meta, and para sites of nitrobenzene; here the ES,min are 1.40 eV (ortho), -1.00 eV (meta), and -1.12 eV (para), in line with the experimental and computational trends of reactivity for VNS found by Mąkosza and co-workers.4,33,35 Furthermore, there is a ES,min of -1.47 eV associated with the C-N bond, corroborating an earlier proposal by Politzer and coworker that C-N bonds of nitroaromatics are sites susceptible to nucleophilic attack.36 These examples show that ES(r) provides insight into a molecules local reactivity for nucleophilic processes, but that ES(r), like any computational chemistry approach, must be applied together with knowledge of potential reaction mechanisms and reaction conditions to be useful for predicting chemistry. The applicability of E(r) to the NAS class of reactions has recently been established by studying a series of congeneric compounds active in the SNAr reaction.25 In addition, the use of E(r) is motivated by a previous study of electrophilic aromatic substitution reactions,37 where the nucleophilic analogue to E(r) (i.e. the average local ionization energy [Ī(r)]38) was successfully


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employed for estimations of relative reaction rates and regioselectivity. By the use of groundstate reactivity descriptors such as E(r), the computational cost can be substantially reduced compared to e.g. elaborate transition-state calculations; this while maintaining good accuracy in the reactivity estimations.

Computational Methods All DFT calculations have been performed within the Gaussian 09 program suite.39 The groundstate geometry optimizations were carried out at the B3LYP40,41/6-31G(d) level of theory, while the local electron attachment energy [E(r)] and the electrostatic potential [V(r)] were evaluated at the 0.004 a.u isodensity surface with the in-house program HS95 (T. Brinck), using the KohnSham42 wave functions obtained from B3LYP/6-31+G(d,p) single-point calculations. For the iodine containing compounds we have employed the LACV3P*//LACVP* basis set combination.43 This is based on the LANL2-DZ basis set where the core electrons are treated with Los Alamos style effective core potentials.44 Gas phase calculations were compared to condensed phase by including solvation effects via the polarizable continuum model (PCM) using the integral equation formalism.45,46 The piperidine solvent was described by a dielectric constant of ε=5.9. For the mechanistic studies, including all transition-state (TS) calculations, we used the M06-2X47 exchange correlation functional in piperidine PCM and the 6311+G(3df,2p)//6-31+G(d,p) basis set combination for all atoms but the iodine atoms, for which LACV3P*//LACVP* were used. The choice of the M06-2X functional is motivated by its excellent performance for main-group thermochemistry and kinetics.47 For comparison, the B3LYP functional was also tested in the mechanistic studies yielding similar trends and geometries as M06-2X while severely overestimating the TS barriers. Harmonic vibrational frequencies were calculated to verify the nature of all stationary points, i.e. zero (one) imaginary


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frequency for ground-state (TS) structures. The thermochemical analysis was carried out employing the harmonic oscillator, rigid rotor and ideal gas approximations, and assuming a standard state of 298.15 K and the experimental 10 M piperidine concentration. Gibbs free energy corrections ∆∆ → to the 10 M concentration from the program default of 0.041 M (i.e. 1bar) were added as: ∆∆ → =

.

= −3.26 kcal ∙ mol

(1)

The E(r) descriptor is defined as & )

' !"#$ = ∑*+,- .

&' (' "#$ ("#$

(2)

where εi is the eigenvalue of the i:th virtual orbital, ρi(r) represents its density at the position r, and ρ(r) is the total density of the occupied orbitals.25 Only virtual orbitals below the free electron limit are included in the summation. Equation 2 is motivated based on Janak's theorem48 and the piecewise linear energy dependence upon electron addition to atomic and molecular systems.49 In our previous study,25 it was shown that E(r) can be divided into contributions from the electrostatic potential, the exchange-correlation energy and the kinetic energy densities of the contributing virtual orbitals. The last term explains the capacity of E(r) to predict strong intermolecular interactions that are not entirely electrostatic in character, but also has significant contributions from charge transfer and polarization. Equation 2 is valid for the generalized KohnSham methods (GKS-DFT),50 which includes methods ranging from local DFT via hybridmethods to pure Hartree-Fock (HF). However within the GKS-DFT class of methods the energies of the virtual orbitals vary rather strongly with the amount of HF exchange in the method, and it has been argued that methods where the LUMO energy is close to -EA (EA = electron affinity) should preferentially be used with eq 2.25 In our previous study we found that


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E(r) computed with standard hybrid functionals, such as B3LYP and PBE0,51 that typically includes 15-25 % HF exchange, have a high predictive power for interactions such as halogen bonding, nucleophilic attack of activated double bonds, and SNAr. Our tests further indicated that these methods provide a more balanced description of the virtual orbital energies, and better E(r) predictions of reactivity, than long range corrected methods such LC-BLYP52 and CAMB3LYP.53 In our previous article25 we also discuss the connection between using E(r) and FMO theory for analyzing electrophilicity. We demonstrate that the two approaches are basically equivalent for small organic molecules that have only one virtual orbital (the LUMO) of negative energy. On the other hand, for molecules of more complex electronic structure and with several low lying virtual orbitals, an FMO analysis based on a single orbital is generally inferior to a multiorbital approach, such as E(r). As an example, an E(r) computation of pentafluoronitrobenzene included four virtual orbitals and was shown, in contrast to the LUMO density, to give a good representation of the stereoselectivity for SNAr. The electrostatic surface potential VS(r) was computed at the same isodensity surface as E(r) and is given by: 01

/"#$ = ∑4 |3

1

−5 #|

(6# 7 89# 7 |# 7 #|

(3)

Here ZA is the charge of A:th nucleus, RA its spatial coordinate and r and r’ represents the coordinates of two electrons. The surface contour graphics were prepared in the UCSF Chimera visualization program.54


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For the statistical validations we have employed the coefficient of determination (R2), crossvalidated R2 (i.e. Q2) and standard error (SE). Q2 was evaluated according to the leave-one-out procedure55 by: ∑@ "=

' : ; = 1 − ∑'AB @ "= 'AB

'

=>$? =C$?

(4)

where D* is the i:th value of y in the data series, DC is the mean value of y over the data series and D>*/* is the predicted value of y=y(F* ) based on a linear regression analysis of the data series with the i:th data point excluded from the regression.


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Results and Discussion This work consists of, all together, six series of electrophilic arenes, with the range of electrophiles chosen so as to facilitate proper evaluation of the ES(r) descriptor: Its ability to estimate relative reactivity as well as its performance in regioselectivity predictions is examined by reducing the influence of other contributions to the compounds reactivities (e.g. steric or entropic effects) besides those reflected by the descriptor (i.e. charge-transfer/polarization and electrostatic interactions25). The experimental reaction rate constants and regioisomeric distributions that are used for comparison have previously been reported in the literature.10–12,14,56– 58

Series 1-4 follow the SNAr mechanism while series 5 and 6 belong to the VNS family of

reactions. For most of the compounds local maxima in the electrostatic potential, VS,max, could not be determined at the specific site of reaction. Hence, the local electrostatic potential, VS,loc, at the ES,min sites (local minima of ES(r) on the 0.004 a.u. isodensity surface, i.e. electrophilic sites) are used for comparison between the two descriptors. For series 1 the performance of the ES,min is, in addition, compared to estimated Gibbs free energy barriers obtained by TS calculations.

SNAr Among the four SNAr series the first (series 1) examines the relative reactivity of a number of brominated nitroarenes with the neutral piperidine as nucleophile and Br-/BrH as leaving group. As mentioned in the introduction, the putative two-step mechanism of SNAr has lately been questioned and found to be correct primarily in cases of reluctant leaving groups (as F-/HF) or highly stabilized intermediates.20,26–28 Given more favorable leaving groups like Cl-/HCl or Br/BrH, as in the case of series 1, the reaction is expected to proceed via a concerted mechanism in the sense that no σ-adduct intermediate is formed. The compounds of series 2-4 reacts with anionic nucleophiles and have F-/FH as leaving group, were the latter presumably leads to the


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putative two-step mechanisms. Another significant difference between the series is that series 1 consists of arenes with only one plausible SNAr site, in contrast to series 2-4 were multiple reaction sites are active.

Series 1 The 1-bromo-4-R-2-nitrobenzene compounds of series 1 (inset of Figure 2) are taken from a study by Berliner and Monack.56 A nitro group in ortho position to the leaving group activates the reaction site while the R substituent in the para position is varied. The activating effect in the SNAr reaction for the different substituents ranges from strongly activating (NO2) to strongly deactivating (H2N) relative to the H compound. Throughout the series the sterical variations at the reacting site are minimal since the site of reaction is situated at a distance far from the substituents. Piperidine acts as both nucleophile and solvent. Since piperidine is a neutral nucleophile, an additional deprotonating step is included in the mechanism compared to Figure 1 (see Scheme 1).

Figure 2. Logarithmized experimental rate constants relative to R=H plotted against ES,min values of series 1, R = H, F, Cl, Br, I, t-Bu, Me, OH, OMe, OEt, COOH, NH2, NMe2, NO2. Note that NO2 is not include in the correlations since it was reported to react too fast under the reaction conditions for a rate constant to be determined.56 The ES,min values are obtained on the 0.004 a.u. isodensity surface in gas phase (left) and in the piperidine solvent (right) represented by explicit solvent molecules and PCM. The asterisk (*) marks the site of reaction.


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Table 1. Experimental rate constants and computed descriptor data at the site of reaction (i.e. position 1) for the compounds of series 1. ES,min values for the ring positions 3 and 5 (ortho and para with respect to NO2) are included in the supporting information.

Gas phase

Piperidine solvation

R=

ln krela)

GH,JKL b)

MH,NOP c,d)

GH,JKL b)

H

0.00

-1.11

16.63

-0.76

Me

-1.93

-0.95

14.14

MeO

-4.02

-0.81

Me2N

-6.71

OH

UVWXSYSZ b)

MH,NOP c,d)

∆[\ c)

∆[\,UVWXSYSZ c)

-0.76

14.13

21.2

21.2

-0.66

-0.66

6.5

22.5

22.5

12.12

-0.49

-0.49

3.64

25.6

25.6

-0.59

3.12

-0.31

-0.31

-4.89

26.9

26.9

-7.45

-0.86

14.02

-0.5

-0.32

5.36

24.9

27.7

H 2N

-8.99

-0.7

6.44

-0.37

-0.27

-1.52

26.2

27.4

Br

2.06

-1.26

20.92

-0.88

-0.88

15.26

19.6

19.6

Cl

1.72

-1.24

19.51

-0.88

-0.88

15.47

20.0

20.0

I

1.65

-1.25

20.24

-0.91

-0.91

22.59

20.1

20.1

F

-1.35

-1.15

20.08

-0.72

-0.72

13.04

22.2

22.2

t-Bu

-1.77

-0.95

13.21

-0.66

-0.66

5.82

22.0

22.0

EtO

-4.19

-0.78

11.34

-0.48

-0.48

2.93

24.8

24.8

COOH

0.92

-1.34

23.31

-1.01

-0.90

16.98

16.4

19.4

e)

-1.74 0.827

31.16 0.730

-1.14

-1.14

27.24

13.5

13.5

0.755

0.612

0.869 0.796

0.978 0.966

0.790 0.703

0.792 0.612

0.960 0.940

1.611

2.014

1.403

0.588

1.775

1.767

0.773

n.r.

NO2 2 f)

R Q2 f)

SE f)

GQ,RST

a)

Pseudo first-order reaction rates in min-1 from ref. 56 at 25°C relative to that of H. b) In eV, explicit=explicit solvent molecules were used, c) in kcal mol-1, d) No VS,max could be found at the reactive site, e) the reaction was reported as too fast to determine a reaction constant under the given conditions, f) compared to ln krel. Br NO2H+ N H R

σH-adduct

BrBr

Br NO2-

NO2 +

H NH+ R

NH+

R

N NO2

N NO2

BrH

HN

NO2 -HBr

R

R

R

σH-adduct

Scheme 1. Showing the concerted SNAr mechanism for the neutral piperidine nucleophile. Shown are also the reversible and non-productive formation of σH-adducts at position ortho and meta with respect to the NO2 group.


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Owing to the good leaving group, Br-/BrH, a concerted reaction mechanism without a σ-adduct intermediate is anticipated for series 1. Consequently we expect a relatively early TS, structurally close to the ground-state geometries from which the ES,min values are obtained. The validity of this assumption was tested by a closer examination of the mechanism for the whole series of R substituents. Ormazábal-Toledo et al. have recently investigated the SNAr reaction of similar reactants: including e.g. the reaction of 1-Bromo-2,4-dinitrobenzene (i.e. R=NO2) with the morpholine nucleophile59 as well as the reaction of mono-, di-, and tri-nitro-Fluoro-benzenes with piperidine.60 They report a step-wise mechanism that passes over a zwitterionic σ-adduct intermediate, which is formed in an initial rate-determining step. This step is assumed to be followed by deprotonation and expulsion of the halide leaving group (alternatively by expulsion of the halide followed by deprotonation) via a two-step process. The formation of the σ-adduct intermediate can be explained by the activation of two nitro groups in the case of 1-Bromo-2,4dinitrobenzene as well as by the poor F-/HF leaving group of 1-Fluoro-2,4-dinitrobenzene. The aforementioned calculations were moreover performed in gas phase. Upon reoptimization in the piperidine solvent, we were not able to identify intermediate σ-adducts for any of the R substituents considered. This also includes the 1-Bromo-2,4-dinitrobenzene (i.e. R=NO2). Instead the first TS leads directly to the expulsion of the Br- leaving group and the formation of the protonated product in a concerted mechanism. Upon expulsion, the Br- coordinates to the amine proton originating from piperidine. HBr may leave from this state via a NO2-mediated and non-rate-limiting proton transfer from the amine to the Br anion, as demonstrated for the H, NO2 (activated) and NH2 (deactivated) substituents in Figure 3. Alternatively a solvent molecule could facilitate the deprotonation. The absence of a σ-adduct intermediate in condensed phase is compatible with the experimental evidence that the reaction of 1-X-2,4-dinitrobenzene with


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secondary amines results in one intermediate for X=Cl, Br, and I, while X=F leads to two intermediates.61 Compared to gas-phase, the lack of σ-adduct intermediates can be rationalized by a stabilization of the Br anion in the solvent. Scheme 1 summarizes the concerted SNAr mechanism for the case of a neutral piperidine nucleophile. It also includes the possible formation of reversible σH-adducts at the hydrogen substituted ortho (position 3) and para (position 5) ring sites with respect to the nitro group. These sites are also activated but due to the reaction conditions the formation of the σH-adducts is unproductive. Instead these sites are potentially active in e.g. the VNS reaction given a suitable nucleophile. ES,min values for addition to these sites are included in the supporting information.

Figure 3. Displays the Gibbs free energy reaction profile for the SNAr reaction with the piperidine nucleophile for compounds H, NO2 and NH2 of series 1. The inset shows the rate-determining TS structure for R=H (distances in Å). The ∆G values are shown at 298.15 K assuming the experimentally specified56 piperidine concentration of 10 M and a 0.04 M HBr concentration (i.e. 50% conversion). TSPT represents the TS of a NO2-mediated proton transfer from the amine towards the coordinated Br anion. The reaction profile of NH2 was obtained with an explicit piperidne solvent molecule coordinated to the NH2 group.

The identification of a concerted mechanism (i.e. lack of an intermediate σ-adduct) with an early rate-determining TS should facilitate the use of ground-state reactivity descriptors for this


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reaction series. Accordingly, a good correlation between ES,min values at the reaction site obtained in gas-phase for the set of electrophiles and logarithmized relative experimental reaction constants (ln krel) was found, with a R2-value of 0.827 and a standard error of 1.611 (Table 1). Compared to other methods, the ES,min performs overall better than VS,loc (R2=0.730 in gas-phase) and much better than the LUMO energies (R2=0.618). It should also be pointed out that the there are no maxima in the surface electrostatic potential VS(r) on the sites of reaction for this series. Hence V(r) is unfit to identify local reactivity in this series. In addition, as can be seen in Figure 3, the relative energetics of the intermediate structures (I) cannot be used as a reactivity indicator since the σ-adduct energies does not reflect the ordering of the TS barriers for the various R substituents. To illustrate the ease of comparing the reactivity for the different reactants by ES(r), Figure 4 shows the descriptor value mapped on the 0.004 a.u. molecular isodensity surfaces for the Me and Br compounds.

Figure 4. ES(r) mapped on the 0.004 a.u. isodensity surfaces of a) Me and b) Br from series 1. Coloring: Red < -1.4 eV < yellow < -0.9 eV < green. The asterisk (*) marks the site of reaction via the SNAr mechansim.

Despite the relatively good correlations found, some obvious anomalies can be recognized in the plot of ES,min against ln krel (Figure 2). The NH2, OH, COOH, and possibly F, compounds appear to belong to a separate trend. Without these entries the gas phase correlation increases to R2=0.998 and within the divergent group the correlation is R2=0.984. These discrepancies could


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have several explanations including, besides the possibility of experimental errors, a more complex mechanism than outlined above, as well as pronounced solvent effects, to mention a few examples. In order to further evaluate the validity of the proposed mechanism we compare calculated Gibbs free energy activation barriers ∆G† (obtained with piperidine PCM solvation) for the first TS with the experimental reaction rates. Somewhat surprisingly, the TS barriers turn out to give weaker correlations than the ES,min (note: ES,min obtained in gas phase) with a R2 of 0.792, despite that the TS calculations, in contrast to ES(r), are performed with implicit consideration of solvent effects. This R2-value corresponds to TS energies obtained with the M06-2X functional, the corresponding R2-value for B3LYP barriers is 0.751. Again the largest deviations in the correlation are seen for NH2, OH, and COOH. The correlation without these entries improves significantly to R2=0.968. The divergent groups span from activating to deactivating, which suggests that a mechanistic change to step-wise for these compounds is not a likely explanation for the deviations. Moreover, even if the mechanism would be step-wise, the first TS, as identified here, is expected to be rate-limiting for the studied compounds due to the good leaving groups and because the reactions were run under an excess of base (piperidine) to deprotonate the product. Hence the TS structures obtained here should be valid. A better rationalization can be found by invoking solvent effects, as discussed below. First it should be noted that the ∆G† and ES,min values, both in piperidine, show a close mutual relationship (R2=0.954), suggesting that ES,min may well be used in lieu of TS calculations for these reactions. The latter is of course attractive since it allows for a considerable reduction of computational time. By including solvation effects and reevaluating the ES,min values, we find that the correlations improve significantly; accounting for piperidine solvation implicitly via PCM yields a R2 value


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of 0.869 (R2=0.790 for VS,loc). The effect of solvation highlights the stabilizing role of the solvent for the hydrogen bond donating substituents OH, NH2 and COOH. After inclusion of PCM solvation, the ES,min values of these compounds are shifted considerably towards lower predicted reactivities, as is ES,min of F. Piperidine has a rather low dielectric constant of ε=5.9. However, owing to the amine group the piperidine solvent is able to form directional interactions that effectively would yield an amplified local dielectric response compared to the solvent’s average response. Hence, in order to fully capture the effects of the piperidine solvent, its ability to form H-bonds with the solute has to be modeled explicitly. The OH, NH2 and COOH compounds are expected to form the strongest H-bonds amongst series 1. Adding explicit H-accepting piperidine solvent molecules in proximity to the aforementioned substituent R groups (and still also applying the PCM solvation) the obtained correlation is excellent, R2=0.977. (Note, furthermore, that inclusion of explicit solvent molecules for the non-hydrogen bonding compounds of series 1, e.g. I or Cl, does not significantly alter their corresponding descriptor values.) Apparently, the inclusion of solvent effects is very important for modeling the reactivity within this particular series of compounds. This explains the anomalies from the gas phase correlations and also the failure to describe the reaction by TS calculations in implicit solvation. Using explicit solvation in the TS calculations, the correlation is increased to R2=0.960. The above is consistent with previous reports regarding the importance of utilizing explicit solvent molecules in the modeling of SNAr reactions.62

Series 2-4 Over the next three series it is shown that besides being able to rank compound reactivity, the ES(r) descriptor is also well-suited for regioselectivity predictions. We find that ES(r) can successfully rank the various reactive sites for multiply fluorinated arenes, i.e. for cases where


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two or more SNAr active sites are present in the same compound. Compared to series 1, the sterical variations of the studied reaction sites are, however, large for the compounds of series 24. Combined with the later TSs owing to the F-/HF leaving group, we thus expect weaker overall reactivity correlations for these compounds compared to series 1. The series 2-4 (Figure 5) have recently been investigated in a theoretical study by Liljenberg et al.,63 with the exception of the augmented series 2’ that has been added in the present work. In the study by Liljenberg et al., very good correlations were found between ln k of experimentally determined reaction constants10–12,58 and the relative energies of the σ-adduct intermediate (referred to as the Nαvalue) at different sites. However, the procedure to determine the Nα-values is computationally demanding compared to evaluation of ES(r). Given e.g. an arene with three active sites, this compound would demand five geometry optimizations (one for each of the three possible intermediate σ-adducts as well as one each for the two reactants), whereas merely one optimization is sufficient for the E(r) descriptor. The performance of ES,min on the compounds of the non-augmented series 2 was reported recently, showing promising initial results.25


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Figure 5. Schematic representation of the compounds of series 2-4.

Most striking for the three series 2 (including 2’), 3 and 4 is that ES(r) is capable of correctly predicting the most active fluorine SNAr site and, where applicable, rank the second and third most active site with only two exception (compound 2o’ and 3g, where the difference in ES,min between the sites are within only 0.1 eV), see Table 2-4. As is illustrated by Figure 6, the most reactive sites can readily be determined from a map of E(r) on a molecular isodensity surface, i.e. ES(r).


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Figure 6. ES(r) mapped on the 0.004 a.u. isodensity surface of compound 4e. Coloring: Red < -1.4 eV < yellow < -1.1 eV < green. The experimental SNAr activity ordered as 4 > 2 > 3.58 ES,min ranks position 4 (ES,min= -1.52eV) as the most reactive followed by position 2 (-1.42eV) and lastly position 3 (-1.39eV).

As mentioned above, because of the F-/FH leaving group, the SNAr reactions of series 2-4 are expected to proceed via the two step addition-elimination mechanism, were the first step is usually rate-determining.2,3 Hence late transition states are anticipated for series 2-4 (since formation of the σ-adduct intermediate is endergonic), and thus the transition state geometry should be significantly shifted from the ground-state structure. Consequently the relatively weak correlations between ES,min and ln k for all series (see Figure 7 and Table 2-4) are not very surprising. However, it is noteworthy that for series 3 and 4 the discrepant entries are those with the reactive sites immediately adjacent to substituent groups other than fluorine. Groups like trifluoromethyl, cyanide and multiple chlorines are likely to create a dissimilar sterical environment than fluorine. These groups may also participate in the reactions via other throughspace (not reflected by the ES,min) rather than through-bond (accounted for in ES,min) interactions and will thus affect reactivity to a different degree. This is a clear difference compared to series 1, where the variations of the neighboring environment of the reactive sites were minimal over the series of compounds. By removing the affected entries from the trends in Figure 7 the correlations are increased from 0.66 and 0.68 to 0.96 and 0.95 for series 3 and 4 respectively.


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(Performing the same kind of exclusion on series 2 will not alter the correlation). The observed changes for series 3 and 4 addresses the inherent inability of E(r) to account for e.g. steric effects. If such effects are not corrected for by for instance a linear combination with Taft constants, as used in the Hammett-Taft relations,6–8 E(r) can only be used efficiently for comparison between compounds (and sites) with similar sterical surroundings. Nonetheless, when the contribution from neighboring groups are kept constant the ES,min values are capable of accurately reproducing reactivity trends for the series 2-4. Note, in addition, that the inclusion of solvent effects by means of PCM does not alter the correlations to any significant degree for these series.


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-1 -1

Figure 7. Logarithmized experimental reaction rate constants (k in mol s ) plotted against ES,min values at the site of reaction for the series 2-4 (including 2’). The outliers marked by full-black squares include the entries with dissimilar neighboring environments at the site of reaction. All reaction rates have been corrected for statistical factors where applicable.


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In comparison, ES,min values are performing as good as or better than the VS,loc for estimations of reactivity trends, except for series 2 (including 2’) where VS,loc gives a correlation with R2=0.908 compared to R2=0.828 for ES,min. However, although VS(r) shows a better correlation than ES(r) for this series, we must again point out that a significant drawback of VS(r) is the fact that local maxima cannot be identified at the sites of reaction. This is in stark contrast to ES(r)’s ability to locate reaction sites at each ring carbon, displayed e.g. in Figure 6. With respect to LUMO energies, ES,min performs much better for the series 2-4 (LUMO’s R2-values for series 2 including 2’, 3, and 4 are 0.396, 0.333 and 0.588 respectively). Compared to the Nα-values determined by Liljenberg et al.,63 the ES(r) descriptor is, however, incapable of reaching the same level of correlation. This may to some extent be attributed to the expected potential energy surface of the reaction with a late rate-determining TS. Since the intermediate σ-adduct, from which the Nα-values are determined, has a geometry that is structurally closer to the TS geometry than the ground-state structure on which ES(r) is computed, the better performance of Nα-values compared to ES(r) is sensible. In contrast, the Nα-values cannot be used for compounds like those in series 1 where the mechanism is concerted and no intermediate σadduct exists. Whereas Nα-values better describe reactions with late TS, ES(r) performs best for reactions with early TS. Hence ES(r) and Nα can in many aspects be seen as complementary descriptors.


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Table 2. Experimental reaction data and descriptor values for series 2 (including 2’).

Posi-

Site prea,b)

Vs,loc

d)

dictione)

tion

ln k

2a

2

-13.38 -1.51

38.82

correct

2b

6

-12.04 -1.5

36.01

correct

2c

eq.

-9.89

-1.82

44.27

n.a.

2d

4

-7.29

-2.27

42.75

correct

2e

4

-6.26

-2.11

41.76

correct

2f

4

-3.68

-2.57

48.30

correct

2g(4)

4

-2.94

-2.26

46.98

correct

2g(6)

6

-3.63

-2.2

45.80

correct

2h(2)

2

0.27

-2.41

50.13

correct

2h(4)

4

1.22

-2.73

50.67

correct

2i

4

0.30

-2.37

48.76

correct

2j’(2)

2

-15.42 -1.11

31.35

correct

2j’(4)

4

-14.17 -1.20

31.86

correct

2k’

2

-5.35

-1.98

41.29

correct

2l’(4)

4

-10.72 -1.78

37.98

correct

2l’(6)

6

-12.05 -1.25

34.93

correct

2m’

4

-10.44 -1.89

37.59

correct

2n’

4

-7.25

-2.16

41.85

correct

2o’(2)

2

-10.10 -1.48

38.01

incorrect

2o’(6)

5

-12.23 -1.58

38.39

incorrect

2p’

eq.

-8.95

-1.54

38.20

n.a.

2q’

4

-7.34

-2.05

41.12

correct

2r’

eq.

6.52

-2.73

56.75

n.a.

R2 f)

0.828

0.908

2 f)

0.786 2.373

0.894 1.730

Q SE f)

Es,min

c)

a)

All reaction rates have been corrected for statistical factors where applicable, b) rate constants in mol-1s-1, c) eV, d) kcal mol-1, e) only SNAr sites included, f) versus ln k.


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Table 3. Experimental reaction data and descriptor values for series 3.

Posi-

Site prea,b)

Es,min

c)

Vs,loc

d)

dictione)

tion

ln k

3a

4

-11.42 -1.68

34.26

correct

3b

eq.

-11.31 -1.93

41.38

n.a.

3c

4

-9.9

36.63

correct

3d

eq.

-9.49

-2.34

47.63

n.a.

3e

4

-9.04

-2.12

42.81

correct

3f

4

-8.29

-2.18

43.06

correct

3g

4

-6.61

-2.37

53.53

incorrectf)

-1.85

R2 g)

0.659 0.648 (0.960)h) (0.935)h)

Q2 g)

0.289

0.371 h)

SE g)

(0.897)

(0.761)h)

1.081

1.098 h)

(0.415) (0.528)h) All reaction rates have been corrected for statistical factors where applicable, b) rate constants in mol-1s-1, c) eV, d) kcal mol-1, e) only SNAr sites included, f) the correct site has a Es,min of 0.05eV higher, g) versus ln k, h)obtained after exclusion of sites with sterical discrepancies. a)


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Table 4. Experimental reaction data and descriptor values for series 4.

Posi-

Site prea,b)

Es,min

c)

Vs,loc

d)

dictione)

tion

ln k

4a

eq.

-19.81 -0.83

25.23

n.a.

4b

2

-14.73 -1.12

25.78

correct

4c

1

-13.63 -1.09

26.44

correct

4d(3)

3

-13.12 -1.17

30.09

correct

4d(1)

1

-9.2

-1.49

31.23

correct

4e(2)

2

-8.8

-1.42

33.73

correct

4e(3)

3

-9.85

-1.39

32.51

correct

4e(4)

4

-5.98

-1.52

33.43

correct

4f

eq.

-9.49

-1.48

34.24

n.a.

4g

-5.71

-1.26

30.81

n.a.

4h

one site eq.

-5.34

-1.33

31.7

n.a.

4i

4

-5.24

-1.45

33.79

correct

4j

eq.

-4.99

-1.4

32.6

n.a.

R2 f)

0.685 0.667 (0.944)g) (0.786)g)

Q2 f)

0.584

0.520 g)

SEf)

(0.901)

(0.593)g)

2.658

2.731 g)

(1.044) (2.041)g) a) All reaction rates have been corrected for statistical factors where applicable, b) rate constants in mol-1s-1, c) eV, d) kcal mol-1, e) only SNAr sites included, f) versus ln k, g) obtained after exclusion of sites with sterical discrepancies.

VNS The lowest ES,min on the arenes of series 1-4 does typically not correspond to a SNAr active site. Instead the lowest ES,min is in most cases found at a ring carbon attached to hydrogen (see e.g. Figure 1). This indicates that hydrogen substituted carbons are more electron deficient (i.e. more electrophilic) than e.g. halide substituted carbons, consistent with experimental findings.4 As pointed out in the introduction, nucleophilic attack at the hydrogen-substituted carbons does not lead to a product unless special nucleophiles are used. This is why the SNAr type of reaction is often the prevalent reaction. Under beneficial condition, the carbons with H substituents can, however, react in the VNS type of reactions. In the series 5 and 6, the reactivity at hydrogensubstituted carbon sites is explored by employing the ES(r) descriptor on two series of VNS


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active arenes. Both of the VNS series follow the general mechanism presented in the lower route of the scheme in Figure 1, with the α-halocarbanion of chloromethyl phenyl sulfone as nucleophile and HCl as leaving group.14,57

Series 5 In series 5 (inset of Figure 9) each compound has two possible, non-equivalent, sites for the VNS reaction (three sites for the H compound): The para positions with respect to the activating nitro group are blocked by the various substituents, thus leaving only the ortho and, in theory, meta positions free to react (for H the para position will also react). Experimentally it is found that the ortho positions are the preferred reaction sites, while the meta positions are non-active.57 In the case of the H substituent the para site is also active in VNS. Interestingly both experiments and computations have, however, identified an ortho directing effect of the nitro group thus yielding the ortho product in some excess over para.35,64 The TS structures of the ortho and para addition to H are shown in Figure 8. These demonstrate that the neighboring nitro group interacts with the nucleophile upon ortho but not para addition, thus allowing for a stabilizing effect of NO2 on the ortho TS. Over series 5 the sterical and neighboring group variations are negligible, owing to the relatively large distance between the active ortho site and the para substituents.

Figure 8. Displays the ortho and para TS structure for VNS addition of the chloromethyl phenyl sulfone carbanion nucleophile to the H compound of series 5 optimized in gas phase at the M06-2X/6-31+(d,p) level of theory. The 0.004 a.u. isodensity contours


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Page 28 of 36

are included to demonstrate the interaction (ortho) and lack of interaction (para) of the nitro group with the nucleophile in the TS. Distances are given in Å.

The good correlation (R2=0.909) between ES,min and ln krel (Figure 9 and Table 5) demonstrates that ES,min can well be used for predictions of relative reactivity also in VNS reactions. While the LUMO energies has a weak correlation (R2=0.737), the prediction from VS,loc is of similar accuracy (R2=0.910) as ES,min in this case, suggesting electrostatics to be important for the formation of the σH-adduct. Note again that no local maxima in VS(r) could be located at the active sites. We also note that the inclusion of solvation effects does not alter the trends significantly.

Figure 9. Correlation trend between experimental data and ES,min values at the site of reaction for series 5 (inset), R=H, OMe, F, Cl, Br, I, CF3, OPh, SMe, SPh, CN, i-Pr, t-Bu, COOiPr.

In the original study of the compounds of series 5, the kinetic data was compared to the Hammett σm constants (see Figure 1 in ref. 57) of the R group. In that comparison, the compounds cCOOC2H5 and SPh were excluded and the R2-correlation between the σm constant and experimental data (ln krel) was determined to 0.89.57 By excluding the mentioned compounds in the ES(r) evaluation the corresponding correlation is 0.91. Obviously ES,min has the potential to


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be used as a substitute for Hammett constants. This would be especially useful for cases where Hammett constants are not available, for instance for previously undocumented or short-lived compounds. We have also found that ES,min and the Hammett constants are complementary to some degree. This is exemplified by the fact that by forming a multi-linear regression, ln krel(predicted) = 6.261σm – 6.826ES,min – 9.422, a R2-value of 0.955 is obtained for the correlation with the experimental ln krel for the VNS reaction. Table 5. Reactivity data and descriptor values for series 5 at the ortho position with respect to the NO2 substituent.

R=

ln krela)

ES,minb,c)

VS,locc,d,e)

Br Cl

4.98 4.83

-1.71 -1.71

17.85 18.12

COOiPr

2.71

-1.4

14.78

H OMe

0.00 -0.12

-1.4 -1.4

12.64 11.69

SMe CF3

2.4 6.46

-1.43 -1.81

12.32 21.14

CN i-Pr

6.96 -1.24

-1.9 -1.3

24.44 10.28

OPh

0.99

-1.39

11.49

t-Bu F

-1.02 3.91

-1.27 -1.72

9.84 17.99

I cC3O2H5

3.78 -0.08

-1.67 -1.32

18.01 11.02

SPh

2.48

-1.58

16.9

0.909

0.910

R2 f) 2 f)

Q 0.885 0.876 0.835 0.829 SE f) a) Relative to R=H, reaction rates from ref. 57, b) eV, c) obtained in gas-phase, d) kcal mol-1, e) no VS,max could be established at the reactive sites, h) versus ln krel.

Series 6 It has been demonstrated that a variety of compounds can be studied with ES(r). In series 6 it is shown that the reactivity probe is not only useful for comparisons of reactions within well-


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Page 30 of 36

defined families of compounds, but also for rather dissimilar molecules reacting via the same mechanism. The compounds of series 6 (Figure 10) were studied experimentally by Seeliger et al,14 and contains nine N-hetero nitroarenes of different ring sizes with varied numbers and positions of the nitrogen heteroatoms. As for series 5, a clear ortho directing effect of the nitro group has been reported for series 6.14

Figure 10. Schematic representation of the compounds of series 6.

Figure 11. Experimental rate constants plotted against ES,min values for series 6.


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Despite the vast mix of compounds included in series 6, ES,min values are able to nicely reproduce the experientially determined reactivity trends. The correlation between ln krel and ES,min has a R2-value of 0.941 and a standard error of only 0.98. This correlation is much stronger than that of the LUMO energies (R2=0.590) and the local VS,loc (0.573), see Table 6. In Figure 11 the ln krel of the compounds is plotted against ES,min and only slight variations from the estimated reaction trend is observed; one can identify compounds 6f, 6h and 6i as minor outliers, possibly also including entry 6c(2). The three former compounds can be considered to react at sterically more hindered sites (due to the methyl group of the adjacent nitrogen) than the rest of series 6. It is moreover clear from e.g. Figure 8 that the chloromethyl phenyl sulfone carbanion nucleophile addition not only gives rise to interactions at the site of reaction but also interacts with neighboring groups. For series 6, neighboring methyl and nitro groups as well as the Nheteroatom of the ring may form interactions with the nucleophile during the course of reaction. This may explain why the expected reactivities (based on the ES,min values) slightly deviates from the experimental values. However, these deviations may well fall within the range of experimental errors and the inherent errors of the applied DFT method.


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Table 6. Reaction rates and descriptor values for the series 6 compounds.

Position ln krela) ES,min b) VS,locc,d) 6a

2 4

8.70 -1.72 11.18 -2.18

21.38 23.77

6b 6c

4 2

11.37 -2.31 5.80 -1.64

28.06 16.46

6

6.51

-1.49

16.75

6d 6e

6 3

9.74 0.00

-1.95 -0.73

19.23 2.26

6f 6g

2 2

1.61 2.20

-1.08 -1.08

11.70 11.30

6h

4 5

2.20 6.31

-0.96 -1.40

22.30 18.28

6i

5

4.53

-1.55

22.66

0.941

0.573

R2 e) 2 e)

0.924 0.429 Q 0.983 2.640 SE e) a) from ref. 14, b) eV, c) kcal mol-1, d) no VS,max could be found at the site of reaction, e) versus ln krel.

Conclusion It is herein established that the DFT based surface local electron attachment energy [ES(r)] descriptor is a useful tool for reactivity predictions for the nucleophilic aromatic substitution reactions of SNAr and VNS. Experimental reactivity trends have been reproduced with good to excellent correlations for six series of congeneric compounds, including reactions with different solvents, temperatures, nucleophiles and leaving groups. Remarkably, such diverse sets of compounds as those of e.g. series 2 and 6, including homo- and heteroaromatic species of different ring sizes, can be accurately described by ES(r). It has, furthermore, been demonstrated that ES(r) is an efficient tool for estimation of regioselectivities, as long as the variations in the neighboring environment are small.


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In the present study it is shown that the ES(r) readily outperforms LUMO for electrophilicity estimations. ES(r) is also found to be overall more reliable than the electrostatic surface potential, VS(r), this since ES(r) in general gives stronger correlations but also because ES(r) is able to locate the reactive sites, whereas VS(r) fails in the majority of the considered cases. For the case of concerted SNAr reactions, the ES(r) descriptor has, furthermore, been found to be a valid substitute to elaborate transition state calculations and hence offers an inexpensive alternative. Considering the descriptors low computational cost and its accuracy, it is anticipated to find uses in large reactivity screenings, in e.g. drug discovery or toxicological studies, but also for general studies of various types of electron accepting chemical reactions and interactions.

Acknowledgment J.H.S. gratefully acknowledge funding from the Excellence award of the School of Chemical Science and Engineering at KTH Royal Institute of Technology. Supporting Information. Coordinates of optimized structures and corresponding energies, as well as ES,min values of ring position 3 and 5 of the series 1 compounds.

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