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Brinck, T., Carlqvist, P., Halldin Stenlid, J. (2016)Local Electron Attachment Energy and Its Use for Predicting Nucleophilic Reactions andHalogen Bonding.JOURNAL OF PHYSICAL CHEMISTRY A, 120(50): 10023-10032https://doi.org/10.1021/acs.jpca.6b10142

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Local Electron Attachment Energy and Its Use for PredictingNucleophilic Reactions and Halogen BondingTore Brinck,* Peter Carlqvist,† and Joakim H. Stenlid

Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, SE-100 44Stockholm, Sweden

*S Supporting Information

ABSTRACT: A new local property, the local electronattachment energy [E(r)], is introduced and is demonstratedto be a useful guide to predict intermolecular interactions andchemical reactivity. The E(r) is analogous to the average localionization energy but indicates susceptibility toward inter-actions with nucleophiles rather than electrophiles. Thefunctional form E(r) is motivated based on Janak’s theoremand the piecewise linear energy dependence of electronaddition to atomic and molecular systems. Within thegeneralized Kohn−Sham method (GKS-DFT), only the virtualorbitals with negative eigenvalues contribute to E(r). In thepresent study, E(r) has been computed from orbitals obtainedfrom GKS-DFT computations with a hybrid exchange-correlation functional. It is shown that E(r) computed on a molecular isodensity surface, ES(r), reflects the regioselectivityand relative reactivity for nucleophilic aromatic substitution, nucleophilic addition to activated double bonds, and formation ofhalogen bonds. Good to excellent correlations between experimental or theoretical measures of interaction strengths and minimain ES(r) (ES,min) are demonstrated.

■ INTRODUCTIONLocal molecular properties computed onmolecular surfaces havebeen used extensively to analyze and predict intermolecularinteractions and chemical reactivity.1−8 The molecular electro-static potential [V(r)] has been the dominating property in suchanalysis, and the predictive power of the surface V(r) [labeledVS(r)] for noncovalent interactions, such as hydrogen bondingand halogen bonding, is well documented.6,9−15 One limitationof VS(r) is that it only reflects the susceptibility towardelectrostatic interaction, and thus it is less well suited to analyzethe propensity for interactions that involve a significant degree ofredistribution of the charge densities of the interacting species,such as donor−acceptor interactions and the formation ofcovalent bonds. To increase the applicability of the local surfaceproperty approach, Sjoberg et al. devised the average localionization energy [I(̅r)] as a complement to V(r) for analyzingsusceptibility toward electrophilic attack.2 The I(̅r) is rigorouslydefined within Hartree−Fock (HF) theory and Kohn−Shamdensity functional theory (KS-DFT) by

ε ρρ̅ =

∑ −I r

rr

( )( )

( )i i iocc

(1)

where εi is the energy of orbital i, ρi(r) is the density of the orbital,and ρ(r) is the total electron density. According to Koopman’stheorem,16 the absolute values of the orbital energies areapproximations to the ionization energies, and I(̅r) can beinterpreted as the average energy needed to ionize an electron at

a point r in the space of a molecule or atom. Bulat et al. haveshown that I(̅r) is invariant to an unitary orbital transformationand that I(̅r) can be written as a function of the local electrontemperature [T(r)],V(r), and the exchange-correlation potential[VXC(r)]. (In the case of a HF determinant, VXC(r) equals theSlater potential.)17

̅ = − + −I kT V Vr r r r( ) 32

( ) ( ) ( )XC (2)

The contribution of kT(r) is particularly interesting because itshows that I(̅r) depends not only on the local potential felt by anelectron at r but also on the local kinetic energy density, that is,3kT(r)/2 = tS(r)/ρ(r), where tS(r) is the local kinetic energydensity and is obtained as tS(r) = −1/2∑ioccψi*(r)∇2ψi(r).17For the purpose of analyzing chemical reactivity, I(̅r) is

normally computed on molecular surfaces defined by a constantelectron density and is then labeled IS̅(r). On such a surface, thedenominator in eq 1 is constant, and IS̅(r) reflects the varyingease of ionization over the surface. The positions where IS̅(r) hasits lowest values, the local surface minima (IS̅,min), are indicativeof sites that are prone to interact with electrophiles. In contrastwith VS(r), IS̅(r) has been found to reflect a molecule’s tendencynot only for electrostatic interaction but also for charge transfer

Received: October 7, 2016Revised: November 24, 2016Published: November 29, 2016

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and polarization.5,8,11 IS̅(r) has been shown to be particularlywell-suited to describe reactivity toward electrophiles in solution,where electrostatic interactions are partly shielded and theirimportance is reduced. For example, IS̅(r) is an effective tool forthe prediction of regioselectivity and relative reactivity ofaromatic substrates toward electrophilic aromatic substitu-tion.2,18−20 Another use of IS̅(r) has been in the analysis ofaqueous basicity; the most basic sites in neutral molecules andanions generally have associated IS̅,min, and the IS̅,min values oftencorrelate well with the pKa values of the conjugate acids withinseries of congeneric molecules.5,18,21

In contrast with the VS(r), which attains both negative andpositive values, IS̅(r) cannot be used to characterize susceptibilityfor nucleophilic attack. In an attempt to develop a correspondingsurface property to IS̅(r) for interactions with nucleophiles, Clarkand coworkers defined the local electron affinity [EAL(r)] usingan analogous expression in terms of the virtual orbitals.7,22

ε ρρ

=∑ −

∑=

=EA r

r

r( )

( )

( )i i i

i iL

LUMOnorbs

LUMOnorbs

(3)

The use of the virtual orbital energies for estimating electronaffinities can be justified by Koopman’s theorem, although thereis no error cancellation between orbital relaxation and electroncorrelation effects, as is typical for ionization energies. However,there are other issues with EAL(r) that need to be considered.First of all, it can be noted that EAL(r) is very sensitive to the sizeof the basis set, as the number of virtual orbitals and their energiesdepend on the number and type of basis functions. Clark hasmostly used EAL(r) together with semiempirical methods, andbecause these generally employ a minimum basis set descriptionthe basis set issue is less severe. To use semiemprical methodswith an explicit d orbital description, he has devised a method toidentify which orbitals to include when computing EAL(r) with anonminimal basis set.22 However, even when using a virtualorbital space corresponding to only the valence orbitals, high-energy orbitals, which have little influence on the reactivity, cancontribute significantly to the EAL(r). For example, an EAL(r)analysis of an aromatic system typically finds the aromaticcarbons to be relatively unreactive due to the contributions ofhigh-energy virtual σ* orbitals.Another problemwith EAL(r) as a local surface property is that

the denominator in eq 3 is defined by the virtual orbital densityand thus varies over an isodensity surface. The susceptibility forelectrophilic attack depends not only on the energies of low-lyingvirtual orbitals but also on the magnitude of their combineddensities. However, with the current expression (eq 3), regionswith low total virtual orbital density are often identified as highlyreactive.It should be recognized that EAL(r) has successfully been used

in a number of applications, including as a descriptor in QSARanalysis for drug design and for the calculation of charge-transport properties of organic-field transistors.23−25 On thecontrary, the use of EAL(r) in the analysis of chemical reactivityhas been relatively sparse, which potentially can be traced tosome of the issues discussed above.The objective of the current work has been to define a new

local surface property that is tuned for predicting chemicalreactivity and intermolecular interactions and that is well-behaved with large basis sets and more exact KS-DFT methods.We will introduce the local electron attachment energy, E(r),which can be seen as a local reactivity descriptor. The capacity ofthe surface E(r), labeled as ES(r), for predicting the local and

global reactivities for a number of chemical systems that interactwith nucleophiles in various interaction types has been analyzed.As will be shown, ES(r) has a predictive capacity that iscomparable to IS̅(r) for the corresponding processes withelectrophiles, and ES(r) is found to provide information that inmany cases is complementary to VS(r).

■ THEORYIn a first effort to modify EAL(r) and to obtain a local propertythat more closely corresponds to the I(̅r), we have defined theexpression

ε ρρ=

∑ −ε=<

EE

rr

r( )

( ) ( )( )

E iE

i iLUMO 0i

0

0

(4)

The first difference compared to EAL(r), is that the denominatoris defined by the ground state density rather than the virtualorbital density as in eq 3. This definition is connected to theintended use of EE0(r) as a local surface property. The use ofsurface properties for analyzing chemical reactivity is based onthe assumption that the short-range repulsive potential, whichdepends on electron−electron interactions, is nearly constantover an isodensity surface; thus the varying reactivity over thesurface will be defined by the variations in the attractive potentialexpressed by the local property. To fulfill this criterion, thedenominator needs to be constant at constant ρ(r), such thatEE0(r) at each point on the surface has an energy contribution (εi− E0) from orbital i that is proportional to the orbital density atthat point. Using a denominator that is a summation of thedensities of the contributing virtual orbitals, as in eq 3, willsignificantly reduce the regioselectivity information that isprovided by the local property; this is particularly obvious ifonly one virtual orbital contributes, since the value of the localproperty then will be the same everywhere.The second difference is the introduction of the energy offset,

E0, such that only orbitals with an energy lower than this value areconsidered. This is not a cutoff in the normal sense, as thecontribution from an orbital to the overall EE0(r) value smoothlyapproaches zero as εi approaches E0. The need for an energycriterion for selecting the active orbitals is obvious, as only thelowest-lying virtual orbitals are expected to contribute to thereactivity and accept electron transfer from donor orbitals. Atfirst glance the selection of the E0 value is more difficult. After all,virtual orbital energies are strongly method-dependent; forexample, virtual orbital energies obtained by HF are generallymuch more positive than those obtained with KS-DFT using alocal density approximation (LDA). Rather than attempting tooptimize a method-dependent E0, we will first determine the besttheoretical value at the most exact DFT level.The starting point for the derivation of E0 will be Janak’s

theorem, which states that the derivative of the total energy withrespect to the orbital occupancy is equal to the correspondingorbital energy.26

ε∂∂ =Eni

i(5)

This theorem holds for a local exchange correlation potential aswell as for a nonlocal potential in the case of the generalizedKohn−Sham (GKS-DFT)method; that is, it is applicable to localLDA as well as hybrid methods, invoking HF exchange and evenregular HF.27,28 The theorem shows that only virtual orbitalswith a negative orbital energy will bind a fractional electron,Δni,28 and that the binding energy is Δniεi when Δni is infinitely

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small. Furthermore, it is known that the exact energy as afunction of fractional electron occupancy is always linearbetween integer electron occupancies for any atomic ormolecular system.27,29 This criterion is normally not fulfilledfor approximate DFT methods, and LDA and GGA methodstypically give convex curves, whereas the HF curve isconcave.27,29 However, for an exact GKS-DFT method thatfulfills the linearity criterion, the energy change upon theaddition of a fractional electron is given by

ε+ Δ − = ΔE M N E M N( ) ( ) LUMO (6)and the electron affinity EA = −εLUMO.27,28 We can expect thatsuch a method that provides accurate electron affinities andenergies of charge-transfer interactions will provide reliableenergies for fractional addition to other orbitals as well by thegeneral formula

ε+ Δ − = ΔE M n E M n( ) ( )i i i (7)Summarizing the findings above, it is clear that the optimal valuefor E0 is zero at the exact GKS level. (In the case of an optimizedeffective Kohn−Sham potential (OEP), −EA = εLUMO +ΔXC,27,30 and thus E0 = −ΔXC, where ΔXC is the derivativediscontinuity.) Setting E0 to zero means that only virtual orbitalswith negative eigenvalues are considered, and eq 4 is reduced to

ε ρρ=

∑ε=<

E rr

r( )

( )( )

i i iLUMO0i

(8)

We will hereafter refer to this quantity E(r) as the local electronattachment energy. The choice of E0 value has the addedadvantage when used together with an exact GKS-DFT methodthat E(r) becomes less sensitive to the size and diffuseness of thebasis set. When adding diffuse functions to a basis set, these willcombine to form virtual orbitals that represent free unboundelectrons. However, at the exact GKS-DFT level, these orbitalsalways have eigenvalues that are equal to or greater than zeroeven at the infinite basis set limit. Thus they will never contributeto E(r).In practical applications it is necessary to use an approximate

GKS-DFT method. On the basis of the discussion above onJanak’s theorem and the linear energy dependence uponfractional electron addition, we will argue that a standard hybriddensity functional method, such as B3LYP or PBE0, that typicallyincludes 20−25% HF exchange is a suitable choice. Thesemethods generally provide accurate thermochemistry andkinetics for main group chemistry, including donor−acceptorinteractions that involve intermolecular charge transfer.31 Theyare also good at reproducing experimental electron affinities.31

Furthermore, the energy dependence upon fractional electronaddition is closer to linear than with the pure generalized gradientapproximation (GGA) or LDA functionals.29 Another obviouschoice would be a functional that includes 100% long-range HFexchange, such as long-range corrected GGA or double hybridfunctionals. However, the orbital energies are rather sensitive tothe choice of shifting parameters, and the optimum parametersare system-dependent.32,33We have found that functionals of thistype generally result in a larger energy difference between theLUMO and the LUMO+1 orbital than is obtained with thestandard hybrid functionals. Our limited tests indicate that thelarge LUMO−LUMO+1 gaps reduce the regioselectivityinformation provided by E(r). Although there is a risk that thestandard hybrid functionals provide orbital energies that areslightly shifted to too low values, this is not likely to have large

effects on E(r); due to the functional form of eq 8, the mostnegative virtual orbitals will dominate E(r), and higher virtualorbitals with energies that are negative but close to zero will havesmall impact as long as they are few and not very localized.Following the derivation of eq 2,17 E(r) can be divided into

different components,

∑ ∑

∑ρ ρ

ρ

= −

+

ε ε

ε=

<

=

<

=

<

E t V

V

rr

r r r

r r

( ) 1( )

[ ( ) ( ) ( )

( ) ( )]

ii

ii

ii

LUMO

0

LUMO

0

XCLUMO

0

i i

i

(9)

where ti(r) is the local kinetic energy density of orbital i, hereindefined as ti(r) =−1/2ψi*(r)∇2ψi(r). The ti(r) component is theonly one that directly depends on the functional forms of thevirtual orbitals. The electrostatic potential [V(r)] and the Kohn−Sham potential [VXC(r)] are defined solely by the occupiedorbitals and the external potential, but the scaling of theircontributions is proportional to the sum of the densities of thecontributing virtual orbitals. Because of the often large variationsof V(r) over a molecular isodensity surface, V(r) has a largeinfluence on the regioselective information provided by E(r).TheVXC(r), on the contrary, is nearly constant over an isodensitysurface and is thus likely to be less influential.It should be noted that we have argued for the functional form

of eq 8 based on Janak’s theorem and the piecewise linear energydependence of fractional electron addition and without invokingconcepts from conceptual DFT. However, it can be shown thatfor some simple molecular systems that E(r) provides similarinformation as the Fukui function for nucleophilic attack, f+(r),when the latter is approximated by ρLUMO(r) within the frozenorbital approximation. In most smaller organic molecules that arenonconjugated the LUMO is the only virtual orbital with asignificant negative eigenvalue. In such systems

ρρ ε ρ≃ ≃

− +E

fEAr

rr

rr

( )2 ( )

( )2 ( )

( )LUMO

LUMO(10)

Thus E(r) entails similar regioselectivity information as f+(r)when both are analyzed on an isodensity surface of a smallmolecule with positive EA. However, E(r) may be better thanf+(r) alone for quantifying the difference in global reactivitybetween systems due to the multiplication of f +(r) by EA in eq10. In addition, E(r) is likely to be more versatile than f+(r) indescribing the reactivity of complex systems. The latter approachhas problems describing systems with degenerate or near-degenerate LUMO and LUMO+1 orbitals. As exemplified inFigure 1, the reactivity of a system with two π regions (2n)separated by a σ region cannot be compared directly to that of asingle π-region system (1). When the length of the σ regionincreases (n increases), the reactivity of each π region in 2n isexpected to converge to the reactivity of the π region in 1. As

Figure 1.Two systems of different size but with similar reactivity of the πregions at large n. The surface E(r) at the π region (CCCO) of 1differs by

shown in Table S1 in the Supporting Information, E(r) correctlypredicts this behavior, whereas f+(r) of 2n converges to 0.5f

+(r) of1. It can be argued that f+(r) should be renormalized for large nwhen LUMO and LUMO+1 are close to degenerate. However,this will not solve the size-consistency problem entirely, as f+(r)will make a discontinuous jump at the n for which the energydifference between the two orbitals becomes below the definedtolerance.It is also known that frontier orbital descriptions do not always

provide a complete reactivity picture in systems, such as aromaticmolecules, where there are several π- or π*-orbitals close inenergy. This has been recognized by Langenaeker et al.34 andAndersson et al.35 Since IS̅(r), which use a similar orbitalexpansion as E(r), is more effective than the ρHOMO(r) forelectrophilic attack on aromatic systems,20 we anticipate thatE(r) may be more successful than ρLUMO(r) for nucleophilicattack in aromatic systems. The validity of this assumption hasbeen investigated in the current study. There are also potentialadvantages of E(r) compared to a frontier orbital description insystems where there are a both low-lying σ* and π* orbitals. Insuch a system, the LUMO has to be of either type, and cannotdescribe the reactivity of the other. It can be expected that E(r)should be able to predict reactivity also in very large systems withmultiple interaction sites, like a protein, or systems with nearinfinite size and a band structure, like a semiconductor. We evensee the potential to use E(r) in connection with periodicboundary conditions to treat infinite systems.In the following study, we have analyzed the potential of E(r)

computed on an isodensity surface [ES(r)] to predict thepropensity for nucleophilic attack in a variety of systems and inrelation to different types of reactions and intermolecularinteractions. To evaluate the predictive capacity of ES(r), wewill compare the positional selectivity obtained by ES(r) to thatof ρLUMO(r) and the global reactivity to the εLUMO and Parr’selectrophilicity index, ω.36 The latter is defined by

ω μη=2

(11)

where μ is the electronic chemical potential and η is the absolutehardness, and they are given by μ = (εLUMO + εHOMO)/2 and η =(εLUMO − εHOMO)/2 in the frozen orbital approximation.36 Thereason for the comparison withω is not to determine which is thebetter electrophilicity descriptor but rather to investigate theeffects of going beyond a frontier orbital description, and thereby

justify the introduction of ES(r) as a complementary tool foranalysis and prediction of interactions with nucleophiles.

■ COMPUTATIONAL METHODSMolecular geometries were optimized and characterized byharmonic frequency analysis at the B3LYP/6-31G* level. Single-point calculations were performed to obtain the occupied andvirtual orbitals at the B3LYP/6-31+G(d,p) level. This level oftheory generally provides virtual orbitals that work well togetherwith eq 8. All KS-DFT computations were performed using theGaussian 09 suite of programs.37

ES(r) and VS(r) were computed on molecular isodensitysurfaces using a modified version of the HS95 programdeveloped by one of the authors (T. Brinck). In previousapplications of the surface property approach, it has beencommon to compute VS(r) or IS̅(r) at molecular surfaces definedby the 0.002 or 0.001 au contours of the electron density. Thesesurfaces encompass 95−98% of a molecules electron density andtypically lie outside of the van der Waals radii of the constitutingatoms.8 However, in using ES(r), we have found generally betteragreements with experimental measures of local reactivity if aslightly higher density value, that is, 0.004 au, is used to define thesurface. A possible explanation for this result is that ES(r) in mostinstances has been used to model interactions that are strongerand more short-ranged than van der Waals interactions.Graphical visualization of surface properties and orbital densitieshas been performed using the UCSF Chimera package.38 Thepositions and magnitudes of local surface minima have beendetermined using a numerical procedure implemented in theHS95 program. The results are in agreement with those obtainedusing an alternative procedure by Bulat et al. that is implementedin the WFA-program.8

Linear regression has been used to analyze correlationsbetween computed descriptors and experimental rate constantsor computed interaction energies. The statistical significance ofthe correlations has been analyzed in terms of correlationcoefficients (R2) and standard errors (SEs). We have alsocomputed the cross-validated correlation coefficient (Q2) bymeans of the leave-one-out procedure.39 A detailed account ofthe results from the statistical analysis is found in SupportingInformation.

Figure 2. (a) Computed ES(r) of pentafluoronitrobenzene (C6F5NO2) at the 0.004 au isodensity surface. Color ranges for ES(r) in eV: red < −2.05,−2.05 < yellow −1.10. (b) LUMO of C6F5NO2. (c) Computed VS(r) of C6F5NO2 at the 0.001 au isodensity surface. Color rangesfor VS(r) in kcal/mol: red > 25, 15 < yellow < 25, −10 < green < 15, −20 < cyan < −10, and blue < −20.



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■ RESULTS AND DISCUSSIONNucleophilic Aromatic Substitution. Figure 2 a shows

ES(r) of pentafluoronitro-benzene. The regions of lowest ES(r)are found over the π-bonds, where also the π*-densities areexpected to be highest. The lowest ES,min are located over orthoand para positions, and their values are −2.11 eV and −2.21 eV,respectively. Due to the C2-symmetry of the molecule, there isalso a second unique ES,min at the ortho positions, with a value of−2.00 eV. The ES,min over the meta positions are significantlyhigher, −1.88 and −1.83 eV. These results give a picture that isconsistent with the experimentally observed ortho-para position-al selectivity of perfluoronitrobenzene in nucleophilic aromaticsubstitution (SNAr) reactions.

40 There is also a relatively lowES,min (−2.06 eV) over the nitrogen, indicating this to be anotherpotential site for nucleophilic attack. Much higher ES,min arefound over the oxygens and fluorines. Their values are in theranges −1.64 to −1.65 and −0.30 to −0.36 eV, respectively. Thelatter are indicative of the fluorine σ* orbitals.Four virtual π* orbitals with negative eigenvalues of −3.50,

−1.84, −1.78, and −1.64 eV contribute to ES(r). This gives agood representation of the electron accepting tendencies and thesusceptibility for nucleophilic attack in this molecule. It can benoted that an analysis of the LUMO, as shown in Figure 2b,provides less information. The LUMO has lobes over the C−Nbond, the nitro oxygens, the ortho-meta C−C bond, and the paracarbon with sizes that decrease in the same order. Thus, theortho-para SNAr positional selectivity is less obvious from theLUMO. Also, the VS(r), shown in Figure 2c, gives a very differentpicture of the nucleophilic reactivity than ES(r). Here the mostpositive VS(r) regions are over the C−N bond and in the centerof the aromatic ring.The good agreement between the SNAr regioselectivity and

the magnitude of the ES,min prompted us to investigate whetherthe ES,min correlates with the relative SNAr reactivities ofcongeners of aromatic substrates. In Table 1, we list the ES,minand experimental rate constants (k)41,42 for the amination of ninefluorine-substituted heteroaromatics, mostly pyridines (seeFigure 3 for structures). In all cases, the lowest ES,min is foundover the carbon that corresponds to the positionally preferredsite for SNAr. For two of the substrates, there is a productdistribution between two isomers, and the individual rateconstants for forming the isomers have been determined. Inthese cases, the second lowest ES,min is found at the positionleading to the minor isomer.There is a linear correlation between the experimental ln k

values and ES,min with a coefficient of determination (R2) of 0.81,

as shown in Figure 3. The R2 value improves to 0.86 if only thereactivity at the most favored reaction site (highest ln k) of eachsystem is considered. The correlations clearly indicate that ES(r)reflects the susceptibility for SNAr in these systems. Thecorrelations are not as good as those that have been obtainedbetween ln k and IS̅,min for electrophilic aromatic substitution(SEAr).

20 This is not surprising considering that this type of SNArreactions have a late transition state that is close in structure tothe product, that is, the sigma-complex, of the rate-determiningstep.43 In contrast, SEAr reactions, and particularly nitrations,have an early transition state that resembles the reaction complexin structure.44 We have also shown that the computed relativesigma-complex (Meisenheimer complex) energies of SNAr withfluorine as nucleofuge correlate very well with the relative rateconstants.43 However, this requires proper consideration ofsolvation effects to obtain stable sigma complexes. Thus, in this

context, it is remarkable that an approach, such as ES(r), that isbased solely on characterization of the isolated reactant in the gasphase, can provide estimates of relative reactivity and positionalselectivity. For comparison, it can be noted that there is nosignificant correlation between ln k of the favored reaction andωfor this reaction series, R2 = 0.12. The correlation between ln kand εLUMO is of similar quality, R

2 = 0.11. We are expecting thatES(r) will work even better for predicting reactivities of SNArwith chlorine or bromine as nucleofuges, since we have foundthese reactions to be concerted with an early transition state thatresembles the reactant in structure.45 This will be a focus of afuture study.

Nucleophilic Addition to Activated Double Bonds.Figure 4 shows ES(r) of benzylidenemalonitrile. The lowest ES,minover the aromatic ring is again found at the ortho and parapositions, consistent with the positional selectivity for SNArassociated with the resonance-withdrawing substituent. How-ever, the overall lowest ES,min is at the β-carbon. This is also theprevalent site for interaction with strong nucleophiles in this typeof molecules. Bernasconi and Killion have investigated themechanism and kinetics for conjugate addition of piperidine to aseries of substituted benzylidenemalonitriles in a 50% DMSO−50% water solution.46 The initial step in these reactions is theformation of a zwitterionic intermediate that has the piperidinenitrogen bonded to the β-carbon. In Figure 5 the ln k for thisinitial process is plotted against the ES,min on the β-carbon for thebenzylidenemalonitriles. There is a good linear correlationbetween ln k and ES,min with R

2 = 0.92. Thus in this series ES(r) isable to quantitatively reproduce the observed reactivity withrelatively high accuracy. It can be noted that ES,min significantlyoverestimates the reactivity of the 4-NMe2 substitutedcompound; the R2 value improves to 0.98 when it is excluded

Table 1. Minima in ES(r) (ES,min) and Logarithm of theExperimental Rate Constants (ln k) for SNAr at theCorresponding Carbon Positions for the Molecules of Figure3a,b

structure positionc ES,min (eV) ln k

a 2 −1.51 −13.383 −1.43 (−)d

b 2 −1.50 −12.046 −1.20 (−)d

c eq −1.82 −9.89d 2 −1.63 (−)d

4 −2.27 −7.29e 2 −1.57 (−)d

4 −2.11 −6.266 −1.68 (−)d

f 4 −2.57 −3.68g 2 −1.94 (−)d

4 −2.53 −2.946 −2.10 −3.63

h 2 −2.41 0.274 −2.73 1.22

I 2 −1.92 (−)d

4 −2.37 0.30R2 0.81

aES(r) was computed at the 0.004 au density surface.bExperimental

rate constants (in L mol−1 s−1) were obtained with NH3 as nucleophilein 60% dioxane−40% water at 25 °C and are taken from refs 41 and42. cOnly positions with an ES,min are listed.

dNo product wasobserved.



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from the correlation. Domingo et al.47 analyzed the reactivity ofthe same series using ω. They also found a linear relationshipwith ln k, but the quality of the correlation is lower and R2 is only0.75. Interestingly, also in their correlation 4-NMe2 is an outlier

and R2 improves to 0.90 when the compound is excluded.Domingo et al. suggest that the deviation of 4-NMe2 can beattributed to solvation effects.To elucidate whether ES(r) can reproduce the reactivity of

activated double bonds toward anionic nucleophiles, wecomputed ES(r) on a series of substituted α-nitrostilbenes. Thekinetics for addition of HOCH2CH2S

− to the β-carbon of thestilbenes in 50% DMSO−50% water solution has beendetermined by Bernasconi and Killion.48 Also, for this series,we find that the lowest ES,min is found at the β-carbon.Furthermore, there is an excellent linear correlation between lnk and ES,min with an R

2 of 0.986 (Figure 6). This confirms that

ES(r) has a capacity for quantitatively ranking substrates forconjugative nucleophilic addition also when the nucleophile isanionic. It can be noted that ω performs better for the α-nitrostilbenes than for the previous series.47 The R2 is 0.95 andthus the correlation again is less than that between ln k and ES,min.

Halogen Bonding. Figure 7 shows ES(r) of methyl bromide.There is an ES,min of −1.14 eV on the methyl group at the

Figure 3. Structures of the heteroaromatic molecules investigated in relation to their SNAr reactivity and the numbering of their positions (to the left).Plot of the logarithm of the experimental rate constant (ln k) versus minimum in ES(r) (ES,min) at the corresponding carbon position (to the right). Datafrom Table 1.

Figure 4. Computed ES(r) of benzylidenemalononitrile at the 0.004 auisodensity surface. Color ranges for ES(r) in eV: red < −2.6, −2.6 <yellow < −0.8, and green > −0.8. The lowest ES,min (−2.79 eV) is foundat the reactive β position. Molecular structure is shown below surface.

Figure 5. Plot of the logarithm of the experimental rate constant (ln k)versus ES,min at the β position for a series of benzylidenemalononitriles.The rate constants (in L mol−1 s−1) are for the conjugate addition ofpiperidine in 50% DMSO−50% water and are taken from ref 46

Figure 6. Plot of the logarithm of the experimental rate constant (ln k)versus ES,min at the β position for a series of α-nitrostilbenes. The rateconstants (in L mol−1 s−1) are for the conjugate addition ofHOCH2CH2S2

− in 50% DMSO−50% water and are taken from ref 48.



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intersection of the three hydrogens, corresponding to theposition for nucleophilic attack in an SN2 reaction. The ES,minbecomes more negative in the order of CH3Cl, CH3Br, CH3I, inagreement with increasing leaving group strength for SN2.However, the lowest ES,min (−1.35 eV) of CH3Br is not found atthe methyl group but at the tip of the bromine opposite to thebromine−carbon bond. A similar picture is given by the VS(r),which has a maximum (VS,max) at the tip of the bromine with amagnitude of 25.7 kcal/mol. However, in the VS(r), the mostpositive areas, with VS,max of 38.2 kcal/mol, are found at themethyl hydrogens. These high positive values reflect thehydrogen-bond-donating properties of the molecule. PositiveVS,max on the halogens has been associated with noncovalentinteractions with nucleophiles in what today is referred to ashalogen bonding.10 Furthermore, the halogen bond strength andpositional selectivity often correlate with the halogen VS,max incongeneric series of halogenated compounds.13,15,49 However,when comparing ES(r) with VS(r), it is clear that the former to agreater extent emphasizes the electrophilic nature of thebromine. This prompted us to investigate whether there is acorrelation between halogen bond strength and ES,min. The ES(r)was computed for a series of methyl chlorides and methylbromides, with varying degree of hydrogen−fluorine substitu-tion, previously studied by Riley and Hobza.50 The halogen bondinteraction energies (ΔEint) for complexes between thesecompounds and formaldehyde were computed at the CCSD-(T)/aug-cc-pVTZ level.50 There is indeed a very good linearcorrelation between ΔEint and ES,min with an R2 value 0.970 andan SE of only 0.09 kcal/mol (Figure 8). The correspondingcorrelation between ΔEint and VS,max is of slightly lower quality(R2 = 0.952, SE = 0.12 kcal/mol)).The good correlation between ΔEint and ES,min could be taken

as an indication that charge transfer is of significant importancefor halogen bonding. This would be in accordance with the earlyinterpretation of halogen bonding as a donor−acceptorinteraction; electron density from the donor is transferred tothe antibonding σ* orbital of the halogen. In recent years, therehas instead been an emphasis on the electrostatic nature of thehalogen bond, and electrostatics together with dispersion have

been indicated to govern the strengths of halogen bonds.14,51,52

The polarization of the σ orbital toward the halogen−carbonbond results in depletion of electron density outside of thehalogen atom opposite to the bond, that is, a so-called σ hole isformed where the electrostatic potential is positive.51 Thelocation of the σ hole largely coincides with the region where theσ* orbital has its highest density. Thus it is logical that thehalogen VS,max and the ES,min are found at the same position. Itshould also be realized that E(r) according to eq 9 has asignificant contribution from V(r), and this could explain thelinear correlation between the halogen VS,max and ES,min (R

2 =0.95).In the case of the halogenated methanes, the LUMO is always

a σ* orbital associated with the heaviest halogen. This is alsoreflected by the good correlation between ΔEint and εLUMO, R2 =0.968. Also,ω correlates well withΔEint (R2 = 0.94), which can betraced to the contribution of εLUMO to ω.To determine if ES(r) can describe the halogen bonding of

more complex systems with multiple interaction sites fornucleophilic attack, we have studied a series of halogenatedbenzenes, of the type C6H(5−y)FyX, where y = 0, 2, 5 and X = Cl,Br, I. This series poses an interesting challenge for ES(r) since themolecules generally have a multitude of negative virtual orbitalsand the LUMO is for half of the molecules an aromatic π* orbitaland for the other half a halogen σ*orbital; C6F5Cl, C6F5Br, andthe iodobenzenes are the molecules of the latter type.Figure 9 shows the ES(r) of 1-bromo-3,5-difluorobenzene, and

there are regions of low ES(r) associated with both the aromaticring and the Br. Interestingly, the lowest ES,min is found at the tipof the heavy halogen despite the fact that the LUMO is anaromatic π* orbital; a feature that 1-bromo-3,5-difluorobenzeneshares with 1-bromo-2,4-difluorobenzene and bromobenzene.There are also higher ES,min associated with the different aromaticcarbons that reflect their varying susceptibility for nucleophilicattack.Riley et al. have investigated the halogen bonding of the

molecules of this series and computed interaction energies forcomplexes with acetone at theMP2/aug-cc-pVDZ(−PP) level.49We have considered the interaction energies for theperpendicular approach toward the heavy halogen (X), that is,

Figure 7. Computed ES(r) (left) and VS(r) (right) at the 0.004 auisodensity surface of methyl bromide. The top and bottom views havethe methyl group and the bromine, respectively, pointing toward theviewer. Color ranges for ES(r) in eV: red < −1.2, −1.2 < yellow < −0.8,and green > −0.8. Color ranges for VS(r) in kcal/mol: red > 45, 10 <yellow < 45, −10 < green < 10, and blue < −20.

Figure 8. Plot of the halogen bond interaction energy versus the halogenES,min for a series of halomethanes. Interaction energies are for theinteraction with formaldehyde, computed at the CCSD(T)/aug-cc-pVTZ level, and taken from ref 50. The ES,min is consistently located atthe tip of the chlorine or bromine.



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constrained complexes with a X−O−C angle of 180°, becausethe fully relaxed structures, in addition to the halogen bond,involve interactions between acetone and the ortho-substituents(F or H) of the halobenzenes.Also, for this series there is a very good linear correlation

betweenΔEint and the halogen ES,min with an R2 = 0.979 and SE =0.18 kcal/mol (Figure 10). This is remarkable considering thatthe donating halogen varies between Cl, Br, and I. Notsurprisingly, the correlations with εLUMO and ω are of muchlower quality, R2 = 0.82 and 0.77, respectively. As expected, andin agreement with the work of Riley et al.,49 we find a goodcorrelation betweenΔEint and the halogen VS,max, R2 = 0.975 andSE = 0.19 kcal/mol. Despite the fact that both ES,min and VS,maxcorrelate well with ΔEint and with similar R2, the linearcorrelation between ES,min and VS,max is less, R

2 = 0.93. Ouranalysis indicates that ES,min and VS,max provide complementaryinformation for describing the halogen bond strength in thissystem. An excellent correlation forΔEint is obtained when ES,minand VS,max are used as independent variables in a multiple linearrelationship, R2 = 0.993 and SE = 0.10 kcal/mol. The cross-validated correlation coefficient Q2 is as high as 0.990, clearlyindicating that the excellent correlation is not the result ofoverfitting. It is also obvious from Figure 10 that there is aconsistent improvement in the correlation going from the one-variable to the two-variable relationship.It is important to remember that there is no uniquemethod for

decomposing the interaction energy of an intermolecularinteraction, and this is one reason behind the conflicting viewson the importance of electrostatics versus charge transfer forhalogen bonding that can be found in current literature.14,52−56

Furthermore, in the classical analysis of donor−acceptorinteractions, the charge-transfer interaction energy (ΔECT)includes terms that in most energy decomposition analyses areconsidered electrostatic. Reed et al. recognized this already intheir review of donor−acceptor interactions when theycompared ΔECT obtained from natural bond orbitals (NBO)to Morokuma energy decomposition analysis.57 An analogy canbe made to E(r), which has a contribution from the electrostaticpotential, V(r), according to eq 9. Still, independent of thedefinition of charge transfer, it is a limitation to only consider theimportance of electrostatics when describing halogen bonding.In a recent study by Rosokha et al., much higher and moregeneral correlations were found when the halogen bondinteraction energy was correlated by a multilinear relationshipswith VS,max and ΔECT (obtained by NBO) than when the samedescriptors where used alone.53 Our results for the halogenatedbenzenes indicate that the halogen VS,max and ES,min, in a similar

manner, provide complementary information for analyzinghalogen bonding. To further explore this complementarity andhow the relative importance of VS,max versus ES,min fordetermining the interaction strength depends on the characterof the halogen bond acceptor will be the objective of a futurestudy.

■ CONCLUSIONSThe local electron attachment energy [E(r)] has beenintroduced with the objective of defining a local property thatis analogous to the average local ionization energy [I(̅r)] but thatreflects susceptibility toward interaction with nucleophiles ratherthan electrophiles. The functional form E(r) is motivated basedon Janak’s theorem and the piecewise linear energy dependenceof electron addition to atomic and molecular systems. Within theGKS-DFT method, only the virtual orbitals with negativeeigenvalues contribute to E(r).Similarly to I(̅r), E(r) is complementary to the electrostatic

potential [V(r)] in that it is best suited to analyze donor−acceptor interactions with a significant component of chargetransfer and polarization. The positions of the lowest values of

Figure 9.Computed ES(r) of 1-bromo-3,5-difluorobenzene at the 0.004au isodensity surface. Color ranges for ES(r) in eV: red < −2.0, −2.0 <yellow < −0.8, and green > −0.8. The lowest ES,min (−2.27 eV) is foundat the tip of the bromine.

Figure 10. Correlations of the halogen bond interaction energy (ΔEint)for a series of halobenzenes of the type C6H(5−y)FyX, where X = Cl, Br, I.ΔEint are for the interaction with acetone, computed at the MP2/aug-cc-pVDZ(−PP) level and taken from ref 49. The top plot shows ΔEintversus the halogen (Cl/Br/I) ES,min. The lower plot shows ΔEint versusΔEint(predicted) = 0.367*ES,min − 1.503*VS,max − 0.352 (ES,min andVS,max in eV).



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E(r) on isodensity surfaces are generally associated with regionsthat are susceptible for nucleophilic attack, and the magnitude ofthe minima (ES,min) at those sites often correlates quantitativelywith the relative reactivity.We have shown that for fluorinated aromatics the lowest ES,min

of the aromatic carbons reflects the positional selectivity fornucleophilic aromatic substitution and that the relative rateconstants of the corresponding reactions correlate with ES,min. Inaromatic olefins that have the double bond conjugated withresonance-withdrawing groups, the lowest ES,min is found at theβ-carbon, which is the site most susceptible to nucleophilicaddition. The lowest ES,min of substituted benzylidenemaloni-triles and α-nitrostilbenes shows high correlation with rateconstants for conjugate addition of piperidine andHOCH2CH2S

−, respectively.Finally, we have analyzed the ES(r) of halomethanes and

halobenzenes. In these systems, the lowest ES,min is found at thetip of the iodine, bromine, or chlorine, which is the interactionsite for halogen bonding. There is a very good linear correlationbetween interaction energy (ΔEint) for halogen bonding of thehalomethanes to formaldehyde and the ES,min. In this series ofmolecules, the halogen VS,max provides a very similar picture asthe halogen ES,min, and there is a good linear correlation betweenthe two descriptors. Also, for the halobenzenes there is a veryhigh correlation between ΔEint and ES,min. However, the ES,mincorrelates less with VS,max, and the complementarity of the twosurface properties is manifested by an excellent dual-variablecorrelation with ΔEint. These results warrant further inves-tigations on the generality of the correlation between halogenbond strength and ES,min and the relative importance of chargetransfer and polarization for halogen bonding.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpca.6b10142.

Computed and experimental data in table format for thesize consistency analysis. Interactions of benzylidenemalononitrale (BMN) and α-nitrostilbene with Michaelacceptors as well as for the halogen bonding of fluorinatedmethyl and arene halides. Summary of the statisticalanalysis of this study. (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] Brinck: 0000-0003-2673-075XPresent Address†P.C.: Novartis, Novartis Sverige AB, Box 1150, 183 11 Tab̈y,Sweden.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTST.B. thanks the Swedish Research Council (VR) for financialsupport. J.H.S. is grateful to the School of Chemical Science andEngineering at KTH for an excellence stipend. Sam Solten isacknowledged for computational assistance.

■ REFERENCES(1) Weiner, P. K.; Langridge, R.; Blaney, J. M.; Schaefer, R.; Kollman,P. Electrostatic Potential Molecular-Surfaces. Proc. Natl. Acad. Sci. U. S.A. 1982, 79, 3754−3758.(2) Sjoberg, P.; Murray, J.; Brinck, T.; Politzer, P. Average LocalIonization Energies on the Molecular-Surfaces of Aromatic Systems asGuides to Chemical-Reactivity. Can. J. Chem. 1990, 68, 1440−1443.(3) Sjoberg, P.; Politzer, P. Use of the Electrostatic Potential at theMolecular-Surface to Interpret and Predict Nucleophilic Processes. J.Phys. Chem. 1990, 94, 3959−3961.(4) Horenstein, B. A.; Schramm, V. L. Correlation of the MolecularElectrostatic Potential Surface of an Enzymatic Transition-State withNovel Transition-State Inhibitors. Biochemistry 1993, 32, 9917−9925.(5) Brinck, T.; Murray, J.; Politzer, P. Molecular-Surface ElectrostaticPotentials and Local Ionization Energies of Group-V-VII Hydrides andTheir Anions - Relationships for Aqueous and Gas-Phase Acidities. Int. J.Quantum Chem. 1993, 48, 73−88.(6) Hagelin, H.; Murray, J. S.; Politzer, P.; Brinck, T.; Berthelot, M.Family-Independent Relationships between Computed MolecularSurface Quantities and Solute Hydrogen Bond Acidity/Basicity andSolute-Induced Methanol OH Infrared Frequency Shifts. Can. J. Chem.1995, 73, 483−488.(7) Ehresmann, B.; Martin, B.; Horn, A. H. C.; Clark, T. LocalMolecular Properties and Their Use in Predicting Reactivity. J. Mol.Model. 2003, 9, 342−347.(8) Bulat, F. A.; Toro-labbe, A.; Brinck, T.; Murray, J. S.; Politzer, P.Quantitative Analysis of Molecular Surfaces: Areas, Volumes, Electro-static Potentials and Average Local Ionization Energies. J. Mol. Model.2010, 16, 1679−1691.(9) Murray, J. S.; Politzer, P. Correlations between the SolventHydrogen-Bond-donating Parameter Alpha and the CalculatedMolecular-Surface Electrostatic Potential. J. Org. Chem. 1991, 56,6715−6717.(10) Brinck, T.; Murray, J.; Politzer, P. Surface Electrostatic Potentialsof Halogenated Methanes as Indicators of Directional IntermolecularInteractions. Int. J. Quantum Chem. 1992, 44, 57−64.(11) Brinck, T. Modified Interaction Properties Function for theAnalysis and Prediction of Lewis Basicities. J. Phys. Chem. A 1997, 101,3408−3415.(12) Brinck, T. In Theoretical Organic Chemistry; Paŕkańyi, C., Ed.;Theoretical and Computational Chemistry; Elsevier: 1998; Vol. 5, pp51−93.(13) Riley, K. E.; Murray, J. S.; Politzer, P.; Concha, M. C.; Hobza, P.Br···O Complexes as Probes of Factors Affecting Halogen Bonding:Interactions of Bromobenzenes and Bromopyrimidines with Acetone. J.Chem. Theory Comput. 2009, 5, 155−163.(14) Riley, K. E.; Murray, J. S.; Fanfrlik, J.; Rezac, J.; Sola, R. J.; Concha,M. C.; Ramos, F. M.; Politzer, P. Halogen Bond Tunability II: TheVarying Roles of Electrostatic and Dispersion Contributions toAttraction in Halogen Bonds. J. Mol. Model. 2013, 19, 4651−4659.(15) Aakeröy, C. B.; Wijethunga, T. K.; Desper, J.; Đakovic,́ M.Electrostatic Potential Differences and Halogen-Bond Selectivity. Cryst.Growth Des. 2016, 16, 2662−2670.(16) Koopmans, T. Über Die Zuordnung von Wellenfunktionen undEigenwerten zu Den Einzelnen Elektronen Eines Atoms. Physica 1934,1, 104−113.(17) Bulat, F. A.; Levy, M.; Politzer, P. Average Local IonizationEnergies in the Hartree− Fock and Kohn− Sham Theories. J. Phys.Chem. A 2009, 113, 1384−1389.(18) Brinck, T.; Murray, J.; Politzer, P.; Carter, R. A RelationshipBetween Experimentally Determined pKAs and Molecular-SurfaceIonization Energies for Some Azines and Azoles. J. Org. Chem. 1991,56, 2934−2936.(19) Liljenberg, M.; Brinck, T.; Herschend, B.; Rein, T.; Rockwell, G.;Svensson, M. Validation of a Computational Model for Predicting theSite for Electrophilic Substitution in Aromatic Systems. J. Org. Chem.2010, 75, 4696−4705.(20) Brown, J. J.; Cockroft, S. L. Aromatic Reactivity Revealed: BeyondResonance Theory and Frontier Orbitals. Chem. Sci. 2013, 4, 1772.



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(21) Brinck, T.; Murray, J.; Politzer, P. Relationships Between theAqueous Acidities of Some Carbon, Oxygen, and Nitrogen Acids andthe Calculated Surface Local Ionization Energies of Their ConjugateBases. J. Org. Chem. 1991, 56, 5012−5015.(22) Clark, T. The Local Electron Affinity for Non-Minimal Basis Sets.J. Mol. Model. 2010, 16, 1231−1238.(23) Kramer, C.; Beck, B.; Clark, T. A Surface-Integral Model for LogPow. J. Chem. Inf. Model. 2010, 50, 404.(24) Güssregen, S.; Matter, H.; Hessler, G.; Müller, M.; Schmidt, F.;Clark, T. 3D-QSAR based on Quantum-Chemical Molecular Fields:Toward an Improved Description of Halogen Interactions. J. Chem. Inf.Model. 2012, 52, 2441−2453.(25) Bauer, T.; Jag̈er, C. M.; Jordan, M. J.; Clark, T. A Multi-AgentQuantum Monte Carlo Model for Charge Transport: Application toOrganic Field-Effect Transistors. J. Chem. Phys. 2015, 143, 044114.(26) Janak, J. F. Proof That ∂ E/∂ ni= εi in Density-Functional Theory.Phys. Rev. B: Condens. Matter Mater. Phys. 1978, 18, 7165−7168.(27) Cohen, A. J.; Mori-Sańchez, P.; Yang, W. Fractional ChargePerspective on the Band Gap in Density-Functional Theory. Phys. Rev.B: Condens. Matter Mater. Phys. 2008, 77, 115123.(28) Peach, M. J.; Teale, A. M.; Helgaker, T.; Tozer, D. J. FractionalElectron Loss in Approximate DFT and Hartree-Fock Theory. J. Chem.Theory Comput. 2015, 11, 5262−5268.(29) Mori-Sańchez, P.; Cohen, A. J.; Yang, W. Many-Electron Self-Interaction Error in Approximate Density Functionals. J. Chem. Phys.2006, 125, 201102.(30) Baerends, E. J.; Gritsenko, O. V.; van Meer, R. The Kohn-ShamGap, the Fundamental Gap and the Optical Gap: The Physical Meaningof Occupied and Virtual Kohn-Sham Orbital Energies. Phys. Chem.Chem. Phys. 2013, 15, 16408−16425.(31) Zhao, Y.; Truhlar, D. G. Design of Density Functionals That areBroadly Accurate for Thermochemistry, Thermochemical Kinetics, andNonbonded Interactions. J. Phys. Chem. A 2005, 109, 5656−5667.(32) Foster, M. E.; Wong, B. M. Nonempirically Tuned Range-Separated DFT Accurately Predicts both Fundamental and ExcitationGaps in DNA and RNA Nucleobases. J. Chem. Theory Comput. 2012, 8,2682−2687.(33) Whittleton, S. R.; Sosa Vazquez, X. A.; Isborn, C. M.; Johnson, E.R. Density-Functional Errors in Ionization Potential with IncreasingSystem Size. J. Chem. Phys. 2015, 142, 184106.(34) Langenaeker, W.; Demel, K.; Geerlings, P. Quantum-ChemicalStudy of the Fukui Function as a Reactivity Index: Part 2. ElectrophilicSubstitution on Mono-Substituted Benzenes. J. Mol. Struct.: THEO-CHEM 1991, 234, 329−342.(35) Anderson, J. S.; Melin, J.; Ayers, P. W. Conceptual Density-Functional Theory for General Chemical Reactions, Including ThoseThat are Neither Charge- Nor Frontier-Orbital-Controlled. 2.Application to Molecules where Frontier Molecular Orbital TheoryFails. J. Chem. Theory Comput. 2007, 3, 375−389.(36) Parr, R. G.; Von Szentpaly, L.; Liu, S. B. Electrophilicity Index. J.Am. Chem. Soc. 1999, 121, 1922−1924.(37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.;Petersson, G. A. et al. Gaussian 09, revision D.01; Gaussian, Inc.:Wallingford, CT, 2009;.(38) Pettersen, E. F.; Goddard, T. D.; Huang, C. C.; Couch, G. S.;Greenblatt, D. M.; Meng, E. C.; Ferrin, T. E. UCSF Chimera, aVisualization System for Exploratory Research and Analysis. J. Comput.Chem. 2004, 25, 1605−1612.(39) Leach, A. R. Molecular Modeling: Principles and Applications;Pearson Education, Ltd.: Harlow, England, 2001.(40) Tanaka, K.; Deguchi, M.; Iwata, S. Ab initio Study of NucleophilicAromatic Substitution of Polyfluorobenzene. J. Chem. Res., Synop. 1999,528−529.(41) Chambers, R. D.; Close, D.; Musgrave, W. K. R.; Waterhouse, J.S.; Williams, D. Mechanisms for Reactions of Halogenated Com-pounds.2. Orienting Effects of Chlorine Substituents in NucleophilicAromatic-Substitution. J. Chem. Soc., Perkin Trans. 2 1977, 1774−1778.

(42) Chambers, R. D.; Martin, P. A.; Waterhouse, J. S.; Williams, D. L.H.; Anderson, B. Mechanisms for Reactions of HalogenatedCompounds.4. Activating Influences of Ring-Nitrogen and Trifluor-omethyl in Nucleophilic Aromatic-Substitution. J. Fluorine Chem. 1982,20, 507−514.(43) Liljenberg, M.; Brinck, T.; Rein, T.; Svensson, M. Utilizing theSigma-Complex Stability for Quantifying Reactivity in NucleophilicSubstitution of Aromatic Fluorides. Beilstein J. Org. Chem. 2013, 9, 791−799.(44) Brinck, T.; Liljenberg, M. In Arene Chemistry: ReactionMechanisms and Methods of Aromatic Compounds; Mortier, J., Ed.;John Wiley & Sons, Inc: Hoboken, NJ, 2015; pp 83−105.(45) Liljenberg, M.; Brinck, T.; Herschend, B.; Rein, T.; Tomasi, S.;Svensson, M. Predicting Regioselectivity in Nucleophilic AromaticSubstitution. J. Org. Chem. 2012, 77, 3262−3269.(46) Bernasconi, C. F.; Killion, R. B. Nucleophilic-Addition toOlefins.24. Is there a Transition-State Imbalance inMalononitrile AnionForming Reactions - Kinetics of Piperidine and Morpholine Addition toSubstituted Benzylidenemalononitriles in Various Me2SO-WaterMixtures. J. Org. Chem. 1989, 54, 2878−2885.(47) Domingo, L. R.; Perez, P.; Contreras, R. Reactivity of the Carbon-Carbon Double Bond Towards Nucleophilic Additions. A DFTAnalysis. Tetrahedron 2004, 60, 6585−6591.(48) Bernasconi, C. F.; Killion, R. B. Nucleophilic Additions toOlefins.23. High Intrinsic Rate-Constant and Large Imbalances in theThiolate Ion Addition to Substituted Alpha-Nitrostilbenes. J. Am. Chem.Soc. 1988, 110, 7506−7512.(49) Riley, K. E.; Murray, J. S.; Fanfrlík, J.; Rezać,̌ J.; Sola,́ R. J.; Concha,M. C.; Ramos, F.M.; Politzer, P. Halogen Bond Tunability I: The Effectsof Aromatic Fluorine Substitution on the Strengths of Halogen-BondingInteractions Involving Chlorine, Bromine, and Iodine. J. Mol. Model.2011, 17, 3309−3318.(50) Riley, K. E.; Hobza, P. Investigations into the Nature of HalogenBonding Including Symmetry Adapted Perturbation Theory Analyses. J.Chem. Theory Comput. 2008, 4, 232−242.(51) Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. HalogenBonding: The Sigma-Hole. J. Mol. Model. 2007, 13, 291−296.(52) Politzer, P.; Murray, J. S.; Clark, T. Halogen Bonding: AnElectrostatically-Driven Highly Directional Noncovalent Interaction.Phys. Chem. Chem. Phys. 2010, 12, 7748−7757.(53) Rosokha, S. V.; Stern, C. L.; Ritzert, J. T. Experimental andComputational Probes of the Nature of Halogen Bonding: Complexesof Bromine-Containing Molecules with Bromide Anions. Chem. - Eur. J.2013, 19, 8774−8788.(54) Mitoraj, M. P.; Michalak, A. Theoretical Description of HalogenBonding - an Insight Based on the Natural Orbitals for ChemicalValence Combined with the Extended-Transition-state Method (ETS-NOCV). J. Mol. Model. 2013, 19, 4681−4688.(55) Wang, C.; Danovich, D.; Mo, Y.; Shaik, S. On the Nature of theHalogen Bond. J. Chem. Theory Comput. 2014, 10, 3726−3737.(56) Politzer, P.; Murray, J. S.; Clark, T. Mathematical Modeling andPhysical Reality in Noncovalent Interactions. J. Mol. Model. 2015, 21, 52.(57) Reed, A. E.; Curtiss, L. A.; Weinhold, F. IntermolecularInteractions from a Natural Bond Orbital, Donor-Acceptor Viewpoint.Chem. Rev. 1988, 88, 899−926.



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