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Role of Reaction Conditions in the Global and Local Two Parabolas Charge Transfer Model Ulises Orozco-Valencia, José L. Gázquez, and Alberto Vela J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12001 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 22, 2018

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The Journal of Physical Chemistry

Role of Reaction Conditions in the Global and Local Two Parabolas Charge Transfer Model Ulises Orozco-Valencia a, José L. Gázquez b and Alberto Vela a * a

Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México, D. F. 07360, México. b Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México, 09340, México.

Abstract The local and global charge transfer approach based on the two parabolas model is applied to several problems aiming to show the importance of incorporating the reaction conditions to evaluate the global and local chemical descriptors. It is shown that by preparing the reactants the chemical potentials of the reacting species determined by the two parabolas model satisfy the condition for the transfer of electrons in the direction dictated by the chemical potential difference. The model is applied to the hydration of alkenes, showing that it recovers Markovnikov’s rule, to aromatic nitration, and to the interaction of nitrobenzenes with 1,3-diethylurea, an electrochemically controlled hydrogen-bonding problem. The applications presented show that to satisfy the charge transfer directionality established by the chemical potential differences obtained from the two parabolas model, one has to incorporate the reaction conditions in the evaluation of the global and local chemical descriptors. The global and local charge transfer predicted along these lines allows one to determine the direction of electron transfer prevailing in the reaction and also the most relevant atoms participating in the interactions between the reactants, aiding in the unraveling of the chemical interactions present in the system under investigation.

*Corresponding author. Email: [email protected] 1 ACS Paragon Plus Environment

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1. Introduction The ensemble theorem establishes that the dependence on the number of electrons ( N ) of any size consistent property, like the energy ( E ) and the density ρ (r) , is a series of straight lines connected at the values of the property for positive integers values of N .1-4 Consequently, its first derivatives with respect to N are constant for any fractional number of electrons and discontinuous when evaluated at every positive integer. The second derivatives are zero for fractional number of electrons and diverge for all integer N .3 Nonetheless, it is customary to approximate E(N ) by a continuous function at every interval,1, 3 approach that has proved to be an important source of concepts and principles in chemistry such as electronegativity, hardnes5s, softness, electrophilicity, Fukui function, the principle of electronegativity equalization and the principle of hard and soft acid and bases, just to name a few.6-18 The first realization of the ensemble theorem in chemical reactivity within density functional theory (CRDFT) was in 1984 when Parr and Yang (PY) introduced the Fukui function, distinguishing at the outset, the left derivative, f − (r) = (∂ ρ (r) / ∂N )υ− (r ) , and the right derivative, f + (r) = (∂ρ (r) / ∂N )υ+ ( r) .19 PY offered an interpretation to the discontinuity in derivatives of N : the left derivative (“−”) corresponds to the cationic branch and represents a nucleophilic process (the species is donating charge), and the right derivative (“+”) corresponds to the anionic branch and represents an electrophilic process (the species is accepting charge). Considering the importance of the ensemble theorem, Gázquez, Cedillo and Vela (GCV) proposed a two parabolas model (2PM),20 that incorporates the derivative discontinuities implied by the ensemble theorem, keeping the possibility of evaluating the second derivatives of the energy with respect to the number of electrons. In the 2PM the change in the energy for the nucleophilic and electrophilic processes are given by ∆E +/− = µ +/− ∆N +/− + 12 η +/− (∆N +/− )2

,

(1)

where the “-” sign describes processes in the interval

−1 ≤ ∆N − ≤ 0

, and the “+” sign those in the

interval 0 ≤ ∆N + ≤ 1. Even though the 2PM distinguishes the first derivatives from the left and from

2 ACS Paragon Plus Environment

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the right, it does not comply completely with the ensemble theorem, since the energy is not a set of straight lines but a set of parabolas. According to the ensemble theorem, the second derivative of E with respect to N can be expressed as3  ∂2 E  = η (N + ∆N ) = ( µ + − µ − ) δ (∆N )  ∂N 2  υ (r )

,

(2)

where δ (N ) is the Dirac delta function, result that establishes that the second derivative is zero for fractional number of electrons and diverges for integer N . GCV assumed that η = µ + − µ − and that both parabolas have the same curvature or hardness, η = η + = η − . With these assumptions and making the parabolas to pass through the energies of the cation, neutral and anion species, one can show that Eqs. (1) lead to the following expressions for the right and left chemical potentials and the global hardness:20

µ + = − 14 (I + 3A) , µ − = − 14 (3I + A) , and η = 12 (I − A) ,

(3)

where I is the first vertical ionization potential and A the vertical electron affinity. These expressions distinguish the donating and accepting charge process, and partially incorporate the requirements of the ensemble theorem. Following the procedure leading to the definition of electrophilicity, GCV introduced the electrodonating, ω − = ( µ − )2 / 2η , and electroaccepting, ω + = ( µ + )2 / 2η , powers, global reactivity descriptors that have been applied and commented in the literature.21-25 On the other hand, inspired in the 2PM, Ramirez, Vargas, Garza and Gázquez (RVGG) proposed that the interaction energy of the reaction A + B → AB can be written distinguishing the direction of charge transfer associated to each species as,26 ∆EAB = ∆EA− + ∆EB+ = µ A− ∆N A− + 12 ηA (∆N A− )2 + µ B+ ∆N B+ + 12 ηB (∆N B+ )2

,

(4)

where A is the donating fragment and B the accepting one. Minimizing Eq. (4) with respect to ∆N A− and imposing charge conservation we obtain that the number of electrons donated by A is given by ∆N A− =

µ B+ − µ A− = −∆N B+ ηB + η A

,

(5) 3

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and the interaction energy is ∆EAB = −

1 ( µB+ − µ A− )2 2 (ηB + η A )

.

(6)

RVGG showed that Eqs. (5) and (6) correctly describe the most stable species in the complexation of metal cations Ca2+, Hg2+ and Pb2+ (electron-acceptors) with bidentate and cyclic ligands (electrondonors).26 Before going further it is necessary to comment some important points about Eq. (5). First, to be consistent with the situation where A is a charge donor and B a charge acceptor, the chemical potentials of the interacting species must satisfy the condition µ B+ < µA− . Second, this latter inequality is feasible when at least one of the interacting fragments is an ionic system, this as a consequence of the displacements in the chemical potentials produced by the extraction or addition of an electron. In Figure 1 we depict the favorable and unfavorable scenarios for the electronic transfer between a donor A and an acceptor B. Figure 1a is the favorable situation corresponding to the interaction between ionic systems, and Figure 1b is the typical unfavorable case expected for the interaction between neutral systems.

Figure 1. Situations for the electronic transfer between a donor A and an acceptor B: a) favorable and b) unfavorable.

It is worth noting that reactivity between ionic systems is fundamental in all branches of chemistry, ranging from canonical interactions such as neutral molecules-cation, neutral molecules-anion, or anion-cation, to more complex situations like those occurring in supramolecular chemistry such as organic ligands-cation, cation-π interactions or anion-π interactions. One way to achieve the 4 ACS Paragon Plus Environment

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inequality µ B+ < µA− is to take into consideration the reaction conditions, for instance, the presence of a catalyst and/or solvent that breaks or prepares the species for reacting. Local reactivity is essential to understand reaction mechanisms in chemistry.27 This involves identifying the most reactive sites in a molecule that is attacked by another molecule. The functional groups in a molecule are primarily responsible in driving a chemical reaction and it is on these sites where chemical bonds are created and broken.28-30 Therefore, the analysis of functional groups in molecules is key for understanding intra and intermolecular reactivity. The comparative study between molecules sharing the same functional group has led to a considerable clarification and organization of chemical information, since the chemical and physical properties of a particular molecule may be inferred from the behavior of molecules possessing the same functional groups.28 These chemical effects influencing the local reactivity of a molecule are commonly called “electronic

effects” and they modify the behavior of a reaction center.28-30 The issue of functional group definition has been treated in CRDFT by methodologies like group electrophilicity31 and group softness.32 The main aim of this work is to apply the global and local two-parabolas model that partially satisfies the ensemble theorem to different chemical situations, paying special attention to the important role played by the reaction conditions in preparing the reactants to exchange electrons, complying with the requirement that the difference in electronic chemical potentials of the interacting species agrees with the expected direction of electron transfer, and also to show that the local model provides an alterative to select the most reactive atoms in the reacting species, information that helps to identify the underlying interactions in a reaction. These requirements are in line with a recent work by Miranda-Quintana and Ayers33 who stress the importance of the reaction surroundings. The structure of this works is the following. In Section 2 we will discuss the theoretical background of how the local criterion is incorporated in Eqs. (5) and (6). The computational details are presented in Section 3. In Section 4 we will apply the global and local model to some chemical reactions, underlying the importance of taking into consideration the reaction conditions to use the global and local 2PM. Finally, the conclusions of this work are presented in Section 5. 5 ACS Paragon Plus Environment


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2. Local model within the 2PM In the work where the concepts of electrodonating and electroaccepting powers were introduced by GCV, they also presented the extension of the global 2PM to a local version that lead to the definition of the local electrodonating and electroaccepting powers.20 In this derivation it is shown that the change in the energy where one distinguishes the donating (-) and the accepting (+) directions of charge transfer is given by ∆E +/− = ∫ f +/− (r)dr  µ +/− ∆N + 12 η (∆N )2 

,

(7)

that allow one to define a local energy change per unit volume for each direction of charge transfer as ∆ε +/− (r) = f +/− (r) [ µ +/− ∆N +/− + 12 η ( ∆N +/− )2 ]

.

(8)

Invoking the same reasoning that was used to introduce the local reactivity in the PP model,34-35 we write Eq. (8) in atomic resolution:

∑

k

∆ε k+/− =

∑

f +/− k k

 µ +/− ∆N +/− + 12 η ( ∆N +/− )2 

,

(9)

where fk+/− is the condensed Fukui function (CFF).36-37 Including a atoms from fragment or reactant A and b from fragment or reactant B, in the same spirit as it was done in Ref. [34], the atomically resolved interaction energy can be expressed as

∑α = ∑α

∆ε ab =

a

∆ε ab

a

∈A

∆εα− +

∑β b

∈B

∆ε β+

f −  µ − ∆N A− + 12 ηA ( ∆N A− )2  + ∈A α  A

∑

b

f +  µ + ∆N B+ + 12 ηB ( ∆N B+ )2  β ∈B β  B

.

(10)

In this last equation nucleophile A participates with a atoms, and the electrophile B with b atoms, resulting in an atomically resolved interaction energy that depends on the number of atoms selected, fact that is indicated by the ab subindex. Minimizing Eq. (10) with respect to ∆N A− , and conserving the number of electrons in the reaction we obtain that the number of electrons donated by fragment A is given by

− ∆N A,ab

(µ ∑ = (η ∑ + B

B

b

+

f β ∈B β

b

+

f β ∈B β

) − (µ ∑ ) + (η ∑ − A

A

a

−

a

−

f α ∈A α f α ∈A α

) = −∆N )

+ B,ab


(11)

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and the corresponding energy change is

( (

)( )(

) )

a −  −  + b + 1  µB ∑ β ∈B fβ − µ A ∑ α ∈A fα  ∆ε ab = − 2 η ∑b f + + η ∑a f − B A β ∈B β α ∈A α

2

.

(12)

In Eq. (11) we changed the notation of ∆N A− to ∆N A,− ab , with the intention of emphasizing that the charge transfer depends on the selected number of most reactive atoms a and b . Considering the participation of all atoms in both systems, by the normalization of the CFF,

∑

all atoms k

fk+/− = 1,

36-37

we

recover Eqs. (5) and (6). The usage of Eqs. (11) and (12) require the fulfillment of the inequality ( µ B+

∑ β fβ ) < (µ ∑α fα ) b

+

− A

a

−

to guarantee that electron transfer complies with the electronic chemical

potential difference. A crucial point in applying this local model is the selection of the number of reactive atoms (a and b). This selection can include atoms constituting functional groups like a double bond, a carbonyl group, a cyano group, etc., or in other words, atoms that can be relevant in the formation of transition states. In this work the selection of atoms considers two points. First, the selected atoms include those with the larger values of the CFFs and the final number of a and b atoms depends on which combination provides the best correlation of the charge transferred predicted with this selection of atoms with the experimental quantity used to measure the reactivity. And second, the selection of reactive atoms must satisfy the condition ( µ B+ ∑ β fβ+ ) < ( µ A− ∑ α fα− ) . It should be noted b

a

that Eqs. (11) and (12) are very similar to Eqs. (25) and (26) of Ref. [34]. The difference, which is not minor, is that in this work the chemical potentials and hardness appearing in Eqs. (11) and (12) are evaluated following the 2PM, that is, using Eqs. (3), while in Ref. [34] these global chemical descriptors of the reacting species were evaluated with the classical PP model, Eq. (5) and (6) of Ref. [34].

3. Computational Details



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All structures were optimized in gas phase with the M06-2X38 and PBE39-40 functionals and with 6311G(d,p) and TZVP basis set. The calculations were done with deMon2k (version 4.4.1)41 and Gaussian 0942. A frequency analysis was done to confirm that all stationary points located by the optimization correspond to minima in the potential energy surface. The vertical ionization potentials and electron affinities were calculated by energy differences, keeping the geometry of the N electron system: I = E(N − 1) − E(N ) and A = E(N ) − E(N + 1) .2 All energies reported are in eV. The condensed Fukui functions were calculated through the response-of-molecular-fragment approach,43 with the scheme proposed by Yang and Mortier36 using the definitions fk+ = qk (N ) − qk (N + 1) , for electrophilic attack, and fk− = qk (N − 1) − qk (N ) , for nucleophilic attack, where qk (N ), qk (N − 1) , and qk (N + 1) are the atomic charges of the system in neutral, cationic and anionic state, respectively. We

used the atomic charges from the Lödwin Population Analysis (LPA),44 Hirshfeld Population Analysis (HPA),45 and Natural Population Analysis (NPA).46-47

4. Applications and results 4.1 Hydration of alkenes As a first application of the local 2PM we study the hydration of alkenes catalyzed in acid medium, RR'C = CR''R''' + H 2 O → RR'C(OH) − C(H)R''R'''

.

(R1)

For the (R1) reaction the nucleophilic attack of the alkene on H2O, the electrophile, is carried out by the C=C functional group, which is the reaction center. The reactive behavior of this group is controlled by the substituents (R, R’, R’’ and R’’’). By donating charge, electron-donating substituents (EDS) activate the C=C center making the alkene more reactive towards hydration.28-30 This mechanism has been widely studied in chemistry, and Markovnikov’s rule play an important role in explaining the formation of the most stable carbocation and the major reactivity of the electrophilic addition. Markovnikov’s rule can be understood using the FMOs involved in the reaction.28-30 Since hydration is catalyzed in acid medium then it is the H3O+ cation (subscript B, the electrophile) who


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attacks the alkene (subscript A, the nucleophile). This consideration is crucial since it provides an acceptor electronic chemical potential ( µB+ ) for H3O+ satisfying the inequality µ B+ < µA− . Table 1. Reactivity properties for a set of alkenes and H3O+ along with global charge transfer, sums of CFF values with atomic charges from NPA, and the local charge transfer. Values obtained with M06-2X/6-311G(d,p). The Log k values are from Ref. [48] and Ref. [49]. − ∆N A, 23

Log k

-0.153 -0.189 -0.191 -0.198

− fC=C 0.857 0.747 0.735 0.699

-0.156 -0.256 -0.267 -0.296

-14.8 -8.6 -8.6 -8.4

6.1

-0.221

0.663

-0.339

-7.8

-6.2 -6.2 -6.2 -5.9 -6.4 -5.9 -5.8

6.2 5.8 5.8 5.9 6.0 6.0 5.9

-0.221 -0.224 -0.224 -0.242 -0.207 -0.239 -0.244

0.668 0.662 0.655 0.617 0.554 0.515 0.505

-0.335 -0.344 -0.349 -0.388 -0.405 -0.456 -0.468

-7.4 -7.1 -7.0 -3.7 -3.6 -0.1 0.2

AB

µB+

ηB

4.7

-9.7

10.0

Alkenes

IA

AA

µ A−

ηA

∆N A−

H2C=CH2 (Me)HC=CH2 (Et)HC=CH2 (n-But)HC=CH2 trans(Me)HC=CH(Me) cis-(Me)HC=CH(Me) cis-(Et)HC=CH(Et) trans-(Et)HC=CH(Et) (Me)2C=CH(Me) (c-Pr)HC=CH2 (MeO)HC=CH2 (EtO)HC=CH2

10.5 9.8 9.7 9.6

-2.9 -3.0 -2.6 -2.6

-7.2 -6.6 -6.6 -6.5

6.7 6.4 6.2 6.1

9.2

-3.0

-6.2

9.2 9.1 9.1 8.8 9.4 8.9 8.8

-3.1 -2.5 -2.6 -2.9 -2.6 -3.1 -3.0

IB 24.7

H3O+


fH+ 0.862


Figure 2. Correlation between the global charge transfer and Log k. Values from Table 1. The linear fit equation and the R2 correlation coefficient are displayed on top of the plot.

Figure 3. Correlation between the local charge transfer and Log k. Values from Table 1. The linear fit equation and the R2 correlation coefficient are displayed on top of the plot.


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In Table 1 we show for a set of alkenes and H3O+ its global properties as well as the global charge transfer ∆N A− . The substituents on the alkenes are alkyl (-Me, -Et and -n-But), cyclopropyl (cPr) and alkoxy (-CH2O and –CH3CH2O), and all of them are EDSs. Table 1 also includes the experimental kinetic constant ( Log k ) for the hydration of these alkenes in acid medium.48-49 The first point to be noted from Table 1 is the fulfillment of the inequality µ B+ < µA− , suggested by the reaction conditions (acid medium) required for the reaction to occur. Table 1 shows that the alkenes with alkoxy substituents or more alkyl groups have the larger ∆N A− , unlike alkenes with one or none alkyl substituents. However, as it can be seen in Figure 2, when we correlate ∆N A− with the experimental rate constants ( Log k ) the correlation obtained is not acceptable. This result illustrates the shortcomings of the global models to establish acceptable correlations with experimental reactivity data. To use Eq (11) we must first identify the most reactive atoms in each reactant. This hierarchization is done using the nucleophilic CFF, for the alkenes, fα− , and the electrophilic CFF of the hydronium ion, fβ+ . For this particular example we select the two nucleophilic atoms conforming the double bond of each alkene, considering them as the reaction center for this hydration reaction. Thus, for reactant A we have that a = 2. On the other hand, for reactant B we will include the three electrophilic protons of H3O+, implying that b = 3. We will denote these FFs as each alkene and

∑β

b=3

∑α

a=2

− for fα− = fC=C

fβ+ = fH+ for the hydronium ion. These quantities are also reported in Table 1

− along with local charge transfer, ∆N A,23 , which was evaluated with the CFFs values. It is important to

note that the total number of reactive atoms, the combination of a and b, was determined after finding that increasing the number of reactive atoms in the alkenes worsens the correlation. One can also verify that the selection satisfies the inequality ( µ B+ ∑ β fβ+ ) < ( µ A− ∑ α fα− ) . Figure 3 depicts the b

a

− correlation between ∆N A,23 and Log k , showing the notable improvement obtained with the local



model. This result suggests that these atoms should be playing an important role in the ratedetermining step of the electrophilic addition. Figure SI.1 in the Supporting Information shows that the correlations with other combination of reactive atoms are worst than that presented in Figure 3. Interestingly, all unsymmetrical alkenes following Markovnikov’s rule have the largest fα− value in the carbon atom having the greater number of hydrogen substituents in the reaction center, implying that the direct nucleophilic attack towards the H3O+ cation takes place in this carbon atom. The unsymmetrical alkenes are shown in Figure 4 along with their respective values of fα− for each carbon − atom. Finally, Table 1 shows that the values of ∆N A, 23 can be used as a hydration reactivity scale

establishing that the larger the amount of charge donated by the alkene to the hydronium ion the larger its corresponding rate constant. This scale predicts the following ordering for this reaction: -EtO > MeO > -c-Pr > -n-But > -Et > -Me > -H. This ordering is very well known and established in the literature.29-30 Here we have shown that the 2PM is capable of reproducing this reactivity trend and it can be used to predict it in similar reactions.


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Figure 4. Nucleophilic CFF values using NPA and LPA (in parentheses) charges of carbon atoms forming the double bond in unsymmetrical alkenes.

4.2 Aromatic nitration Electrophilic aromatic substitution is a paradigmatic reaction in chemistry.29-30 The effect of the substituents on the aromatic ring as well as the preferential orientation of electrophilic attack are topics widely known and discussed in the chemical literature.29-30 For CRDFT this problem has been challenging since several attempts have failed to predict the preferential orientation experimentally observed.50-53 Globally, the aromatic nitration reaction can be written as R-C6 H 5 + HNO 3 → R-C 6 H 4 -NO2 + H 2 O

(R2)

where R can be an EDS (activator) or an EWS (deactivator) and this substituent is responsible of driving the preferential orientation of the attacking electrophile. Note that if we use the neutral 13 ACS Paragon Plus Environment


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reactants, as indicated in (R2), then we have an unfavorable situation like that shown in Figure 1b, and hence we cannot use the 2PM to determine the charge transfer and its mechanism. However, the experimental conditions for reaction (R2) involve an acid medium (HNO3-H2SO4 mixture) producing in situ the NO2+ cation that is the electrophile.30 Hence, we use as reactant the NO2+ cation instead of neutral nitric acid. Under these conditions, the chemical potentials of the 2PM arrange according to Figure 1a, allowing the charge transfer in the correct direction. In Table 2 we present the values for the ionization potentials, electron affinities, chemical potentials and hardnesses for a set of benzene molecules monosubstituted by the functional groups indicated in the first column. The experimental kinetic constants ( Log krel ) to aromatic nitration, relative to benzene, are also reported in the last column of this table. These aromatic compounds are considered the A systems. The same properties for the NO2+ cation (B system) are also reported at the bottom of Table 2. The global charge transferred, ∆N A− for each aromatic ring substituted is also included. For the NO2+ cation we use a C2v geometry for determining its reactivity properties, considering that we are modeling a previous step towards the formation of the σ-complex, which is the rate-determining step where the NO2+ is bonded to the aromatic ring and determines the preferential orientation.54-55 In other words, we study the aromatic nitration using the association reaction R-C 6 H 5 + NO2+ → R-C 6 H 5 − NO+2 .

(R3)

with NO2+ in a C2v geometry.


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Table 2. Reactivity properties for a set of aromatic rings R-substituted and the NO2+ cation along with global charge transfer, sums of CFF values with atomic charges from LPA, and the local charge transfer. Values obtained with M06-2X/6-311G(d,p). The Log krel values are from Ref. [30]. R -N(CH3)3 -NO2 -CF3 -CO2Et -Cl -CH2Cl -Me -OH NO2+

+

∑α

a=4

IA

AA

µ A−

ηA

∆N A−

13.4 10.3 10.0 9.5 9.3 9.4 9.0 8.7

2.6 0.4 -1.3 -0.6 -1.4 -1.0 -1.9 -1.8

-10.7 -7.8 -7.2 -7.0 -6.6 -6.8 -6.3 -6.1

5.4 4.9 5.6 5.0 5.4 5.2 5.5 5.2

-0.430 -0.734 -0.742 -0.801 -0.811 -0.809 -0.839 -0.876

IB

AB

µB+

ηB

fO+

23.4

12.7

-15.4

5.4

0.44

fα−

0.56 0.68 0.68 0.67 0.64 0.56 0.53 0.54

− ∆N A, 41

Log krel

-0.140 -0.255 -0.303 -0.359 -0.432 -0.559 -0.653 -0.671

-7.92 -7.22 -4.59 -2.43 -1.48 -0.15 1.40 3.00

−/+ The µ A/B values reported in Table 2 show that the inequality µ B+ < µA− is satisfied for all the

monosubstituted benzenes, guaranteeing that the 2PM, with the reactants prepared in the way described above, can be used to determine the direction and amount of electron transfer in this reaction. The global analysis indicates that the monosubstituted benzenes with EDS such as –OH and –Me have the most negative values of ∆N A− . Similarly, those systems with EWS such as –N(CH3)3+ have the least negative values of ∆N A− and, consequently, donate less charge to NO2+. Although it seems that ∆N A− predicts an acceptable reactivity ordering, we find a poor correlation with Log krel (y

= −22.6x −19.5 and R2 = 0.64). To improve this correlation we will apply the local model described above by selecting four atoms (a = 4) with the largest nucleophilic CFF values on the aromatic rings of the monosubstituted benzenes and for NO2+ we selected one atom (b = 1), the oxygen atom, which has the largest electrophilic CFF. The atoms selected for the monosubstituted benzenes are depicted in Figure 5. Figure SI.2 in the Supporting Information provides further support for this selection.



Figure 5. Reactive atoms selected for each monosubstituted benzene along with the nucleophilic CFF evaluated with NPA and LPA (in parentheses) atomic charges.


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Figure 6. Correlation between the local charge transfer and Log krel. Values from Table 2. The linear fit equation and the R2 correlation coefficient are displayed on top of the plot.

Using the values for the sums of the CFFs of the selected atoms the local charge transfer − ∆N A, 41 was evaluated according to Eq. (11) and are also included in Table 2. With this selection of − reactive atoms we find the correlation between ∆N A, 41 and Log krel which is depicted in Figure 6, that

is clearly better than that obtained with the global model. These results allow us to select the atoms that play the most important role in the ratedetermining step of the reaction, either because they are directly involved in the bonding with NO2+ or because they have the ability to reshuffle the electronic density after the attack by NO2+. It is worth noting that the atoms on the aromatic ring correspond to those sites with the experimentally observed preferential orientation. To elaborate this point further, in Table 3 we present the nucleophilic CFF values for the ortho, meta and para positions of the systems under consideration together with the experimental yield for each isomer. As we can see, in all cases, with the sole exception of –Me, the largest nucleophilic CFF matches the preferential orientation observed experimentally, independently 17 ACS Paragon Plus Environment


Page 18 of 40

of the population analysis chosen to determine the atomic charges that enter in the evaluation of the CFFs. We close this discussion reiterating that the applicability of the 2PM requires the inclusion of the reaction conditions to calculate the reactivity descriptors.

Table 3. The largest nucleophilic CFF values obtained with atomic charges from NPA and LPA (in parentheses) for the carbon atoms in the ortho, meta and para positions of each monosubstituted benzene. Values obtained with M06-2X/6-311G(d,p). The experimental nitration yield is from Ref. [30].

R

ortho

meta

para

Exp.

0.27 (0.21) 0%

0.29 (0.21) 89%

0.06 (0.07) 11%

Exp.

0.20 (0.17) 5%

0.21 (0.17) 93%

--- (0.02) 2%

Exp.

0.21 (0.17) 6%

0.21 (0.17) 91%

--- (0.02) 3%

Exp.

0.27 (0.17) 24%

0.28 (0.18) 72%

0.04 (0.01) 4%

Exp.

0.06 (0.08) 31%

0.03 (0.06)

Role of Reaction Conditions in the Global and ... - ACS Publications

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