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Journal of Molecular Structure: THEOCHEM 940 (2010) 103–114

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Journal of Molecular Structure: THEOCHEM

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DFT studies of b-elimination reactions in water solution with different bases:Theory vs experiment

Edoardo Mosconi a,b, Filippo De Angelis b,*, Leonardo Belpassi a,b, Francesco Tarantelli a,b, Sergio Alunni a

a Dipartimento di Chimica, Università degli Studi di Perugia, via Elce di Sotto 8, I-06213 Perugia, Italyb Istituto CNR di Scienze e Tecnologie Molecolari (ISTM), c/o Dipartimento di Chimica, Università di Perugia, Via elce di Sotto 8, I-06213 Perugia, Italy

a r t i c l e i n f o

Article history:Received 10 August 2009Received in revised form 9 October 2009Accepted 9 October 2009Available online 13 October 2009

Keywords:Elimination reactionDFTpKa

Transition state

0166-1280/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.theochem.2009.10.016

* Corresponding author.E-mail address: [email protected] (F. De Angeli

a b s t r a c t

We describe a theoretical investigation of a prototype b-elimination reaction in systems activated by thepyridine ring. The reactions investigated, the acetohydroxamic-induced and OH�-induced b-eliminationwith the nitrogen protonated N-[2-(2-pyridyl)ethyl]quinuclidinium substrate, offers a unique opportu-nity to test computational methodologies for the study of b-elimination reactions in solution since forthis system detailed kinetic experimental data have been obtained. We calculated the pKas of the aceto-hydroxamic acid and of the substrate, for which experimental estimates are available. We then thor-oughly characterized the reactive free-energy profile. Our study establishes that the reaction proceedsvia a quasi reversible E1cb mechanism for the reaction induced by acetohydroxamate base, and irrevers-ible E1cb mechanism for the reaction induce by OH� base, involving a stable carbanion intermediate.Except for a discrepancy in the reproduction of the pKa of the acetohydroxamic acid and of the H2O,the calculated free-energy profile is in excellent agreement with the experiment, showing the generalreliability of the present approach.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Base-induced b-elimination reactions, with formation of a car-bon–carbon double bond, are one of the most fundamental chem-ical reactions and understanding the mechanisms with which theytake place in different substrates and solution environments is ofrecognized importance. In particular, being able to distinguish be-tween concerted and stepwise mechanisms is a very relevant issueboth in chemistry [1–16] and biochemistry [17]. The nature of theborderline between concerted and stepwise mechanisms is yet un-clear [7,8,15] and an obviously important aspect of this problem isthat of establishing whether there is smooth continuity or distinctdiscontinuity between the E2 concerted and the E1cb stepwisemechanisms. Distinguishing the E2 concerted process (AxhDHDN)from the E1cb irreversible mechanism ðAxhD�H þ DNÞ is a difficulttask [1–4,7,8,18]. In fact, while the E1cb reversible mechanismðAxhDH þ D�NÞ can be revealed [1–4] by the presence of H/D ex-change [19], by studies of acid–base catalysis [19] and by the in-verse solvent isotope effect [20,21] the E2 mechanism showsmany of the same characteristics of an E1cb irreversible mecha-nism. In previous studies [19,21–24] of b-elimination reactions insystems activated by the pyridine ring, we have found a high valueof the Proton Activating Factor, PAF, defined as the ratio of the sec-

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s).

ond-order-rate constant for the nitrogen protonated substrate, NH+

to that for the unprotonated substrate, N (PAF = kNH+/kN). The valuefound with 2-(2-fluoroethyl)pyridine is PAF = 3.6 � 105 (acet-ohydroxamate base, 50 �C, l = 1 M KCl) whereas with N-[2-(2-pyr-idyl)ethyl]quinuclidinium PAF is 5.2 � 106. The high values of PAFobserved were interpreted in terms of an E1cb mechanism, with anintermediate carbanion strongly stabilized by resonance. There areseveral biological processes where the stabilization of a carbanionby a quaternized nitrogen atom, part of a heteroaromatic system, isimportant. One example [17] is the mechanism of action of a cofac-tor related to the B6 vitamin, the pyridoxal phosphate. In this sys-tem, the protonated pyridine ring provides the necessarystabilization of the intermediate carbanion formed in the elimina-tion, transamination, decarboxylation and racemization reactionsinvolving this cofactor in the amino acids metabolism. Another[17] example is the chemistry of thiamine pyrophosphate, wherethe carbanion formed in the decarboxylation of b-chetoacids pre-sents an enamine-type structure. Also the enzymatic b-eliminationreaction of ammonia from L-histidine, catalyzed by histidineammonia-lyase, has been proposed to occur via an E1cb mecha-nism, with activation provided by the nitrogen-protonated imidaz-ole ring [25].

Previous theoretical studies on b-elimination reactions havemainly focused on prototype substrates (mostly CH3CH2X, withX = halogen) and were generally limited to the gas-phase [26–32]. Among the many different theoretical studies, of particular rel-

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Scheme 1. Thermodynamic cycle used to calculate the pKa of the species involvedin the reaction.

104 E. Mosconi et al. / Journal of Molecular Structure: THEOCHEM 940 (2010) 103–114

evance is the series performed by Gronert [26], Saunders [28] andJensen [29] using mainly ab initio (MP2-MP4) calculations. Animportant study by Bickelhaupt et al. [27] presented a two-dimen-sional scan of the potential energy surface for the CH3CH2F sub-strate using Density Functional Theory (DFT) calculations. Morerecently, the CH3CH2F substrate has been the subject of intensivetheoretical investigations based on ab initio molecular dynamicssimulations in the gas-phase [30–32], aimed at providing a de-tailed description of the free-energy landscape for the competingelimination and substitution reactions. We recently reported acombined DFT and experimental investigation on b-eliminationreactions in 2-(2-halogenethyl)-1-methylpyridinium (halogen = F,Cl and Br) substrates in solution [33], which represent borderlinecases between E1cb and E2 reaction mechanism. In a subsequentstudy we also investigated the reaction dynamics of the OH�-base-induced b-elimination reaction with 2-(2-fluoroethyl)-1-methylpyridinium, by means of Car–Parrinello Molecular Dynam-ics simulations [34].

Here, we report the results of a theoretical investigation in watersolution of a typical b-elimination reaction of systems activated bythe pyridine ring. The reaction investigated, the b-elimination inthe nitrogen protonated N-[2-(2-pyridyl)ethyl]quinuclidinium sub-strate in the presence of acetohydroxamate/acetohydroxamic acidbuffers and in presence of OH� base, offers a unique opportunity

Scheme 2. Schematic representatio

Table 1Experimental rate constants and associated activation free energies in kcal/mol. B� (OH�)

kB�

1 [M�1 s�1] kBH�1 [s�1] k2 [s�1]

k 24.8 9.9 � 107 2.6 � 106

DG# 15.5 6.5 8.7

a Data refers to N-[2-(4-pyridyl)ethyl]quinuclidinium substrate.

to test computational methodologies for the study of b-eliminationreactions, since for this system detailed kinetic experimental datahave been obtained [19,21,24]. We initially calibrated the computa-tional methodology by calculating the pKas of the acetohydroxamicacid, of the substrate and of the OH� base for which experimentalestimates are available. We then thoroughly characterized the reac-tive free-energy surface connecting the reagents to the final prod-ucts, arriving at a complete description of the reaction profile.

2. Theoretical approach

The B3LYP exchange–correlation functional [35], as imple-mented in the Gaussian03 program package [36], was used forall our calculations, with a 6-31++G** basis set [37]. Geometryoptimizations were performed in water solution by means ofthe conductor-like polarizable continuum model (C-PCM) [38–43] using three different options: the default UA0 solvation ra-dii, specific spheres (SPH) added on the hydrogen mostly in-volved in the reaction, and UAHF [44] solvation radii. Theevaluation of the Gibbs free energies in solution, and of theabsolute pKas, was performed as follows [33,38–43]. The Gibbsfree energy in solution of species i is defined as: Gi

sol =Gi

vac + DGisolv, where Gi

vac is its Gibbs free energy in vacuumand DGi

solv is the free energy of solvation (see Scheme 1). Givac

is computed at the geometry optimized in vacuum, includinga frequency calculation to take into account the vibrational con-tribution to the total partition function. The translational androtational contributions are evaluated by standard statisticalmechanics (particle in a box and rigid rotor models). DGi

solv isestimated as the difference between the result of a C-PCM cal-culation and of a corresponding reference calculation in vac-uum, both at the geometry optimized in solution. The pKa isdefined as the negative logarithm of the dissociation constantof the process AHaq ! A�aq þHþaq and we have that pKa =DGaq,AH/2.303RT. The free energy of deprotonation in water iscalculated again as: DGaq,AH = DGg,AH + DDGsolv,AH (see Scheme 1).For the proton (H+) free-energy values, we used the knownexperimental data: Gg,H+ = �6.28 kcal/mol and DGsolv,H+ =�263.98 kcal/mol (Ref. [40]). A term �RTln24.46 is added toconvert the unit of measurement from the atmosphere for thegas phase to mol/l for the liquid phase. For comparison, the

n of the reaction mechanism.

refer to the acetohydroxamate (hydroxyl) base.

k�2 [M�1 s�1] kOH1 [M�1 s�1] kH2O

�1 [s�1]

2.5 � 103� 421 4.2 � 104

12.8 13.8 11.1

Table 2Values of Gvac (Hartree), DGsolv (kcal/mol) of the acetohydroxamic acid and its N-deprotonated conjugate-base and calculated pKas using different computational methods. Allvalues refer to the more stable A conformer of the acetohydroxamic acid.

Gvac UA0 SPH UAHF

DGsolv pKa DGsolv pKa DGsolv pKa

B3LYPB� (N) �283.804978 �58.7 – �58.8 – �63.7 –BH �284.351977 A �12.7 21.2 �5.4 15.7 �15.5 19.6

B No min – No min – No min –C No min – �2.6 13.7 �11.8 16.8

MP2B� (N) �283.012220 �58.9 – �58.6 – �63.0 –BH �283.555823 A �12.2 19.1 �4.7 13.8 �15.3 18.4

B �12.6 19.4 �5.1 14.1 �15.3 18.4C �9.7 13.7 �2.2 12.0 No min –

Table 3Values of Gvac (Hartree), DGsolv (kcal/mol) of the acetohydroxamic acid and its O-deprotonated conjugate-base and calculated pKas using different computational methods. Allvalues refer to the more stable A conformer of the acetohydroxamic acid.

Gvac UA0 SPH UAHF

DGsolv pKa DGsolv pKa DGsolv pKa

B3LYPB� (O) �283.794018 �63.3 �61.0 �68.4BH �284.351977 A �12.7 22.8 �5.4 19.2 �15.5 21.1

B No min – No min – No min –C No min – �2.6 17.1 �11.8 18.4

MP2B� (O) �282.995155 �64.2 – �61.8 – �69.4 –BH �283.555823 A �12.2 23.1 �4.7 19.3 �15.3 21.5

B �12.6 23.3 �5.1 19.6 �15.3 21.5C �9.7 21.2 �2.2 17.5 No min –

Fig. 1. Optimized geometries of the three different conformers of acetohydroxamic acid, acetohydroxamate base and related Newman-projections.

E. Mosconi et al. / Journal of Molecular Structure: THEOCHEM 940 (2010) 103–114 105

pKa of the acetohydroxamic acid was calculated using also theMP2 method, with the same 6-31++G** basis set employed forthe DFT calculations.

The transition states were located by performing first a con-strained geometry optimization along an appropriate reaction coor-dinate, and then using this starting point for a fully unconstrained

Fig. 2. Optimized geometrical structures of the acetohydroxamic acid and its anion using explicit micro-solvation (five water molecules).


saddle-point search. If not otherwise stated, the results discussed inthe following have been obtained using non-standard solvationparameters (SPH), adding solvation spheres on the two hydrogensbound to C1, to the pyridil-bound hydrogen and to the O-bound pro-ton of the N-deprotonated acetohydroxamic acid.

3. Results and discussion

The reaction investigated here is the b-elimination in the nitro-gen protonated N-[2-(2-pyridyl)ethyl]quinuclidinium substrate, toproduce quinuclidine and 2-vinylpyridine, in the presence of eitheracetohydroxamate, the conjugate base of the acetohydroxamic

Fig. 3. Optimized geometrical structures of the OH-base and of H2O using threewater molecules as micro-solvation.

acid (CH3CONHOH/CH3CONOH-), or of the OH� base. Previousexperimental studies [19,21,24] and our theoretical study havedetermined that this reaction proceeds by a partially reversibleE1cb mechanism [45] in acetohydroxamate/acetohydroxamic acidbuffer and by an irreversible E1cb mechanism with the OH� base(this work). This mechanism is a two-step process: with referenceto Scheme 2, in the first step (A) the base abstracts a proton fromthe substrate to form a carbanion intermediate; in the second step(B) the elimination of the quinuclidine leaving group takes place,with formation of the olefin product.

We report in Table 1 the measured kinetic rate constants andthe associated activation free energies for the first and secondsteps of the reaction (for the experimental procedure see Refs.[19,24]). From the combination of the rate constants, and theknowledge of the pKa of the reactants, the entire energy profileof the reaction can be determined. It is worth noting that k-1 andk2, which determine the kinetic stability of the carbanion, are com-parable so that in the reaction conditions (in acetohydroxamate/acetohydroxamic acid buffer) we can classify this reaction mecha-nism as a partially reversible one, in which the carbanion interme-

Table 4Values of Gvac (Hartree), DGsolv (kcal/mol) of the micro-solvated H2O and is conjugate-base OH� along with calculated pKas using different definitions of the solvation radii.

Gvac DGsolv

SPH1 SPH3 UAHF

4H2O �305.711310 �16.2 �20.7 �18.6OH� + 3H2O �305.176350 �71.7 �78.0 �76.6pKa – 8.7 7.2 6.7


diate, once formed, has a comparable probability of returning tothe reagents or evolving towards the products; as we shall discusslater in greater detail. In contrast, using the OH� base, the pKa ofthe reactants (in particular the pKa OH�/H2O) moves the positionof the intermediate system (carbanion and water) and the reactionmechanism becomes an irreversible E1cb one.

We start our theoretical analysis by investigating the acid–baseproperties of the acetohydroxamate anion and of the OH� baseswith the respective conjugated acids (acetohydroxamic acid andsolvated H2O), which are the bases employed experimentally.

Fig. 4. (a) Optimized structures of the gauche and anti substrate conformers with their Nand C2. (b) Optimized structures of the carbanion (C), olefin product (P) and quinuclidin

The acetohydroxamic acid has two acidic hydrogens, one boundto nitrogen and one bound to oxygen. Previous experimental andtheoretical studies [46,47] reported that N-deprotonation is themost effective process in solution. The experimental pKa of the ace-tohydroxamic acid is 9.4 [20]. The calculated pKa values for N-deprotonation, obtained employing different levels of theory, arereported in Table 2. We have also calculated the pKa values forthe O-deprotonation process (see Table 3), obtaining larger valuescompared to N-deprotonation. This confirms that the N-deproto-nation is the most likely process in water solution. This may be re-

ewman-projections (the arrows point to the reaction site) and definitions of D for C1e (Q).

Table 6Optimized geometrical parameters (bond lengths in Å, angles in �) in solution for thesubstrate (S) gauche and anti conformers (first and second entry, respectively), thecarbanion (C), the olefin product (P) and of transition states of the reaction (TS1, TS1–OH, TS2). In parenthesis are shown the values of the geometry optimized in vacuum.

S C P TS1 TS1–OH TS2

Cpy–C1 1.50–1.51 1.38 1.46 1.45–1.43 1.46 1.42(1.51) (1.38) (1.46) (1.46) (1.46) (1.42)

C1–C2 1.54–1.54 1.47 1.34 1.50–1.52 1.51 1.39(1.55) (1.47) (1.34) (1.53) (1.51) (1.38)

C2–Q 1.52–1.51 1.58 – 1.55–1.52 1.54 2.11(1.52) (1.58) (1.53) (1.55) (2.20)

a 109–108 118 113 111–110 110 115(108) (118) (116) (109) (111) (115)

b 111–111 117 119 114–115 113 119(111) (117) (119) (112) (113) (119)

c 118–110 125 128 122–117 121 126(110) (125) (125) (114) (122) (126)

a’ 107–111 114 120 110–112 113 118(111) (114) (120) (112) (113) (119)

b’ 108–108 108 117 107–108 107 114(109) (108) (116) (108) (109) (114)

c’ 112–110 112 123 113–112 110 122(110) (112) (123) (111) (108) (123)

DC1 22–31 0 0 13–19 17 0(31) (0) (0) (25) (15) (0)

DC2 33–31 26 0 30–28 30 6(30) (26) (1) (29) (30) (4)

Table 5Values of Gvac (Hartree), DGsolv (kcal/mol) of the substrate acid and calculated pKasusing the B3LYP functional and different definitions of the solvation radii.

Anti

Gvac DGsolv (total free energy in solution)

UA0 SPH UAHF

�655.427998 �155.2(�655.982125)

�149.9(�655.974317)

�163.6(�655.995578)

pKa – 15.3 13.8 16.5GaucheNo minimum �156.3 �151.9

(�655.968141)�164.4(�655.988416)

pKa – 16.1 15.3 17.0


lated to the possibility that the N-deprotonated species establishesan intra-molecular hydrogen bond between H1 and the carboxylicoxygen, stabilizing the anion. Moreover we have to consider an-other stabilization induced from the intra-molecular hydrogenbond, see Fig. 1, that is the formation of a five heteratomic ringin a very conjugated system with a good charge delocalization.For the O-deprotonated species, see Fig. 1, we can find a weak in-tra-molecular hydrogen bond interaction between H2 and N, andwe have not a formation of a stabilizing heteratomic ring, in factthe distance from H2 and N is 2.45 Å being hydrogen is in b-posi-tion respect to the N. From the other hand, for the N-deprotonatedspecies, we have a H1–O hydrogen bond distance of 1.86 Å and theH1 is c-position respect to the carboxylic oxygen. In our previouswork [45] we have found altogether three different conformersof the acetohydroxamic acid in solution and only one stable con-former in vacuo; the acetohydroxamate anion has only one con-former both in vacuo and in solution, see Fig. 1. The threeconformers differ essentially in the value of two dihedral angles,<H1–O–N–C and <H2–O–N–C. The A, B and C conformers are char-

Fig. 5. Selected optimized configurations extracted from the linear transit scan alongconformer, along with main optimized geometrical parameters (Å, �).

acterized by <H1–O–N–C angles close to 100�, 70� and 0�, respec-tively. Note that these structural differences are associated notonly to rotations around the single bonds but also to changes inthe pyramidalization of the nitrogen bonds (Fig. 1). While the acet-ohydroxamate anion is planar and the hydroxylic hydrogen ispointing towards the carboxylic oxygen, probably interacting withintra-molecular hydrogen bond, all of the acid conformers are non-planar. This observations underline that the intra-molecular

the N. . .HC1 distance for the acetohydroxamate anion attacking the anti substrate


hydrogen bond, in this condition, is not favored in a polar environ-ment and the minimum energy condition is characterized by thesolvation of the acid hydrogen H1 out the plane. This is confirmedby the fact that, at all levels of theory, the A conformer is the morestable species in solution, while in some of the calculations no min-imum was found in correspondence of one or both of the otherconformers, Tables 2 and 3. Considering the more stable A con-former, we find that B3LYP tends to overestimate the pKa com-pared to MP2. We also notice that the pKa value in closestagreement with the experimental one (12.0 vs 9.4) is obtainedfor the C conformer at the MP2 level, considering explicit solvationspheres on acidic hydrogens. A slightly improved agreement be-tween theory and experiment is obtained by considering DGsolv

values obtained at the Hartree–Fock level on the MP2 optimizedgeometries (10.7 vs. 9.4 for the C conformer). The only conformerconsidered in Ref. [47] is probably our C conformer.

By looking at the data in Table 2, which shows the free energiesin vacuum (Gvac) and the DG of solvation (DGsolv) of the acetohy-droxamic acid (BH) and its conjugate base (B�) along with the cal-culated pKas, one notices that the main source of variabilitybetween DFT and MP2 results resides in the description of solva-tion effects. We tried to perform calculations on the acetohydrox-amate base using a different basis set, 6-31G** and AUG-cc-pVTZ.We obtain very inconsistent pKa values for the calculation with6-31G** (29.7 vs. 9.4) confirming that the diffuse functions give abetter description for the characterization of the solvation effects;using a larger basis set, AUG-cc-pVTZ, we obtain a value of pKa of17.4 similar to the values calculated using 6-31++G**. We thereforeinvestigated by DFT the effect of explicit solvation on the calcu-lated pKas and considered an extended model with five water mol-ecules surrounding the acetohydroxamic acid. By doing so at theB3LYP/UAHF level, we obtain a pKa of 12.6 which substantially im-

Fig. 6. Selected optimized configurations extracted from the linear transit scan along thewith main optimized geometrical parameters (Å, �).

proves the values of 16.8 and 19.6 found without explicit solvationfor the C and A conformers, respectively. Even including explicitsolvation, the disagreement between theory and experiment forthe pKa of acetohydroxamic acid (about 3 pK units) is somewhatlarger than what we would typically expect from the presentmethodology. Focusing our attention on the geometry of the acet-ohydroxamate solvated by five water molecules shown in Fig. 2,we can see that the structure of the acid solvated and in solutionat B3LYP level is similar to the structure of the C conformer, withtwo water molecules pointing towards the carboxylic oxygen andone molecule pointing towards the nitrogen atom, another onepointing towards hydroxylic hydrogen and the last one pointingtowards the hydroxylic oxygen. For what concerns the geometryoptimized in vacuo, we can see that the water molecules tend togive an inter-molecular hydrogen-bond. The geometry of the sol-vated base is planar and we have two water molecules aroundthe nitrogen atom, interacting with the negative charge generatedafter deprotonation. For what concerns the explicit micro-solvationusing the MP2 method, we essentially obtain the same pKa (13.6),with however a different position of the water molecules and a dif-ferent conformation of the acid in solution: in this case we obtain ageometry close to the A conformer and we have three water mol-ecules around the carboxylic oxygen and one around the hydrox-ylic hydrogen and another one pointing to the nitrogen atom. Forthe MP2-calculated geometry of the base and the acid in vacuowe obtain an intensification of the inter-molecular hydrogen bondbetween water molecules. As will be discussed in the following,however, the acid–base properties of the deprotonating agentmainly influence the thermodynamics of the first reaction step,i.e. the formation of the carbanion from the substrate, while thereaction barrier is only marginally sensitive to the base. This con-clusion is experimentally supported by the evidence that using

HO. . .HC1 distance for the OH� base attacking the anti substrate conformer, along


OH- in place of acetohydroxamate leads to a free energy barrieronly slightly lower (13.8 kcal/mol vs. 15.5 kcal/mol) [19].

For the study of the OH� base, we have used, as previously re-ported [33], three water molecules along with PCM to describe sol-vation effects. We show in Fig. 3 the optimized geometry of theOH� base and of its conjugate acid (H2O) and in Table 4 we report

Fig. 7. (a) Geometry optimization of first transition state of the reaction in vacuum (left) a(b) Geometry optimization of first transition state of the reaction in vacuum (left) and instate of the reaction in vacuum (left) and in solution (right).

the respective values of free energies in vacuo and the DG of solva-tion and pKa (B3LYP/6-31++g** level of theory) using different sol-vation radii. It can be noticed that the two waters are placedaround the oxygen of the OH� base and another one is pointingthe hydrogen of the base as a tetrahedral geometry with a distancet HOH–OH� of 1.66 Å and an angle of about 111� and with a dis-

nd its two different conformers in solution (right) using the acetohydroxamate base.solution (right) using the OH� base. (c) Geometry optimization of second transition

Table 7Free energies in vacuo (Hartree) and DG of solvation (kcal/mol) for all the species andtransition states involved in the reaction.

Species Gvac DGsolv (gauche) DGsolv (anti)

S �655.427998 �151.9 �149.9C �655.150537 �36.8 �36.8BH �284.351977 �5.4 �5.4B� �283.804978 �58.8 �58.84H2O �305.711310 �16.2 �16.2OH� + 3H2O �305.176350 �71.7 �71.7TS1 �939.462923 �51.6 �45.7TS1–OH �960.839149 �62.0 –TS2 �655.143984 �35.0 �35.0Quinuclidine �329.171123 1.9 1.92-Vinyl-piridinium �325.980270 �47.6 �47.6


tance H2O–HO� of 1.66 Å and an angle of 113�. We can see that thevalues of the pKa calculated using the different parameterization ofthe solvation spheres give results far from the expected value of 14,confirming the difficulty in properly describing the OH� base bycalculations including a limited number of explicit water mole-cules, neglecting also dynamics effects. We now turn to the inves-tigation of the acid–base properties of the substrate (nitrogenprotonated N-[2-(2-pyridil)ethyl]quinuclidinium). Interestinglyby previous work [45], we found only one stable substrate con-former in vacuo, corresponding to the anti conformer of Fig. 4and we obtain both the gauche and anti conformers in water solu-tion (see the corresponding optimized structures and Newmanprojections in Fig. 4). The gauche conformer is more stable thanthe anti conformer by 1.4 kcal/mol in terms of solution free ener-gies. The calculated pKa values for both substrate conformers arereported in Table 5 along with the corresponding energy contribu-tions. As can be seen, we calculate values of 15.3 and 13.8 for thegauche and anti conformers and we can underline that using dif-ferent parameterizations of the solvation spheres (UA0, SPH,UAHF) we obtain converging results. The former value (15.3), asso-ciated to the more stable conformer, is in excellent agreement withthe experimental value of 16 that can be estimated by applying theTaft’s equation [48,49].

A useful geometrical parameter which allows us to follow theevolution of the first reaction step is the parameter D [45], seeFig. 4, defined as D = [360�(a + b + c)], where a + b + c is the sumof the three bond angles of the carbon site undergoing deprotona-tion. This parameter characterizes the pyramidalization of the car-bon in a to the pyridine ring (C1), going from zero for an sp2 carbonatom to 31.5� for a tetrahedral sp3 site. The D values are reportedin Table 6 along with the main geometrical parameters in vacuoand in solution for the substrate (S), the carbanion (C), the olefinproduct (P) and the first and second transition states, consideringboth the acetohydroxamate and the OH� bases (TS1, TS1–OH,TS2). As can be noticed from Table 6, the optimized structuresare only slightly affected by solvation; recall, however, that differ-ent substrate conformers (gauche and anti) are more stable in solu-tion and in vacuo, respectively.

We notice that while the Cpy–C1 and C1–C2 distances show val-ues close to typical single carbon–carbon bonds in the reagent, inthe carbanion a considerable shortening of both parameters takesplace, reflecting the conjugation of these two carbon–carbon bondsand this is suggestive of the changing of hybridization of the C1 car-bon atom from tetrahedral to planar. In particular, the largest var-iation involves the Cpy–C1 bond length (from 1.50 Å to 1.38 Å), dueto the presence of the nitrogen protonated ligand. On the contrary,the C2–N bond with the quinuclidine leaving group is slightly elon-gated in the carbanion compared to the reagent (1.58 Å and 1.52 Å,respectively), indicating a weakening of the C2–N bond which pre-ludes the loss of the leaving group. We notice that in the carbanionthe value of D = 0� confirms the sp2 hybridization of the C1 carbon.The geometrical parameters of the carbanion are consistent withthose of an enaminic structure. In the olefin product, an inversionin the lengths of the Cpy–C1 and C1–C2 distances takes place withrespect to the carbanion, and the C1–C2 distance (1.34 Å) comesto be close to that of a typical carbon–carbon double bond.

To locate the transition state for the first reaction step we per-formed a linear transit scan of the potential energy surface of thesystem composed by the substrate and the base (acetohydroxa-mate, or OH� base). Following our previous work [33,34], we se-lected the distance between the nitrogen or oxygen atom of thetwo bases and the C1-bound hydrogen atom of the substrate (inanti position to the leaving group) as an approximate reactioncoordinate (RC), see Figs. 5 and 6. We then simulated the attackof the bases to the substrate by progressively reducing this dis-tance from a value of 2.0 Å (in steps of 0.1 Å) while fully relaxing

all the other degrees of freedom. We considered only the base at-tack to the C1-bound hydrogen in anti position to the leavinggroup, since this hydrogen was found to be the more reactive sitein our previous studies of b-eliminations in similar substrates[33,34,45]. We show in Figs. 5 and 6 selected snapshots takenalong the linear transit scan.

At values of the approximate RC close to 1.9 Å, the geometry ofthe substrate is essentially that of the isolated reagent. As the baseapproaches further, however, significant changes in the substrategeometry take place. At a RC value of 1.3 Å the C1–H bond is appre-ciably elongated (1.30 Å for the reaction with the acetohydroxa-mate base and 1.38 with OH� base) and, further reducing the RCleads to breaking of the C1–H bond and to the formation of thecarbanion. This is accompanied, as expected, by a change in theC1 hybridization from sp3 to sp2 (see values of D in Figs. 5 and 6).

Starting from the maximum energy structure encounteredalong the RC scan, we have fully optimized the geometry of thetransition state of TS1 in solvent for both the gauche and anti sub-strate conformers, finding optimized structures characterized byC1–H distances of 1.38 Å and 1.43 Å, respectively. For the TS1 in va-cuo we obtain a C1–H distance of 1.43 Å; for TS1–OH we obtain aC1–H distance of 1.31 Å in vacuo and 1.26 Å in solution, seeFig. 7. The gauche TS1 conformation is the more stable one by2.6 kcal/mol, in line with the relative stability of the two sub-strates. Again in line with what we found for the substrate, in va-cuo only the conformation of the transition state corresponding tothe anti conformation of the substrate exists. For the TS1–OH weobtain only one conformer in vacuo and in solution that is similarto the gauche conformer of the TS1.

The substrate is characterized by an essentially tetrahedralgeometry (D = 31� in vacuum and D = 22� in solution), while thecarbanion is planar (D = 0�). TS1 and TS1–OH are characterized,respectively, by D = 25� and D = 15� in vacuo, D = 13� andD = 17� in solution, still showing, therefore, a significant pyrami-dalization of the C1 carbon.

We proceeded in the same way to study the transition state ofthe second reaction step (TS2) and also in this case we used theparameter D for the characterization of carbon in b position tothe pyridine ring, which is about to lose the exiting group quinucli-dine. For the optimized structure of TS2 we find D = 6� in solutionand D = 4� in vacuo for the transition state, that is a transition statewith a geometry similar to that of the products, see Fig. 7. TS2 hasonly one conformation in vacuo and in solution. Pointing our atten-tion to the bond distance of the TS2 we can see that we obtain avalue of the C2–Q distance of 2.20 Å that is considerably elongatedwith respect to the reagents (1.52 Å) and respect to the carbanion(1.58 Å) that remark the TS2 is product-like.

We now have sufficient information to provide a thoroughdescription of the entire reaction profile. In Table 7, we reportthe free energies in vacuo and the DGsolv for the relevant species

Fig. 8. (a) Calculated reaction profile for the substrate in its gauche conformation (red profile) and the experimental reaction profile (blue) induced by the acetohydroxamatebase. (b) Calculated reaction profile (red) using the experimental pKa of acetohydroxamic acid compared to the experimental reaction profile (blue) (For interpretation ofreferences in color in the figure legends 8 and 9, the reader is referred to the web version of this article).


involved in the reaction. In Figs. 8 and 9 we show a schematic rep-resentation of the reaction energy profile (for a substrate in the

more stable gauche conformation). Notice that, to evaluate freeenergies, a term �1.89 kcal/mol must be added (subtracted) to

Fig. 9. (a) Calculated reaction profile for the substrate in its gauche conformation (red profile) and the experimental reaction profile (blue) induced by the OH� base. (b)Calculated reaction profile (red) using the experimental pKa of H2O compared to the experimental reaction profile (blue). (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)


the products energies for associative (dissociative) bimolecularreactions [33]. As can be noticed, the calculated activation free en-

ergy of the first step (12.8 kcal/mol for the reaction induced by theacetohydroxamate base and 12.4 kcal/mol for the reaction induced


by OH� base) is in good agreement with the experimental esti-mates (15.5 kcal/mol, 13.8 kcal/mol, respectively), the slightunderestimation being possibly due to the self-interaction errortypical of the exchange–correlation functional, which usually leadsto such underestimation in hydrogen and proton transfer reactions[50]. As is evident from Figs. 8 and 9, the main discrepancy be-tween the calculated and experimental profiles concerns the ther-modynamics of the first step where for the reaction involving theacetohydroxamate base, instead of an appreciably endothermicreaction (+8.7 kcal/mol), we calculate a slightly exothermic reac-tion (�0.5 kcal/mol); for the reaction involving OH� base, insteadof an experimental value of DG0

1 ¼ 2:2 kcal=mol, we calculated avalue of DG0

1 ¼ 9:1 kcal=mol. The thermodynamics of the first stepis dictated entirely by the difference in pKas of the base and thesubstrate, so that we can attribute this inaccuracy to the overesti-mation of the pKa of the acetohydroxamic acid and OH� which wediscussed above. While this apparently spoils the overall absoluteaccuracy of the computed profile, leading to an undue stabilizationof the reaction products, it does not affect at all the relative ener-getics of the second step of the reaction, i.e. the dissociation ofthe carbanion into the olefin and quinuclidine products, but onlyshifts it to lower energy. In particular, we note that the computedactivation energy for the second step is again only slightly under-estimated. As a result, if we just replace the computed pKa value forthe acetohydroxamic acid with its experimental estimate of 9.4,and the pKa value for the OH� with 14, the calculated free-energyprofile is at once brought into excellent agreement with the exper-imental one (see Figs. 8 and 9). Moreover, not only accuratelyreproduces the kinetics and thermodynamics of the reaction inabsolute value, but also leads to a qualitatively correct descriptionof the reaction mechanism, which is confirmed to be, in the reac-tion conditions [24] of partially reversible E1cb type, with an acti-vation free energy for the forward second step slightly higher thanthat for the reverse first step for the reaction with the acetohydr-oxamate base and irreversible, with an activation free energy forthe forward second step smaller than that for the reverse first stepfor the reaction with OH� base.

4. Summary and conclusions

We have presented a theoretical DFT investigation of a typicalb-elimination reaction induced by the attack of different bases ona pyridine-activated substrate. The aim of our study was to tune,and assess the accuracy of, a suitably general theoretical approachto simulate such important reactions. We have completely charac-terized the structure and free-energy in solution of the reactants,products and reaction intermediates, including a thorough confor-mational study and thus reproducing the entire reaction profile.The first step of the reaction is the substrate deprotonation by ac-tion of a base (acetohydroxamate or OH� in our case), leading tothe formation of a carbanion intermediate. In a second step, the lat-ter ejects a leaving group (quinuclidine in our case) and forms anolefinic product. The thermodynamics of the first step is essentiallythe result of the balance of the acid–base equilibria of the substrateand attacking base. Due to the difficulties in the theoretical repro-duction of the pKa of small base molecules in solution, this is inac-curately reproduced. On the contrary, the relative energy of thesubstrate and carbanion is very satisfactorily calculated and so isthe activation energy of the deprotonation, because the transitionstate is typically close in structure to the substrate and essentiallyindependent of the base. The energetics of the second step, with a‘‘late” transition state is also very accurately reproduced. As a re-sult, except for a rigid shift due to the incorrectly estimated pKa,the entire reaction free-energy profile is in excellent agreement(to within less than 3 kcal/mol) with the experimental findings

and, in particular, it confirms the partially reversible E1cb mecha-nism of the reaction. Given the nature of these b-eliminations, weexpect the level of accuracy obtained in the present work to berather generally attainable, establishing an efficient and reliabletool for predictive theoretical studies. The weak aspect of themethodology, namely the unreliable description of the acid–baseequilibrium of small acid molecules in solution, is at least partlyattributable to defects in the solvation model and, if necessary,can be corrected by explicit micro-solvation. In any case, it maybe argued to constitute a relatively minor problem both becausethe pKa of such species is typically well known, and because it af-fects only marginally the other details of the reaction profile.

References

[1] W.H. Saunders Jr., Cockerill, Mechanism of Elimination Reaction , Wiley-Interscience Publication, New York, 1973. vol. 2, pp. 60–68.

[2] E. Baciocchi, in: S. Patai, Z. Rappoport (Eds.), The Chemistry of Halides, PseudoHalides and Azides, Supplement D, Wiley Chichester, UK, 1983.

[3] J.R. Gandler, in: S. Patai (Ed.), The Chemistry of Double Bonded FunctionalGroup, Wiley Chichester, UK, 1989.

[4] W.H. Saunders Jr, Acc. Chem Res. 9 (1976) 19.[5] J.R. Gandler, W.J. Storer, D.A. Ohlberg, J. Am. Chem. Soc. 112 (1990) 7756.[6] A. Thibblin, J. Am. Chem. Soc. 111 (1989) 5412.[7] R.A. More O’Ferrall, P.J. Warren, J. Chem. Soc., Chem. Commun. 12 (1975) 483.[8] R.A. More O’Ferrall, F. Larkin, P.J. Walsh, Chem. Soc., Perkin Trans. 2 (1982)

1573.[9] F. Larkin, R.A More O’Ferrall, Aust. J. Chem. 36 (1983) 1831.

[10] A. Thibblin, J. Am. Chem. Soc. 110 (1988) 4582.[11] M. Ölwegård, I. McEwen, A. Thibblin, P. Ahlberg, J. Am. Chem. Soc. 107 (1985)

7494.[12] W.P. Jencks, Chem. Soc. Rev. 10 (1981) 345.[13] D.R. Marshall, P.J. Thomas, C.J.M. Stirling, J. Chem. Soc., Perkin Trans. 2 (1977)

1914.[14] N.S. Banait, W.P. Jencks, J. Am. Chem. Soc. 112 (1990) 6950.[15] A. Thibblin, Chem. Soc. Rev. (1993) 427.[16] W.P. Jencks, Acc. Chem. Res. (1980) 161.[17] R.H. Abeles, P.A. Frey, W.P. Jencks, Biochemistry, Jones and Bartlett Publisher,

1992.[18] F.G. Larkin, R.A. More O’Ferrall, D.G. Murphy, Collect. Czech. Chem. Commun.

64 (1999) 1833.[19] S. Alunni, A. Conti, R. Palmizio Errico, J. Chem. Soc., Perkin Trans. 2 (2000) 453.[20] J.R. Keefe, W.P. Jencks, J. Am. Chem. Soc. 105 (1983) 265.[21] S. Alunni, A. Conti, R. Palmizio Errico, Res. Chem. Intermed. 27 (2001) 653.[22] S. Alunni, A. Busti, J. Chem. Soc., Perkin Trans. 2 (2001) 778.[23] S. Alunni, V. Laureti, L. Ottavi, R. Ruzziconi, J. Org. Chem. 68 (2003) 718.[24] S. Alunni, L. Ottavi, J. Org. Chem. 69 (2004) 2272.[25] M. Langer, A. Pauling, J. Rétey, Angew. Chem. Int. Ed Engl. 34 (1995) 1464.[26] S. Gronert, J. Am. Chem. Soc. 113 (1991) 6041.[27] F.M. Bicklehaupt, E.J. Baerends, N.M.M. Nibbering, T. Ziegler, J. Am. Chem. Soc.

115 (1993) 9160.[28] W.H. Saunders Jr, J. Org. Chem. 62 (1997) 244.[29] S.S. Glad, F. Jensen, J. Am. Chem. Soc. 116 (1994) 9302.[30] M. Mugnai, M. Cardini, V. Schettino, J. Phys. Chem. A (2003) 2540.[31] B. Ensing, A. Laio, F.L. Gervasio, M. Parrinello, M.L. Klein, J. Am. Chem. Soc. 126

(2004) 9492.[32] B. Ensing, M.L. Klein, Proc. Nat. Ac. Sci. 102 (2005) 6755.[33] S. Alunni, F. De Angelis, L. Ottavi, M. Papavasileiou, F. Tarantelli, J. Am. Chem.

Soc. 127 (2005) 15151.[34] F. De Angelis, F. Tarantelli, S. Alunni, J. Phys. Chem. 110 (2006) 11014.[35] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.[36] M. J. Frisch, et al., Gaussian 03, Revision B.05, Gaussian, Inc., Pittsburgh PA,

2003.[37] R. Ditchfield, W.J. Herhe, J.A. Pople, J. Phys. Chem. 54 (1971) 724.[38] V. Barone, M. Cossi, J. Phys. Chem. A 102 (1998) 1995.[39] M. Cossi, N. Rega, G. Scalmani, V. Barone, J. Comp. Chem. 24 (2003) 669.[40] G.A.A. Saracino, R. Improta, V. Barone, Chem. Phys. Lett. 373 (2003) 411.[41] M.P. Liptak, G.C. Shields, Int. J. Quant. Chem. 85 (2001) 727.[42] C.O. da Silva, E.C. da Silva, M.A.C. Nascimento, J. Chem. Phys. 103 (1999) 11194.[43] C.O. daSilva, E.C. daSilva, M.A.C. Nascimento, J. Phys. Chem. A 104 (2000) 2402.[44] V. Barone, M. Cossi, J. Tomasi, J. Chem. Phys. 107 (1997) 3210.[45] E. Mosconi, F. De Angelis, F. Tarantelli, S. Alunni, A. Sgamellotti, Chem. Phys.

Lett. 480 (2008) 100.[46] N. Mora-Diez, M.L. Senent, B. Garcia, Chem. Phys. 324 (2005) 350.[47] L. Senent, A. Niño, C. Muñoz Caro, S. Ibeas, B. Garcia, G. Leal, F. Secco, M.

Venturini, J. Org. Chem. 68 (2003) 6535.[48] R.W. Taft, J. Am. Chem. Soc. 74 (1952) 3120.[49] M.J. Cook, A.R. Katritzky, P. Linda, R.D. Tack, Chem. Commun. (1971) 510.[50] M. Lundberg, P.E.M. Siegbahn, J. Chem. Phys. 122 (2005) 224103 (and

references therein).

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