Chemical Physics 359 (2009) 132–140

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Chemical Physics

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Theoretical calculation of atmospheric reactions. The case ofCH3–CHxOH(CH3)1�x–CHy(CH3)3�y, (x = 1,0; y = 2,1) + Cl

Andrés Garzón a,*, Mónica Moral b, Alberto Notario b, José Albaladejo a, Manuel Fernández-Gómez c

a Universidad de Castilla-La Mancha, Departamento de Química Física, Facultad de Ciencias Químicas, Avenida de Camilo José Cela, 10, 13071 Ciudad Real, Spainb Universidad de Castilla-La Mancha, Instituto de Tecnología Química y Medioambiental (ITQUIMA), Laboratorio de Química de la Atmósfera, Campus Universitario s/n,13071 Ciudad Real, Spainc Universidad de Jaén, Departamento de Química Física y Analítica, Paraje las Lagunillas, s/n, 23071 Jaén, Spain

a r t i c l e i n f o

Article history:Received 16 July 2008Accepted 23 March 2009Available online 27 March 2009

Keywords:Atmospheric reactionTheoretic mechanismAlcohol2-Butanol2-Methyl-2-butanol3-Methyl-2-butanol2,3-Dimethyl-2-butanolChlorineClRadical

0301-0104/$ - see front matter � 2009 Published bydoi:10.1016/j.chemphys.2009.03.017

* Corresponding author. Tel.: +34 953 21 33 78.E-mail address: agarzon@ujaen.es (A. Garzón).

a b s t r a c t

In this work, the reactions of Cl with a series of secondary alcohols: 2-butanol, 2-methyl-2-butanol, 3-methyl-2-butanol, and 2,3-dimethyl-2-butanol have been studied through ab initio Möller–Plesset sec-ond order perturbation treatment (MP2) calculations with 6-311G** basis sets. Optimized geometriesand vibrational frequencies have been obtained for transition states and molecular complexes appearingalong the different reaction pathways. Furthermore, molecular energies have been calculated at Qua-dratic Configuration Interaction with Single, Double, and Triple Excitations (QCISD(T)) level in order toget an estimation of activation barriers. The theoretical rate constant was also calculated for the mainreaction pathways using the Transition State Theory. The main aim of this work is to extend, from a the-oretical point of view, the knowledge of this kind of reactions that play a significant role in atmosphericchemistry.

� 2009 Published by Elsevier B.V.

1. Introduction

Alcohols are directly emitted into the atmosphere from biogenicand anthropogenic sources. They are used as industrial solventsand fuel additives, and in rural and forested areas, vegetation hasalso been found to be a significant source of unsaturated and satu-rated alcohols [1,2]. However, they are also formed in the tropo-sphere by photooxidation of non-methane hydrocarbons [3]. Inparticular, 2-butanol is present in coating formulations [4] and isemitted by solvent use and road traffic [5]. Other alcohols, suchas 2-methyl-2-butanol, have been detected in ambient air ofsemi-rural and urban locations [6] and 3-methyl-2-butanol wasfound as a metabolite from microorganisms grown on humidbuilding materials and synthetic media [7].

The oxidation of these volatile compounds in the troposphere ismainly initiated by reaction with OH radicals during the daytimeand with NO3 radicals at night. However, in recent years, the oxi-dation by chlorine atoms has gained great importance in the studyof atmospheric reactions because they may exert some influence inthe boundary layer, particularly in marine and coastal environ-

Elsevier B.V.

ments, and in the Arctic troposphere during springtime. Chlorineatoms may be key species in the atmospheric chemistry of marineenvironments where the ratio [Cl]/[OH] could be a factor of 1000higher than usual [8]. The main source of tropospheric Cl atomsis believed to be the photolysis of chlorine-containing moleculesgenerated by heterogeneous reactions of sea salt aerosols [9,10].It has also been proposed that Cl atoms, produced in the photolysisof Cl2 emitted from industrial processes, may enhance hydrocarbonoxidation rates and ozone production in urban environments[11,12]. Concerning to the oxidation mechanisms of alcohols, thisoxidation produces aldehydes, ketones, and organic nitrates as ma-jor products [13]. Therefore, alcohols have a potential to contributeto the adverse effects that are caused by anthropogenic organic airpollutants, e.g. photochemical oxidant formation and haze.

In a previous paper, we reported relative and absolute rate coef-ficients for the Cl with 2-butanol, 2-methyl-2-butanol, 3-methyl-2-butanol, and 2,3-dimethyl-2-butanol reactions [14]. In that work,some products were also identified and the corresponding reactionmechanisms were proposed. Now, the purpose of this work is toanalyse those reactions from a theoretical point of view, in orderto get additional elements to confirm the previously proposedreaction mechanisms. Although there are some preceding theoret-ical works about primary alcohols (e.g. methanol, ethanol,. . .) with

A. Garzón et al. / Chemical Physics 359 (2009) 132–140 133

Cl reactions [15–17], this study is the first one dealing with second-ary alcohols reactions.

As concerns primary alcohols, Jodkowski et al. [16] performed atwofold theoretical study at the MP2 level with 6-311G* and 6-311G** basis sets both for geometries and vibrational frequenciesand at the G2 model for energies on the hydrogen abstraction reac-tion from methanol with chlorine and bromine atoms. The authorsconcluded that these reactions proceed via the formation of inter-mediate molecular complexes with a favored hydroxymethylchannel with, in the case of the chlorine atoms, a very low energybarrier which may explain the relatively high value of the rateconstant.

Later, Rudic et al. [17] studied the reactions of hydrogenabstraction from methanol, ethanol and dimethyl ether (DME) bychlorine atoms. They carried out ab initio calculations at the MP2level with 6-311G** basis sets as regards optimized geometricalstructures and vibrational frequencies of molecular complexesand transition states on the reaction pathways while the energieswere refined at the G2 level. They concluded that reactions of chlo-rine atoms with ethanol and DME show transition states with verylow barriers and molecular complexes very similar to thosereported previously for the methanol case.

As a consequence of a crossed molecular beam experiment onthe abstraction of hydrogen from methanol by chlorine, a quantumdiffusion Monte Carlo (DMC) study on this reaction has also beenreported [18]. In this paper, an intrinsic reaction coordinate, IRC,calculation at MP2/6-311++G** identifies a direct reaction pathwayat odds with previous statements according to which this reactionproceeds through intermediates. Also, an estimate of reaction bar-rier at DMC and MP2 level of theory, DMC heats of reaction, DMC,MP2 and DFT/B3LYP atomization energies and heats of formationwere calculated.

Other previous work in this sense was carried out by our groupabout a set of reactions between primary alcohols, CH3–(CH2)n–OH,n = 0–4 and chlorine [15]. Critical points of the potential energysurface were optimized at the MP2 (with all electron correlatedfor n = 0–2 and Frozen Core approximation for n > 2) level with6-311G** basis sets. Activation energies and enthalpies at roomtemperature were calculated at the QCISD(T) level corrected withthe ZPE and thermal corrections estimated at MP2/6-311G**.

2. Computational details

Ab initio calculations were carried out using Gaussian’03 [19]set of programs. Geometries of reagents, transition states (TSs)and molecular complexes (MCs) were optimized at the Möller–Plesset second order perturbation theory with all electrons corre-lated, MP2(Full), and the 6-311G** basis sets. An initial conforma-tional analysis was carried out for the reagents in order to obtainthe least energetic conformation. Afterwards, a second conforma-tional analysis was also performed for each TS in order to confirmour initial choice for the most favored reaction pathway. All con-formational analysis were also carried out at the MP2(Full)/6-311G** level and convergence problems were solved by use ofOpt = CalcFC, SCF = Tight, and Int = Ultrafine options. The natureof the stationary points was assessed through the frequencies ofthe normal vibrations calculated through energy analytical secondderivatives. First order saddle points, which are related to transi-tion states, must show an imaginary value for the frequency asso-ciated to the eigenvector describing mainly the product formationstep while real minima of the potential energy hypersurface, whichare related to stable species must show all positive real values forvibrational frequencies.

For open-shell structures, spin contamination has been takeninto account since, as known, if the value of the final total spin

hS2i differs from s(s + 1), s being 1/2 times the number of unpairedelectrons, by more than 10% it may affect the energetic and geom-etry of the system. This effect increases, in general, as a bondstretches what turns out to be interesting for transition stateswhich contains elongated bonds [15]. In our systems, the spinexpectation values hS2i before annihilation of contaminants differfrom the theoretical value, 0.75, by no more than ca. 5%. Therefore,the spin contamination can be considered negligible. Single pointscalculations for reactants, molecular complexes, transition statesand selected products have been computed at quadratic CI (single,doubles and triples), QCISD(T), level on geometries at the MP2 levelwith 6-311G** basis set.

Relevant zero-point energies and thermal corrections calculatedwith MP2 have been considered into the final values of QCISD(T)energies. Barrier energies, DE�, classical and zero point corrected,as well as activation enthalpies and energies at 298.15 K have alsobeen calculated for the main reaction pathways. The calculatedactivation energies at 298.15 K, obtained through the expressionEa = DH� + 2RT [15,20] were compared with the previously re-ported experimental activation energies [14]. Enthalpies at298.15 K relative to the reactants were also calculated for molecu-lar complexes, transition states and products of these reactionpathways. Finally, for each reaction pathway a theoretical rate con-stant was calculated using the Transition State Theory (TST). Theseconstants were compared with the corresponding experimentalrate constants reported in literature [14].

3. Results and discussion

This kind of reactions between saturated alcohols and tropo-spheric radicals such as OH, NO3 or Cl proceed via hydrogenabstraction. This fact has been observed both in different experi-mental works [14,21–23] and theoretical studies [15–18]. In ourprevious work about primary alcohols, CH3�(CH2)n�OH, n = 0–4with Cl reactions, all possible pathways were studied [15]. Never-theless, due to the larger size of these secondary alcohols and theloss of symmetry, the number of chemically different hydrogenatoms and possible transition states increases significantly. In thissense, only main reaction pathways such as hydrogen abstractionover �CH– and –CH2– groups were studied. In several experimentaland theoretical works, it has been observed that attacks to HO–and –CH3 groups are minority reaction pathways [15–18,21–23].

3.1. 2-Butanol with Cl reaction

Two enantiomers are possible for this alcohol: R-2-butanol andS-2-butanol. Since they are chemically indistinguishable, only oneof them was studied, R-2-butanol. Transition states calculatedwere noted as TSn where n indicates the position of the hydrogenatom that suffers the attack. Thus, we have kept the same numer-ation that in previous works [15,24] where the HO– group-attack isnoted as TS0, the �CaH– group-attack is noted as TS1, etc. In thisreaction only TS2, TS3 syn and TS3 anti were calculated, which cor-respond at �CH– and –CH2– groups exclusively. We have also dis-tinguished between syn and anti depending on the Cl atom is onthe same plane that HO– group or at the opposite one respectively.Likewise, molecular complexes calculated were noted as MCnwhere n indicates the position of the hydrogen atom that is at-tacked. Nevertheless, MC0 is a molecular complex previous to tran-sition states wherein chlorine interacts with oxygen at largedistance (>2.5 Å).

In Fig. 1, the rotational barrier for O�Ca�Cb�Cc dihedral angleof TS2 at MP2(Full)/6-311G** level is plotted. The conformer 1 isthe initial conformation obtained for TS2 coming from a previousconformational analysis for the reagent (2-butanol). Two more

Fig. 1. Rotational barrier for O�Ca�Cb�Cc dihedral angle of TS2 in 2-butanol + Clreaction calculated at MP2(Full)/6-311G** level. Degrees of the dihedral angleindicate differences in the dihedral angle with respect to the initial conformationobtained for TS2 coming from a previous conformational analysis for the reagent (2-butanol). Different conformers are plotted in Newman conformation.

134 A. Garzón et al. / Chemical Physics 359 (2009) 132–140

energetic conformers were calculated: conformer 2 and conformer3 with MP2 energies 0.8 and 0.7 kcal mol�1 higher than conformer1. Although the energy differences between conformers 2 and 3with respect to the conformer 1 are small, the rotational barriersare 5.1 and 3.6 kcal mol�1, respectively. In order to facilitate thestudy, we only take into the account the initial conformer calcu-lated for TS2. Conformational analyses were also performed forTS3 syn and TS3 anti which are showed in the Supplementarymaterial. In both cases, high rotational barriers, between 3 and7 kcal mol�1, were calculated. For TS3 syn, other two conformerswere obtained. Both conformers have MP2 energies 0.7 and1.0 kcal mol�1 higher than the initial conformer TS3 syn. For TS3anti, two conformed were also obtained with MP2 energies 0.1and 0.5 kcal mol�1 higher than TS3 anti.

Optimized MP2(Full)/6-311G** geometries of transition states(TSn) corresponding to �CH– and –CH2– groups are representedin Fig. 2. Molecular complexes (MCn) corresponding to the mainreaction pathway in terms of energy are also represented inFig. 2. As an example, the critical points (molecular complexes,transition states, and products) of the potential energy surface(PES) for the main reaction pathway are represented in the Fig. 3.An energy-stabilized-molecular complex (MC0) previous to thetransition state, in which the Cl atom is situated at 2.55 Å of theO atom was found. Also, the Cl atom is situated at 2.74 Å of the hy-droxyl hydrogen atom, 3.06 Å of the hydrogen of �CaH– group, and3.12 Å respect to the nearest hydrogen of –CbH3 group. Thesebond-distances are comparable with MC0 corresponding to pri-mary alcohols with Cl reactions where d(Cl���O) � 2.53 Å andd(Cl���HO–) � 2.87 Å [15].

Subsequently, the reaction passes through the correspondingtransition states. When Cl approaches the alcohol along the bondCa–H, a named-TS2-transition state can be outlined. The most sig-nificant structure parameters are d(Ca���H) = 1.119 Å andd(H���Cl) = 2.119 Å and a(Ca���H���Cl) = 148.9�. There are some dif-ferences with respect to primary-alcohols-TS2 in which the dis-tance H���Cl varies from 1.802 Å for methanol to 1.967 Å for 1-pentanol and the angle a(Ca���H���Cl) is closer to the linearity(�172�). Associated with an out-of-phase stretching of Ca���H andCl���H distances, an imaginary frequency exists whose value is73i cm�1 while for the corresponding primary-alcohols-TS2 theirvalues vary from 236i cm�1 for methanol to 123i cm�1 for 1-pent-anol. On the other hand, abstraction of hydrogen from the –CbH2–

moiety yields two non-equivalent transition states, TS3 syn andTS3 anti. In both TS3, values for Cl���H and Cb���H distances are�1.46 Å and �1.35 Å, respectively, while values for the angle de-fined by Cl���H���Cb are 173.9� for TS3 syn and 176.1� for TS3 anti.Both values of Cl���H and Cb���H distances and the angle Cl���H���Cb

are similar to those for primary-alcohols-TS3. The imaginary fre-quency associated with stretches of Cb���H and Cl���H distancesare 916i cm�1 for TS3 syn and 888i cm�1 for TS3 anti.

In Table 1, the energies of transition states evaluated atQCISD(T)/6-311G**//MP2(Full)/6-311G** can be read. Accordingly,and assuming the less energy consuming reaction pathway, themost favorable route for reaction between 2-butanol with Cl is thatpassing through TS2. In our previous experimental work about thisreaction two reaction pathways were proposed as the main ones[14]. Both pathways yield peroxyacetyl nitrate (PAN) as final reac-tion product according to the reaction mechanism of the Fig. 4. Thismechanism is proposed on the basis of detected reaction productsand typical photooxidation tropospheric mechanisms. In the lightof this theoretical study, it seems that the most favorable pathwayis that yielding 2-butanone as a previous product to PAN and acet-aldehyde. The value determined for the experimental activationenergy, Ea,exp, (�0.35 kcal mol�1, [14]) lies between Ea calculatedfor TS2 (�0.89 kcal mol�1) and Ea calculated for TS3 syn and anti(0.22 and 0.53 kcal mol�1). These results seem coherent consider-ing that the experimental activation energy is a global activationenergy wherein a greater contribution of the most favoured reac-tion pathway (TS2) must exist. Good agreements between experi-mental and theoretical activation energies were obtained in ourprevious study on primary alcohols with Cl reaction, especiallyfor the alcohols with the shortest hydrocarbon chains [15].

The theoretical rate constants for the main pathways were alsoevaluated through the TST assuming a preequilibrium betweenMC0 and reactants and TS, in such a way that the rate constantfor the overall reaction can be written as

k ¼ k1k2

k�1 þ k2� kk2; ð1Þ

where k1 and k�1 are the forward and reverse rate constants for theformation of MC0, k2 is the rate constant for the passage to productsand k is the equilibrium constant between reactants and MC0(k = k1/k�1). We assume that k�1� k2, even though the energy bar-rier for k�1 is some higher than for k2 since the evaluation of k�1 isnot trivial due to the inexistence of TS in the formation of MC0 (seeTable 2). This supposition means that the calculated rate constantmay not be the rate-determining step.

The equilibrium constant, k, can be obtained from the total par-tition functions for both the prereactive complex (QMC0) and reac-tants (QR), while k2 can be calculated through the classical TSTexpression from the total partition functions for transition state(Q�), with no tunneling factor in mind

K ¼ QMC0

Q Rexp

E�1

RT

� �Q z

Q MC0

kbTh

� �exp

E2

RT

� �: ð2Þ

Table 3 displays the values of the experimental and calculatedrate constants at 298.15 K. For the most favorable route of the reac-tion 2-butanol + Cl, i.e. that passing through TS2, the calculatedrate constant (kTST) is over 10 times the experimental value forthe whole reaction (kexp) while for the pathways through TS3’s, kTST

turns out to be nearer to the experimental k.Finally, in Table 2 the QCISD(T)/6-311G**//MP2(Full)/6-311G**

relative enthalpies calculated at 298.15 K, with respect to the re-agents, of the molecular complexes (HMC), transition states (HTS),and products (Hproducts) for the main pathway (less costly in en-ergy) of each reaction can be seen. A relative enthalpy of�4.67 kcal mol�1 was calculated for the initial molecular complex

MC0 TS2

TS3 syn TS3 anti

MC2

2.119

1.119 1.519

1.519

148.9º 1.4142.548

0.962

1.437

2.743

110.8º

3.123

3.057

176.1º

1.500 1.511

1.355

1.459

1.093

1.429

1.356

1.505

1.462

1.502

173.9º 1.092

1.418

1.811

1.323

174.0º 1.370

1.497

Dihedral angles:

<(H-O-Cα-Cβ) = 174.3º

<(H-O-Cα-Cl) = 73.3º

Dihedral angles:

<(O-Cα-Cβ-Cγ) = 57.8º

<(Cl-Cα-Cβ-Cγ) = 10.1º

Dihedral angles:

<(H-O-Cα-Cβ) = 178.6º

<(O-Cα-H-Cl) = 55.8º

Dihedral angles:

<(H-O-Cα-Cβ) = 172.8º

<(O-Cα-Cβ-Cl) = 69.7º

Dihedral angles:

<(H-O-Cα-Cβ) = 176.6º

<(O-Cα-Cβ-Cl) = 169.2º

Fig. 2. Optimized geometries at MP2(Full)/6-311G** level for molecular complexes, MCn, and transition states, TSn, regarding to 2-butanol + Cl reaction.

A. Garzón et al. / Chemical Physics 359 (2009) 132–140 135

MC0 and of �9.86 kcal mol�1 for MC2. This molecular complexshows the initial evolvement of HCl, since a formal H–Cl link ap-

-12.00

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

2.00

En

thal

py

/ kca

l mol

-1

Main reaction pathway

CH3CH(OH)CH2CH3 + Cl

CH3C(OH)CH2CH3 + HClMC0

MC2

TS2

Fig. 3. Calculated QCISD(T)/6-311G**//MP2/6-311G** relative enthalpies at298.15 K, with respect to the reagents, of the transition state (HTSn) and molecularcomplexes (HMCn) for the main pathway of 2-butanol + Cl reaction.

pears, d(H–Cl) = 1.323 Å, as well as a partial breaking of the Ca–Hbond, d(C–H) = 1.811 Å. The relative enthalpy calculated for finalproducts was �5.26 kcal mol�1, therefore this reaction pathwayis exothermic in character.

3.2. 2-Methyl-2-butanol with Cl reaction

In the present reaction only transition states corresponding to –CbH2– were calculated since the molecule has not neither �CH–groups nor other –CH2– groups, different to –CbH2–. However,two different transition states can be differentiated: TS3 syn andTS3 anti. In the first one, the Cl atom is situated in the same planeof HO– group unlike TS3 anti. Although both TSs were optimizedfrom optimized structure of 2-methyl-2-butanol (reagent), a laterconformational analysis was also carried out. For TS3 syn, twoother different conformers were obtained, both with a higherMP2 energy than the initial conformer (0.4 and 0.6 kcal mol�1),one of them (0.4 kcal mol�1) corresponding with an enantiomerof TS3 anti. For the case of TS3 anti, a more energetic conformerthan 0.3 kcal mol�1 as well as another nearly energy-equivalentone to the initial conformer were obtained. This last conformer cor-

Table 1Calculated QCISD(T)/6-311G**//MP2(Full)/6-311G** classical barrier heights ðDEzclassicalÞ, zero-point energy corrected barrier heights ðDEzcorrectedÞ, enthalpies of activation at 298.15 KðDEz298:15 KÞ, and energies of activation at 298.15 K (Ea,298.15 K) for the different pathways of each studied reaction.

Alcohols Transition states DEzclassical (kcal mol�1) ðDEzcorrectedÞa (kcal mol�1) DH�

298.15 Ka (kcal mol�1) Ea 298.15 K

a (kcal mol�1) Ea,expb (kcal mol�1)

2-Butanol TS2 �1.25 �1.67 �2.08 �0.89 �0.35TS3 syn 3.96 �0.64 �0.97 0.22TS3 anti 4.25 �0.38 �0.66 0.53

2-Methyl-2-butanol TS3 syn 3.66 �1.01 �1.23 �0.04 �0.65TS3 anti 3.92 �0.77 �1.02 0.17

3-Methyl-2-butanol TS2 �1.44 �1.75 �2.16 �0.97 �0.38TS3 0.54 �3.99 �4.18 �2.99

2,3-Dimethyl-2-butanol TS3 0.05 �4.51 �4.61 �3.43 �0.44

a ZPE and thermal correction at 298.15 K were computed at MP2 level.b Ref. [14].

CH3

CH3

OH

2-butanol

CH3

CH3

O

2-butanone

1) ·Cl / -HCl2) O2 / -HO2

CH3CH3

OH

O

CH3

H

O

CH3 C

O

+acetaldehyde

1) ·Cl / -HCl2) O2

3) NO2

1) O2

2) NO2

CH3

O O

NO2

O

peroxyacyl nitrate

1) ·Cl / -HCl2) O2

3) NO / -NO2

1) ·Cl / -HCl2) O2

3) NO / -NO2

CH3CH3

O

O

CH3 CH

OH

O2 / -HO2

Fig. 4. Proposed reaction mechanism of 2-butanol with Cl atoms under tropospheric conditions.

Table 2Calculated QCISD(T)/6-311G**//MP2(Full)/6-311G** relative enthalpies at 298.15 K, with respect to the reagents, of the molecular complexes (HMC), transition states (HTS), andproducts (Hproducts) for the main pathway of each reaction.

Alcohols Reaction pathway corresponding to HMC0a (kcal mol�1) HTSn

a,b (kcal mol�1) HMCna (kcal mol�1) Hproducts

a,c (kcal mol�1)

2-Butanol TS2 �4.67 �2.08 �9.86 �5.262-Methyl-2-butanol TS3 syn �5.12 �1.23 �6.39 0.153-Methyl-2-butanol TS3 �4.71 �4.18 �7.53 �0.942,3-Dimethyl-2-butanol TS3 �5.22 �4.61 �8.81 �1.90

a ZPE and thermal correction at 298.15 K were computed at MP2 level.b Corresponding with the enthalpy of activation at 298.15 K (ðDEz298:15 KÞ) for the main reaction pathway.c Corresponding with the reaction enthalpy at 298.15 K (DH298.15K) for the main reaction pathway.

136 A. Garzón et al. / Chemical Physics 359 (2009) 132–140

responds with an enantiomer of TS3 syn. The smallest torsionalbarriers were obtained to change from TS3 anti to TS3 syn and viceversa (2.7�3.1 kcal mol�1). The rest of barriers are between 4.0 and6.4 kcal mol�1 (see Supplementary material for more information).

Optimized Geometries MP2(Full)/6-311G** for TS3 syn and antiare represented in Fig. 5. Concerning the main geometric parame-ters, no substantial differences between both TSs were found. Incomparison with TS3 syn the distance Cl���H experiences a slightshortening in TS3 anti while the distance H���Cb suffers a slightenlargement. Furthermore, the angle a(Cb���H���Cl) for TS3 anti is�4� closer to the linearity than that for TS3 syn (�172�). Imaginaryfrequencies for TS3 syn and TS3 anti are 926i cm�1 and 837i cm�1,

and appear as associated to vibrations where the most importantcontributions are the stretches of Cb���H and H���Cl distances. Ascan be seen in Table 1, the activation energy at 298.15 K,Ea,298.15 K, for TS3 syn is only 0.21 kcal mol�1 smaller than that forTS3 anti. In this case, the experimental activation energy, Ea,exp,(�0.65 kcal mol�1) does not seem to be in a good agreement withthe calculated activation energies for the less energetic pathways(�0.04 and 0.17 kcal mol�1). On the other hand, Ea,exp for 2-methyl-2-butanol was obtained by the fitting of an Arrhenius-likeequation, ln k vs. (1/RT), in the range of temperature 270–352 Kwhere that plot shows a linear behavior [14]. Nevertheless,although Ea,exp for 2-methyl-2-butanol was the smallest of the ser-

MC0 TS3 syn

TS3 anti MC3 syn

1.804 1.297

1.449

1.497

0.963

2.932

178.3º

1.3531.465

172.4º1.503

1.512

1.425

1.093

2.539 2.891

3.030 3.723

118.9º 1.443

1.372

1.451

176.5º

1.519 1.501

1.437

Dihedral angles:

<(H-O-Cα-Cβ) = 176.4º

<(O-Cα-Cβ-Cγ) = 58.7º

<(Cl-Cα-Cβ-Cγ) = 93.3º

Dihedral angles:

<(H-O-Cα-Cβ) = 176.0º

<(O-Cα-Cβ-Cγ) = 66.5º

<(O-Cα-Cβ-Cl) = 179.5º

Dihedral angles:

<(H-O-Cα-Cβ) = 177.1º

<(O-Cα-Cβ-Cγ) = 49.3º

<(Cl-Cα-Cβ-Cγ) = 86.6º

Dihedral angles:

<(H-O-Cα-Cβ) = 173.7º

<(O-Cα-Cβ-Cγ) = 45.9º

<(O-Cα-Cβ-Cl) = 68.2º

Fig. 5. Optimized geometries at MP2(Full)/6-311G** level for molecular complexes, MCn, and transition states, TSn, regarding to 2-methyl-2-butanol + Cl reaction.

Table 3Calculated theoretical rate constants through the TST for the main reaction pathways and comparison with the experimental values reported [14], both at 298.15 K.

Compound Reaction pathway (kTST ± 2s) � 1011 (cm3 molecule�1 s�1) (kexp ± 2s) � 1011 (cm3 molecule�1 s�1)

2-Butanol TS2 157 11.0 ± 0.3TS3 syn 5.72TS3 anti 4.16

2-Methyl-2-butanol TS3 syn 11.4 7.4 ± 0.2TS3 anti 5.96

3-Methyl-2-butanol TS2 236 12.0 ± 0.3TS3 1270

2,3-Dimethyl-2-butanol TS3 3400 10.5 ± 2.1

A. Garzón et al. / Chemical Physics 359 (2009) 132–140 137

ies of secondary alcohols (see Table 1), this reaction turns out to bethe slowest of the series at least within the range of temperaturestudied. Therefore, it seems coherent that the calculated value ofEa,298.15 K for the main pathway of 2-methyl-2-butanol reaction isthe highest of the series. The calculated kTST are comparable tothe experimental value for this reaction (see Table 3) and theseare the slowest of the series, too.

Molecular complexes MC0 and MC3 syn, previous and subse-quent, respectively to the most energy favorable transition state(TS3 syn), were also calculated. Optimized Geometries MP2(Full)/6-311G** for these molecular complexes are represented in Fig. 5.As can be seen, the most significant differences in comparison withMC0 for 2-butanol is the enlarged Cl���H–O and Cl���H–CcH2 dis-tances, that amount to 2.891 Å and 2.723 Å, respectively. As con-cerns MC3 syn, it is a structure where HCl molecule interacts

with O atom instead of with Cb atom. The distance O���HCl is1.80 Å, similar to d(Ca���HCl) of MC2 of 2-butanol. Both molecularcomplexes are structures less energetic than TS3 syn, but the en-thalpy of reaction at 298.15 K (DH298.15 K) is slightly endothermic(see Table 2). According to our previous experimental study [14],where PAN and acetone were detected as main reaction products,this pathway (through TS3) was proposed as the most favorable,too.

3.3. 3-Methyl-2-butanol with Cl reaction

Once again, two enantiomers are possible for this compound: R-3-methyl-2-butanol and S-3-methyl-2-butanol. Nevertheless, sincethey are chemically indistinguishable, only one of them was stud-ied, R-3-methyl-2-butanol. Thus, two transition states correspond-

138 A. Garzón et al. / Chemical Physics 359 (2009) 132–140

ing to �CaH– and �CbH– groups were calculated for this system:TS2 and TS3, respectively. The conformational analysis carriedout for TS2 yields two other conformers other than the startingone. Both conformers have higher MP2 energies (0.1 and0.5 kcal mol�1) than the initial conformer TS2. For TS3, two addi-tional closed-in-energy conformers were calculated where theleast energetic one has a MP2 relative energy of �0.1 kcal (see Sup-plementary material).

TS2, like TS2 of 2-butanol, shows Ca���H distances some tenthsof Å shorter and H���Cl distances almost 1 Å longer than any otherTSn (see Fig. 6). This fact has already been observed in previoustheoretical works dealing with alcohols with Cl reactions [15,17].These transition states are more similar to reagents than othertransition states. Also, TS2 usually is more energy favorable thanthe remaining TSn. These differences could be caused by the prox-imity of HO– group which can stabilize the structure by means ofthe free electron-pairs of the oxygen atom. Also, TS2 shows lowerimaginary frequencies than other TSn. An imaginary frequency of49i cm�1 was observed for TS2 which is associated with an out-of-phase stretching of Ca���H and Cl���H distances. In Fig. 6, the opti-mized geometries MP2(Full)/6-311G** for TS3 can also be seen. Ascompared with other TS3, Cb���H and H���Cl distances remain essen-tially constant. Nevertheless, it can be observed a light shorteningof Ca���H distance and a somewhat elongated Cl���H distance,caused by steric hindrances. The imaginary frequency associatedto stretches of Cb���H and Cl���H distances for TS3 is 673i cm�1.

As regards the classical barrier ðDEzclassicalÞ, i.e. QCISD(T) energywithout thermal corrections, the reaction pathway correspondingto TS2 is the least energetic. Nevertheless the pathway throughTS3 is the most favored in terms of energy considering MP2 ther-mal corrections (see Table 1). Therefore, Ea,298.15 K for TS3 is smaller

MC0

TS3

2.740

2.544

3.031110.5º 1.438

0.962

β

αγ

1.308

1.497 171.9º

α

β

γ1.515

1.509

1.509

1.419

Dihedral angles:

<(H-O-Cα-Cβ) = 160.8º

<(O-Cα-Cβ-Cγ) = 55.1º

<(Cl-Cα-Cβ-Cγ) = 6.9º

D

<(H

<(O

<(C

Dihedral angles:

<(H-O-Cα-Cβ) = 171.4º

<(O-Cα-Cβ-Cγ) = 45.8º

<(O-Cα-Cβ-Cl) = 67.0º

Fig. 6. Optimized geometries at MP2(Full)/6-311G** level for molecular complexes,

than Ea,298.15 K for TS2 and that is why we consider the main reac-tion pathway that through TS3. In this case, both Ea,298.15 K calcu-lated for TS2 and TS3 are smaller than experimental activationenergy (Table 1). These results are coherent considering the exper-imental activation energy like a global activation energy with agreater contribution of the most favored reaction pathways (TS2and TS3). Nevertheless, the differences between experimentaland theoretical activation energies are higher than those for thecase of 2-butanol. This fact could be induced by the presence ofmore methyl groups, which generate new feasible although lessaccessible (higher energy barriers) reaction pathways and hin-drances to attack on the most favored positions, �CaH� and�CbH�.

The calculated kTST’s for the main pathways (TS2 and TS3) liebetween 20 and 100 times the experimental rate constant. kTST

for this reaction is higher than those for the reactions of 2-butanoland 2-methyl-2-butanol. This increase parallels the decrease ofEa,298.15 K for TS3 due to the increase of the number of methylgroups.

In Table 2 relative enthalpies calculated at 298.15 K with re-spect to the reagents, of the molecular complexes, transition states,and products for this pathway are included. As it can be seen, bothMC0 and MC3 are structures less energetic than TS3, and theenthalpy at 298.15 K (DH298.15 K) points that this reaction is exo-thermic in character. The most relevant geometrical parametersof MC0 appear in Fig. 5. A noticeable similarity with anotherMC0’s can be observed as it can be deduced from Cl���O (2.54 Å)and H–Ca (3.03 Å) distances. Similar comments deserve the caseof MC3, for which the distance (Cl)–H���O keeps around 1.81 Å.

Bearing in mind Scheme 1 of Ballesteros et al. [14] and on thebasis of our theoretical results the pathway that directly yields

TS2

MC3

1.521 1.525

2.218

1.114

169.0º

1.418

α

β

γ

1.297 1.812

177.4º

1.442

1.522

1.498

0.962

α

β γ

Dihedral angles:

<(H-O-Cα-Cβ) = 176.0º

<(O-Cα-Cβ-Cγ) = 57.7º

<(Cl-Cα-Cβ-Cγ) = 66.5º

ihedral angles:

-O-Cα-Cβ) = 177.0º

-Cα-Cβ-Cγ) = 49.8º

l-Cα-Cβ-Cγ) = 89.6º

MCn, and transition states, TSn, regarding to 3-methyl-2-butanol + Cl reaction.

A. Garzón et al. / Chemical Physics 359 (2009) 132–140 139

PAN and acetone is more favorable than those that yield 3-methyl-2-butanone as primary reaction product. In this sense a differencein Ea,298.15 K of �2 kcal mol�1 has been calculated between bothpathways. These were already detected by Ballesteros et al. [14],although they were not able to state about the main pathway reac-tion due to the unfeasibility to quantify products.

3.4. 2,3-Dimethyl-2-butanol with Cl reaction

A transition state TS3 corresponding to a �CbH– group was cal-culated for this system. The later conformational analysis yieldedtwo additional conformers with closed MP2 energies. One of themis an enantiomer of the initial conformer proposed for TS3 emerg-ing from the conformational analysis of the reagent 2,3-dimethyl-2-butanol. The most interesting geometric parameters of MC0, TS3and MC3 can be seen in Fig. 7. Different energy barriers and rela-tive enthalpies calculated at 298.15 K, with respect to the reagents,for the various stationary points appearing along this pathway canbe seen in Tables 1 and 2. Ea,298.15 K calculated for this reaction isthe smallest of the series and is very much smaller than experi-mental activation energy (�0.44 kcal mol�1). Like in the case of3-methyl-2-butanol, the difference between experimental and the-oretical activation energies increase with the number of methylgroups and the comparison becomes of increasing complexity.For this reaction, kTST for the main reaction pathway is the highestof the series due to the fall in the value of the calculated Ea,298.15 K,and the difference between experimental and theoretical rate con-stant is the largest, too.

As can be seen in Fig. 7, the Cl���O distance for MC0 keeps nearlyconstant, �2.54 Å as compared with other MC0’s structure. Like-

MC0

MC3

1.801

1.44

0.963

β

αγ

1.529

2.541

1.529

0.964

1.537

1.445

βαγ

100.3º

Dihedral angles:

<(H-O-Cα-Cβ) = 178.3º

<(O-Cα-Cβ-Cγ) = 60.9º

<(Cl-Cα-Cβ-Cγ) = 96.6º

Fig. 7. Optimized geometries at MP2(Full)/6-311G** level for molecular complexes, M

wise, TS3 shows the longest Cl���H (1.29 Å) and the shortest H���Cb

(1.52 Å) distances as well as the greater departure from linearity,a(Cl���H���Cb) = 169.5�. These results are in agreement with anexplanation on the basis of steric hindrances due to the greaternumber of methyl moieties in the proximity. In MC3, a O���H–Cldistance of 1.80 Å was observed. Finally, both molecular com-plexes, MC0 and MC3, are structures less energetic than TS3 andthe values of enthalpy of reaction at 298.15 K (DH298.15 K) pointsto the reaction is exothermic, too (see Table 2).

4. Conclusions

This work is a continuation of our previous theoretical andexperimental studies about the reactions of primary and secondaryalcohols with chlorine atoms [14,15]. Critical points of the poten-tial energy surface were calculated for the less energetic pathwayof each reaction. Thus, molecular complexes, previous and subse-quent to the corresponding transition states, were calculated forthe mentioned pathways. The calculation of this kind of molecularcomplexes has already been described in experimental and theo-retical previous works [14–17].

The calculated values for the activation energies at 298.15 K,Ea,298.15 K, of the main pathways for 2-butanol + Cl reaction arecoherent with the experimental activation energy [14]. Neverthe-less, the differences between experimental and theoretical activa-tion energies are higher for the rest of the series. Likely, this factcan be caused by the presence of additional methyl groups thatgenerates more possible reaction pathways and steric hindrances.Also, the energy differences discussed are at the borderline of theexpected accuracy of the applied methods. Particularly the single

TS3

1.298

8

177.5º

1.516

1.289

169.5º

1.510

1.511

1.526

1.427β

α

γ

Dihedral angles:

<(H-O-Cα-Cβ) = 178.6º

<(O-Cα-Cβ-Cγ) = 49.3º

<(Cl-Cα-Cβ-Cγ) = 87.5º

Dihedral angles:

<(H-O-Cα-Cβ) = 171.9º

<(O-Cα-Cβ-Cγ) = 49.8º

<(O-Cα-Cβ-Cl) = 62.8º

Cn, and transition states, TSn, regarding to 2,3-dimethyl-2-butanol + Cl reaction.

140 A. Garzón et al. / Chemical Physics 359 (2009) 132–140

point calculations at QCISD(T) level might pile up small errors fromnot optimal geometries, which could explain the decreasing agree-ment with increasing system size.

In general, TS2s have a particular geometry, more similar to thereagents than the rest of TSn’s, where Ca���H and H���Cl distancesturn out to be 1.1 and 2.1�2.2 Å, respectively, and the imaginaryfrequencies are significantly low (49i and 73i cm�1). Comparablegeometric parameters and imaginary frequencies were calculatedfor primary alcohols such as 1-butanol and 1-pentanol. Activationenergies calculated for TS2 of 2-butanol and 3-methyl-2-butanolhave energies (�0.89 and �0.97 kcal mol�1, respectively) near toother TS2s calculated for linear alcohols such as 1-propanol, 1-butanol, and 1-pentanol (�0.76, �0.92, and �0.97 kcal mol�1).For TS3s of the series, there are more differences in the geometricparameters and activation energies. In general, TS3s of 2-butanoland 2-methyl-2-butanol have higher activation energies thanTS3s of 3-methyl-2-butanol and 2,3-dimethyl-2-butanol becauseof the increase of methyl groups. Nevertheless, this decrease inthe activation energy for TS3 is not observed in the experimentalactivation energy. One possible explanation may be that the in-crease of steric hindrances in this pathway could reduce its weightin the whole mechanism. Thus, 2-butanol and 3-methyl-2-butanolhave comparable reaction rates while the rest of alcohols without apathway through TS2 have slower reaction rates [14].

The calculated kTST’s follow the same trend that Ea,298.15 K, wherethe fastest pathway seems to be through TS2 for 2-butanol and TS3for the rest of the series. Therefore, in the same way that forEa,298.15 K, the difference between the experimental and theoreticalrate constants increases with the system size, too.

Acknowledgments

Ab initio calculations were done on a ia64HP Server rx 2600 atthe University of Jaén and resources of the Supercomputing Serviceof Castilla-La Mancha University. The authors gratefully thank theSpanish Ministerio de Educación y Ciencia (Projects BQU 2003-08221 and CGL2004-03355/CLI), the Junta de Comunidades deCastilla-La Mancha (Project PAI-05-062) and the Consejería deInnovación, Ciencia y Empresa (Junta de Andalucía, (FQM337 con-tract)) for the financial support of this research work.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.chemphys.2009.03.017.

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