theoretical and computational study of sulfur compounds … · theoretical and computational study...

Theoretical and Computational Study of Sulfur Compounds Reactivity in PrebioticChemistry: The Whitesides Network of Thiols and Thioesters

Joao Miguel dos Santos Nicolau InesFacultat de Quımica, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain. and

Departamento de Engenharia Quımica, Instituto Superior Tecnico, Av. Rovisco Pais 1049-001 Lisboa, Portugal.*

Advisors: Josep Maria Bofill Villa ; Iberio de Pinho Ribeiro Moreira and Co-tutor: Luis Filipe Veiros*

Abstract: Networks of organic reactions containing sulfur may have played a role in the originsof life. Sulfur atoms are similar to other hydrogen bond donors, like -N-H. They are more directionaland hydrophobic being perfect for catalysis in polar and apolar media. Using ab initio quantumchemistry methods we propose to study the Whitesides organic chemistry network. This networkconsists in a set of biologically relevant organic reactions like amide formation, thiolate-thioesterexchange, thiolate-disulfide interchange and conjugate addition. Interesting dynamics appear asbistability and oscillatory behaviour in the autocatalytic thiol network. The root cause for sulfuractivation energies and reactivities will be analyzed through valence bond theory.

I. INTRODUCTION

An understanding of chemical reactivity begins withan understanding of chemical bonding, the forces whichrender atoms aggregated to form molecules. Londonand Heitler introduced quantum mechanics into reactiv-ity problems, in chemistry.

The principle of activation, that is, the postulate thatonly those molecules with combined energy equal orgreater than some critical value can react, is likewisea statistical concept, but the actual value of this criti-cal energy depends on electronic changes in the reactingmolecules and cannot be found without a knowlodge ofquantum laws2.

Additionally, the rate constants of the Whitesides3 re-actions were calculated by theoretical methods in the gas-phase using Transition State Theory (TST). The reagentmolecule(s) are supposed to be in thermodynamic equi-librium with the Transition State (TS) which passes toproducts at a specific frequency and it is only applied tosingle microscopic rate constant as a result of collisionsof two molecules (or unimolecular reactions) to render aconfiguration of maximum potential energy.

Valence Bond (VB) theory formalism decomposeschemical systems into a linear combination of chemicallymeaningful structures (molecular states), in which theelectrons occupy localized orbitals by combining relevantatomic orbitals. Therefore, VB looks for the probabilityof finding a molecule at a given molecular state. A VBcorrelation diagram, which traces the VB configurationsalong the reaction coordinate, and by mixing of configu-rations, projects the root cause of the energetic barrier,the nature of the transition state, and the origins of re-action intermediates4.

In the present work, it was proposed to study a set ofbiologically relevant organic reactions that present someinteresting features as autocatalysis, bistability and os-cillatory behaviour. The reactions network is completewith an initial (trigger) and final (inhibition) conjugateaddition of the produced thiols (RSH) over time. The

triggering reaction is very quick and so, the productionof thiols is delayed until all maleimide is consumed. Sim-ilarly, as the autocatalytic process develops, there will bean exponential growth of thiols and acrylamide will reactwith the formed thiols to slowly inhibit thiol production.

Control theory enables to probe and model the reac-tions dynamics that take place in a continiously stirredtank reactor (CSTR) that can simulate a cell for this pur-poses. Feedback and control are universal processes thataffects a single cell microbes or even a multicellular com-plex system that can be a condition for a definition of life.Cells are in a constant state of feeedback and responseto numerous stimuli, which some of are self-regulated10.

For the sake of comprehension of the reader, this com-plex network of thiols and thioesters can be divided intothe following processes:

i Trigger - Generation of RSH by hydrolysis of L -alanine ethyl thioester and destruction of RSH byconjugate addition to maleimide (see Fig.1).

FIG. 1: Hydrolisis of AlaSEt and conjugate addition of thiolsto maleimide

ii Positive Feedback - autoamplification by auto-catalysis: RSH generates a positive feedback loopvia thiol-disulfide interchange and native chemicalligation (see Fig.2).

iii Negative Feedback - inhibition of RSH by con-jugate addition to acrylamide (see Fig.3).

Theoretical and Computational Study of Sulfur Compounds Reactivity in Prebiotic Chemistry: TheWhitesides Network of Thiols and Thioesters Joao M. S. N. Ines

FIG. 2: Native chemical ligation and thiol-disulfide exchangereactions

FIG. 3: Conjugate addition of thiols to acrylamide

iv Refill - Compounds 1, 2, 9, 10 are fed into thereactor continuously.

v Washout - all compounds are removed by the out-let port of the reactor.

II. COMPUTATIONAL DETAILS

Ab initio quantum mechanical gas-phase calculationswere performed using GAMESS program[11]. Optimiza-tions employed the Quadratic Approximation algorithmand all stationary points were characterized by comput-ing the Hessian matrix. The electronic structure calcula-tions are based in Hartree Fock theory capable of study-ing closed shell systems. In order to properly describethe sulfur chemistry, it was used a split valence basisfunction, namely a 6-31G** basis set. More specifically,this uses six primitive functions for core orbitals anddoubly-split functions combining contracted basis func-tions of three primitive functions with one uncontractedbasis function for valence orbitals. Polarization functionsmust be added to reasonably sized bases in order to avoidnon-physical results and incorrect descriptions of the po-larity of the molecule. Polarization of the valence-shell ofsulfur is crucial to incorporate the anisotropic nature ofmolecular orbitals originating from chemical bonds. Onecan question also the non inclusion of diffuse functions tostudy anions in a more reliable way. For the sake of timeconstrains, the diffuse functions, solvation and electroniccorrelation were left for future calculations.

For each TS, Intrinsic Reaction coordinate (IRC) wasconducted by the second-order method of Gonzales andSchlegel (GS2) to connect reactants and products. Thisapproach is based on implicit trapezoid method thatcombines an explicit Euler step with an implicit Eulerstep.

All resulting structures (except TS) were shown to beminima by confirming that all harmonic frequencies were

real; the transition states were shown to contain only oneimaginary frequency. The difference in enthalpic energy(in kcal mol−1) is computed at 298 K using the thermo-chemistry computations in the GAMESS11 program.

The set of ordinary differential equations were solvednumerically using the built-in ode45 in Matlab12 pro-gram. The general code was developed by Whitesidesand co-workers.

All 2-D representations were carried out in Chemdrawprogram, while the 3-D structures and molecular orbitalswere obtained by Wxmacmolplt13 software.

III. RESULTS AND DISCUSSION

A. Thiolate-thioester exchange

Thiolate-thioester exchange describes the reaction be-tween a thioester and a thiolate to produce anotherthioester and thiolate as products belonging to a class oforganic reactions that reversibly generate covalent bondsin water17.

FIG. 4: Thiolate-thioester reaction between AlaSEt and CS−

Optimum conditions were set by Whitesides and hisco-workers3 with near neutral pH 7.5-8 and at roomtemperature (25 degree C) allowing this reaction to takeplace in biological medium6. Based on the pKa valuefor cysteamine (CSH) the estimation for thiol/thiolatepopulations at equilibrium can be calculated. Thiolatehas a significantly lower molar percentage between0.001-0.1 in the solvent3. Therefore, four different routescan be considered as potential mechanisms to model thereaction:

1. Anionic concerted mechanism - the nucleophileis the CS− and EtS− the leaving group (see Fig. 4).This mechanism is considered to be the dominantdue to a lower energy pathway and it will be subjectto study in more detail.

2. Neutral and concerted mechanism - attack ofthe sulfur atom of CSH at the carbonyl carbon ofAlaSEt and simultaneously departure of EtSH (seeFig. 5).

2 Barcelona, September 2017


FIG. 5: Neutral and concerted TS 2. All distances are givenin Angstrom (�A).

3. Neutral stepwise mechanism - additional pro-toton transfer after the the sulfur attack to the car-bonyl (see Fig. 6).

FIG. 6: Hypothetical neutral stepwise transition state

4. Anionic stepwise mechanism - sulfur atom ofCS− attacks the carbonyl carbon to form a tetrahe-dral intermediate, and subsequently the ethanethi-olate anion leaves (see Fig. 7).

FIG. 7: Hypothetical anionic stepwise transition state

The stepwise transition state mechanisms 3) and 4)were not located in this work. Analysis of the optimizedstructures for ionic concerted transition state reveals anenthalpy of activation (∆H ) of 10.83 kcal mol−1. Thiol-thioester exchange (neutral) requires an enthalpic acti-vation of 66.43 kcal mol−1. It is worthy to notice thatthe energy barrier in 1) is relatively small, which can beovercome by means of thermal activation of the processand dominates over the neutral specie. Energy distribu-tion matrix found in Pulay analysis at transition stateshows two additional vibrational modes in the neutralconcerted mechanism corresponding to torsional modes.The extra modes can be the root cause for higher activa-tion energy corresponding to the concerted nucleophilic

attack and proton transfer between the two sulfur atoms.The stretching mode concerning S20-C1 (see Figures 5and 8) is commonly shared in both mechanisms but thevibrational contribution in the neutral form is lower.

Thiolates are favoured in terms of lower activation en-ergy as result of higher electron density, therefore thestudy of anionic species prevailed upon neutral thiols infurther reaction mechanisms.

The exothermicity of the reaction is -7.66 kcal/mol,upon calculation of the standard enthalpy of formation.As the reaction becomes less exothermic, the reactant-like structure moves along the reaction coordinate chang-ing its distances of resulting transition state.

FIG. 8: Potential energy profile for the thiolate-thioesterexchange reaction accounting the zero point energy correc-tion. Energy of activation relative to reactants in kcal mol−1

with Zero Point Energy correction. All distances are given inAngstrom (�A).

In TS 1 (see Fig.8), the shorter distance S20-C1 is at-tributed to weaker nucleophile-electrophile interaction ofCS− 18. The angle formed by S12-C1-O11 in the TS is105.3 degree, which is in good agreement with the the-oretical angle for a nucleophile approach on a trigonalunsaturated moiety of 107-109 degree. Sulfur p-orbitaland carbonyl π*-orbital interaction is favored within thisrange. Variations in the angle are caused by electrophilespecific repulsive and attractive electrostatic and Van derWaals interactions 22. According to Corbett17, the differ-ence in electronegativity in the nucleophile influences theHOMO-LUMO energy difference. The calculated energygap between frontier molecular orbitals relative to theneutral and anionic species is 13.69 and 5.99 eV, respec-tively. This confirms that thiols are poor nucleophiles.

Examination of ionic Valence Bond (VB) structuresprovides information on the reactivity of covalent bonds.Ionic structures are simply secondary VB configurationsof polar covalent bonds and its influence must be inves-tigated. Fig. 9 displays the VB configuration mixingdiagram (VBCMD) containing the reactants, products,promoted states and the foreign excited states. Reac-tants and product states are localized in active bonds,



FIG. 9: Qualitative VB configuration mixing diagram forthiolate-thioester exchange reaction.

whereas the promoted states are obtained from electronicexcitations and bonds that do not make part of the activebonds. Fundamental curves are built up from the groundstates and σ-charge transfer(σ-CT) state that are able todescribe this single-step reaction. The mechanism is pro-vided by a direct backside attack. The concertedness ofthis process is ruled by a σ-CT state and a π-CT lyingclose in energy. Because of low energy difference betweenthis two state, the reaction proceeds in a single step andthe tetrahedral intermediate does not take part of themechanism of the reaction. In gas phase, the anionicintermediate cannot be stabilized. One possible explana-tion is given by the fact that the large electron cloud ofsulfur atoms increases the repulsion to such high levelsthat is not possible for carbonyl carbon atom to coordi-nate simultaneously to two sulfur atoms. One can alsoquestion if this intermediate is stable in aqueous mediaby solvent interaction. Given the small barrier for theconcerted process and a possible low stabilization by sol-vent, this intermediate may not be found.

B. Intramolecular rearrangement

Native chemical ligation (NCL) is one of the most usedchemoselective strategies for the formation of a peptidebond. This method takes advantage of the high nucle-ophilicity of the thiolate anion, as well as its ability asa leaving group. It consists in the following elementarysteps: the unprotected peptide-α-thioester reacts withanother unprotected peptide containing an N-terminalcysteine residue by thiol-thioester exchange yielding anintermediate. It is followed by a quick and entrop-ically favourable intramolecular rearrangement (S→Nacyl transfer, see Fig.10) yielding an amide bond at theligation site7. For a succesful intramolecular rearrange-ment to take place, the amine moiety must attack thecarbonyl to form a five-membered cyclic transition state.The equilibrium of the S→N/N→S acyl transfer ratiois thermodynamically favoured, pushing the equilibriumtowards the amide product. Intramolecular reactions areentropy reduction-facilitated via the loss of the transla-tional entropy, which accompanies the bringing togetherof the reactants. However, using different conditions and

FIG. 10: S→N acyl transfer

methodology, the S→N acyl transfer can be reversed inorder to synthesize thioesters by a different approach19.Harding and Owen reported that thioesters with an hy-droxyl group, under dilute alkali conditions, isomerize tothe oxygen ester with high yield compared with the hy-drolysis process20. For the intramolecular rearrangment,the mechanism proceed by a concerted and neutral tran-sition state TS 3 (see Fig.11). The nucleophilic attack of

FIG. 11: Potential energy profile for the intramolecular rear-rangement reaction accounting the zero point energy correc-tion. Energy of activation relative to reactants in kcal mol−1


thiolate proceeds via single TS 3 with an enthalpy of ac-tivation of 40.9 kcal mol−1. Notice that this high kineticbarrier is compensated thermodynamically by means ofthe standard enthalpy of formation with a value of -54.5kcal mol−1. Such high barrier may be attributed to anincrease of steric effects during the formation of the 5-membered ring in TS 3, increasing the ring tension. Inaqueous media, the proton transfer can be easily medi-ated by the solvent, thus lowering the energetic cost ofthe overall reaction. In TS3 (ν = i 82.22 cm−1) , theC1-N15 bond is partially weakend and the bond length isenlarged from 1.36 �A to 1.54 �A. The S12-C1 distance is2.61 �A and shows that this is a late transition state dueto the nature of the product stability. This reaction isexothermic by -13.6 kcal mol−1.

Table I gives the information concerning which modesare vital in TS3 by means of Pulay analysis. The protontransfer is accomplished throughout the IRC procedure.The assisted proton donation by the positively chargedamine moiety it is essential to stabilize the thiolate. First,



vibrational mode vibrational contribution (%)Stretching 12 1 0.82

Torsion 11 1 2 6 0.22Torsion 12 1 11 5 -0.15Torsion 15 1 11 2 0.09

TABLE I: Major vibrational contributions in energy distribu-tion matrix for intramolecular rearrangment

because the N15-H17 distance is 1.01 �A and remains un-changed from reactant to products. Second, the torsionangle contributions involve the right positioning of thecarbonyl for a tetrahedral geometry to accomodate theentering sulfur with an angle of 114 degree. This angleinfluences the orientation of sulfur lone pair of electronsto interact with the carbonyl π* orbital.

Valence bond diagrams are helpful to understand thereactivity mechanisms with simple valence bond struc-tures. In Fig.12, structure 7 does not provide a low en-

FIG. 12: Qualitative VB Configuration Mixing Diagram forthe S→N acyl transfer

ergy pathway for the TS3, specially in the gas phase, dueto steric effects during the formation of the 5-memberedring. The boat-type configuration adopted in TS3 bystructure 7 also increase the energy in comparison to amore stable chair-type conformation. It is also expectedthat the solvent will decrease largely the TS 3 energeticbarrier due to the fact that charge is not present in re-actants nor products, hence the energy in TS3 and theactivation energy must decrease.

C. Thiolate-disulfide interchange

Disulfide bond plays an essential role in biological pro-cesses. Reversible creation/disruption of the S-S bond incelullar systems is a nonequilibrium dynamic process andis governed kinetically, not thermodynamically9. Fig. 13shows an SN2 type nucleophilic substitution of a thiolatein disulfides with another thiolate.

Depending on the pKa of the enviroment, the neutraland anionic form are present. Assuming the pKa ex-tracted from previous work and, according to Whitesidesand co-workers, the molar ratio of ionic/neutral species

FIG. 13: Thiolate-disulfide exchange reaction. Notice thattwo molecules of cysteamine are formed in this two parallelreactions.

are presented in table II.

Compound pKa pH 7.5 pH 83, CSSC 9.0 3.3 % 9.7 %4, EtS− 10.5 0.1 % 0.3 %

5− 8.2/9.7 0.1 % 0.7 %

TABLE II: pKa values and estimated populations for reac-tants and cystamine at equilibrium

Based on the relative populations and given the dra-matic differences in nucleophilicity, the present study willfocus on the above species. Therefore, the effect of pH isimportant to establish the kinetics of the thiol-disulfideinterchange. Protonation-deprotonation are usually fastand can be treated as a pre-equilibrium assumption9.

RSH −−⇀↽−− RS− + H+ (1)

KRSHa =

[RS−][H+]

RSH(2)

In this way, the apparent rate constant will be pH de-pendent described by equation (3),

kapp = k1KRSH

a

KRSHa + [H+]

(3)

where, k1 is pH independent. Thus, the kinetics ofthiolate-disulfide exchange is intrinsically related to thepH media, and an optimum value is found when mostof the thiol is deprotonated. Thiol-disulfide interchangereaction has not been observed experimentally8. Thereason must be attributed to the dramatic difference ofnucleophilicity. Thiolate-disulfide interchange reactionsare favoured approximatly by three orders of magnitudein aprotic solvents rather than in water9. The theoreti-cal argument is based on the more delocalized negative



charge in the transition state. Investigation on the ge-ometry of the transition state for the reaction of CSSCwith two different nucleophiles was chosen to compare thereactivity of both thiolates 4 and 5. The reaction Fig.13 summarizes both thiolate-disulfide exchange reactionsinvolved in the autocatalysis of thiols.

FIG. 14: Potential energy profile for the thiolate-disulfide re-action with EtS− accounting the zero point energy correc-tion. Energy of activation relative to reactants in kcal mol−1


FIG. 15: Potential energy profile for the thiolate-disulfidereaction with 5− accounting the zero point energy correc-tion. Energy of activation relative to reactants in kcal mol−1


The transition state models predict, as expected, aconcerted mechanism for both reactions. The enthalpyof activation for reactants 5 and 4 are 21,89 (see Fig.15) and 17.01 (see Fig. 14) kcal mol−1, respectively.The pKa values of the nucleophiles are in agreement withWilson and co-workers21 observations based on Brønstedequation. Higher pKa values for attacking thiolates arerelated to higher rate. The potential energy surface con-sists of an entrance and exit ion-dipole complex. In TS4and TS5 the steric effects are small to describe the barri-

ers, mostly, when the difference is mainly localized in thealkyl substitution at carbon β to sulfur. All sulfur atomsare bonded to a -CH2- moiety displaying very low sterichindrance. This factor can influence positively the orien-tation of the electronic lone pair directed along the axisof the covalent bonds. The p-orbital (HOMO) of the in-coming sulfur must interact with the σ∗- orbital (LUMO)of the S-S disulfide bond. The relative higher barrier in5 is presumably due to steric effects of substituents atthe carbon-β to sulfur. The SN2 reaction geometry of

Geometry parameters TS 4 TS 5d1(S8-S4) 2.49 2.56d2(S4-S3) 2.48 2.41

α(S8-S4-S3) 176.65 175.54δ1(C9-S8-S4-C5) 84.00 72.93δ2(C2-S3-S4-C5) 89.17 86.46

TABLE III: Geometrical comparison of distances (d), angle(α, values in degrees), and dihedral angles (δ, values in de-grees) for both thiolate-disulfide TS.

the transition state is given in table III. It summarizesthe important distances, angle and dihedral angles of TS4/TS 5 by comparing distances and angle in the incom-ing and outgoing sulfur moieties along the axis. Themore symmetrical TS 4 shows almost identical distancesbetween sulfur atoms and it is 1 degree closer to ideal180 degree, in comparison to TS 5 . In order to avoidelectronic repulsion between the sulfur substituents, thedihedral angle, δ2 must be the closest to 90 degree. Forthis reason, the energy barrier in TS 4 is lower. Exper-imental evidence based on Brønsted coefficients pointsthat the charge distribution is higher in the two terminalsulfurs is confirmed by computational results 8. The neg-ative charge is accumulated in the sides, while the centralsulfur possesses a positive charge.

Valence bond state correlation diagram presents theHeitler-London mixing structures 1-4. The ground stateat the reactant geometry is 1 which gets gradually desta-bilized as the S1-S2 bond is homolyzed and the threeelectron overlap repulsion increases in S3-S2 interaction.

FIG. 16: Qualitative VB State Correlation Diagram for thethiolate-disulfide reaction.

Structure 2 represents the excited state and inter-changes with 1 along the reaction coordinate as a resultof one-electron transfer from the thiolate to the S1 sul-fur, resulting in a triplet excitation. The charge transfer



states σ-CT are closer to ground states mostly due effec-tive electron delocalization which is expressed by a lowerenergy profile in the transition state.

D. 1,4 Conjugate addition

The conjugate addition of thiolates to acrylamide andmaleimide (see Fig. 17) displays very different kineticand thermodynamic behaviour in the Whitesides3 net-work of reactions.

FIG. 17: 1, 4 conjugate addition mechanism present in triggerand inhibition mechanisms, respectively. First, nucleophilicaddition of EtS−, second proton transfer and final tautomericequilibrium.

Sustainable oscillations are dependent on the triggerand inhibition mechanisms that control the thiol pro-duction. When the electron density of a carbon-carbonbond is reduced by strongly electron-withdrawing sub-stituents, nucleophilic addition turns to be possible. Con-jugation of a double bond to a carbonyl group trans-mits the electrophilic character of the carbonyl carbonto the β-carbon of the double bond. These conjugatedcarbonyl are called enones or α, β unsaturated carbonyls.Usually, in conjugate addition, the rate-determining stepis the nucleophilic addition2. Since carbon is weaklyelectronegative, carbanions are extremely poor leavinggroups and addition can only occur if the resulting car-banion is strongly stabilized by positive substituents.Rate of nucleophilic addition is expected to be greater,the more nucleophilic is the attacking nucleophile andthe less basic resulting carbanion. 1,2 addition nucle-ophile adds to the carbon which is in the one position.The hydrogen adds to the oxygen which is in the twoposition. 1,4 the Nucleophile is added to the carbon β tothe carbonyl while the hydrogen is added to the carbonα to the carbonyl. During the addition of a nucleophilethere is a competition between 1,2 and 1,4 addition prod-ucts and it is the nature of the nucleophile that mostlydictates which mechanism is favoured.

Thiolates are weak bases and therefore, the preferred1,4 addition dominates. This means that the stability ofcarbonyl group is guaranteed and the reaction is con-trolled thermodynamically. The model proposed onlyconcerns the nucleophilic attack by thiolate and it as-sumes that there is a proton assisted mechanism to theformed carbanion.

FIG. 18: Potential energy profile for the 1,4 conjugate addi-tion reaction with acrylamide accounting the zero point en-ergy correction. Energy of activation relative to reactants inkcal mol−1 with Zero Point Energy correction. All distancesare given in Angstrom (�A).

As usual, the reactions undergo a single transition stateor concerted mechanism. Enthalpy of activation in TS7 (see Fig.18) is 27.25 kcal mol−1, while there is a sharpdrop in TS 6 (see Fig.19) with an enthalpy of activationof 4.34 kcal mol−1. This energetic difference must beinvestigated by electronic effects in the transition state.In both cases, the attacking thiol is the same, the maindifference is related to conjugation effects in acrylamide(10) and maleimide (9). Maleimide is an anti-aromaticheterocyclic molecule with two carbonyl π-bonds, onemethylene π-bond and the electronic p-lone pair of nitro-gen. This conjugation lowers the activation barrier andstabilizes the resulting carbanion structure 11a. Acry-lamide also displays planarity but only possesses one π-bond conjugated with one carbonyl π-bond and the p-lone pair of nitrogen. This has a dramatic behaviourchange in both, energy barrier and product stabilization.Initial H-bond stabilization by the amine may also con-tribute to a larger activation. The resulting carbanioncannot successfully stabilize the negative charge at α-carbon by conjugation.

Thermodynamically, there is an equilibrium betweenstructures 9 + 4− and 11 and it is a endothermal re-action by 0.66 kcal mol−1. In TS 7 the reaction equi-librium is more displaced to the thermodynamic morestable reactants and the endothermicity of reaction wascalculated to be 25.54 kcal mol−1. The thermodynam-



FIG. 19: Potential energy profile for the 1,4 conjugate addi-tion reaction with maleimide accounting the zero point energycorrection. Energy of activation relative to reactants in kcalmol−1 with Zero Point Energy correction. All distances aregiven in Angstrom (�A).

ics of the system is incomplete due to the stabilizationof the proton-assisted mechanism in solution by the sol-vent and tautomeric equilibrium. For this reason, thevalues presented here are kinetically more reliable thanthermodynamically. The transition state geometry isslightly different in terms of nucleophile-electrophile dis-tance and planarity. TS 7 shows a C1-S11 distance of2.22�A compared with 2.30�A in TS 6. The approximationof attacking sulfur along the reaction coordinate towardsmaleimide distorts the planarity of the ring by 10 degreecompared with 2 degree in the case of acrylamide.

Valence bond theory was used, once again, as a tool tounderstand the quantum chemical aspects that generateenergy barriers in transition state.

FIG. 20: Qualitative VB Configuration Mixing Diagram forthe 1,4 conjugate addition of EtS− reaction with acrylamide

Figure 21 and 22 show that thiolates add to the β-carbon in a concerted mechanism with no further sta-bilization of structures 2, 7, 5. Despite of no furtherstabilization of the π-CT, the carbonyl plays an impor-tant role in electron delocalization. Conjugate additionimplies the formation of a σ-bond and the partial π-bond-breaking.

Despite of similar charge transfer excitations, TS 6 has

FIG. 21: Qualitative VB Configuration Mixing Diagram forthe 1,4 conjugate addition of EtS− reaction with maleimide

an additional carbonyl moiety capable of higher stabiliza-tion. The presence of an electron withdrawing group, asthe α-NH / α-NH2 moieties may raise the LUMO orbitalenergy of the carbonyl by n →π∗ interaction. This delo-calization leads to some degree of charge separation andpolarization of the amide.

E. Thioester Hydrolysis

The acyl group of a thioester can be transferred to awater molecule in a hydrolysis reaction, resulting in acarboxylate. In Fig. 22, it is presented a SN2 reactionbetween an hydroxyl anion and AlaSEt that yields a car-boxylic acid and the leaving thiolate anion.

FIG. 22: Hydrolisis of AlaSEt to carboxylic acid. The firstthiols are generated in this reaction.

Thioester hydrolisis can be acid or base mediated.However, the base catalyzed reaction favors the thiolate-thioester competition mechanism in solution that isneeded for the autocatalytic loop to proceed more effi-ciently. Therefore, it is very important to keep in mindthat the kinetics of hydrolisis is pH dependent. The nu-cleophilic attack of hydroxyl anion towards the thioesterproceeds via single TS 8 without barrier. It is a sur-prising result but it is important to remember that is agas-phase calculation. The formed carboxylic acid showsto be a very stable product in comparison to a more la-bile C-S bond in the thioester molecule. The calculatedstandard enthalpy of formation is -57.96 kcal mol−1. Dueto such high exothermal reaction, the transition state re-sembles the reactants, as referred in Hammond postulate.



FIG. 23: TS 8 structure for the hydrolisis reaction. Distanceunits in Angstrom (�A).

In TS8 (see Fig. 23), the C1-S7 bond is just slightlyweakend by 0.1 �A. This may be associated with a longnucleophile interaction. The O20-C1 distance is 2.4 �Aand it is more common in soft bases as the thiolate an-ion. It was found that the two frontier molecular orbitals,HOMO-LUMO, have 5.06 eV energy gap. As a conse-quence, a better interaction is confirmed by the O20-C1-O3 angle of 109.41 degree.

FIG. 24: Relevant molecular orbitals representations for hy-drolisis TS 8

Valence bond theory allows to make an interpretationof the nature of the energetic barrier in TS 9 by analysisof the promoted states 2, 3, 5, 6, 7.

Fig. 25 puts in evidence the energy differences in σ-CTπ-CT in order to accomodate the one-electron excitationprovided by the electronic lone pair of hydroxyl nucle-ophile. It is clear that the dominant mechanism is a di-rect backside attack in the C-S bond and it is enhancedby the carbonyl π ∗ conjugation. The formation of thetetrahedral intermediate is once again avoided. The ex-planation may be given by the energetic difference ofsupra-LUMO to LUMO orbital and a greater electron

FIG. 25: Qualitative VB Configuration Mixing Diagram forthe hydrolisis reaction

cloud surrounding sulfur atom. The last effect producesa greater degree of electron density, together with oxy-gen, resulting a high increase in steric strain in TS 8.

IV. RATE CONSTANTS MODELLING

The network dynamics should display bistabily and os-cillatory behaviour as a consequence of the triggering,auto-amplification and inhibition balance.

The set of differential equations can be solved for dif-ferent space velocities (FνV) and initial concentrations.The space velocities are dependent on the initial concen-trations in order to achieve sustained oscillations in thiol(RSH) concentrations. Therefore, if one fixes the initialconcentrations, there will be a transition from dumpedoscillations to sustained oscillations for a range of spacevelocities.

The values for the theoretical rate constants (k) werecalculated under thermodynamic formulation of transi-tion state theory:

k =kBT

hexp

{∆S°R

}exp

{−∆H°RT

}M1−m (4)

where kB is the Boltzmann constant, h is Planck’s con-stant and T is the Kelvin temperature. The free energy ofactivation, ∆ G° , can be divided into contributions fromenthalpy of activation, ∆ H° , and entropy of activation,∆ S° . The units correction factor to distinguish an uni-molecular reaction from a bimolecular is introduced byM, the molarity. It vanishes for an unimolecular reactiondue to its molecularity (m).

Deviations from the experimental rate constants areattributed to solvent interactions with reactants and TScomplexes, which affect the activation energies. The pHdependence is also determinant and controls the ratioof anionic/neutral species in solution. This factor is ofgreat importance when the rate of hydrolisis around neu-tral pH is very small compared with Kent ligation. Inorder to observe thiol concentration oscillations, the con-jugated addition must have the greatest rate constantin order to trigger the autocatalysis. The first thiolate



Reaction k [s−1 M1−m] experimentalthiolate-thioester exchange 67.60 0.41

S→N acyl transfer 3.30 ·10−20

thioester hydrolysis 3.13 ·1011 7.00 ·10−6

thiolate-disulfide interchange of 5 1.70 ·10−6 0.44thiolate-disulfide interchange of 4 1.37 ·10−2 0.44

1,4 conjugate addition to maleimide 2.01 ·107 1501,4 conjugate addition to acrylamide 7.18 ·10−11 0.014

TABLE IV: Theoretical rate constant values for the reactionsin gas-phase using thermochemistry at 298 K.

is formed in the hydrolisis, which enables the thiolate-disulfide reaction with CSSC and formation of CSH inthe network. However, all thiols are inactive by reactionwith maleimide. Once is consumed, the autocatalyticloop is activated and the thiol population increases butthe conjugate addition to acrylamide will inhibit the thiolpopulation. Therefore, the inhibition rate constant mustplay a gradual role in the dynamics with a small rateconstant.

V. CONCLUSION

The results in Hartree-Fock level of theory showthat all mechanisms studied are concerted via a sin-gle TS. Factors like sulfur size, polarizability and nu-cleophilic strength influence its reactivity reflecting thenon-observed π-CT mixing. Intermediates may not beable to be stabilized in the gas-phase due to the elec-tronic repulsion in tetrahedral intermediates, for the caseof nucleophilic attack on carbonyl. One can imagine thatthe absence of intermediates is an important feature ofsulfur reactivity that avoids side reactions in the originsof life.

In future work, the introduction of solvent and elec-tronic correlation must be taken in consideration toproper describe the activation energies. Concentrationprofiles in autocatalytic cycle must be introduced in fu-ture work, with proper energy barriers calculations thatlead to more accurate rate constants.

[1] Isaacs, N.S. Physical Organic Chemistry. John Wiley &Sons, Inc, New York.(1987)

[2] Lowry, T.H.; Richardson, K.S. Mechanism and Theory InOrganic Chemistry. Vantage Art Inc, New York.(1976)

[3] (a) Semenov, S.N.; Kraft, L.J.; Ainla, A.; Zhao, M.;Baghbanzadeh, M.; Campbell, V.E.; Kang, K.; Fox,J.M.; Whitesides, G.M. Autocatalytic, bistable, oscilla-tory networks of biologically relevant organic reactions.Nature 537: 656-668 (b) Taylor, A.F. Small molecularreplicators go organic. Nature 537:627 (2016)

[4] Shaik, Sason.; Shurki, A. Valence Bond Diagrams andChemical Reactivity. Angew. Chem. Int. Ed. 38: 568-625 (1999)

[5] Bruice, T.C.; Benkovic, S.J. Bioorganic mechanisms: vol-ume I. W.A. Benjamin, Inc, New York.(1966)

[6] Bracher, P.J.; Snyder, P.W.; Bohall, B.R.; Whitesides,G.M. The Relative rates of Thiol-Thioester Exchangeand Hydrolysis for alkyl and Aryl Thioalkanoates in Wa-ter. Orig Life Evol Biosph. 41: 399412 (2011)

[7] Dawson, P.E.; Churchill, M.J.; Ghadiri, M.R.; Kent,S.B.H. Modulation of reactivity in native chemical lig-ation through the use of thiol additives. J. Am. Chem.Soc. 119: 43254329 (1997)

[8] Singh, R.; Whitesides, G.M. (1993) The chemistry ofsulphur-containing functional groups: Thiol-disulfide in-terchange. Supplement S. John Wiley & Sons Ltd. 119:4325-4329

[9] Nagy, P. Kinetics and Mechanisms of Thiol-DisulfideExchange Covering Direct Substitution and ThiolOxidation-Mediated Pathways. Antioxidants & RedoxSignaling. 18: 16231636 (2013)

[10] Whitesides, G.M.; Ismagilov, R.F. Complexity in Chem-istry. Science. 284: 8992 (1999)

[11] Schmidt, M.W.; Baldridge, K.K; Boatz, J.A.; Elbert,S.T.; Gordon, M.S.; Jensen, J.H.; Koseki, S.; Nguyen,K.A. General Atomic and molecular Electronic Structure

System. J. Comput. Chem. 14: 13471363 (1993)[12] MATLAB version 7.10.0. Natick, Massachusetts: The

MathWorks Inc., (2010)[13] Bode, B. M. and Gordon, M. S. J. Mol. Graphics Mod.,

16, 1998, 133-138.[14] Dewar, M.J.S.; Dougherty, R.C. (1975) The PMO The-

ory of Organic Chemistry: A Plenum, Rosetta Edition,New York.

[15] Swain, C.G.; Scott, C.B. Quantitative Correlation of Rel-ative Rates. Comparison of Hydroxide Ion with OtherNucleophilic Reagents toward Alkyl Halides, Esters,Epoxides and Acyl Halides. J. Am. Chem. Soc. 75:141147 (1953)

[16] Edwards, J.O.; Pearson, R.G. The Factors DeterminingNucleophilic Reactivities. J. Am. Chem. Soc. 84: 1624(1962)

[17] Corbett, P.T.; Leclaire, J.; Vlal, L.; West, K.R.; Wietor,J.L.; Sanders, J.K.M. Dynamic Combinatorial Chem-istry. J. Am. Chem. Soc. 106: 36523711 (2006)

[18] Wang, C.; Guo, Q.X.; Fu, Y. Theoretical Analysis of theDetailed Mechanism of Native Chemical Ligation Reac-tions. Chem. Asian J. 6: 12411251 (2011)

[19] Burke, H.M.; McSweeney, L.; Scanlan, E. Exploringchemoselective S-to-N acyl transfer reactions in synthesisand chemical biology. Nat. Commun. 8: 116 (2017)

[20] Jencks, W.P.; Corder, S.; Carriuolo, J. The Free Energyof Thiol Ester Hydrolysis. J. Bio. Chem. 235: 36083614(1960)

[21] Wilson, J.M.; Bayer, R.J.; Hupe, D.J. Structure-reactivity correlations for thiol-disulfide interchange re-action. J. Am. Chem. Soc. 99: 79227926 (1977)

[22] Klopman, G. Chemical Reactivity and Reaction Paths.John Wiley & Sons, Inc, New York.(1974)

[23] Kent, P.R.C. Techniques and Applications of QuantumMonte Carlo, PhD thesis, Robinson College, Cambridge(1999)


theoretical and computational study of sulfur compounds … · theoretical and computational study...

Documents