SCRF study of the conformational equilibrium of chorismate in water

Sergio Madurga and Eudald Vilaseca*

Departament de i Centre de Recerca en Facultat deQu•�mica F•�sica Qu•�mica T eorica, Qu•�mica,Universitat de Barcelona, i 1, 08028-Barcelona, Catalunya, Spain.Mart•� FranquesE-mail :eudald=qf.ub.es

Received 10th May 2001, Accepted 27th June 2001First published as an Advance Article on the web 13th August 2001

The conformational equilibrium between the diequatorial and diaxial forms of chorismate molecule in waterhas been studied with a self-consistent reaction Ðeld (SCRF) model. Conformational energies in the gas phasehave been calculated at the MP2/6-31&G*//HF/6-31G* level, and solvation energies have been obtained withPCM/6-31G* and PCM/6-31&G* calculations. The cavity deÐnition of the united atom model forHartreeÈFock (UAHF) was used in the polarizable continuum model (PCM) calculations. The conformationalenergy surface as a function of the two main degrees of freedom of the principal side-chain has beenconstructed for the chorismate molecule in the gas phase and in water solution. These surfaces allow a moreexhaustive search for conformational minima and the calculation of the entropic contribution to theconformational equilibrium. Five diaxial minima, three of them not described before, two diequatorial minimaand a planar ring minimum have been detected. One of the new diaxial minima is essential to correctlyreproduce the experimental diaxialÈdiequatorial proportions in water.

1 Introduction

Chorismate is a key molecule in the biosynthesis of aromaticamino acids and other metabolites in microorganisms andplants.1,2 In the path to phenylalanine and tyrosine, choris-mate undergoes a transformation to prephenate that is for-mally a Claisen rearrangement. A transformation that mayoccur in aqueous solution3h5 or in the presence of the enzymechorismate mutase,6h15 in which case the reaction rate isincreased by a factor greater than 106. A good description ofthe catalyzed transformation can help to Ðnd inhibitors ofchorismate mutase that may act as herbicides, fungicides andantibiotics.16 As a Ðrst step, however, a complete understand-ing of this rearrangement in solution is needed.

The theoretical studies published until now on the Claisenrearrangement of chorismate in solution3,4 do not reproducecorrectly the experimental equilibrium constant. This may beattributed to an insufficient characterization of the conforma-tional equilibrium of chorismate molecule in solution. Thus, amore exhaustive analysis of the conformational properties ofchorismate is required. In particular, modiÐcation of the posi-tion and relative stability that the gas phase conformationsexperience in solution and the possible appearance of newconformational minima due to solvent interactions should beconsidered.

Chorismate can be found in two di†erent dispositionsdepending on the position of the ether and the hydroxyoxygen atoms with respect to the cyclohexadienyl ring. Theycan be labeled as diaxial and diequatorial, respectively (Fig. 1).The equilibrium between these two forms is clearly favorablefor the diequatorial conformation due to an internal hydrogenbond between the hydroxy group and the side-chain carbox-ylate that enhances its stability. Experimental data, based on1H NMR studies, yield a proportion of 88% for the die-quatorial form in water at 298.15 K.5 This proportion issmaller than in the gas phase since the water moleculescompete in breaking the internal hydrogen bond.

Performing ab initio calculations at the RHF/6-31G* level,Wiest and Houk17 found one minimum for chorismate in thediequatorial form and one minimum for its diaxial form in thegas phase. These results were used by Carlson and Jorgensen3to study the chorismate conformational equilibrium and itsrearrangement to prephenate in aqueous solution by means offree energy perturbation (FEP) simulations. They obtained afree energy di†erence for the conformational equilibriumbetween the diaxial and diequatorial forms of 3.6 kcal mol~1,a result that is clearly higher than the experimental value (1.2kcal mol~1). Davidson et al.4 performed new ab initio calcu-lations at a higher level of accuracy for the chorismate in thegas phase and found another diaxial minimum. However, dueto its high energy, consideration of this minimum does notalter the diaxialÈdiequatorial equilibrium. Thus, the Davidsonet al. study of the chorismate conformational equilibrium inwater using discreet techniques (FEP with Monte Carlo) andcontinuum models such as the self-consistent isodensity pol-arizable continuum model (SCIPCM) yielded similar resultsto those of Carlson and Jorgensen. In a more recent paper15 aconformational search for the chorismate molecule in the gasphase was performed at the AM1 semiempirical level followedby an ab initio MP2 reoptimization using the standard6-31G* basis set. This procedure yielded a new diequatorial

Fig. 1 DiaxialÈdiequatorial conformational equilibrium of choris-mate.

3548 Phys. Chem. Chem. Phys., 2001, 3, 3548È3554 DOI: 10.1039/b104108h

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minimum whose relative importance in water was notassessed.

In the present work the description of the conformationalequilibrium of chorismate in solution is improved in twoways : by performing a more exhaustive search and character-ization of conformational minima in solution, and by calcu-lating the contribution of the conformational entropy of eachminimum in solution. This entropic contribution is obtainedby constructing the conformational energy surface of choris-mate as a function of the main degrees of freedom of its prin-cipal side-chain.

2 Computational detailsStationary and partially optimized points of the gas phasepotential energy surface of chorismate were calculated at theHartreeÈFock level using a 6-31G* basis set. Electron corre-lation was considered by carrying out calculations at the MP2level with the 6-31&G* basis set on the optimized structures.The] functions are a di†use set of s and p orbitals on eachnon-hydrogen atom introduced to describe properly the elec-tronic structure of anions. Vibrational frequency analyseswere performed on all optimized structures to verify that theyare true minima.

Relative solvation free energies among conformations werecalculated using a continuum description of the solvent basedon an SCRF method. The PCM approach with the cavitydeÐnition given by the UAHF of Tomasi and coworkers18,19was employed. In the UAHF model the atomic radii of thespheres used to build the molecular cavity are adjusted byintroducing chemical considerations such as hybridization,formal charge and Ðrst neighbor inductive e†ect. With theseoptimized radii the mean error with respect to the experimen-tal absolute solvation energies is about 0.2 and 1 kcal mol~1for neutral molecules and ions, respectively. The errors in therelative solvation energies among molecular conformationsare expected to be smaller due to the cancellation of system-atic errors.

PCM models perform a normalization of the polarizationcharge appearing on the cavity surface to correct the e†ect ofnumerical approximations and the e†ect of the escapedcharge. Although there are several normalization procedures,the most suitable for anions is the ICOMP \ 4 option in thePCM version implemented in GAUSSIAN 98. In this pro-cedure, the e†ect of the escaped electronic charge outside thecavity is corrected with an additional set of charges on thecavity surface distributed according to the solute electronicdensity in each point of the surface.20

PCM calculations have been performed at the ab initio HFlevel. In order to test the stability of the results with respect tothe inclusion of di†use functions two basis sets have beenemployed, 6-31G* and 6-31&G*. All gas phase and PCM cal-culations were performed using the GAUSSIAN 98 package21on an IBM SP2 computer.

3 Gas phase conformational surfaceFor each molecular disposition, diaxial and diequatorial, theconformational diversity of chorismate is due to the mobilityof the three side-chains attached to the cyclohexadienyl ring.However, the major contribution to this conformationaldiversity comes from the enol pyruvoyl group, the greater andmore Ñexible side-chain. The hydroxy side-chain presents onlya single rotation that adopts two orientations. For the die-quatorial chorismate form the OH group is directed awayfrom the ring to participate in the internal hydrogen bond,whereas for the diaxial form the OH group is directed towardsthe ring. The third side-chain is a carboxylate group thatadopts a rather rigid disposition coplanar with the cyclo-hexadienyl ring since its double bonds are in resonance with

the ring p electrons. Thus, a systematic search of the choris-mate conformational minima should start by considering themobility of the enol pyruvoyl group for each of the twomolecular dispositions, diaxial and diequatorial.

Since the rotations around the two CÈO bonds of the etheroxygen, rotational angles and (Fig. 2), are the main/1 /2degrees of freedom of the enol pyruvoyl side-chain, the confor-mational behavior of chorismate was studied in terms of them.Thus, for each molecular disposition the conformationalenergy surface as a function of these two internal rotationangles was analyzed. In particular, the conformational minimawere located and the energy surface around them calculated.

3.1 Conformational minima search

In a Ðrst step, a rapid exploration of the diaxial and the die-quatorial conformational energy surfaces was done by choos-ing a set of 57 points and performing for each one a(/1, /2)HF/6-31G* ab initio calculation keeping the angle value/1Ðxed and completely optimizing the rest of the molecularcoordinates. These calculations showed the situation of thesurface low energy zones. After that, for a better location of allthe minima and to facilitate the construction of the energysurface around each one, a grid of conformations was(/1, /2)considered in the low energy zones. A preliminary study wasalso carried out with semiempirical AM1 calculations but itwas abandoned because of the signiÐcant di†erences observedbetween the HF and AM1 conformational energy surfaces.

For the chorismate molecule in the diaxial form a 30¡ ] 30¡grid for the and rotations in the ranges [190¡ to [40¡/1 /2and [180¡ to 180¡, respectively, was considered (Fig. 3a). Thisgrid encloses all the diaxial minima corresponding to the side-chain oriented away from the ring. Outside this grid theenergy is rather high due to steric repulsions between the enolpyruvoyl side-chain and the cyclohexadienyl ring. However,there is a small region, corresponding to the side-chain locatedover the cyclohexadienyl ring, in which a little stabilization isobserved. This region was also explored considering a newgrid of points in the ranges of 18¡ to 118¡ and [132¡ to 0¡ forthe and rotations, respectively (Fig. 3a). For the choris-/1 /2mate molecule in the diequatorial form two rectangular gridsof conformations were considered. The value ranges for the /1and rotational angles were [152¡ to [71¡ and [120¡ to/219¡ for the Ðrst grid, and 0¡ to 120¡ and [110¡ to [30¡ forthe second one (Fig. 4a). For each one of the 109 points of the

Fig. 2 Chorismate molecule in the diaxial form with the two rota-tional angles, and of the enol-pyruvoyl side chain at the zero/1 /2 ,value disposition.

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Fig. 3 Conformational energy map for the diaxial form of choris-mate. (a) MP2/6-31&G*//HF/6-31G* gas phase surface, (b) solutionsurface obtained with the solv model. Contour lines are drawn at 1kcal mol~1 intervals starting from the absolute minimum. Dashedlines in (b) correspond to an energy of (with T \ 298.15 K) over2kBTeach local minimum and show the regions considered to evaluate theentropic contribution to the conformational equilibrium.

four grids, the energy was calculated at the HF/6-31G* levelby completely optimizing the rest of the molecular coordi-nates.

In the next step, the exact positions of the chorismate con-formational minima were located by performing full opti-mizations of all the internal coordinates starting at the grid

Fig. 4 Conformational energy map for the diequatorial form of cho-rismate. (a) MP2/6-31&G*//HF/6-31G* gas phase surface, (b) solutionsurface obtained with the solv model. Contour lines are drawn at 1kcal mol~1 intervals starting from the absolute minimum. Dashedlines in (b) correspond to an energy of (with T \ 298.15 K) over2kBTeach local minimum and show the regions considered to evaluate theentropic contribution to the conformational equilibrium. The energyobtained for a set of ten conformations situated outside the contourmap region are also indicated.

points that appear as local minima. Six conformationalminima were found. Four minima (AX1, AX2, AX3 and AX4)correspond to the diaxial chorismate form and two minima(EQ1 and EQ2) to the diequatorial form (Table 1 and Fig. 5).All minima were checked with vibrational frequency analyses.

Table 1 Dihedral angles and HF/6-31G* relative energies of the gas phase conformational minima of chorismate. Relative energy valuesobtained at higher level ab initio calculations are also shown. Angles in degrees and energies in kcal mol~1

EQ1 EQ2 AX1 AX2 AX3 AX4

/1 [121.54 78.56 [162.60 [108.48 [154.40 78.04/2 69.51 [72.93 [126.52 119.76 [2.81 [82.42/form [70.03 [63.77 [157.17 [160.24 [147.05 [139.37HF/6-31G*//HF/6-31G* 0 3.2 11.8 11.6 13.8 17.4HF/6-31&G*//HF/6-31G* 0 3.5 11.3 11.2 12.9 17.2MP2/6-31G*//HF/6-31G* 0 2.1 11.4 11.6 13.1 16.6MP2/6-31&G*//HF/6-31G* 0 1.9 10.1 10.6 11.7 14.8

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Fig. 5 Representation of the gas phase diaxial and diequatorialminimum structures obtained with the HF/6-31G* optimizations. TheNF1 (new form) conformation, only found in solution, is also dis-played.

Finally, the energy of all the grid points and the conforma-tional minima were recalculated at the MP2 level using a6-31&G* basis set.

The and angles and the energy values obtained for/1 /2the six minima are shown in Table 1. The MP2 resultsobtained with a 6-31G* basis set are also included for com-parison. The clear di†erences between the relative energyvalues obtained with the two basis sets indicate that thedi†use functions are important in the energetic description ofthese conformations. In Table 1 it can also be seen that thedihedral angle, that the hydroxy oxygen and the ether/form ,oxygen form around the CÈC ring bond, takes characteristicvalues for the diequatorial and the diaxial dispositions. In thediaxial conformations is situated in the range [160¡ to/form[140¡, whereas in the diequatorial form it is restricted to the[70¡ to [60¡ interval.

As can be seen in Fig. 5, three of the four diaxial minima,AX1, AX2 and AX3, correspond to the ““extendedÏÏ diaxialform of chorismate (with the side-chain away from the ring)and one, labeled as AX4, to the ““compact ÏÏ diaxial form (withthe side-chain over the ring). The minimum labeled as AX2 isthe same as found by Wiest et al.17 and Davidson et al.,4 and

the AX4 conformation coincides with the new minimumobtained by Davidson et al. with MP2/6-31G*//HF/6-31G*calculations.4 The other two diaxial minima (AX1 and AX3)have not been described before. The AX1 conformation is themost stable diaxial minimum, while the AX3 minimum is only1 kcal mol~1 higher than AX2. This means that considerationof these new minima is necessary to improve the description ofthe conformational behavior of chorismate. It should be notedthat these four diaxial minima have the OH group orientedtowards the ring. As was shown by Davidson et al.4 with theAX2 and AX4 conformations, no diaxial minima are foundwhen the OH group is oriented away from the ring.

For the diequatorial form, we found the same minimum,EQ1, that was reported in previous papers4,17 and a newminimum, EQ2, only detected in the recent work of etMart•�al.15 Both diequatorial minima present an intramolecularhydrogen bond between the hydroxy group and the side-chaincarboxylate (Fig. 5).

3.2 Conformational energy surface around each minimum

In order to construct a detailed energy surface around eachlocal minimum, additional conformational points(/1, /2)were considered in their proximities. Then, the same calcu-lation procedure described before (MP2/6-31&G*//HF/6-31G* and MP2/6-31G*//HF/6-31G*) was performed at eachpoint. At the end, a total of 203 chorismate conformationswere studied at the ab initio MP2 level. The analytical confor-mational energy surface was obtained by means of a bicubicspline interpolation procedure.22 In Fig. 3a and 4a the diaxialand the diequatorial MP2 energy surfaces obtained with the6-31&G* basis set are represented. The corresponding 6-31G*surfaces are very similar.

In Table 2 the relative energies and geometrical parametersof the conformational minima of the MP2/6-31&G*//HF/6-31G* Ðtted surface are shown. These minima are betterdescribed than the corresponding minima of Table 1 sincethey correspond to a higher level computed surface, and thisenergy recalculation implies a sort of optimization.(/1, /2)Relative energies practically do not change (di†erences arearound 0.1 kcal mol~1), and the dihedral angles have(/1, /2)a maximum change of 13¡. This angular variation is related tothe relatively Ñat region in the proximities of each minimum.

A Ðnal aspect to be noted is that the diaxial conformationalenergy surface, Fig. 3a, shows a new minimum that did notappear in the HF/6-31G* calculations. This new minimum,labeled as AX5, is observed when the energies of the (/1, /2)grid points are recalculated at the MP2/6-31&G* level. It isalso detected if the surface points are recalculated either at theMP2/6-31G* or the HF/6-31&G* level (Table 2). A globaloptimization of the AX5 conformation at the HF/6-31&G*level and a vibrational frequency analysis conÐrmed that AX5is a true minimum with the and values equal to [94.6¡/1 /2and 24.8¡, respectively (Fig. 5). Its HF/6-31&G* energy is[832.490 40 Eh .

4 Liquid phase calculationsThe study of the solvent e†ect on the conformational equi-librium of a solute molecule, using either an explicit or a con-

Table 2 Relative energies of chorismate minima of the Ðtted gas phase conformational surfaces calculated at di†erent ab initio levels.(/1, /2)The tabulated and angles correspond to the minima of the MP2/6-31&G*//HF/6-31G* surface. Angles in degrees and energies in kcal/1 /2mol~1

EQ1 EQ2 AX1 AX2 AX3 AX4 AX5

HF/6-31G*//HF/6-31G* 0 3.2 11.8 11.5 13.8 17.4 ÈHF/6-31&G*//HF/6-31G* 0 3.5 11.3 11.1 12.9 17.3 12.4MP2/6-31&G*//HF/6-31G* 0 2.0 10.0 10.7 12.0 15.0 11.9/1 [121.0 76.6 [173.5 [110.8 [155.6 71.8 [88.9/2 56.7 [61.0 [139.5 131.3 [0.6 [86.0 17.7

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tinuum solvation model, can be done in di†erent ways. Themost common procedure consists of calculating the solvationenergy for each gas phase conformational minimum, addingthe resulting value to the corresponding gas phase energy toobtain the new relative conformational energies, and, Ðnally,obtaining from them the new conformer populations.However, this procedure can lead to wrong predictions sincethe structures of the conformational minima are altered whenthe solute molecule is introduced into the liquid phase. Theconformational minima in the gas phase and in solution arenot fully coincident. Moreover, some minima may appear ordisappear in solution. Thus, an optimization in solutionshould be done to Ðnd the geometry and relative energies ofthe new conformational minima.

In order to overcome the difficulties of performing opti-mizations in solution, an indirect optimization procedure,restricted to the two main degrees of freedom (the and/1 /2rotational angles), has been introduced. First, the solvationenergy is calculated for each one of the conforma-(/1, /2)tional points used to construct the gas phase conformationalenergy surface. Second, new relative energies are obtained forall these points by adding the solvation energy to the(/1, /2)conformational gas phase energy. Then, after a Ðtting pro-cedure a new conformational energy surface for the choris-mate in solution is obtained. Finally, the minima in this newsurface are located and taken as a good approximation to theconformational minima in solution.

The standard and the proposed procedures yield clearly dif-ferent results for chorismate molecule in water solution. Thus,for PCM calculations with a 6-31G* basis set, the di†erencesin the relative conformational energies between the two pro-cedures are 0.9, 1.3, 0.8 and 0.6 kcal mol~1 for the AX1, AX2,AX3 and AX4 minima, respectively. The amount of these dif-ferences indicates that the two procedures are not equivalentand, consequently, the procedure that implies the optimizationin solution is preferred. Another important point to improvethe description of the conformational equilibrium of choris-mate molecule in water is to consider the conformationalentropic contribution to the relative stability of the conforma-tions. There is a di†erent entropic contribution for each con-formational minimum depending on the shape of the surfacein its surroundings. Moreover, for a given minimum thisentropic contribution di†ers from gas phase to solution due tothe di†erent shape of the conformational energy surface.

4.1 Conformational minima of chorismate in water

As in the gas phase study, two conformational energy surfaces,diaxial and diequatorial, were constructed for chorismate inwater as a function of and the two rotational angles of/1 /2 ,the enol pyruvoyl side chain (Fig. 2). The solvation energy ofthe chorismate conformations were calculated with theUAHF-PCM method. The energy of each conforma-(/1, /2)tion in solution was obtained as the summation of its gas

phase energy (calculated in the previous section at the MP2/6-31&G*//HF/6-31G* level) plus the solvation energy obtainedfrom the PCM/6-31G*//HF/6-31G* or the PCM/6-31&G*//HF/6-31G* calculations. Thus, two solvation models are con-sidered, depending on the basis set used in the PCMcalculations. They will be referred to as solv and solv],respectively. All the conformations considered in the gas phasehave been recalculated with this procedure. The Ðnal surfaces,obtained after a Ðtting procedure, are shown in Fig. 3 and 4.Di†erences in the positions of the minima, in the surface shapeand in the relative energies are analyzed.

In Fig. 3a and b the diaxial surfaces for chorismate in thegas phase and in solution are compared. Although the gasphase minima are also minima in the solution surface, thereare signiÐcant di†erences. Thus, the AX5 minimum presents insolution a better deÐned well, and the AX4 minimum shows insolution a wider well that indicates a favorable entropic e†ect.In general, the well shapes and the and angles of the/1 /2liquid phase minima are di†erent from the corresponding gasphase values. The new angle values and relative energies of thesolution minima are collected in Table 3. Another importantdi†erence is the new maximum that appears in the solutionsurface between the AX2, AX3 and AX5 minima.

The diequatorial surfaces for chorismate in the gas phaseand in solution are shown in Fig. 4a and b. The gas phaseEQ1 and EQ2 minima are also found in solution. However,their energy wells present some di†erences in shape and in thelocation of their minimum (Table 3). Additional (/1, /2)points were calculated outside the areas surrounding the EQ1and EQ2 minima to conÐrm that these other regions are moreenergetic, and, that there is not any other diequatorialminimum in solution.

An additional search for conformational minima in solutionwas done by Ðxing the ring geometry close to a planar dis-position. Thus, the dihedral angle, that characterizes the/form ,diequatorial and the diaxial dispositions of chorismate wasoptimized starting from a value close to a planar ring dis-position and for di†erent values of the and angles. A/1 /2new minimum (NF1) with a, dihedral angle of [105¡/form ,was found (Fig. 5). This angle value di†ers from the character-istic values of the diequatorial and diaxial minima (Table 1)indicating that this new conformational minimum belongs toneither the diequatorial nor the diaxial chorismate forms. Thisminimum is only present in the conformational surface insolution. No minimum is observed in the same posi-(/1, /2)tion of the gas phase conformational surface. See Table 3 forits geometric and energetical values. In the construction of theconformational surfaces 22 points were employed for the EQ1region, 33 for EQ2, 88 for AX1, AX2, AX3 and AX5, 23 forAX4 and 37 for NF1.

The obtained relative Gibbs energies of the conformationalminima in solution are shown in Table 3. Both models(*Gmin)(solv and solv]) show an important reduction in the Gibbsenergy di†erence between the diequatorial and diaxial

Table 3 Dihedral angles and relative Gibbs energies and entropic correction of these Gibbs energies of the conformational(*Gmin) (*Gent)minima of chorismate in water obtained from the Ðtted conformational surfaces in solution. The values obtained with the solv and solv](/1, /2)models (solvation energy calculated using PCM with the 6-31G* and the 6-31&G* basis set, respectively) are indicated. The corresponding gasphase thermal corrections of the HF/6-31G* optimized structures are also shown. Angles in degrees and energies in kcal mol~1

EQ1 EQ2 AX1 AX2 AX3 AX4 AX5 NF1

Solv model /1 [120.0 69.8 [160.5 [83.3 [163.7 65.9 [83.0 66.8/2 42.4 [91.9 [130.5 105.6 0.3 [96.4 17.4 2.6*Gmin 0 2.4 3.1 3.1 3.3 7.7 1.6 4.0*Gent 0 0.01 0.29 0.09 0.45 [0.87 0.13 0.37

solv] model /1 [120.3 68.5 [160.4 [83.6 [164.2 76.4 [83.5 67.0/2 57.7 [92.9 [130.5 107.3 0.2 [98.7 18.1 2.7*Gmin 0 1.9 2.5 2.6 2.6 7.2 1.1 3.6*Gent 0 0.67 0.75 0.37 1.25 [0.47 0.79 0.88

Gas phase thermal correction 0 0.68 [0.66 [0.72 [0.58 [0.51 È È

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minima. The chorismate diaxial minima are signiÐcantly morestabilized in water solution than the diequatorial ones due tothe absence of the internal hydrogen bond and the consequentfavorable interaction between the solvent and the hydroxyand carboxylate groups of the side chains. The greatest solva-tion energies of the AX5 (10 kcal mol~1) and AX3 (9 kcalmol~1) minima are due to the more extended disposition ofthe enol pyruvoyl side-chain (Fig. 5) that puts the carboxylategroup more separated from the rest of the molecule, allowinga better interaction with the continuum model of water. Thetwo diequatorial minima show similar solvation energiesdespite the internal hydrogen bond being formed with a di†er-ent disposition of the carboxylate group. The reduction of therelative Gibbs energies is more signiÐcant in the solv] model.Although for both solvation models the values are quite*Gminsimilar, there is a systematic di†erence of about 0.5 kcalmol~1 due to the clearly smaller solvation energy of the EQ1minimum when the PCM is used with a basis set with di†usefunctions.

The most stable diaxial conformation in solution is the AX5minimum, the one that does not appear in the conformationalsurface calculated at the HF/6-31G* level. It is situated only1.1È1.6 kcal mol~1 above the absolute minimum, the EQ1conformation. Thus, its consideration is very important in thedescription of the diaxialÈdiequatorial conformational equi-librium. It should be noted that this minimum was notdescribed in previous studies.3,4 On the other hand, the con-tribution of the minimum found only in solution, NF1, is verypoor due to its high energy.

4.2 Conformational equilibrium

Although the calculation of the conformational populationscan be done considering only the Gibbs energy of each con-formational minimum, better results are obtained*Gmin ,when the entropic correction due to the shape of its surround-ing energy well in the conformational energy surface is takeninto account. This correction is calculated by considering theentropic contribution of all surface points situated under acontour set at above each local minimum. It can be2kBTexpressed in terms of a Gibbs energy increment, and*Gent ,calculated as where the*Gent\ [kBT ln(&

ie~(*Gi~*Gmin)@(kBT))

summation is extended to all points of a 0.1] 0.1 degree gridhaving Thus, the relative population*G

i[ *Gmin¹ 2kBT .

between two minima A and B can be expressed as,

NANB

\;i

e~*GiA@(kBT)

;j

e~*GjB@(kBT)\

e~(*GmAin`*GeAnt)@(kBT)e~(*GmBin`*GeBnt)@(kBT)

(1)

According to this expression a conformational minimum isrepresented by a local minimum plus the surface region situ-ated within a contour set at above it. Relative popu-2kBTlations are calculated at 298.15 K. The entropic regionscorresponding to the diaxial and diequatorial minima at thistemperature are indicated in Fig. 3b and 4b. The obtained

Gibbs energy corrections are shown in Table 3. Their*Gentvalues are an indication of the relative di†erences in thesurface shape of the conformational minimum wells. The

greater values observed in the solv] model are due to thewider well that in this model presents the EQ1 minimum.Apart from the highest diaxial minimum (AX4), this correctionenhances the importance of the diequatorial minima.

An interesting comparison can be made between the *GentGibbs energy correction calculated in the liquid phase and thegas phase thermal correction (Table 3). There is a clear dis-crepancy in three of the Ðve compared values that can beattributed to the di†erent shape of the liquid and gas phaseconformational energy contour maps as can be seen by com-paring Fig. 3a with 3b and 4a with 4b. Thus, the usualapproximation of employing the gas phase thermal correctionfor the liquid phase energies is not good enough in the case ofchorismate in water.

The relative populations of chorismate conformationalminima in water at 298.15 K obtained with the solv andsolv] models using eqn. (1) are shown in Table 4. The die-quatorial populations including the conformational entropiccontribution in solution energy terms) are 94(*Gmin] *Gentand 95% for the solv and solv] model, respectively. Thehighest diaxial population corresponds to the AX5 minimum.The presence of this minimum, not found in previous calcu-lations, turns out to be fundamental for the diaxialÈdiequatorial equilibrium. Its contribution reduces thediequatorial weight to values that are reasonably near to theexperimental range, 83 to 92%.5 This reduction would be notpossible if only the AX1 and AX2 minima were considered.

This great coincidence does not mean that the two modelsare practically identical since they give slightly di†erent valuesfor the and energy terms. So, the populations*Gmin *Gentobtained with both models for the EQ1 minimum di†er in 10percentage units when only the contribution is con-*Gminsidered. However, this di†erence is considerably reduced whenthe contribution is added. This means that in the solv]*Gentmodel this minimum has a wider well.

5 ConclusionsAn exhaustive search for the conformational minima of cho-rismate molecule in the gas phase and in solution was carriedout by studying its ab initio conformational energy surface asa function of the two rotations of its main side-chain. A con-formational surface was constructed for each of the two cho-rismate dispositions, diaxial and diequatorial. Five diaxialminima, three of them not found before, and two diequatorialminima have been detected in the gas phase. The fact that allthe minima in these energy surfaces were conÐrmed to be trueminima through global optimization indicates that the and/1rotational angles of the enol pyruvoyl side-chain are a/2good choice for describing the conformational mobility ofchorismate. As expected for anions, the inclusion of di†usefunctions in the basis set is found necessary to properlydescribe the relative conformational energies.

In order to determine the conformational equilibrium ofchorismate in water, its conformational energy surface in solu-tion was constructed from the gas phase surface by calculatingthe solvation energy for each point. Solvation energies wereobtained from PCM calculations at the HF level with the

Table 4 Conformational proportions of chorismate minima in water at 298.15 K obtained from the Ðtted conformational surfaces in(/1, /2)solution with the two solvation models. and indicate whether the entropic contribution from the surface is con-%(*Gmin ] *Gent) %(*Gmin)sidered or not

EQ1 EQ2 AX1 AX2 AX3 AX4 AX5 NF1

Solv model %(*Gmin) 90.9 1.6 0.5 0.5 0.3 0.0 6.1 0.1%(*Gmin ] *Gent) 92.2 1.6 0.3 0.4 0.2 0.0 5.2 0.1

Solv] model %(*Gmin) 80.7 3.3 1.2 1.0 1.0 0.0 12.6 0.2%(*Gmin ] *Gent) 93.7 1.2 0.4 0.6 0.1 0.0 3.9 0.1

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cavity deÐnition of the UAHF model. Two basis sets wereemployed in order to analyze the role of the di†use functions.With both solvation models the diaxialÈdiequatorial relativepopulations measured experimentally in water were correctlyreproduced. It is worthy of note that the AX5 minimum, notfound in previous calculations, is fundamental to obtaining acorrect description of the diaxialÈdiequatorial equilibrium.The entropic contribution of the conformational energy wellsalso plays an important role in the sense of favoring the die-quatorial disposition. This contribution is rather di†erentfrom one solvation model to the other, however both modelsyield similar conformational populations compatible with theexperimental values.

The construction of the conformational energy surface hasbeen useful in locating the true minima in solution and visual-izing the di†erences in shapes with the corresponding gasphase minima. This surface allowed a sort of indirect opti-mization, since the minima in solution di†er geometricallyfrom the gas phase minima. The signiÐcant di†erencesbetween the entropic contribution obtained from these sur-faces and the thermal correction calculated in the gas phaseindicate that further work is needed in order to properlyinclude thermal corrections in solution.

AcknowledgementsFinancial support from the Spanish Ministerio de Ciencia y

(Project BQU2000-0642-CO3-03) and from theTecnolog•� aComissionat per a Universitats i Recerca de la Generalitat deCatalunya (1999SGR00177) is acknowledged. The Centre de

de Catalunya C4-CESCA is also acknow-Supercomputacio�ledged for providing us with computer capabilities. S.M. bene-Ðted from a grant from the Universitat de Barcelona.

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