Modeling the Microhydration of Protonated Alanine - American

9896

J. Phys. Chem. B 2008, 112, 9896–9902

Modeling the Microhydration of Protonated Alanine Catherine Michaux† and Johan Wouters Laboratoire de Chimie Biologique Structurale, Faculte´s UniVersitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium

Eric A. Perpe`te‡ and Denis Jacquemin* Laboratoire de Chimie The´orique Applique´e, Faculte´s UniVersitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium ReceiVed: April 22, 2008; ReVised Manuscript ReceiVed: May 28, 2008

The microsolvation of protonated L-alanine with one, two, or three water molecules has been investigated using a MP2/6-311++G(d,p) approach fully accounting for the basis set superposition errors. A conformational analysis for unhydrated AlaH+ reveals only three minima which have been characterized and compared to the neutral case. We have built a logical tree for the successive hydration stages. This tree shows that the most stable complexes in each step are related and that a systematic approach can be used to grasp the stepwise hydration process. The addition of extra water molecules to the first or second solvation shells leads to the opposite evolution of the hydrogen-bond stretching mode. Comparisons with experimental enthalpies, entropies, and Gibbs free energies clearly demonstrate the adequacy of the approach. Our results also strongly suggest that several di- and trihydrated complexes should coexist under the experimental conditions. I. Introduction Stepwise solvated molecular complexes have recently attracted the attention of a huge number of theoretical and experimental works mainly treating biomolecules or metal ions.1–11 To accurately determine the thermodynamical parameters related to the solute-solvent complexation, most measurements use mass spectrometry (MS),10–12 though the lack of precise structural information might constitute a dramatic drawback. To circumvent this limitation, the MS experiments can be coupled to the determination of the vibrational signatures.8,13 Nevertheless, the resulting spectra might not be straightforwardly interpretable, as several microsolvated structures often coexist. In practice, theoretical calculations are often mandatory or, to say the least, helpful to extract a maximum of information from the experimental data. Broadly speaking microsolvation studies can be classified in to three groups: (i) The evaluation of aqueous effects on metal ions.1–3 (ii) The investigation of the relationships between stepwise hydration and the consequent modifications of the electronic properties, typically the electroaffinities and ionization potentials, of DNA bases.5,14–18 For instance, for the adenine-uracil base pair, the vertical detachment energy increases by 40% when going from the unhydrated to the dihydrated compound.5 (iii) The determination of the relative energies of the nonionized and zwitterionic forms of amino acids (AA).6–8,19–29 For the two simplest AA, Gly and Ala, recent investigations featuring from 1 to 8 and 1 to 10 surrounding water molecules have been reported by Aikens and Gordon,30 and Chuchev and DelBruno.31 Both concluded that the addition of more and more solvent molecules * To whom correspondence should be addressed. E-mail: [email protected]. Research Associate of the Belgian National Fund for Scientific Research. † Post-Doctoral Researcher of the Belgian National Fund for Scientific Research. ‡ Research Associate of the Belgian National Fund for Scientific Research.

leads to relatively more stabilized zwitterions. Much fewer works tackled protonated AA, AAH+,13,19,32–34 although for such systems accurate experimental data are available,10,12 which make meaningful and straightforward the theory/experiment comparisons of the thermodynamic quantities of the complexation process. In the present work, we investigate the microhydration of AlaH+ with refined ab initio tools, and our results are extensively compared with Wincel’s experimental values.10 An obvious limitation of all major theoretical approaches is that the number of possible minima dramatically increases with the cluster size. Consequently, most works rely on initial molecular dynamics and/or Monte Carlo steps to generate a large number of probable starting geometries.13,30 However, the structures eventually obtained in this way are so numerous that a subsequent treatment with state-of-the-art theoretical tools still remains difficult; one often ends up in resorting to semiempirical, low-level ab initio, or even chemical intuition, to perform the screening. Such procedures may look fashionable but cannot be viewed as totally safe. Indeed, using a smaller basis set (for instance) could lead to the disappearance of some valid minima for AAH+.33 In a recent investigation dealing with the microhydration of the protonated glycine,34 we found that an evolutionary logic is suitable to predict the most stable GlyH+-(H2O)n complex on the basis of the energetics and structures of the previous generation, that is, the ensemble of GlyH+-(H2O)n-1 compounds. For comparisons with gas-phase experiments, it is valid to build up the complexes following a stepwise approach, as three- (or more-) body collisions seem very unlikely in the actual low-pressure experimental setup.10,12 For GlyH+, our computational approach yields an excellent accuracy on the successive hydration enthalpies. However, the transferability of this systematic approach to other AAH+ is still to be considered. Therefore, we here selected protonated L-alanine,35 a more complex situation than GlyH+ (AlaH+ lacks the GlyH+ symmetry), to confirm/infirm the efficiency of our procedure and, more importantly, determine the structures

10.1021/jp803476k CCC: $40.75  2008 American Chemical Society Published on Web 07/23/2008

Microhydration of Protonated Alanine

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9897

encountered for the experimental complexes with one to three surrounding water molecules. II. Computational Protocol All calculations have been performed with the Gaussian03 package.36 We followed the computational protocol developed33 and tested34 for the protonated glycine, and details regarding the adequacy of the involved theoretical methodologies can be found in these earlier investigations. Full geometry optimizations and vibrational frequency determinations have been analytically achieved at the second-order Møller-Plesset (MP2) level, using a basis set featuring both polarized and diffuse atomic functions on each atomic center, namely, 6-311++G(d,p). Recently, Riley and Hobza have shown that MP2 generally returns accurate hydrogen bond energies for protein like systems and that a triple-ζ atomic basis set with both polarized and diffuse function is an effective choice.37 Likewise, the MP2 interaction energies obtained for H-bonded thymine-adenine structures agree very well with coupled-cluster [CCSD(T)] values.38 We are therefore confident that such an approach is suitable for our purpose. Note that, at any point, neither intermediate semiempirical nor cheap ab initio optimization schemes were introduced. In order to numerically attain accurate enthalpies, the self-consistent field (SCF) convergence criterion has been systematically tightened to 10-9 au, and the force minimizations were carried out with the tightest Gaussian03 optimization threshold; that is, the minimum of the potential energy surface was considered for a root mean square (rms) force smaller than 1 × 10-6 au only, but for the conformational profile (see section III A) for which a tight threshold (1 × 10 -5 au) was selected. The basis set superposition errors (BSSE) were taken into account by using the wellestablished counterpoise (CP) procedure.39 These BSSE corrections have been applied not only to the (internal) complexation energies but also to all the geometry optimizations and vibrational frequency calculations, following the procedure designed in ref 40. Therefore, the values presented here are completely BSSE-free, even the vibrational contributions to the entropy. We redirect the readers to refs 41–45 for discussions of BSSE effects. Except when noted, all the thermodynamic functions have been computed for T ) 298.15 K and P ) 1012.95 mbar, using the standard thermochemistry model implemented in Gaussian03. No vibrational scaling factor has been applied, except in section III C where the usual MP2 scaling factor of 0.95 has been used.46,47 III. Results and Discussion A. Conformation of the Unhydrated AlaH+. Before studying the stepwise hydration process, we searched after the stable conformers of AlaH+. In general, for AA, this type of conformational analysis is performed by varying the dihedral angles, t1, that is, N-CR-C-O(H), and t2, that is, H-N-CR-C. 48,49 However, in the AlaH+ protonated system, the nitrogen lone pair has left, and the charged ammonium group clearly presents a sp3 structure, so the investigating of t2 is rather useless. For t1, we have performed a fully relaxed MP2/6-311++G(d,p) scan using 20° steps (Figure 1). It turns out that two minima were located with t1 values of 186° (A) and 17° (B), with the former being more stable by 3.9 kcal/mol (in ∆E terms). The (harmonic and unscaled) O-H stretching frequencies of these conformers are alike, 3758 and 3760 cm -1 for A and B, respectively, while the N-H ammonium differentiates with frequencies (relative intensities) of 3375 (0.25), 3486 (0.50), and 3539 (0.42) cm-1

Figure 1. Relative internal energy profile of AlaH+ as a function of the t1 dihedral angle. The structures of the two minima are sketched.

Figure 2. Relative internal energy profile of AlaH+ as a function of the t3 dihedral angle (for t1 ) 186°).

for A but 3417 (0.24), 3514 (0.50), and 3528 (0.47) cm-1 for B. The lower frequency modes correspond to symmetric stretching of the three N-H bonds, that are slightly shorter in B than in A. In a second step, keeping constant these optimal t2 values, we vary the t3 (CR-C-O-H) twisting angle in a relaxed fit. For B, a rotation around t3 provokes steric hindrance and electrostatic repulsion between the ammonium and carboxylic protons, that costs more than 20 kcal/mol. For A (see Figure 2), a new structure could be found, C, but it lies much higher on the energy scale (∆E ) 9.65 kcal/mol) and is therefore unlikely to appear experimentally. In the Cambridge Structural Database (CSD),50 the conformer A of AlaH+ occurs more frequently (15 hits on 18; see the Supporting Information) than conformer B. For A, the t1 values range from 153 to 215°, in agreement with the energetic profile of Figure 1 that shows a quite constant energy in this domain. According to the experimental studies by Blanco et al. on neutral alanine,51 three conformers can be detected. The lowestenergy conformer (t1 )167°), experimentally observed in the gas phase, corresponds to A while the second one (t1 ) -11.5°), where the hydrogen atom of the hydroxyl group is bonded to the nitrogen lone pair, cannot obviously exist in AlaH+. The third predicted conformer, less stable and not yet observed in the gas phase, is similar to our B AlaH+ but lies only 1 kcal/ mol above the neutral reference. For the conformer A of AlaH +, nonsymmetrical bifurcated hydrogen bonds of NH · · · O)C type are observed with distances of 2.13 and 2.88 Å, contrasting with neutral Ala in which the hydrogen bonds are more alike (2.70 and 2.88 Å).51 This clearly highlights that the similarities

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Michaux et al.

Figure 3. L-AlaH+-(H2O)n tree for the A conformer. The color of each box indicates the relative stability (in G terms) of each complex within its generation in a continuous scale going from green (0.0 kcal/mol) to red (g10.0 kcal/mol) with yellowish-green (2.0 kcal/mol), yellow (4.0 kcal/mol), and orange (7.0 kcal/mol) intermediates. The most stable complex is underlined. See text for more details.

Figure 4.

L-AlaH+-(H2O)n

tree for B and C. See Figure 3 for more details.

between neutral and protonated AA are definitely limited, impeding any straightforward generalization of the studies performed for the former. This is actually in agreement with our previous investigation of GlyH+.34 B. Family Tree of Stepwise Hydrated AlaH+. In Figures 3 and 4, we present the logical tree for complexes with one, two, and three water molecules for, respectively, the most stable (A), less stable (B), and least stable (C) conformers of AlaH+ defined in the previous section. Figure 5 provides a sketch of the four most stable complexes in each generation, and a sketch of each aggregate can be found in the Supporting Information. The relative Gibbs free energy (G) of the complexes of Figures 3 and 4 are listed in Table 1. Following ref 34, generic nomenclature and building rules have been applied to obtain the family tree: (i) G0, G1, G2, and G3 are the successive generations, that is, they correspond

to the ensemble of structures with 0, 1, 2, and 3 water molecules, respectively. (ii) A prime (′) is added to distinguish microhydrated structures with t1 angles differing by a few degrees only. (iii) The bold number denotes the first-shell complexation sites: 1 (COOH), 2 (CMe side of NH3+), 3 (CH side of NH3+), or 4 (back of NH3+); see Figure 5. (iv) Italics are for second and third solvation shells and indicate to which Gn-1 water the Gn water is bonded. (v) Superscripts a, b, and c are used to distinguish the relative position of the second-shell water molecules with respect to the first-shell ones, and similarly for the third hydration shell with aa, ab, and so forth. (vi) Any child incorporates the full name of its ancestors, for example, A44b4bb has A44b as parent, A4 as grandparent, and A as greatgrandparent. (vii) The descendants of a compound less stable than 3.0 kcal/mol have not been looked for, as the unstable structures at Gn do not provide more stable complexes at



Figure 5. Four most stable (from left to right) AlaH+ structures at G0, G1, G2, and G3.

TABLE 1: Relative G (P ) 1013 mbar and T ) 298.15 K) Values in kcal/mol for the AlaH+-(H2O)n Structuresa generation

label

G

generation

label

G

generation

label

G

generation

label

G

G0 G0 G0 G1 G1 G1 G1 G1 G1 G1 G1 G1 G1 G1 G1 G1 G1 G2 G2 G2 G2 G2 G2 G2 G2 G2 G2 G2

A B C A1 A′1 A2 A3 A4 B1 B′1 B2 B3 B4 C1 C2 C3 C4 A11a A11b A′11a A′11b A21 A22a A22b A31 A32 A33a A33b

0.00 3.21 9.54 3.35 3.36 1.58 0.89 0.00 6.29 6.30 3.40 4.07 3.65 11.38 10.27 9.48 9.89 6.34 5.89 6.23 5.93 2.30 4.78 3.50 1.18 0.97 4.14 2.61


A41 A′41 A42 A43 A44a A44b B11a B11b B′11a B′11b B21 B22a B22b B23 B24 B31 B33a B33b B41 B43 B44a B44b A211a A211b A212a A212b A212c A311a

1.42 1.08 0.37 0.00 2.02 3.00 9.44 10.88 9.46 10.85 4.55 7.94 7.75 3.66 2.38 4.17 7.77 7.29 3.66 2.27 5.76 4.86 4.84 5.15 4.83 3.08 7.24 3.95


A311b A313a A313b A313c A321 A322a A322b A323a A323b A323c A33b3a A33b3ba A33b3bb A411a A411b A414a A′411a A′411b A′414a A′414b A421 A422a A422b A422c A424a A424b A424c A424d

4.45 4.25 2.06 6.10 1.18 3.72 2.52 3.51 2.29 4.83 5.82 5.14 5.12 3.71 3.44 1.94 3.21 3.04 2.48 1.91 0.39 2.88 1.80 2.42 1.33 1.49 5.86 3.45


A431 A432 A433a A433b A433c A434a A434b A434c A434d A44a4aa A44a4ab A44a4b A44b4a A44b4ba A44b4bb B241 B242a B242b B244a B244b B244c B431 B432 B433a B433b B434a B434b B434c

0.00 0.02 2.60 1.39 2.42 0.80 0.83 5.18 2.74 5.88 5.89 4.95 4.66 5.82 5.81 2.32 5.83 5.69 4.19 3.33 5.98 2.31 2.29 5.59 5.36 4.86 4.17 5.35

a

For each generation, the most stable complex is used as reference to compute G.

Gn + 1, as demonstrated in ref 34 and confirmed below. (viii) To release the evolutionary pressure, a child is always linked to its most stabilized parent in Figures 3 and 4. For instance, A31 is said to be the son of A3 (G ) 0.89 kcal/mol) and not of A1 (G ) 3.35 kcal/mol). Let us first describe the essential structural characteristics of typical complexes. At G1, 14 minima have been unraveled by our approach, almost twice the number obtained for GlyH+. The differences between A1 and A′1 (B1 and B′1) are mostly limited to small perturbations of the t1 angle from -168° to -174° (from -16° to +16°). As these minima have nearly the same energy, it is likely that a dynamic conversion from one conformer to the other would occur. All the monohydrated A

present t1 angles within 15° of planarity and hydrogen bond lengths of 1.66 Å (A1 and A′1), 1.74 Å (A2 and A3), and 1.78 Å (A4), that is, about 0.02 Å longer than those in GlyH+.33 The vibrational spectra of AlaH+-H20 complexes are characterized by a strong absorption corresponding to the H-bond stretching mode. In the harmonic approximation,52 we foresee very large red-shifts53 with respect to A and a strong intensity enhancement for the O-H stretching mode (-508 cm-1 for A1 and -514 cm-1 for A′1) when water binds to site 1. In other words, for A the disappearance of the 3758 cm-1 absorption (see Section III.A), bears witness to the bonding of a water molecule to the COOH. Indeed, in A2, A3, and A4 this frequency is almost unchanged: 3768, 3768, and 3766 cm-1,

9900 J. Phys. Chem. B, Vol. 112, No. 32, 2008 respectively. For these ammonium-bonded structures, the corresponding IR absorptions at 3486 and 3539 cm-1 in A are only slightly altered (A2, 3457 and 3551 cm-1; A3, 3465 and 3546 cm-1; and A4, 3451 and 3517 cm-1), while a strong bathoand hyper-shift is noted for the third stretching: -283, -257, and -193 cm-1 for A2, A3, and A4, respectively.54 At G2, we obtain 17 minima for the conformer A, whereas only 10 could be found for the simplest AAH+.34 Second-shell structures show up and the water molecules tend to pack in pyramidal orientations, but for bridging structures that have the second H2O binding to the CdO group. These structures, such as A22a (see the Supporting Information), remain a minority. The addition of the second water molecule in the first shell significantly increases the H-bond length(s), whereas for the second-shell structures opposite trends are observed. For instance, the 1.78 Å distance in A4 becomes 1.84 Å in A43 and A42, 1.81 Å in A41, 1.80 Å in A′41, but 1.68 Å in A44a and A44b. Accordingly, the vibrational signatures follow antagonistic behaviors for an extra first- or second-shell water: the most active stretching mode of A4 varies by +98 cm-1 for A43, but by -178 cm-1 for A44a.55 These trends are consistent with previous experimental and theoretical works.13,34 For triply hydrated AlaH+, numerous bridging structures have been found with either the third water molecule stacked in between the two first water molecules on the ammonium side (e.g., A434d) or linking the water molecules placed at the 1 and 2/3 positions (e.g., A313c). The evolution of the geometrical and vibrational parameters found at G2 are conserved at G3. For instance, focusing on the same H-bond and stretching mode as above, we got similar changes: A432 (1.88 Å, +164 cm-1), A434a (1.74 Å, -52 cm-1) and A44b4a (1.60 Å, -382 cm-1).55 Due to the mechanical stress inherent to bridging architectures, any interpretation is difficult, as illustrated by A434d (1.82 Å, +88 cm-1) and A434c (2.01 Å, +197 cm-1).55 However, as such structures are unlikely to appear experimentally (see below), we can conclude that tracking the characteristics of the N-H and O-H stretching mode while increasing microhydration is a powerful tool to determine the actually observed structures. Let us now turn toward an assessment of the predictive efficiency of the family tree. As shown in Figure 3, the most stable complexes of all G belong to the same branch: A (G0), A4 (G1), A43 (G2) and A431 (G3). In addition, the best structure at Gn combines the most stable structures from Gn-1. For instance, A43 is obtained from A4 and A3, the only two complexes within a 1 kcal/mol stability at G1. While it is understandable that filling two favorable hydration sites yields the lowest-G structure, such conclusion only holds if no repulsive interactions between water molecules take place. In the present case, a prediction of the energy steadiness for doubly hydrated complexes can be made by simply adding the relative G of monohydrated structures. Indeed, such a crude procedure (that obviously is unsuited for second-shell structures) gives the accurate ordering for the three first structures, A43, A42, and A32, that are of interest for further comparisons with experiment. Likewise, the three most stable G3 complexes, namely, A431, A432, and A421 directly derive from the five best G2 aggregates. On top of that, A434a is the lowest-G second-shell triply hydrated structure that combines A43 and A44a, which are the most stable first- and second-shell complexes at G2, respectively. Our building rules also allow the relative G to worsen when going down the tree but, of course, in the leading branch. This phenomenon is completely systematic for the A-family complexes. If one notes a ∼1 kcal/mol improvement between the best B isomers at G1 and G2, these complexes

Michaux et al. remain more than 3 (2) kcal/mol above the reference A4 (A43). It is also striking that this a 1 kcal/mol does not pertain at G3, suggesting that only lineage from A could be detected by today’s experiments, which can, at best, isolate AAH+-(H2O)3 or AAH+-(H2O)4 complexes.10,12,13 All these conclusions are in agreement with our initial investigation of GlyH+ 34 and confirm that such a systematic procedure is a valid protocol to discover AlaH+-(H20)n structures. Indeed, as all lowest-G complexes belong to the same branch, the computational resources could be straightforwardly focused on the sound AAH+ structures, what is obviously necessary as the complexity of the studied AA increases. Larger complexation free energies are obtained when the extra molecules are placed on the CH side than on the CMe side of the ammonium group. Indeed, for the A conformers, Table 1 demonstrates that type-3 structures are systematically more stable than the corresponding type-2 complexes, with the typical G differences ranging from 0.50 to 1.00 kcal/mol. For AlaH+, the first water binds to the back of the ammonium group (site 4), similarly to GlyH+. However, the difference with respect to the carboxylic complexation is much larger for the former (3.35 kcal/mol) than for the latter (2.02 kcal/mol).33 Likewise, the stability difference between the back and the side NH3+ structures (see Figure 5) is much larger for AlaH+ (A3: 0.89 or A2: 1.58 kcal/mol) than for GlyH+ (0.36 kcal/mol), meaning that while both forms can experimentally coexist for glycine,34 only one conformer should pertain for alanine (see next section). CP-MP2/6-311++G(d,p) calculations performed for the monohydrated protonated valine by Rizzo et al.13 reveal that, at G1, an A3-like is favored over an A4-like (A1-like) complex by 1.57 (3.08) kcal/mol. This illustrates the risk of expanding conclusions drawn about the most stable structure(s) of a given AAH+ to another. The second- and third-shell complexes are not favored in the early generations of AlaH+ because the direct bonding to the charged moieties is always more advantageous for any of the positively charged monohydrated conformers. Nevertheless, while the best second-shell G2 structure (A44a) is 2.02 kcal/mol above the A43 reference, the differences sharply fall at G3 with A434a being only 0.80 kcal/mol less stable than the A431 G3 reference. These values are smaller than the corresponding G for GlyH+:34 3.24 kcal/mol at G2 and 1.44 kcal/mol at G3, suggesting that bulkier AAH+ should more easily lead to second-shell structures. This trend is also in agreement with the investigation of ValH+ by Rizzo and coworkers.13 Note that the best double-second-shell and third-shell aggregates of G3 present relative G larger than 4.5 kcal/mol and are therefore unlikely to be detected. Likewise, bridging structures such as A22a, A33a, or B11b do not allow better stabilization. On the contrary, they are frequently the less stable structures in their category: noncyclic second-shells are always preferred as illustrated by the G of A434a (0.80 kcal/mol, noncyclic) versus A434d (2.74 kcal/mol, cyclic). In fact, at G3, the best cyclic structures (A422a and A433a) present one water molecule not involved in a bridge and stay more than 2.50 kcal/ mol above the corresponding reference structure. This situation strongly contrasts with the case of neutral and zwitterionic Ala,31 for which the low-G complexes possess cyclic hydrogen bonds around the carboxylic moiety, while for the zwitterionic form, water molecules tend to form bridges between the NH3+ and COO- groups. C. Comparisons with Experimental Data. Recently, Wincel reported mass spectrometry measurements of the successive hydration enthalpies and entropies of four protonated AA.10 While he listed ∆Hn, ∆Sn, and ∆Gn under standard conditions



TABLE 2: Comparison between Successive (Gas-Phase) Hydration Enthalpies (kcal/mol) and Entropies (cal/mol · K) of AlaH+ Obtained from Experiment (Ref 10) and Theory (This Work)a -∆Hn

-∆Sn

-∆Gn

n

complex

experiment

theoryb

experiment

theoryb

theoryc

experiment

1

A4 (100%) average

14.8 ( 0.3

15.41 15.41

20.6 ( 0.8

22.24 22.24

21.19 21.19

2

A43 (64%) A42 (36%) average

13.2 ( 0.2

13.72 13.62 13.68

22.4 ( 0.4

29.27 30.17 29.59

28.63 29.55 28.96

12.2 ( 0.2

11.06 11.82 10.96 9.68 11.09

24.2 ( 0.4

24.49 27.09 25.49 22.55 25.22

24.63 27.18 25.64 22.77 25.36

3

A431 (37%) A432 (30%) A421 (20%) A434a (13%) average

theoryb

theoryc

8.8 ( 0.5

8.89 8.89

9.20 9.20

6.7 ( 0.3

5.15 4.78 5.02

5.23 4.96 5.13

5.1 ( 0.3

3.87 3.88 3.49 3.07 3.70

3.84 3.86 3.45 3.01 3.66

Following the experiment, all values are obtained for T ) 293 K and P ) 1000 mbar. Computed straightforwardly using T ) 293 K and P ) 1000 mbar. c Calculated consistently with the experimental data, that is, (i) considering the ∆Sn value at experimental temperature to be equal to that at 293 K and (ii) applying the G ) H - TS formula at T ) 293 K to compute G. a

(293 K and 1000 mbar), the actual experiments were performed at very low pressure (10 mbar) and at higher temperature. For AlaH+, the experimental temperatures are typically 420 K for n ) 1, 390 K for n ) 2, and 350 K for n ) 3. Therefore, prior to any extensive theory/experiment comparisons, one should recognize the complexe(s) in each generation, that were actually detected with this experimental setup. For sure, the temperature has a non-negligible influence on the relative G. For instance, while A4 is more stable than A3, A2, and A1 by 0.89, 1.58, and 3.35 kcal/mol, respectively, and under standard conditions, these differences amount to 1.46, 2.35, and 3.86 kcal/mol within the reported experimental setup.56 Note that using CP-CCSD(T) internal energies to correct the CP-MP2 ∆U has a completely negligible influence as the relative stabilities become 1.53, 2.41, and 4.00 kcal/mol, for A3, A2, and A1, respectively. This confirms the reliability of the MP2 methodology for such complexes. At 420 K, the thermal energy is 0.83 kcal/mol, and only A4 should consequently pertain. A43 remains the most stable complex of G2 but with larger (smaller) differences for complexes without (with) water bound to the carboxylic group. Indeed, the corrected ∆G are A43 (+0.00 kcal/mol), A42 (+0.45 kcal/mol), A4′1 (+0.96 kcal/mol), A31 (+1.13 kcal/mol), A41 (+1.29 kcal/mol), and A32 (+1.33 kcal/ mol). Using the Boltzmann formula, we calculate a 0.64-A43/ 0.36-A42 proportion in the experimental conditions (T ) 390 K; RT ) 0.77 kcal/mol). At G3, the first five most stable structures at 350 K (RT ) 0.70 kcal/mol) are A431 (G ) 0.00 kcal/mol), A432 (G ) 0.14 kcal/mol), A421 (G ) 0.44 kcal/ mol), A434a (G ) 0.70 kcal/mol), and A434b (G ) 0.75 kcal/ mol). This means that a slight proportion of second-shell complexes is detectable. Indeed, a Boltzmann distribution yields the following: 37% of A431, 30% of A432, 20% of A421, and 13% of A434a. Note that, for GlyH+, no second-shell structures were predicted to be experimentally detectable even with three or four water molecules complexed.34 The computed ∆Hn, ∆Sn, and ∆Gn values of AlaH+-(H20)n complexes with n ) 1, 2, and 3 are compared to the experimental data in Table 2. The van’t Hoff plots being linear, Wincel deduced that the ∆Sn values are almost independent of temperature,10 and our results confirm this result with a variation limited to 5% for ∆S1. Anyway, we have computed the thermodynamical data following both a direct procedure (calculation under standard conditions) and the indirect scheme by Wincel. Keeping in mind that our estimated theoretical inaccuracies are (0.5 kcal/mol for ∆H and ∆G, and (2.0 cal/mol · K

b

for ∆S,33 the results are in perfect agreement with experiment for the first hydration step. For the second water molecule, we obtain an accurate ∆H2 value, but we overestimate the entropic contribution by ∼30%, consequently leading to a too small ∆G2. For the last microsolvation step, we are close to the experiment for all parameters, although we slightly undershoot the free enthalpy of complexation. Apart from the difficulty to achieve accurate experimental values for such systems, several factors could explain the residual theory/experiment discrepancies: (i) the experiments are not performed at a constant temperature but use a range of values (e.g., between 410 and 370 K for G2), so that the relative weights of the complexes might not be ensured; (ii) the actual complex composition is very sensitive to the relative stabilities, so that very small errors on relative G might impact on the calculated ∆Gn; and (iii) Table 2 lists successive hydration contributions, so that the theoretical errors tend to propagate with increasing n. The ∆Hn and ∆Gn values are systematically slightly smaller for AlaH+ than for GlyH+,10 what our approach correctly reproduces except for ∆G1 for which we obtain equal values for the two protonated amino acids.34 Despite the above mentioned limitations, Table 2 demonstrates the adequacy of our CP-MP2/6-311++G(d,p) computational scheme to provide the energetic data for AlaH+-(H20)n. IV. Conclusions Using a MP2/6-311++G(d,p) approach including full counterpoise corrections, the structures and energetics of AlaH+-(H20)n (n ) 0, 1, 2 and 3) have been investigated. For AlaH+, only three conformers could be identified, since the interactions with the nitrogen lone pair, that were essential in neutral Ala, are removed. In strong contrast with the case of Ala, structures with bridging water molecules are not favored for AlaH+. The various complexes can be classified in a systematic tree whose proper reading allows to diminish the computational effort for structural determinations. Indeed, the most stable compounds at each microhydration step belong to the same branch of the tree. In addition, a set of relevant structures at a given generation is sufficient to predict the best structures at the next generation, whatever the stability of the branch. This, at least, limits the effort to a few guess compounds. We basically obtain a good agreement with the successive experimental hydration enthalpies, entropies, and Gibbs free energies measured by Wincel, though we overshoot ∆S2. In

9902 J. Phys. Chem. B, Vol. 112, No. 32, 2008 addition, our results allow us to suggest that the experimental setup probably detects a mixture of two AlaH+-(H20)2 and four AlaH+-(H20)3 structures, with one of the latter presenting a second-shell hydration. As the binding of an extra H2O directly to AlaH+ or to another water molecule can be distinguished by antagonistic evolutions of the intense H-bond stretching mode, the actual presence of second-shell structures could be deduced from systematic IR studies. Acknowledgment. C.M., E.A.P., and D.J. thank the Belgian National Fund for Scientific Research for their respective positions. All calculations have been performed on the Interuniversity Scientific Computing Facility (ISCF), installed at the Faculte´s Universitaires Notre-Dame de la Paix (Namur, Belgium), for which the authors gratefully acknowledge the financial support of the FNRS-FRFC and the “Loterie Nationale” for the Convention No. 2.4578.02 and of the FUNDP. Supporting Information Available: Cartesian coordinates for the molecules of Table 2, CSD refcodes for the unhydrated AlaH+, and representation of all complexes here investigated. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Shepler, B. C.; Wright, A. D.; Balabanov, N. B.; Peterson, K. A. J. Phys. Chem. A 2007, 111, 11342–11349. (2) Ali, S. M.; De, S.; Maity, D. K. J. Chem. Phys. 2007, 127, 044303. (3) Jagoda-Cwiklik, B.; Wang, X. B.; Woo, H. K.; Yang, J.; Wang, G. J.; Zhou, M. F.; Jungwirth, P.; Wang, L. S. J. Phys. Chem. A 2007, 111, 7719–7725. (4) Jalili, S.; Akhavan, M. Theor. Chem. Acc. 2007, 118, 947–957. (5) Kim, S.; Schaefer, H. F. J. Phys. Chem. A 2007, 111, 10381–10389. (6) Rodziewicz, P.; Doltsinis, N. L. ChemPhysChem. 2007, 8, 1959– 1968. (7) Blom, M. N.; Compagnon, I.; Polfer, N. C.; von Helden, G.; Meijer, G.; Suhai, S.; Paizs, B.; Oomens, J. J. Phys. Chem. A 2007, 111, 7309– 7316. (8) Bush, M. F.; Prell, J. S.; Saykally, R. J.; Williams, E. R. J. Am. Chem. Soc. 2007, 129, 13544–13553. (9) Belau, L.; Wilson, K. R.; Leone, S. R.; Ahmed, M. J. Phys. Chem. A 2007, 111, 7562–7568. (10) Wincel, H. Chem. Phys. Lett. 2007, 439, 157–161. (11) Beyer, M. K. Mass Spectrom. ReV. 2007, 26, 517–541. (12) Wincel, H. Int. J. Mass Spectrom. 2006, 251, 23–31. (13) Kamariotis, A.; Boyarkin, O.; Mercier, S.; Beck, R.; Bush, M.; Williams, E.; Rizzo, T. J. Am. Chem. Soc. 2006, 128, 905–916. (14) Hanus, M.; Kabelac, M.; Rejnek, J.; Ryjacek, F.; Kabelac, M.; Hobza, P. J. Phys. Chem. B 2004, 108, 2087–2097. (15) Abo-Riziq, A.; Crews, B.; Grace, L.; de Vries, M. S. J. Am. Chem. Soc. 2005, 127, 2374–2375. (16) Hu, X.; Li, H.; Liang, W.; Han, S. J. Phys. Chem. B 2005, 109, 5935–5944. (17) Mazzuca, D.; Marino, T.; Russo, N.; Toscano, M. THEOCHEM 2007, 811, 161–167. (18) Lange, A.; Herbert, J. M. J. Chem. Theory Comput. 2007, 3, 1680– 1690. (19) Ai, H.; Bu, Y. J. Chem. Phys. 2004, 120, 2208–2214. (20) Simon, S.; Sodupe, M.; Bertran, J. Theor. Chem. Acc. 2004, 111, 217–222. (21) Chaudhari, A.; Sahu, P. K.; Lee, S. Y. THEOCHEM 2004, 683, 115–119. (22) Li, P.; By, Y.; Ai, H. J. Phys. Chem. B 2004, 108, 1405–1413. (23) Chaudhari, A.; Lee, S. Y. Chem. Phys. 2005, 310, 281–285. (24) Lemoff, A. S.; Bush, M. F.; O’Brien, J. T.; Williams, E. R. J. Phys. Chem. A 2006, 110, 8433–8442.

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JP803476K

Modeling the Microhydration of Protonated Alanine - American

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