2430
J. Phys. Chem. B 2008, 112, 2430-2438
Microhydration of Protonated Glycine: An ab initio Family Tree 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: October 16, 2007; In Final Form: December 14, 2007
The incremental hydration of the glycine cation is investigated using an ab initio approach fully correcting for basis set superposition errors and explicitly incorporating electron-correlation effects. Structures with zero to four surrounding water molecules have been determined. It is demonstrated that the successive aggregates follow a Darwinian family tree, the most stable complexes systematically belonging to the same branch of the tree. In strong contrast with neutral glycine, the direct hydrogen bonding to the glycine cation is favored over bridging water structures. The agreement between experimental and theoretical hydration enthalpies and Gibbs free energies is impressive, as ab initio estimates almost systematically fit the experimental error bars. For GlyH+-(H2O) and GlyH+-(H2O)3, we show that two structures are generated by the experimental setup. The present approach also resolves most of the previous theory/experiment discrepancies and provides patterns for the evolution of the vibrational spectra: a decrease of the hydrogen-bond stretching frequency indicating second-shell water molecules. Additionally, the impact of bulk solvent solvation is investigated, as four discrete water molecules still do not fully hydrate the protonated glycine.
I. Introduction Water plays a role in stabilizing biomolecular structure and facilitating biological function. Water can generate small active clusters and macroscopic assemblies, that are able to transmit information on various scales.1 Protonation and microhydration of proteins or DNA are of fundamental importance in biochemical processes such as proton transport, water-mediated catalysis, molecular recognition, protein folding, and so forth. Indeed, proton transfer is crucial for many enzyme reactions, and intraprotein water networks could constitute proton-binding sites in proteins, that are as essential for biological functions as amino acids (AA).2 For instance, the proton pumping photocycle of bacteriorhodopsin involves a cluster of water molecules at the proton release site close to the molecular surface.3,4 Similarly for the carbonic anhydrase II the rate-determining step of its catalytic reaction is the proton transfer from a zinc-bound water molecule to a histidine residue via a bridge made of two water molecules.5 In addition, water efficiently participates in molecular recognition by mediating the specific interactions between binding partners.6,7 Water molecules are, for example, abundant in protein-protein interfaces (10 water molecules per 1000 Å2 of interface area) and form hydrogen bonds either with the backbone polar groups or the charged side chains. Understanding such a binding mechanism may be crucial in drug design, for example, how two monomers of HIV-protease, a major drug * Corresponding author. Research Associate of the Belgian National Fund for Scientific Research. E-mail:
[email protected]. † Post-Doctoral Researcher of the Belgian National Fund for Scientific Research. ‡ Research Associate of the Belgian National Fund for Scientific Research.
target in combating AIDS, can combine to form an active dimer form. Designing an inhibitor binding at the interface would be a way to prevent dimerization of the enzyme.8 Bound water molecules can also help to mediate an antigen-antibody association, like the Fv fragment of the anti-hen egg white lysozyme antibody D1.3 in its free, or antigen-bound forms.9 The interaction between a ligand and a protein is also mediated by water molecules. For example, in a concanavalin A-trimannoside complex, a water molecule plays a crucial role by anchoring the reducing sugar unit to the protein.10 Solventinduced effects contribute to the binding Gibbs energy between a drug and its target and could therefore improve the clinical efficiency of the drugs.11 Many protein-DNA interfaces are also highly solvated, and water is directly involved in proteinDNA recognition.12 Bridging water molecules have for instance a dual role in promoting the histone protein-DNA association not only by providing further stability to direct protein-DNA interactions but also by enabling the formation of many additional interactions between more distantly related elements.13 Peptide solvation is one of the major factors in the protein folding,14 as the hydration forces mediate the collapse of the chain and stabilize the native structure.7 Imai et al. also suggest hydration entropy gain to be a substantial driving force in protein folding.15 The understanding of these hydration effects at the molecular level requires the characterization of the interactions between biomolecules and their environment. Due to its relevance in many fields, the microhydration process of nucleic acid bases16-18 or amino acids19-21 has received widespread attention.22 In this report, we will focus on the microhydration of AA, building blocks of peptides and proteins, and particularly of protonated glycine (GlyH+), the simplest and smallest among the amino acids. This cationic system has been selected because
10.1021/jp710034r CCC: $40.75 © 2008 American Chemical Society Published on Web 02/01/2008
Microhydration of Protonated Glycine recent gas-phase successive hydration enthalpies have been measured for GlyH+-(H2O)n (n ) 1-4).19 Numerous theoretical works have been devoted to the solvation and microsolvation,23,24 on the one hand, of DNA bases for which the impact of water on electroaffinities and ionization potential has been unveiled17,25-33 and, on the other hand, of AA for which the nonionized/zwitterion equilibrium is treated by many investigations.34-49 However, indeed, few works tackled AAH+.37,50-52 Besides, most of these studies use a density functional theory (DFT) approach, which is able to model hydrogen bonds in some biomolecules53,54 and give some valuable chemical insights41,48,51,52,55 but is not always fully adequate to investigate weakly bonded complexes,56,57 especially when conventional hybrids are used. We have to mention a couple of studies from 2006 that tackle problems similar to the case treated herein. First, for the microhydration of uncharged AA, the most comprehensive investigation we are aware of is from Aikens and Gordon.58 They determined an astonishing number of MP2/6-31++G(d,p)//HF/6-31G(d,p) Gly-(H2O)n (n ) 1-8) minima, partly using the effective fragment potential approach.59-61 There is also the joint theoretical/experimental study of ValH+ and ValLi+ water complexes by the Rizzo group,51 though, while the B3LYP functional used in ref 51 could simulate vibrational spectra and help in identifying the successive complexation site(s) of protonated valine, a strong mismatch was unravelled: the B3LYP lowest-energy conformers do not always match the experimental facts.51 To generate the (starting) structures, both works rely on a first molecular dynamics step51,58 and/or a Monte Carlo procedure.58 In the framework of microhydration investigations, the advantage of performing an initial molecular dynamics run is clear: it allows a huge number of reasonable starting geometries to be generated without assumptions. However, these geometries are generally so numerous (200 in ref 58) that directly optimizing them with a high-level electroncorrelated approach is almost impossible, and eventually the chemical intuition or even an affordable intermediate ab initio stage is often necessary.51 In this work, our main goal is to assess the existence/nonexistence of building rules for AAH+-water complexes. Such rules would obviously allow to focus the computational resources on the most interesting structures. If a systematic buildup of the complexes appears dangerous to simulate solvated chemicals, it makes sense to perform such construction when simulating gas-phase measurements. Indeed, it appears very unlikely that direct five-body collisions take place to create the experimentally detected GlyH+-(H2O)4 structure: the actual complexes are also generated step by step. Our second target is to provide help in interpreting the measurements. Indeed, in most cases, the available experimental data for (gasphase) AAH+-water structures are quite sparse: hydration enthalpies and/or vibrational spectra in a limited spectral region.19,21,51 This paper is organized as follows: In section II, we summarize our theoretical tools; we try to categorize each complex so as to create a systematic family tree for structures with one, two, and three surrounding water molecules in section IIIA; in section IIIB, we determine the most stable GlyH+(H2O)4 structure; section IIIC is a comparison of theoretical and experimental hydration energies, and in section IIID, the relationships between micro- and macrosolvation are investigated. II. Computational Considerations The calculations have been performed, with the Gaussian 03 program,62 following our recently purpose-designed computa-
J. Phys. Chem. B, Vol. 112, No. 8, 2008 2431 tional procedure.50 All geometry optimizations and vibrational frequency determinations have been analytically achieved at the second-order Møller-Plesset (MP2) level, using the extended 6-311++G(d,p) atomic basis set that includes both polarization and diffuse functions. The MP4(SDQ)//MP4(SDQ) hydration energies are within 0.40 kcal/mol of the MP2//MP2 results, and CCSD(T) calculations indicate that the correct figure is bracketed by the MP2 and MP4(SDQ) values.50 Though B3LYP provides valid geometries, it yields inconsistent interaction energies for the GlyH+-H2O complex, and could not be used to compute hydration energies in the present case.50 MP2 is therefore clearly a very interesting compromise in regards to its accuracy/cpu-time balance. In order to ensure numerically accurate enthalpies, the self-consistent field (SCF) convergence criterion was systematically tightened to 10-10 au, and the force minimizations were carried out until the root mean square (rms) force was smaller than 1 × 10-6 au. This latter parameter corresponds to the best geometry optimization threshold available in Gaussian 03 (so-called Verytight option). Except when noted, all thermodynamic functions have been computed using T ) 298.15 K and P ) 1012.95 mbar using the standard thermochemistry model implemented in Gaussian 03. This model is quite crude, and some deviations with respect to experiment are therefore to be expected, especially for the entropic contribution. Note that no vibrational scaling factor has been applied, except in section IIIC where comparisons with experiment are carried out and for which the usual MP2 scaling factor of 0.95 has been used.63,64 We have demonstrated in ref 50 that both rotational-vibrational couplings and anharmonicities have a very small impact on the hydration Gibbs free energies (between 0.05 and 0.20 kcal/mol). Accordingly, the thermodynamic contributions are computed in the standard harmonic approach in the following. However, it has to be emphasized that, for this type of complexes, the hydrogen-bond stretching frequencies are very sensitive to anharmonic factors,36,50 so that purely straightforward comparisons with experimental vibrational spectra could be tricky for these intense peaks. The basis set superposition errors (BSSEs) have been removed using the well-established counterpoise (CP) procedure.65 We want to highlight that the BSSE corrections have been applied not only to the (internal) complexation energies but also to all of the geometry optimizations and vibrational frequency calculations.66 In that sense, the values presented here are completely BSSE-free, including the H-bond distance and the vibrational contributions to the entropy. The CP correction on the entropic term is not to be neglected, as we have shown that it can tune T∆S by 1 kcal/mol for some complexes,50 consistently with the Simon et al. investigation on hydrogen-bonded complexes.66 Of course, computing MP2 CP corrections for GlyH+-(H2O)n was a major computational task: when n is incremented, not only the size of the complex increases but also the number of fragments. Consequently the required cpu time for the vibrational analysis scales approximatively with a factor of 1, 3, 9, 20, and 42 for n ) 0, 1, 2, 3, and 4, respectively. To build up the complexes, numerous starting geometries have been considered, though we only report here the different (and stable) final stationary points. In addition, all optimizations began with the accurate level of theory, that is, CP-MP2/6311++G(d,p). No intermediate semiempirical nor cheap ab initio scheme was introduced, as such mixed-methods procedures could be risky. For instance, keeping the same level but using a smaller basis set [CP-MP2/6-31G] could lead to the disappearance of some fertile seeding structures.50 We hold that
2432 J. Phys. Chem. B, Vol. 112, No. 8, 2008
Michaux et al.
Figure 1. GlyH+-(water)n family tree. The color of each box indicates the relative stability (free enthalpy) 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 the text for more details.
all possibilities have been unravelled for directly bonded water molecules, whereas, for the second-shell complexes, that exhibit much smoother potential energy surfaces, we are confident that the majority of possible structures were established. Eventually, we state that CP-MP2 hydration ∆H and ∆G are within ∼0.5 kcal/mol of the fully converged theoretical values. For instance, the MP2 hydration Gibbs free enthalpy of the A3 complex (see below) is only 0.3 kcal/mol larger than the fully corrected ∆G.50 Likewise, we estimate the typical CP-MP2/6-311++G(d,p) (in)accuracy on ∆S to be close to 2.0 cal/mol‚K. In section IIID, the bulk solvent effects are evaluated by means of the conducting polarizable continuum model (CPCM),67,68 that divides the model into a solute part (the complex) lying inside a cavity, surrounded by the solvent (water) continuum. III. Results and Discussion A. A Darwinian Family Tree. In Figure 1, we present the genealogy of GlyH+-(H2O)n complexes for n ) 0, 1, 2, and 3, whereas Figure 2 depicts the three most stable complexes in each generation. The relative Gibbs free energies of the complexes of Figure 1 are listed in Table 1. To help in reading the family tree, the following nomenclature has been applied: (i) G0, G1, G2, and G3 are the successive generations; that is, they correspond to the ensemble of structures with zero, one, two, or three water molecules, respectively; (ii) the letters A, B, and C designate the three types of conformers
of GlyH+ that were identified (see G0 in Figure 2); (iii) the bold number denotes the first-shell complexation sitess1, 2, or 3 (see below and G1 in Figure 2); (iv) italics are for second (and third)-shell solvation, 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 (aa, ab, ...); (vi) any children incorporate the full name of their ancestors; for example, A222a has A22 as a parent, A2 as a grandparent, and A as a great-grandparent. In addition, two evolutionary rules have been illustrated. On the one hand, a significantly less stable Gn - 1 complex does not yield the most favorable Gn structure (this is confirmed below). Therefore, in Figure 1, we have used a relative G threshold of 4.0 kcal/mol for automatic discarding. For instance, children of C1 (G ) 9.14 kcal/mol) have not been looked for. This 4.0 kcal/mol value is about half of the first and second experimental hydration energies of GlyH+.19 On the other hand, to keep “alive” as many productive tree branches as possible, an existing descendant, whatever its stability, is always attributed to its most favorable parent. For this reason, B32 is linked to B3 (G ) 3.04 kcal/mol) and is not labeled B23, as would be a descendant of B2 (G ) 3.45 kcal/mol). Before analyzing the relative stabilities of the several complexes, it is worth to describe the main structural features. For the records, each aggregate listed in Figure 1 and Table 1 has been sketched in the Supporting Information. First, we have
Microhydration of Protonated Glycine
J. Phys. Chem. B, Vol. 112, No. 8, 2008 2433
TABLE 1: Relative G in kcal/mol for the GlyH+-(water)n Structuresa generation
label
G
generation
label
G
generation
label
G
G0
A B C A1 A2 A3 B1 B2 B3 C1 C2 A11a A11b A21 A22 A22a A22b A31 A32 A33a A33b B11a B11b B21 B22 B22a B22b B31 B32 B33a B33b
0.00 3.58 8.37 2.02 0.36 0.00 6.57 3.45 3.04 9.14 8.89 7.19 6.64 1.69 1.39 5.13 3.56 1.74 0.00 3.24 3.32 12.67 11.35 5.40 4.43 9.17 8.63 4.88 2.77 6.17 6.18
G3
A211a A211b A212a A212b A221 A222a A222b A222c A22b2a A22b2ba A22b2bb A311a A311b A313a A313b A313c A321 A322 A322a A322b A322c A323a A323b A323c A323d A33a3b A33a3aa A33a3ab A33b3ba A33b3ba
5.03 5.82 5.53 6.55 0.91 4.26 3.14 5.91 6.24 6.48 6.48 4.40 4.48 3.06 3.16 3.19 0.01 0.00 3.16 1.69 2.78 1.44 1.65 3.76 6.06 5.02 6.22 6.21 7.26 7.25
G3
B321 B322 B322a B322b B323a B323b A2212a A2212b A2212c A2212d A3212a A3212b A3212c A3212d A3213a A3213b A3213c A3213d A3221 A3222a A3222b A3222c A3223a A3223b A3223c
2.92 2.63 6.57 6.30 4.68 6.70 4.78 2.91 5.04 6.27 2.82 1.03 2.57 5.14 0.99 1.25 3.28 5.59 0.00 2.55 1.53 3.72 1.11 3.01 5.85
G1
G2
G4
a For each generation (that is n), the most stable complex is used as an energetic reference, and the superscripts refer to the different complexes displayed in Figure 1. P ) 1013 mbar, and T ) 298.15 K.
only found three different GlyH+ conformers corresponding to well-defined and -characterized minima, the two most stable being the trans (A) and cis (B) forms. This contrasts with neutral Gly for which Barone, Adamo, and Lelj unravelled several conformers.69 Indeed, in Gly, stabilizing interactions between the carboxylic acid and the amino lone pair could appear, which is obviously impossible for GlyH+. At G1, eight minima are found, with the 1, 2, and 3 sites corresponding to a water molecule attached to the carboxylic moiety, the side of the ammonium group, and the back of the ammonium group, respectively. While the ValH+-H2O equivalents to A1, A2, and A3 have been reported with B3LYP/6-31++G(d,p) in ref 51, only two GlyH+-H2O complexes (no A2) were given in a 2004 B3LYP/6-31G(d) investigation.37 For more details about the A1, A2, and A3 geometries and spectra, we refer the reader to ref 50. At G2, the second-shell structures can appear and these water molecules are packed in (relative) pyramidal orientations, as expected. The only three significant exceptions to this finding are A22a, B11a, and B22b that present more coplanar water molecules due to an extra hydrogen bond arising between the second water and the carbonyl group. All of these three complexes correspond to bridging minima structures that have been found to be dominant in nonionized and zwitterionic glycine.58 Despite numerous attempts, no bridging counterpart of B11a could be detected when starting from the A conformation. Note that many more complexes with bridging waters have been identified in the work of Aikens and Gordon for microhydrated Gly,58 as the total positive charge in GlyH+ favors direct hydrogen bonds. For the records, systematic CP-MP2/6311++G(d,p) geometry optimizations have been performed using the best Gly-(H2O)n (n ) 1 and 2) minima of ref 58 as starting structures70 and all led to the minima previously identified in Figure 1.71 This is a solid clue that we should
actually have unravelled all relevant complexes, at least for G1 and G2. At G2, one can also create a complex with water molecules on both sides (A22, see Figure 2), as there are two energy-equivalent and symmetry-related complexation sites of type 2. Direct binding of the second water to glycine (or to the first-shell water) could be easily distinguished by antagonistic evolutions of the geometrical and vibrational signatures. Indeed, with additional first-shell (second-shell) water molecules, the water-GlyH+ H-bonds lengthen (shorten). For instance, the H-bond distance of A2 (1.72 Å) increases when adding the second water molecule in the first shell (1.77 Å in A22) but decreases when the second shell is involved: 1.62 Å (A22a) and 1.64 Å (A22b). Consequently, the vibrational frequencies of the related (most intense) IR stretching modes are also affected: +117 cm-1 from A2 to A22 but -233 cm-1 (-191 cm-1) from A2 to A22a (A22b). This latter finding is completely consistent with the theoretical and experimental trends noted in ref 51 and allows one to straightforwardly determine to which solvation shell an extra water molecule pertains, on the basis of the measured hydrogen stretching spectra. At G3, the same phenomena could be unravelled with a H-bond distance from GlyH+ to water (at site 2) of 1.78 Å in A221, 1.69 Å in A222b, and 1.61 Å in A22b2bb. The variations in the stretching frequencies (A2 as reference) are +137, -51, and -281 cm-1 for A221, A222b, and A22b2bb, respectively. A new possibility shows up at G3,51 that is A222c, where the third water molecule is linked to the first solvation shell but still very slightly interacts with the carbonyl. In the latter complex, the distance between the two side water molecules and the ammonium hydrogen atom is 1.74 Å, but the second-shell water remains 2.27 Å away from the carbonyl oxygen. Similarly, a structure with the third water bridging the molecules bonded to the ammonium and carboxylic moiety was unveiled (A212b).
2434 J. Phys. Chem. B, Vol. 112, No. 8, 2008
Figure 2. Representation of the three most stable (from left to right) GlyH+ structures with zero, one, two, three, and four water molecules. Cartesian coordinates are available in the Supporting Information.
Let us now investigate the relative stabilities of the complexes. The main striking fact deduced from Figure 1 is that the lowest-G complexes of all generations belong to the same branch of the tree: A (G0), A3 (G1), A32 (G2), and A322/A321 (G3), with the two latter being extremely close in energy (see section IIIC). In addition, the ideal G2 structure, namely, A32, has its roots in A3 but at G2 it incorporates the second-shell water molecule in the first shell similarly to its uncle A2. That is, A3 and A2 were the two most stable complexes of G1. In the same way, A322 and A321 are combinations of A32, A22, A31, and A21, that are the only four complexes of G2 with G e 2.0 kcal/ mol. In other words, the most favored parent complexes give the children with the highest stability. Additionally, in most cases, our Darwinian-tree-building rules lead to generationrelative G getting worse as n increases; for example, all four B2x complexes at G2 are relatively less stable than B2 at G1. Only two exceptions can be noticed: the B (G0), B3 (G1), B32 (G2), and B322 (G3) series, and A221 that is relatively more stabilized than A22. However, in both cases, the generational improvement remains very modest: 0.5 kcal/mol at most, clearly justifying our Darwinian rules. Specifically, our 4.0 kcal/mol discarding threshold seems totally safe, if not conservative. For instance, assuming the 0.91 kcal/mol upgrade between G0 (B) and G3 (B322) would remain constant throughout the descending tree (at larger n), a B descendant could only become a competitor to an A complex at generation 12, much above today’s experimental availability (G3 or G4 for AAH+-water structures).19,21,51 Another striking point is that the second- and third-shell water molecules are not favorable, with respect to direct H-bond to the protonated glycine that is always preferred.
Michaux et al. For instance, at G2, the most stable second-shell complex, namely, A33a, remains 3.24 kcal/mol above the A32 reference. In addition, structures with 1a or 1b water tend to be even more unstabilized, and the same statement holds for bridging complexes. Therefore, it is quite clear that the two first solvent molecules are directly attached to the ammonium group. This is in strong contrast with nonionized Gly for which the low-G structures typically possess bridging water molecules on the COOH side.58 While GlyH+ behaves more like zwitterionic Gly, the best minima still significantly differ, as a bridging A22alike complex is foreseen for zwitterionic Gly at G258,71 but is more than 5 kcal/mol above A32 for GlyH+. At G3, third-shell (or doubly occupied second-shell) complexes are (much) more unstable than the second-shell structures, for example, A33a3b and A33a3aa are 5.02 and 6.22 kcal/mol above the G3 reference. This means that the shorter the AAH+-water bond, the less stable the complex; that is a counterintuitive conclusion. The amount of charge on the free hydrogen atoms of the ammonium group decreases when n increases: +0.39e for A, +0.33e for A3, and +0.26e for A32.72 Therefore, the difference between first and second-shell complexes is much smaller at G3 (1.44 kcal/mol for A323a) than at G2 (3.24 kcal/mol). It is also worth to underline that bridging water structures like A222c, A212b, A322c and A322d are significantly less stable than their nonbridging counterparts. This is probably related to the significant stress implied by such systems: the local structures implying first-shell waters are so strongly altered that the benefit from any double H-bonding is lost. Eventually, starting with the Gly-(H2O)3 minima of ref 58 CP-MP2/6-311++G(d,p) optimizations led to structures previously identified,73 or descendent of unstable G1 and G2 parents, that happen to be significantly high in energy (at least +5 kcal/mol),74 confirming the reliability of our approach. In the Supporting Information, one can find the electrostatic potential computed for the most stable structures of the three first generations. For A, it is clear that complexation on the NH3+ side could have been predicted, as it is the most positively charged area. However, with this simple picture, A3 and A2 appear almost equally probable. The situation is similar at G1 for A3. For A32, the free hydrogen of the ammonium moiety is surrounded by the most positive potential area and one would foresee a favored A322 at G3, although A321 is in fact equally stabilized. In short, the electrostatic potential computed for Gn could provide only initial insights for the complexation site at Gn + 1. Eventually, it is interesting to compare our relative G at each n with the ValH+ energies reported by Rizzo and co-workers for three complexes.51 Although the AA used are not exactly the same (especially the two complexation sites are not equivalent in ValH+), we demonstrate below that our approach solves most of the previously encountered theoretical/experimental discrepancies. For G1, our results are very similar to Rizzo’s, though the Gibbs energy difference between the A1like and A3-like compounds is only 1.2 kcal/mol in this investigation. Of course, part of the difference might originate in the use of different AA: Val is bulkier than Gly. For this reason, we have performed CP-MP2/6-311++G(d,p) test calculations on ValH+-H2O and it turned out that the “best” ammonium-hydrated compound is more stable than the carboxylic centered complex by 3.1 kcal/mol. This means that the water complexation at the COOH side is even less probable in ValH+ than in GlyH+ which shows a 2.0 kcal/mol difference between A1 and A3. In any case, it is clear that the first water molecule fits best at the ammonium side for both AAH+. At
Microhydration of Protonated Glycine G2, the two most stable B3LYP/6-31++G(d,p) ValH+ compounds are (i) a mixed ammonium-carboxylic complex (0.00 kcal/mol) and (ii) a structure with two NH3+ bonded water molecules (+0.33 kcal/mol), the latter being in better agreement with the available experimental vibrational spectra.51 Contrary to B3LYP, CP-MP2 correctly foresees a double complexation on the ammonium side for AAH+ (A32: 0.0 kcal/mol versus A21: 1.69 kcal/mol). Therefore, our results for G1 and G2 are completely consistent with the conclusions of ref 51: In particular, the [B3LYP] stabilization arising from hydrogen bonding to the carboxylic OH seems to be systematically oVerestimated with respect to putting a second water molecule on a protonated ammonium. At G3, the ValH+ complex best fitting the experiment presents water molecules bonding with all of the hydrogen atoms of the ammonium, and possibly a mixed (one carboxylic, two ammonium waters) contribution, but definitely no “cyclic” compound.51 Again, keeping in mind that COOH complexation is less favored in protonated valine than in GlyH+, the agreement with our findings is perfect, that is, A322 (0.00 kcal/mol), A221 (0.91 kcal/mol), and A222c (5.91 kcal/mol).75 However, in that case, B3LYP incorrectly predicts a high-energy A322-like complex (2.75 kcal/mol) and a stabilized A222c-like (0.57 kcal/mol) complex.51 We think that the overstabilization of the latter could originate in the apparent lack of BSSE correction in ref 51. Indeed, the A222c aggregate is very ‘packed’, so that BSSE would incorrectly favor it. Subsequently, we confidently can state that our computational approach is able to restore a correct theory/experiment agreement concerning the ordering of microhydrated G1-G3 structures. B. Building up the Next Generation. Even with the knowledge accumulated in the previous section, accurately foreseeing the most gifted G4 kid may not look like a walkthrough. Following the obtained building rules, one would go for A3221 because its roots are the three G3 structures with the smallest G, that is A322, A321, and A221. However, as noted above, the second-shell compounds tend to become more and less unstable with n: 3.24 kcal/mol for A33a but 1.44 kcal/ mol for A323a. If such a 1.80 kcal/mol improvement pertained at the next generation, the best G4 complex could contain one second-shell water molecule. To alleviate these uncertainties, we have generated all G4 individuals being descended from the three most stable G3 parents (which are within 1 kcal/mol), but for the 1a and 1b substitution, as such patterns are obviously not promising. This led to the 19 structures listed in Table 1 and depicted in the Supporting Information. It turns out that A3221 is clearly the most stable G4 structure, though four second-shell structures are within 1.0-1.2 kcal/mol: A3212b, A3213a, A3213b, and A3223a. It should be emphasized that, as noted previously, the relative stability tends to decrease when going down the tree but, of course, in the leading branch. For instance, all four A2212a, A2212b, A2212c, and A2212d are 4.78, 2.91, 5.04, and 6.27 kcal/mol above the reference, whereas their father was only off by 0.91 kcal/mol. Consequently, the results obtained at G4 do not contradict the conclusions for the three first generations: one can build up AAH+-(H2O)n complexes in a systematic way. Indeed, the naturally foreseen structure, A3221, is indeed the most stable and only descendants of the leading tree branch are to be searched for. Following chemical common sense and using B3LYP/631++G(d,p) calculations, Rizzo’s group proposed three complexes for ValH+-(H2O)4 that are labeled A3221 (H4-C), A3222c (H4-B), and A2212c (H4-A) in our (Rizzo) notation.51 From comparison with experimental spectroscopic data, they concluded that only the two latter, containing the bridging water
J. Phys. Chem. B, Vol. 112, No. 8, 2008 2435 molecules, could correspond to the detected molecular assembly, although it was not possible for them to rule out other (nonbridging) second-shell structures.75 Our best second-shell aggregates are within 1.0-1.2 kcal/mol of the A3221 reference, that is about the same energy separating carboxylic OH complexation in ValH+ and in GlyH+ (1.1 kcal/mol, see above). Subsequently, it is possible that the A3221-like ValH+-(H2O)4 does not dominate the G4 generation for ValH+, as suggested by Rizzo. Further calculations, that are beyond the scope of the present contribution, would be required to obtain a definitive answer. Nevertheless, we can definitely state that only nonbridging second-shell water could possibly be detected experimentally: the G of 2c structures are too large, impeding any substantial presence of bridging complexes. Note that the prediction of four directly bonded water molecules in GlyH+ appears consistent with Wincel’s experimental findings, who detected G1-to-G4 complex for GlyH+, AlaH+, and PheH+ but only G1-to-G3 for ProH+ that has three available acidic hydrogen molecules instead of four in the other AAH+.19 As bridging second-shell water structures appeared nonfavored, these experimental findings seem to indicate that only first-shell complexes could be detected with the experimental setup of ref 19, although theoretical investigations of AlaH+ and ProH+ would be helpful. C. Successive Hydration Energies: Comparisons with Experimental Data. The most recent measurements for gasphase hydration energies of protonated glycine are the 2007 mass spectrometry experiments by Wincel.19 The reported ∆Hn, ∆Sn, and ∆Gn are corrected for standard conditions (293 K and 1000 mbar),19 though the actual measurements have been carried out at much higher temperature, typically around 440 K for n ) 1, 390 K for n ) 2, 350 K for n ) 3, and 320 K for n ) 4, and with a very low pressure (around 10 mbar). Therefore, establishing meaningful theory/experiment analogies has a prerequisite: the determination of the complexes presenting the smallest G’s in these experimental conditions, that is, the aggregate(s) actually present in the reaction chamber. Without surprise, the impact of the temperature on the relative G listed in Table 1 is certainly not negligible. For instance, while A3 is more stable than A2 (A1) by 0.36 (2.03) kcal/mol under standard conditions, the difference amounts to 0.67 (1.87) kcal/mol within the actual experimental setup (a 0.95 vibrational scaling factor is used to obtain these values). At 440 K, the thermal energy is ∼0.9 kcal/mol and both ammonium complexes do coexist. As these structures are related by internal rotation, a rapid conversion between the two complexes is likely to happen. However, the transition state connecting A3 and A2 is 1.28 kcal/mol high, impeding a significant dynamical conversion. Boltzmann relative weights are 52% (A3) and 48% (A2), taking into account that two symmetry-equivalent 2 sites exist. Again, these facts appear to be completely consistent with the ValH+-H2O experiment that suggests both A2 and A3 are probably present but with a majority of A3.51 At G2, A32 clearly remains the best complex under T ) 390 K and P ) 10 mbar with the relative G values unchanged for A21 (1.71 kcal/mol) and A31 (1.80 kcal/mol) but significantly increased for A22 (1.90 kcal/mol). Obviously, the complexation on site 2 is relatively more sensitive to the entropic contribution than on the 1 and 3 positions. This suggests that experiments carried out at lower (higher) temperature could significantly increase (decrease) the 2/3 ratio. In addition, we note that second-shell water structures do not significantly benefit from higher temperature.76 For G3, A322 and A321 are equally stabilized under the conditions used in Table 1, though at higher temperature the latter that possesses only one side
2436 J. Phys. Chem. B, Vol. 112, No. 8, 2008
Michaux et al.
TABLE 2: Comparisons between Successive (Gas-Phase) Hydration Enthalpies (in kcal/mol) and Entropies (cal/mol‚K) of GlyH+ Obtained from Experiment (ref 19) and Theory (This Work)a -∆Hn n
complex
1
A3 (52%) A2 (48%) Total A32 (100%) Total A321 (72%) A322 (28%) Total A3221 (100%) Total
2 3 4
experiment
15.4 ( 0.7 13.9 ( 0.4 12.8 ( 0.3 10.6 ( 0.6
-∆Sn theoryb
experiment
16.30 16.59 16.44 14.05 14.05 11.29 12.31 11.57 11.19 11.19
20.4 ( 1.6 22.4 ( 1.4 24.8 ( 0.9 22.2 ( 2.0
-∆Gn
theoryb
theoryc
24.78 26.96 25.83 23.75 23.75 23.92 27.32 24.87 27.28 27.28
23.61 25.80 24.66 23.23 23.23 24.07 27.42 25.00 27.82 27.82
experiment
9.4 ( 1.2; 9.7d 7.3 ( 1.0; 7.2d 5.5 ( 0.6; 5.4d 4.1 ( 1.2
theoryb
theoryc
9.04 8.70 8.88 7.08 7.08 4.28 4.31 4.29 3.17 3.17
9.38 8.93 9.16 7.30 7.30 4.24 4.28 4.25 3.04 3.04
a Following the experiment, all values are obtained for T ) 293 K and P ) 1000 mbar. When several complexes coexist, the Boltzmann total is given. See the text for more details. b Computed straightforwardly using T ) 293 K and P ) 1000 mbar. c Calculated consistently with the experimental data, that is, (1) considering the ∆Sn value at experimental temperature to be equal to that at 293 K and (2) applying the G ) H TS formula at T ) 293 K to compute G. d Values taken from ref 77.
TABLE 3: Estimated Relative Gibbs Free Energies (kcal/mol) in Bulk Water (See Text for More Details) generation G0 G1
label A B C A1 A2 A3 B1 B2 B3 C1 C2
G 0.00 0.71 3.14 2.65 0.06 0.00 3.45 1.10 0.65 5.29 2.94
generation
label
G2
A11a
water is favored. At T ) 350 K, the G difference is 0.17 kcal/ mol, that is, much smaller than the thermal energy (∼0.7 kcal/ mol), but contrary to the G1 case, the two systems are not related by a simple internal rotation. Applying the Boltzmann distribution formula leads to 72% of A321 and 28% to of A322, as A321 presents a twofold degeneracy. For G4, A3221 remains the most stable complex at T ) 320 K and P ) 10 mbar. While the relative G values of A3213a and A3212b are now decreased to 0.92 and 0.96 kcal/mol, respectively, they remain significantly larger (40%) than the thermal energy in the experimental setup. Now that the structures and energetics of the detected GlyH+-(H2O)n for n ) 1-4 have been assigned, it is possible to compare the theoretical enthalpies and entropies with the experimental data. These results are summarized in Table 2. For each case, we have computed the ∆Sn at 293 K as well as at the experimental temperature. From the linearity in van’t Hoff plots, Wincel considered ∆Sn to be temperature-independent. Indeed, we obtain small differences, although a slight decrease of ∆S1 with increasing temperature is observed: a 5% difference between 440 and 293 K. Likewise, the ∆Gn values in Table 2 have been directly computed from calculations, as well as following the procedure reported in ref 19. As in ref 19, we present successive hydration energies, so that the theory/ experiment discrepancies should have a tendency to propagate with n. Nevertheless, considering our estimated theoretical inaccuracies ((0.5 kcal/mol for ∆Hn and ∆G; (2.0 cal/mol‚K for ∆S, see section II), one gets a very impressive theory/ experiment agreement at each microhydration step, especially for the data computed so as to simulate the experimental processing. In fact, the only two possible mismatches are the first and fourth generation entropic contributions that are overshot by theory, and the speed of decrease of ∆Hn and ∆Gn when n increases that we slightly overestimate. Indeed, the experiment predicts a ∆H3 (∆G3) value 17% (41%) smaller than
A11b A21 A22 A22a A22b A31 A32 A33a A33b B11a
G 5.03 4.10 2.24 1.67 3.40 1.96 2.81 0.00 1.61 1.79 6.77
generation G2
label b
B11 B21 B22 B22a B22b B31 B32 B33a B33b
G 5.15 2.83 1.69 7.88 7.39 3.32 0.97 2.62 2.63
∆H1 (∆G1), whereas CP-MP2 predicts variations of 30% (52%). Despite these two drawbacks, Table 2 demonstrates the adequacy of CP-MP2. To the best of our knowledge, such a remarkable consistency has not been previously reached for this type of complex. As feedback, this agreement also supports our structural identification for the present complexes. Indeed, hazardously selecting A1 at G1 and A21 at G2 (two reasonable complexes) leads to a ∆H1 value of 13.9 kcal/mol and a ∆H2 value of 15.0 kcal/mol; that is, an incorrect selection would, without appeal, produce a qualitatively incorrect growth of hydration enthalpies with n. D. From Micro- to Macrosolvation. At this stage of the study, it is also worth considering the impact of the bulk solvent on the relative stabilities of the complexes. As it is not straightforward to perform counterpoise corrections simultaneously with PCM calculations,78 we have estimated the relative G value in water by using the difference of total energy between MP2 and PCM-MP2 calculations for the gas-phase optimized structures. Such a procedure is similar to what can be found for neutral glycine in ref 58. The results for G0-G2 are listed in Table 3. The first striking conclusion from this table is that the most stable structures pertain to gas-phase hydrated complexes, A, A3, and A32 at G0, G1, and G2, respectively, though the differences between the various conformers of a single generation are significantly dimmed: now, B is only less stable than A by 0.71 kcal/mol (3.58 kcal/mol in gas-phase) and B32 is 0.97 kcal/mol off A32 instead of 2.77 kcal/mol. While longrange solvation effects have a tendency to equalize the G value, it seems that complexation with the COOH group is (relatively) less probable in water than in the gas phase. The solvation energy of the G0 structures is 81 ( 3 kcal/ mol for all three conformers. This huge amount is directly related to the cationic nature of the investigated molecule that is obviously strongly stabilized in a dielectric medium. This PCM
Microhydration of Protonated Glycine solvation energy decreases to approximatively 75 and 70 kcal/ mol for G1 and G2, respectively. In addition, summing the successive CP-MP2 hydration G values of Table 2, one obtains 23 kcal/mol, suggesting that four water molecules are far from totally solvating GlyH+ (∼81 kcal/mol). This is not a surprising result, as even eight water molecules cannot fully hydrate neutral Gly.58 IV. Conclusions and Outlook Using a MP2/6-311++G(d,p) approach combined with a full counterpoise correction, GlyH+-(H2O)n complexes (n ) 0, 1, 2, 3, and 4) have been systematically classified in a family tree, based on their structures and energetics. It appears that a Darwinian-like logic can be used to build such protonated AA complexes, as the most stable complex at any stage systematically gives the best structure at the next generation. Note that, for the purpose of comparisons with gas-phase experiments, such conclusions are also supported by the fact that three-body, fourbody, ... , molecular collisions are unlikely: it is indeed highly probable that the complexes build step by step. The data generated from the family tree also allow, on the one hand, previous inconsistencies between theoretically predicted and experimentally detected structures to be elucidated and, on the other hand, an impressive accuracy on successive hydration enthalpies and Gibbs free energies to be achieved, even though the measurements sometimes imply a mixture of complexes. Indeed, the computed complexation energies often lie within the experimental error bars. For GlyH+, it is clearly demonstrated that the first two water molecules bind to the ammonium, whereas the following two bind to the two remaining hydrogen-bond donors of AAH+. Bridging water structures that contain second-shell molecules are much less favorable up to G4. This strongly contrasts with nonionized glycine in which water tends to form bridges around the COOH group. We have also confirmed that the vibrational signature in the hydrogen stretching region could help in identifying the structures: a significant increase (decrease) of the circular frequency of the very intense H-bond stretching mode is observed when the incremental water appears in the first (second) solvation shell. We are currently investigating the microhydration of protonated alanine and proline. Acknowledgment. C.M., E.A.P., and D.J. thank the Belgian National Fund for Scientific Research for their respective positions. The authors are indebted to Profs. J.M. Andre´ and D.P. Vercauteren for their long-lasting continuous support and efficient help. 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 number 2.4578.02 and of the FUNDP. Supporting Information Available: Full Gaussian reference, Cartesian coordinates for the molecules of Figure 2, extra complexes obtained from Aikens and Gordon data, electrostatic surfaces for selected complexes, and representation of all complexes investigated here. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Chaplin, M. F. Nat. ReV. Mol. Cell Biol. 2006, 7, 861-866. (2) Garczarek, F.; Gerwert, K. Nature 2006, 439, 109-112.
J. Phys. Chem. B, Vol. 112, No. 8, 2008 2437 (3) Garczarek, F.; Brown, L. S.; Lanyi, J. K.; Gerwert, K. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3633-3638. (4) Shibata, M.; Kandori, H. Biochemistry 2005, 44, 7406-7413. (5) Fisher, Z.; Hernandez Prada, J. A.; Tu, C.; Duda, D.; Yoshioka, C.; An, H.; Govindasamy, L.; Silverman, D. N.; McKenna, R. Biochemistry 2005, 44, 1097-1105. (6) Ben-Naim, A. Biophys. Chem. 2002, 101-102, 309-319. (7) Levy, Y.; Onuchic, J. N. Annu. ReV. Biophys. Biomol. Struct. 2006, 35, 389-415. (8) Levy, Y.; Caflisch, A.; Onuchic, J. N.; Wolynes, P. G. J. Mol. Biol. 2004, 340, 67-79. (9) Bhat, T. N.; Bentley, G. A.; Boulot, G.; Greene, M. I.; Tello, D.; Dall’Acqua, W.; Souchon, H.; Schwarz, F. P.; Mariuzza, R. A.; Poljak, R. J. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 1089-1093. (10) Naismith, J. H.; Field, R. A. J. Biol. Chem. 1996, 271, 972-976. (11) Wang, H.; Ben-Naim, A. J. Med. Chem. 1996, 39, 1531-1539. (12) Janin, J. Structure 1999, 7, 277-279. (13) Davey, C. A.; Sargent, D. F.; Luger, K.; Maeder, A. W.; Richmond, T. J. J. Mol. Biol. 2002, 319, 1097-10113. (14) Baldwin, R. L. J. Mol. Biol. 2007, 371, 283-301. (15) Imai, T.; Harano, Y.; Kinoshita, M.; Kovalenko, A.; Hirata, F. J. Chem. Phys. 2007, 126, 225102. (16) Kabelac, M.; Hobza, P. Phys. Chem. Chem. Phys. 2007, 9, 903917. (17) Kim, S.; Schaefer, H. F. J. Chem. Phys. 2007, 126, 064301. (18) Belau, L.; Wilson, K. R.; Leone, S. R.; Ahmed, M. J. Phys. Chem. A 2007, 111, 7562-7568. (19) Wincel, H. Chem. Phys. Lett. 2007, 439, 157-161. (20) Derbel, N.; Hernandez, B.; Pflu¨ger, F.; Liquier, J.; Geinguenaud, F.; Jaı¨dane, N.; Ben Lakhdar, Z. B.; Ghomi, M. J. Phys. Chem. B 2007, 111, 1470-1477. (21) Wincel, H. Int. J. Mass Spectrom. 2006, 251, 23-31. (22) de Vries, M. S.; Hobza, P. Annu. ReV. Phys. Chem. 2007, 58, 585612. (23) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 1133-1152. (24) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2006, 110, 16066-16081. (25) Hanus, M.; Ryjacek, F.; Kabelac, M.; Kubal, T.; Bogdan, T. V.; Trygubenko, S. A.; Hobza, P. J. Am. Chem. Soc. 2003, 125, 7678-7688. (26) Hanus, M.; Kabelac, M.; Rejnek, J.; Ryjacek, F.; Kabelac, M.; Hobza, P. J. Phys. Chem. B 2004, 108, 2087-2097. (27) Abo-Riziq, A.; Crews, B.; Grace, L.; de Vries, M. S. J. Am. Chem. Soc. 2005, 127, 2374-2375. (28) Hu, X.; Li, H.; Liang, W.; Han, S. J. Phys. Chem. B 2005, 109, 5935-5944. (29) Close, D. M.; Crespo-Hernandez, C. E.; Gorb, L.; Leszcynski, J. J. Phys. Chem. A 2005, 109, 9279-9283. (30) Kabelac, M.; Zendlova, L.; Reha, D.; Hobza, P. J. Phys. Chem. B 2005, 109, 12206-12213. (31) Mazzuca, D.; Marino, T.; Russo, N.; Toscano, M. J. Mol. Struct. (THEOCHEM) 2007, 811, 161-167. (32) Kim, S.; Schaefer, H. F. J. Phys. Chem. A 2007, 111, 1038110389. (33) Lange, A.; Herbert, J. M. J. Chem. Theory Comput. 2007, 3, 16801690. (34) Mercier, S. R.; Boyarkin, O. V.; Kamariotis, A.; Guglielmi, M.; Tavernelli, I.; Cascella, M.; Rothlisberger, U.; Rizzo, T. R. J. Am. Chem. Soc. 2006, 128, 16938-16943. (35) 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, 73097316. (36) Chaban, G. M.; Gerber, R. B. J. Chem. Phys. 2001, 115, 13401348. (37) Ai, H.; Bu, Y. J. Chem. Phys. 2004, 120, 2208-2214. (38) Ai, H.; Bu, Y.; Li, P.; Sun, L. J. Phys. Chem. A 2004, 108, 41584162. (39) Simon, S.; Sodupe, M.; Bertran, J. Theor. Chem. Acc. 2004, 111, 217-222. (40) Chaudhari, A.; Sahu, P. K.; Lee, S. Y. J. Mol. Struct. (THEOCHEM) 2004, 683, 115-119. (41) Lemoff, A. S.; Williams, E. R. J. Am. Soc. Mass Spectrom. 2004, 15, 1014-1024. (42) Li, P.; By, Y.; Ai, H. J. Phys. Chem. B 2004, 108, 1405-1413. (43) Chaudhari, A.; Lee, S. Y. Chem. Phys. 2005, 310, 281-285. (44) Lemoff, A. S.; Bush, M. F.; O’Brien, J. T.; Williams, E. R. J. Phys. Chem. A 2006, 110, 8433-8442. (45) Remko, M.; Rode, B. M. J. Phys. Chem. A 2006, 110, 1960-1967. (46) Alonso, J. L.; Cocinero, E. J.; Lesarri, A.; Eugenia Sanz, M.; Lopez, J. C. Angew. Chem., Int. Ed. Engl. 2006, 45, 3471-3474. (47) Rodziewicz, P.; Doltsinis, N. L. ChemPhysChem 2007, 8, 19591968.
2438 J. Phys. Chem. B, Vol. 112, No. 8, 2008 (48) Derbel, N.; Hernandez, B.; Pfliiger, F.; Liquier, J.; Geinguenaud, F.; Jaidaine, N.; Lakhdar, Z. B.; Ghomi, M. J. Phys. Chem. B 2007, 111, 1470-1477. (49) Costa, D.; Lomenech, C.; Meng, M.; Stievano, L.; Lambert, J. F. J. Mol. Struct. (THEOCHEM) 2007, 806, 253-259. (50) Michaux, C.; Wouters, J.; Jacquemin, D.; Perpete, E. A. Chem. Phys. Lett. 2007, 445, 57-61. (51) Kamariotis, A.; Boyarkin, O.; Mercier, S.; Beck, R.; Bush, M.; Williams, E.; Rizzo, T. J. Am. Chem. Soc. 2006, 128, 905-916. (52) Marino, T.; Toscano, M.; Russo, N.; Grand, A. J. Phys. Chem. B 2006, 110, 24666-24673. (53) Sponer, J.; Leszczynski, J.; Hobza, P. J. Phys. Chem. 1996, 100, 1965-1974. (54) Sirois, S.; Proynov, E. I.; Nguyen, D. T.; Salahub, D. R. J. Chem. Phys. 1997, 107, 6770-6781. (55) Pasker, F. M.; Solca, N.; Dopfer, O. J. Phys. Chem. A 2006, 110, 12793-12804. (56) Paizs, B.; Suhai, S. J. Comput. Chem. 1998, 19, 575-584. (57) Antony, J.; Grimme, S. Phys. Chem. Chem. Phys. 2006, 8, 52875293. (58) Aikens, C. M.; Gordon, M. S. J. Am. Chem. Soc. 2006, 128, 1283512850. (59) Adamovic, I.; Freitag, M. A.; Gordon, M. S. J. Chem. Phys. 2003, 118, 6725-6732. (60) Jensen, J. H. J. Chem. Phys. 1996, 104, 7795-7796. (61) Jensen, J. H.; Gordon, M. S. J. Chem. Phys. 1998, 108, 47724782. (62) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (63) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-16513. (64) Halls, M. D.; Schlegel, H. B. J. Chem. Phys. 1999, 111, 88198824. (65) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553-566. (66) Simon, S.; Duran, M.; Dannenberg, J. J. J. Chem. Phys. 1996, 105, 11024-11031.
Michaux et al. (67) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 29993094. (68) Default parameters have been used, but for radii ) UAKS and noaddsph, for the cavity building. (69) Barone, V.; Adamo, C.; Lelj, F. J. Chem. Phys. 1995, 102, 364370. (70) For both G1 and G2, we have used the six nonionized and five zwitterionic geometries given by Aikens and Gordon. The extra proton was added on the amine (nonionized) or carboxylic (zwitterionic) group. No other parameter was modified prior to the force minimization process. (71) CP-MP2/6-311++G(d,p) gave the following changes (Aikens and Gordon notation for starting points, our notation for final structures): 1N1-a f A1; 1N6-a f A1; 1N2-a f B1; 1N6-b f A1; 1N8-a f B1; 1N8-b f B1; 1Z-a f A2; 1Z-b f B2; 1Z-c f B2; 1Z-d f B2; 1Z-e f C2; 2N1-a f A11b; 2N1-b f A11b; 2N2-a f B11a; 2N6-a f A11b; 2N6-b f A11b; 2N2-b f B11a; 2Z-a f A22a; 2Z-b f B22b; 2Z-c f B22b; 2Z-d f A22; and 2Z-e f A22. (72) Charges have been computed at the MP2 level within the MerzKollman approach. (73) CP-MP2/6-311++G(d,p) led the following changes: 3N1-ar f A321 and 3Z-f f A222a. (74) The new CP-MP2/6-311++G(d,p) minima are the following: 3N1-a f A11b1a; 3N6-a f A11b1a; 3N6-c f A11b1bb; 3N3-h f C212a; 3Z-a f A22a2b; and 3Z-b f B22a2b. These new minima and relative energies are displayed in the Supporting Information. (75) It seems that no A321-like structure was found for ValH+. Even unravelled, such complex would show a (relative) Gibbs free energy larger in ValH+ than in GlyH+, because of a water molecule complexed on the carboxylic OH. (76) We obtained the following: A11a, 7.18 kcal/mol; A11b, 6.34 kcal/ mol; A22a, 5.73 kcal/mol; A22b, 3.73 kcal/mol; A33a, 3.25 kcal/mol; A33b, 3.37 kcal/mol, with the experimental conditions. (77) Klassen, J. S.; Blades, A. T.; Kebarle, P. J. Phys. Chem. 1995, 99, 15509-15517. (78) Cammi, R.; Delvalle, F. J. O.; Tomasi, J. Chem. Phys. 1988, 122, 63-74.
