Microsolvation of Uracil and Its Conjugate Bases: A DFT Study of the

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Microsolvation of Uracil and Its Conjugate Bases: A DFT Study of the Role of Solvation on Acidity Steven M. Bachrach* and Michael W. Dzierlenga Department of Chemistry, Trinity University, 1 Trinity Place, San Antonio, Texas 78212, United States

bS Supporting Information ABSTRACT: The effect of microsolvation on the deprotonation energies of uracil was examined using DFT. The structures of uracil and its N1 and N3 conjugate bases were optimized with zero to six associated water molecules. Multiple configurations (upward of 93) of these hydrated clusters were located at PBE1PBE/6-311þG(d,p). Trends in these geometries are discussed, with the waters generally forming chains with small numbers of waters (one
three), rings (three
five waters), or cages (five
six waters). The difference in energy between the N1 and N3 conjugate bases is 13 kcal mol
1 in the gas phase, and it decreases with each added water up to four. At this point the energy difference has been halved, but addition of a fifth or sixth water has little effect on the energy difference. This is understood in terms of the water structures and their ability to stabilize the negatively charged atoms in the conjugate bases.

1. INTRODUCTION The acidity of uracil is a fascinating case for the study of the role of solvation. Nakanishi has measured the solution phase pKa of uracil to be 9.5, giving the conjugate base formed by loss of the N3 proton.1 This conjugate base is in equilibrium with the one derived from proton loss at N1. Furthermore, they found that the pKa values of 3-methyluracil (10.0) and 1-methyluracil (9.8) are quite similar, all suggesting that the aqueous-phase acidity of the N1 and N3 protons are essentially identical. On the other hand, the relative acidities of the two nitrogen sites are dramatically different in the gas phase. Kurinovich and Lee performed bracketing measurements using Fourier transform mass spectrometry on uracil.2 They determined the deprotonation energy (DPE) of the N1 proton is 333 ( 4 kcal mol
1 and that of the N3 proton is 347 ( 4 kcal mol
1. (Subsequently, Lee3 and Gronert4 independently bracketed the deprotonation energies of the C5 and C6 sites; they are at least 16 kcal mol
1 less acidic than the nitrogen protons.) Miller performed kinetic gasphase acidity experiments and confirmed the deprotonation energy of uracil is 333 ( 4 kcal mol
1; this is associated with the loss of the N1 proton.5 These deprotonation energies are well reproduced by computations. For example, B3LYP/631þþG/(d,p) predicts the two deprotonation energies are 332.4 (N1) and 345.8 (N3) kcal mol
1,6 and 334.2 (N1) and 346.6 (N3) using the aug-cc-pVTZ basis set at 298 K.7 The two DPEs are 334.5 (N1) and 346.6 (N3) kcal mol
1 at G3(298 K).5 The two nitrogen sites are of distinctively acidities in the gas phase (their DPEs differ by about 13 kcal mol
1), yet they are equivalent in water. Lee2 has argued that this difference comes about for two reasons. First, the N1 conjugate base is more stable than the N3 conjugate base because the formal nitrogen anion in the former is adjacent to one oxyanion (in the benzenoid r 2011 American Chemical Society

resonance structure of Scheme 1) while the nitrogen anion is adjacent to two oxyanions in the latter. Second, due to its larger dipole moment the N3 conjugate base will be stabilized to a greater extent by the dielectric field associated with water than will be the N1 conjugate base. These two effects essentially cancel, making the two conjugate bases nearly isoenergetic in water. The acidity of uracil thus seems like an excellent system to use to judge the ability of microsolvation to model solvation effects. Additionally, it complements our recent microsolvation studies of amino acids8,9 toward defining the number of explicit water molecules needed to begin to describe bulk water effects. There have been a number of microsolvation studies of uracil,6,10
16 but only two dealing with its acidity and these papers17,18 investigated only the acidity at N1. Kurinovich and Lee have estimated the differences in the N1 and N3 acidity using PCM.2 In this work, we will sequentially microsolvate uracil (U), its N1 and N3 conjugate bases (N1 and N3, respectively) to investigate how the relative acidities of these two sites vary with the number of associated water molecules. We will discuss the previous microsolvation studies as we present our results for the microsolvation with one to six water molecules.

2. COMPUTATIONAL METHODS We employ here the same computational methodology we have previously used to study the microsolvation of glycine8 and cysteine.9 Specifically, initial configurations formed of either uracil, its N1 or N3 conjugate base, and one to six water molecules were generated by guess, guided by both previous Received: March 17, 2011 Revised: April 29, 2011 Published: May 12, 2011 5674

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The Journal of Physical Chemistry A Scheme 1. Resonance Structures of Uracil

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Scheme 3. NPA Charges in U, N1, and N3

Scheme 2. Water-Binding Regions of U, N1, and N3

studies and results with fewer water molecules. The geometries of these clusters were then completely optimized at B3LYP/631þG(d).19 Analytical frequencies were computed at this level to confirm that the clusters are local energy minima and to obtain zero-point vibrational energy (ZPVE). These clusters were then reoptimized at PBE1PBE/6-311þG(d,p)20 and the B3LYP ZPVE were added to the PBE1PBE energies to provide enthalpies at 0 K. The recent benchmark study of DFT performance for describing hydrogen bonding finds PBE1PBE (also called PBE0) to provide excellent hydrogen bonding energies and distances of the hydrogen bonds.21 Energies are not corrected for basis set superposition error (BSSE) due to the inherent overestimation of the correction within the Boys and Bernardi22 counterpoise (CP) or other similar23
25 procedures.26 We anticipate that BSSE is likely to be small in these computations due to the large, diffuse basis employed. An alternative approach toward generating cluster geometries involves molecular dynamics or Monte Carlo methods. We cannot discount the possibility that we may have missed some low-energy clusters that these alternative methods might have located. However, these random guess procedures will also generate many highlying configurations by placing waters in much less favorable regions, like near the alkenyl fragment. With clusters involving a large number of waters, we believe that the random approach will waste a great deal of time pursuing noncompetitive structures and therefore prefer our guided intuitive approach. This procedure provides excellent agreement in relative energies of the small microsolvated clusters of glycine and cysteine relative to energies computed at highly correlated levels.8,9 In addition, as will be discussed below, the gas phase DPE experimental values are reproduced extremely well with this computational method. Microsolvated clusters of uracil will be designated as U-Nx, where N indicates the number of water molecules in the cluster and x sequentially indexes the configurations in increasing energy; i.e. x = a indicates the lowest energy cluster, x = b indicates the second lowest energy cluster, etc. The clusters of the N1 and N3 conjugate bases are similarly labeled as N1-Nx and N3-Nx. All computations were performed with the Gaussian-09 suite.27

3. RESULTS We will first report the structures of the microsolvated clusters, taking in turn the clusters of uracil, then the clusters of the N1

conjugate base, and last the clusters of the N3 conjugate base. The resultant deprotonation energies will be summarized at the end of this section. There are four regions about a uracil molecule (U) or its conjugate bases (N1 or N3) to which water can form hydrogen bonds. These are labeled as regions A
D in Scheme 2. Region A offers the N1
H as a proton donor and the oxygen on C2 (referred to hereafter as O2) as a proton acceptor. Regions B and C offer the N3
H as a proton donor and either O2 (region B) or the oxygen on C4—hereafter referred to as O4—(region C) as proton acceptor. Region D is likely to be the poorest location of these four for a water molecule to bind; while O4 is a suitable proton acceptor, the C5
H is a much weaker proton donor than an N
H group. In the conjugate bases, some of the regions will behave differently. Region A0 in N1 (see Scheme 2) has two strong accepting sites, at the formal N1 anion and the C2 oxygen. In N3, regions B0 and C0 each have the formal N3 anion as an acceptor site, along with the O2 or O4 acceptor site, respectively. The natural population analysis28 charges of the hydrogen bond donor and acceptor sites of U, N1, and N3 are shown in Scheme 3. These charges indicate, as expected, that the N
H group will be a good hydrogen bond donor, the oxygens are good acceptor sites, and the formal nitrogen anions in N1 and N3 also carry large negative charge and will be good acceptors. In fact, in both anions, the two oxygens and the formal nitrogen anion all have very similar charges of around
0.7 e, suggesting that they would all equivalently participate as acceptors. We build configurations by placing the waters into one of these binding regions. A chain of hydrogen bonded waters might occupy a region, even rings and cagelike structures of hydrogen bonded waters are likely, based on past experience. In addition, with a larger number of water molecules, multiple binding regions may be simultaneously occupied. Trends in preferential occupation of each region will guide the construction of new configurations, as we add additional water molecules to make successively larger clusters. Another guiding principle is to try to balance the number of donating and accepting hydrogen bonds made to each water molecule. In particular, a water molecule involved in two hydrogen bonds as a double donor or double acceptor is energetically unfavorable to a water acting as a single acceptor and a single donor. Uracil Microsolvated Clusters. Uracil Monohydrate. There are four possible configurations of uracil monohydrate, shown in Figure 1, created by placing a water molecule into each of the four binding regions A
D. The water is capable of donating a proton to a carbonyl oxygen and simultaneously accepting a proton from an N
H or C
H group. Bridging across these sites leads to nonideal hydrogen bond angles, which are best when the X 3 3 3 H
Y angle is near 180°. These clusters have been the subject of a number of computational studies,6,10,11,13,16 and a summary of these results is listed in Table 1. All computational methods reach the same conclusion: U-1a is the preferred arrangement with 5675

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Table 1. Relative Energies (kcal mol
1) of the Uracil 3 1 Water Clusters U-1a

U-1b

U-1c

U-1d

a

MP2/DZPi

0.0

1.55

1.93

3.24

B3LYP/6-31þþG(d,p)b B3LYP/6-31þG(2d,p)c

0.0 0.0

1.48 1.46

2.06 2.15

3.26

B3LYP/6-31þþG*d

0.0

1.69

2.24

4.02

B3LYP/DZPþþe

0.0

1.54

2.14

3.07

PBE1PBE/6-311þG(d,p)f

0.0

1.49

2.06

3.37

a

CP corrected energies, ref 10. b Reference 6. c Reference 11. d Reference 13. e Reference 16. f This work.

Figure 1. Optimized structures of the lowest energy configurations with one water of U, N1, and N3.

water in region A hydrogen bonded to N1
H and the O2 atom. Furthermore, the relative energies of the configurations are extremely consistent across computational methods. Uracil Dihydrate. There are potentially 18 different configurations of the uracil 3 2 water cluster: a two-water chain can bridge the donor/acceptor sites of one region, with the free hydrogens on each water syn or anti (eight configurations); a two-water chain in one region, with a single water bridging the donor/acceptor sites (four configurations); and one water in two regions (six configurations). We initiated geometry optimizations for all of these variants, and were able to locate 17 unique configurations, shown in Figure S2 in the Supporting Information; the two lowest energy configurations are displayed in Figure 2 as well. A number of computational studies of the uracil 3 2 water cluster have been reported.11,13,14,16 None report as exhaustive a search of the configurational space as we have done here. The relative energies of the eight lowest energy clusters (all clusters within 4 kcal mol
1 of the minimum energy structure), along with previous computational results, are listed in Table 2. As with the uracil 3 1 water clusters, the differing computational methods

Figure 2. Optimized structures of the lowest energy configurations with two waters of U, N1, and N3.

provide very similar relative energies and relative orderings of the configurations. The five lowest energy clusters have the waters occupying regions A and C. The two lowest energy clusters, U-2a and U-2b, have a two-water chain that bridges, via hydrogen bonds, the N1 hydrogen and O2 (region A). They differ in their orientation of the free hydrogens on the water, an anti relationship in the lowest energy cluster U-2a and a syn relationship in the other. U-2c and U-2e are similar to the two lowest clusters, except with the twowater chain bridging the N3 hydrogen and O4 (region C). U-2d has a single water in region A and the second in region C. A few trends are already evident within the one- and two-water clusters of uracil. Water preferentially locates into region A. The 5676

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Table 2. Relative Energies (kcal mol
1) of the Uracil 3 2 Water Clusters B3LYP

PBE1PBE

B3LYP

MP2

B3LYP

PBE1PBE

6-31þG

B3LYP

MP2

B3LYP

6-311þG

6-31þþG*a

DZPb

DZPþþc

6-311þG(d,p)d

(2d,p)a

6-31þþG*b

DZPc

DZPþþd

(d,p)e

0.0

0.0

0.0

0.0

0.0

U-3a U-3b

0.0

0.0

0.0


0.66 0.0

0.31

U-3c

U-2c

2.50

2.68

1.94

2.37

2.38

U-3d

0.76

0.95

U-2d

2.92

3.66

1.11

3.37

2.52

U-3e

2.67

U-3f

2.19

3.17

3.09

U-3g

2.24

4.06

U-2a U-2b

U-2e U-2f

3.38

U-2g 4.61

U-2h a e

Table 3. Relative Energies (kcal mol
1) of the Uracil 3 3 Water Clusters

Reference 11. This work.

b

Reference 13.

c

Reference 14.

3.61 d

U-3h a

0.32 1.01 1.30 1.40

1.46 1.63

2.72

1.78

Reference 13. b Reference 14. c Reference 16. d This work.

Reference 16.

Figure 3. Optimized structures of the lowest energy configurations with three waters of U, N1, and N3.

next best region is C. Clusters having a water in region D are invariably much higher in energy than all others. The free hydrogens in two-water chains are anti, though the energetic consequence of this arrangement is small. Therefore, since comprehensive examination of all clusters having three or more water molecules becomes increasingly computationally expensive, we will focus on clusters that emphasize these trends. In particular, few clusters with water present in region D will be

examined and not all syn/anti arrangements of free waters will be sampled. Uracil Trihydrate. We optimized 22 clusters formed from uracil and three water molecules. Most of these clusters have the waters in regions A
C. The two lowest energy clusters are shown in Figure 3, while all 22 clusters are drawn in Figure S3 in the Supporting Information. The relative energies of the eight lowest energy clusters are listed in Table 3, along with results from previous computations. The three studies reporting computed uracil 3 3 water clusters all indicate that U-3b is the lowest energy cluster.13,14,16 This cluster has a two-water bridge in region A and the third water in region C, consistent with the preferences found in the 1- water and 2-water clusters described above. However, we find that U-3a, a cluster formed of a three-water chain that bridges the N1 hydrogen and O2 within region A, is actually 0.66 kcal mol
1 lower in energy than U-3b. This configuration was not considered in any previous study. U-3c differs from U-3b in having the free hydrogens on the two-water chain syn rather than anti. U-3d and U-3e have a two-water chain in region C and the third water in region A, differing in the syn/anti relation of the free water hydrogen atoms. The water binding preference is clearly for region A. Both twoand three-water chains can effectively hydrogen bond to uracil in this region. Uracil Tetrahydrate. Only limited studies (four or fewer configurations) of the cluster of four water molecules with uracil have been examined.13,14 We have located 25 different configurations of the uracil 3 4 water cluster. These configurations were built off of the trends observed in the smaller clusters. The structures are drawn in Figure S4 in the Supporting Information, and the two lowest energy clusters are reproduced in Figure 4. The three lowest energy clusters each have a two-water bridge in regions A and C, differing only in the orientation of the free hydrogens on these waters. The next three lowest configurations introduce a ring formed by hydrogen bonding between the four waters. In U-4d, the four-water ring spans regions B and C, with hydrogen bonds connecting the water ring to the two oxygen atoms. U-4e and U-4f each have a four water ring that hydrogen bonds to the uracil, the former in region A and the later in region B. U-4g has the three-water chain in region A, as found in U-3a, with the fourth water in region C. van Mourik’s MP2 study of four uracil tetrahydrates14 offers very different results than ours, favoring water-ring-containing clusters. The lowest energy cluster has a three water ring in region A and the fourth water in region C. Optimization of this structure at B3LYP leads to the 5677

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Figure 4. Optimized structures of the lowest energy configurations with four waters of U, N1, and N3.

water-ring cleaving and ultimately to U-4g. An alternative configuration having a three-water ring in region A and one water in region C (U-4y) lies over 5 kcal mol
1 above U-4a. Further, van Mourik’s second lowest energy structure (with a two-water bridge in region A and another in region C) has an unfavorable orientation of the free hydrogens on water; a better conformation will reduce the energy such that this configuration is likely to be the lowest in energy. Furthermore, the lack of zeropoint vibrational energies in his study favors water rings; with four water clusters the difference in ZPVE can be as much as 1 kcal mol
1. The water rings (and cages as we will see below) are often preferred in terms of electronic energy over the water chains, but ZPVE favors the latter, occasionally reversing the ordering of the clusters. Uracil Pentahydrate. No reports of the clusters of uracil with five water molecules have been previously reported. Building upon the trends seen in the smaller clusters, we have optimized the geometries of 19 clusters. Trivial variants of many of these, generated by altering the anti/syn relationship of free hydrogens on the water molecules, could be obtained but we limit ourselves here to sampling a few low-energy variants. The structures of these clusters are shown in Figure S5 (Supporting Information) and the lowest two configurations are drawn in Figure 5. The lowest energy cluster U-5a has a three-water chain in region A and a two-water chain in region C, consistent with trends seen above, especially in the lowest energy trihydrate cluster U-3a. The second lowest energy cluster reverses the locations of these two chains. The third lowest energy structure U-5c has a two-water chain in region A, a common theme seen above, along with a three-water chain that crosses regions B and C, donating a hydrogen to both oxygen atoms and accepting a hydrogen from N3. U-5d has a five-water ring that

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Figure 5. Optimized structures of the lowest energy configurations with five waters of U, N1, and N3.

hydrogen bonds to the uracil in regions B and. The next two higher energy clusters contain four-water rings. Uracil Hexahydrate. We located 30 clusters of uracil with six water molecules. Again, we used the smaller clusters as guides to constructing initial geometries of the hexahydrates. The two lowest energy clusters are drawn in Figure 6, while all of them are shown in Figure S6 in the Supporting Information. The two lowest energy clusters have a three-water chain in regions A and C, differing in the relative orientations of the free hydrogen on the water molecules. This is consistent with the lowest clusters having three (U-3a) or five waters (U-5a). The next three lowest energy clusters (U-6c, U-6d, and U-6e) have a two-water chain in region A and a four-water ring that spans regions B and C. The next lowest configuration again has a threewater chain in region A and a three-water chain that spans regions B and C. Clusters possessing a five- or six-water ring are more than 2 kcal mol
1 higher in energy than U-6a. N1 Microsolvated Clusters. N1 Monohydrate. There are four configurations of the conjugate base of uracil formed from loss of a proton from N1 associated with one water molecule. These four have the water in regions A
D (see Scheme 2). These are shown in Figure S1 in the Supporting Information, with the two lowest energy configurations also drawn in Figure 1. Optimization of a configuration with the water donating a hydrogen to N1 and accepting a hydrogen from C6 leads to N1-1a. As might be expected, the lowest energy configuration has the water in region A0 , where the formal anion is present on N1. Significantly higher in energy is N1-1b, with the water in region B. In this and the other two higher configurations, the water does not directly interact with N1, the site of considerable negative charge, which leads to their higher energies. N1 Dihydrate. We located seven configurations of the N1 3 2 water cluster. These are drawn in Figure S2 (Supporting Information) 5678

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Figure 6. Optimized structures of the lowest energy configurations with six waters of U, N1, and N3.

with the two lowest energy structures reproduced in Figure 2. Both of these clusters (N1-1a and N1-1b) have the waters in region A0 : a two-water chain that bridges the N1 and C2 oxygen. They differ in which water is the double hydrogen donor. N1-2c also has a two-water chain in region A0 , but a single water molecule supplies the two hydrogens for donation to the uracil conjugate base. The next two clusters each have one water in region A0 ; they differ in having the second water in region B (N1-2d) or region C (N1-2e). N1 Trihydrate. The 14 clusters of N1 with three water molecules are shown in Figure S3 in the Supporting Information. The three lowest energy clusters have all three waters in region A0 . N1-3a has a three-water ring with the hydrogen not involved in the water ring making a hydrogen bond to N1 or O2, so that each water is donating two hydrogens and accepting one. N1-3b has a three-water chain that bridges N1 and O2. N1-3c also has a three-water ring, but this ring has one water acting as a double donor to the neighboring waters. This ring then makes two hydrogen bonds to the N1 moiety. The fourth lowest energy configuration has one water in region B and a two-water chain in region A0 . The clear trend with these clusters having three or fewer waters is to place the water molecules in region A where they can best interact with the dominant negative charge on N1 and O2. N1 Tetrahydrate. Nineteen different configurations of the N1 conjugate base of uracil with four water molecules were optimized. These structures are shown in Figure S4 in the Supporting Information, with the two lowest energy configurations drawn in Figure 4. The five lowest energy clusters all have a four-water ring hydrogen bonded to the conjugate base in region A0 . The sixth-lowest energy structure N1-4f, only 0.76 kcal mol
1 above

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N1-4a, has a three water ring in region A0 (just as in N1-3a) and the fourth water in region C. N1 Pentahydrate. We located 27 clusters formed of the N1 conjugate base and five water molecules. The two lowest energy clusters are displayed in Figure 5, and all configurations are drawn in Figure S5 (Supporting Information). Most of the 15 lowest energy clusters have a five-water cage in region A0 , which fall into two groups: (a) those that have one water acting as the donor for the hydrogen bond to N1 and two waters donating to the C2 oxygen and (b) those that have two waters donating to N1 and one water donating to the oxygen. The lowest energy structure N1-5a and the third and fourth lowest clusters (N1-5c and N1-5d) are of type (a). N1-5b has a five-water ring in region A0 , also with one water hydrogen bonded to N1 and two waters hydrogen bonded to oxygen. N1-5e is the lowest energy cluster of type b. N1 Hexahydrate. The 27 configurations we located of six water molecules associated with the N1 conjugate base of uracil are shown in Figure S6 (Supporting Information), with the two lowest energy clusters reproduced in Figure 6. The six lowest energy clusters, which span 2.5 kcal mol
1, have the six waters in a cage structure hydrogen bonded to N1 and O2 in region A0 . The seventh and eight lowest energy clusters (N1-6g and N1-6h) have the six waters in a chain that crosses from region A0 into regions B and C, with the waters donating to N1, twice to O2, accepting a hydrogen from N3 and donating to O4. N3 Microsolvated Clusters. N3 Monohydrate. The four possible configurations of the N3 conjugate base with one water are shown in Figure S1 (Supporting Information). The lowest two configurations are drawn in Figure 1 as well. The formal negative charge is at N3 with delocalization into both oxygen atoms, making regions B0 and C0 prime candidates for the water to occupy. The lowest energy structure N3-1a has the water in region C0 , where water donates a hydrogen to N3 and O4. The second lowest configuration N3-1b has the water in region B0 . Even though the O4 should have significant negative charge capable of acting as a strong hydrogen bond acceptor and so the cluster with water in region D might be favorable, the third lowest energy cluster has the water in region A, indicating the much more favorable hydrogen bond donating ability of the N
H group over the C
H group. N3 Dihydrate. We located 10 configurations of the N3 conjugate base associated with two water molecules; these are drawn in Figure S2 (Supporting Information), with the two lowest energy clusters also shown in Figure 2. The lowest energy structure N3-2a has one water in region B0 and in region C0 ; each water donates to the carbonyl oxygen and to the N3 formal anion. The next two lowest energy clusters are almost equal in energy and are similar in structure: a two-water chain bridges the oxygen and N3, in region B0 for N3-2b and in region C0 for N3-2c. N3-2d, only slightly higher in energy than the previous two clusters, has one water in region A and one in region C0 , indicating the strong preference seen already for a water to locate into region A—even in the N3 conjugate base where the formal anionic charge is far removed. N3 Trihydrate. The 20 optimized configurations of the N3 conjugate base with three water molecules are shown in Figure S3 (Supporting Information), with the two lowest energy clusters drawn in Figure 3. The lowest energy cluster N3-3a has a threewater chain that spans regions B0 and C0 , with hydrogens donating to both oxygens and N3. The next two clusters are close in energy and both have one water in region A and a 5679

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Table 4. Computed Relative Deprotonation Energies of Uracil at N1 vs N3 no. of water molecules

rel DPEa

0

13.34

1 2

12.02 10.33

3

9.15

4

6.52

5

6.65

6

7.30

PCMb

4.28

6 þ PCMc

3.00

a

Computed according to reaction 1c at PBE1PBE/6-311þG(d,p). b IEFPCM (water) computation at PBE1PBE/6-31þG(d,p) using the gas-phase geometry. c IEFPCM (water) computation at PBE1PBE/631þG(d,p) using the gas-phase geometry of N1-6a and N3-6a.

two-water chain that bridges N3 and an oxygen, with this chain in region C0 in N3-3b and in region B0 in N3-3c. N3-3d is very similar to N3-3a differing in the orientation of the hydrogen bonding within the water chain. N3-3e and N3-3f have a three water ring located in region C0 in the former and region B0 in the latter cluster. N3 Tetrahydrate. We optimized 28 clusters formed from the N3 conjugate base and four water molecules. These are drawn in Figure S4 (Supporting Information), and the two lowest energy structures are also shown in Figure 4. The lowest energy cluster N3-4a has a four water ring that spans regions B0 and C0 ; each water acts as a donor in a hydrogen bond to uracil—one hydrogen bond to each oxygen and two hydrogen bonds are formed to N3. N3-4b has the same three-water chain as found in the lowest energy N3 3 trihydrate cluster (N3-3a) with the fourth water in region A. N3-4c differs from N3-4b in the orientation of the hydrogen bonds within the three-water chain. N4-4d has a three-water ring in region C0 and the fourth water is in region B0 , donating a hydrogen to the C2 oxygen and to the water ring. N3 Pentahydrate. The 50 optimized configurations of the N3 conjugate base with five water molecules are shown in Figure S5 (Supporting Information), with the two lowest energy configurations also drawn in Figure 5. These two lowest energy configurations, N3-5a and N3-5b, have a four water ring in regions B0 and C0 , just as in the lowest energy configuration with four four waters (N4-4a), with the fifth water in region A; they differ in the clockwise versus counterclockwise arrangement of the hydrogen bonds within the water ring. N3-5c has a five-water chain that spans regions A, B0 , and C0 , with hydrogen bonds made to N1
H, two to O2, and one to N3 and to O4. N3-5d again has the four-water ring in regions B0 and C0 (like N3-5a and N3-5c) but with the fifth water in region D. The next two lowest energy clusters have a five-water ring that spans regions B0 and C0 . N3 Hexahydrate. Ninety-three different configurations of the N3 conjugate base with six water molecules were optimized. These are drawn in Figure S6 (Supporting Information) and the two lowest energy structures are reproduced in Figure 6. The six lowest energy configurations, which span only 0.5 kcal mol
1, have similar arrangements of the water molecules: they form a chain that spans regions A, B0 , and C0 , acting as donors in hydrogen bonds to O4 and N3 and twice to O2, and accepting the hydrogen from N1. They differ in the orientation of the free hydrogen on each water. (N3-6e also has one differing orientation

of a hydrogen bond within the chain.) N3-6g displays a cubelike structure, with two waters donating a hydrogen to N3 and two others donating a hydrogen to O4. This cluster is actually lower in electronic energy than N3-6a—N3-6e, but its zero-point vibrational energy raises it above these five clusters. Another interesting low-energy cluster is N3-6k, which is 0.98 kcal mol
1 higher in energy than N3-6a. This cluster has the four-water ring as found in N3-4a with a two-water chain in region A. Deprotonation Energies. One might compute the variation of the deprotonation energy (DPE) of uracil depending on the degree of microsolvation according to reactions 1a and 1b. However, these reactions make the assumption that the proton leaves alone with all water molecules remaining associated with the uracil conjugate base, likely a very poor assumption. One can, however, combine reactions 1a and 1b to give reaction 1c, which provides the relative deprotonation energies at N1 and N3. U 3 ðH2 OÞn f N1
3 ðH2 OÞn þ Hþ

ð1aÞ

U 3 ðH2 OÞn f N3
3 ðH2 OÞn þ Hþ

ð1bÞ

N1
3 ðH2 OÞn f N3
3 ðH2 OÞn

ð1cÞ

In evaluating the relative DPEs of N1 and N3 using reaction 1c, we use the energy of the lowest energy configuration of N1 and N3 with a given degree of microsolvation. It should be noted that this invariably implies that not only the proton has been lost but the water molecules rearrange to best interact with the resulting anion. These relative DPEs are presented in Table 4. It should be noted that this is an approximation; a Boltzmannweighted average free-energy should be used. However, since we did not comprehensively seek out all configurations, using the energy of the lowest configurations should provide a reasonable compromise.

4. DISCUSSION Experimentally, the two possible deprotonations from uracil, loss of either the N1 or N3 proton, are quite different in the gas phase, with the DPE for loss of the N1 proton 14 kcal mol
1 lower than that from N3.2 In solution, however, the pKa values for loss of these protons are indistinguishable.1 Thus, one might expect that sequential microsolvation would lead to diminishing the difference in the relative deprotonation energies leading to N1 and N3. In other words, sequential association of more and more water to the N1 and N3 conjugate bases should bring their energies closer together. No previous work has addressed sequential microsolvation to the difference in deprotonation energies at the two nitrogen sites. However, the Wetmore group has examined the effect of adding one water to uracil and its effect on the deprotonation at N1.17,18 They find a decrease in the DPE of about 5 kcal mol
1 with one associated water, relative to the gas-phase result. This is consistent with our result of a decrease in the DPE at N1 of 5.3 kcal mol
1. Inspection of Table 4 shows that this expectation is true for addition of one
four water molecules. The energies reported here come from the difference in energy of the lowest energy configuration of N1 and N3 at the particular level of hydration. Addition of the first water reduces the energy difference between N1 and N3 by 1.3 kcal mol
1, and the second water reduces the gap by another 1.7 kcal mol
1. The third water lowers the gap by 1.1 kcal mol
1, and the fourth water makes a large difference, 5680

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The Journal of Physical Chemistry A decreasing the energy gap by 2.6 kcal mol
1. With four associated water molecules, the energy difference between N1 and N3 has been reduced by half, standing now at 6.5 kcal mol
1. However, adding a fifth water molecule makes little change to the energy gap, and the sixth water actually increases the gap by 0.7 kcal mol
1. What accounts for this plateau in the trend of a decreasing energy gap? One cause of concern is that the lowest energy configurations might not have been located. While we have performed extensive searching of the configuration space, it has not been exhaustive and we may have missed a lower energy cluster of N3 with five or six waters. (For that matter, a lower energy cluster of N1 might also have been missed.) However, we have optimized a large number of configurations of N3 with five and six water molecules, sampling a wide variety of water arrangements, and we feel that it is unlikely that we might have overlooked a significantly more stable cluster. According to natural population analysis shown in Scheme 3, the charge distribution in uracil has both N
H groups slightly negative (
0.19 e for N1
H and
0.22 e for N3
H) and both oxygen atoms are quite negative (
0.61 e for O2 and
0.59 e for O4). In forming the N1 conjugate base, N1 becomes very negative (
0.64 e), O2 and O4 have identical charges of
0.71 e, and N3
H also becomes more negative, with a charge of
0.26 e. Similarly, in forming the N3 conjugate base, the charge on N3 becomes much more negative (
0.68 e), the two oxygens are more negative (
0.73 for O2 and
0.70 e for O4), while the N1
H group also becomes more negative (
0.25 e). Therefore, one might predict that waters will preferentially occupy region A0 of N1 and B0 and C0 of N3 in order to donate hydrogen(s) to the most negative atoms of these anions. For the N1 conjugate base, the best hydrated structures all have every water in region A0 , associated with the two very negative N1 and O2 atoms. In N1-1a, the water donates both of its hydrogens toward making hydrogen bonds with N1 and O2. With the second water, in the best cluster N1-2a, each water acts as a donor, one to N1 and the other to O2, and the waters are linked by a hydrogen bond. In N1-3a, the three waters form a hydrogen-bonded chain, which then donates one hydrogen to N1 and one to O2. The best cluster with four waters, N1-4a, has a four-water ring which is associated to N1 through a hydrogen bond to N1 and to O2. With five waters (N1-5a), a new type of hydrogen bonding pattern emerges: there are two hydrogen bonds formed to O2 originating from two different waters. The waters hydrogen bond together into fused three- and fourwater rings. Lastly, with six waters (N1-6a) a cage structure is formed where the water oxygen atoms along with N1 and O2 are the corners of a cube. Thus, one sees a hierarchy of water shapes—from chains to rings to cages—as the number of water molecules increases. The chain, ring, and cage structures were also observed in microsolvation of amino acids,8,9 formamide,29 and phenol.30
32 Critical at each degree of microsolvation is maintaining the hydrogen bonds to both N1 and O2, along with maximizing the hydrogen bonding between the water molecules. In going from one to four water molecules associated with the N3 conjugate base, the waters arrange in a chain and then a ring shape, while attempting to maintain an association with all of the formal anionic centers (N3 and the two oxygens). The major difference in the clusters of N3 compared to N1 is that in the former, the sites of negative charge span a larger volume, forcing the waters to reach farther away. With three waters, each can donate a hydrogen to one of the anionic sites, but this demands a water chain that ends up with at least one water being a double

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hydrogen bond donor (see N3-3a). It is not until four waters are associated with N1 that a water structure is possible that can both provide hydrogen bonds to each anionic center and have each water participate as a donor and acceptor of at least one hydrogen bond. The four-water ring is a structural motif often found in microsolvation,8,9,29
32 and this ring allows each water to donate a hydrogen to one of the anionic centers. This results in N3 having a bifurcated hydrogen bond structure. This water arrangement is particularly effective in stabilizing the N3 conjugate base; note that the difference in DPE between the two bases drops by 2.6 kcal mol
1 with the addition of the fourth water, reflective of the stabilization afforded in N3-4a. With the addition of a fifth or sixth water molecule to N3 one might anticipate the formation of water cages, as seen in N1-5a and (especially) N1-6a. However, the lowest energy cluster of N3 with five waters (N3-5a) has the same four-water ring seen in N3-4a with the fifth water in region A. (In fact the second and fourth best clusters also have this four-water ring.) None of the lowest 10 energy configurations have a water cage or cagelike structure. A five-water ring appears in the fifth lowest energy structure and also in a few of the next higher energy clusters. This suggests the very favorable interactions between the four-water ring and the three highly anionic centers of N3. There is no apparent position for a fifth water in regions B0 and C0 that can improve upon the hydrogen bonding interactions and so it finds a home in region A. A similar situation holds true for the clusters of N3 with six waters. The six lowest energy configurations have a six-water chain that spans regions A, B0 , and C0 . These are one-water extensions to the third lowest energy cluster with five waters (N3-5c). The waters in these structures provide hydrogen donors to O4 and N3 and O2 (2 H-bonds) and accept the hydrogen from N1, so all of the heteroatoms of N3 are involved in at least one hydrogen bond. A total of 10 hydrogen bonds are formed in clusters N3-6a
f. N3-6g, the lowest energy configuration that exhibits a cage structure, has 11 hydrogen bonds. One might have expected it (N6-3g) to be the lowest energy configuration, based both on the higher number of hydrogen bonds and on the propensity for microsolvation cages. In fact, its electronic energy is lower than that of N3-6a
f, but when ZPVE is included, it rises above the energy of these six clusters. The cage structure in N6-3g exhibits one major failing—it does not extend into region B0 . The waters hydrogen bond only to N3 and O4; a six-water cage cannot readily span the distance from O4 to O2. Therefore, this highly negatively charged atom (O2) is not stabilized through interaction with water, diminishing the potential stabilizing role that cage structures can provide. The lowest energy cagelike water structure that does reach to both O2 and O4 is N3-6p; 15 other clusters have a lower energy, and it is 1.18 kcal mol
1 higher in energy than N3-6a. Each sequential addition of water stabilizes both conjugate bases. This can be seen in the decreasing DPE with increasing microsolvation, as defined by reactions 1a and 1b. The values of these DPES are listed in Table S1 in the Supporting Information. For both N1 and N3, there is a large decrease (5
6 kcal mol
1) with the addition of the first water molecule. For N1, the next three added waters each decrease the DPE by 1
2 kcal mol
1. The decrease is greater with the next two added waters: 2.9 kcal mol
1 with the fifth water and another 3.7 kcal mol
1 with the sixth. These jumps in decreased DPE are due to the very favorable water cage structure and its ability to stabilize the N1 base. The trend is markedly different of the sequential solvation of N3. The second, third, and fourth added water molecules each 5681

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The Journal of Physical Chemistry A

Figure 7. Optimized structure of N3 with nine water molecules.

diminish the DPE of N3 (reaction 1b) by 3
4 kcal mol
1. This larger effect of the microsolvation than that with N1 leads to the overall trend in decreasing energy difference between the two conjugate bases with one to four added waters. However, the fifth added water reduces the DPE of N3 by 2.8 kcal mol
1 and the sixth reduces it further by 3.0 kcal mol
1, reductions that are smaller than that observed for N1. Neither the fifth nor sixth added waters lead to water structures that as effectively stabilize the N3 conjugate base as do these waters in stabilizing the N1 conjugate base. In order to observe a significant stabilizing by further added water, it will be necessary to build a cage water structure that can span regions B0 and C0 , from O2 to O4, contributing two water donors to each of these oxygen atoms and two donor hydrogens to N3. This can be accomplished with nine water molecules, as in Figure 7. This optimized structure contains two face-fused cubes, with O2, N3, O4 and each water oxygen occupying the corners. Each water participates in three hydrogen bonds and each of the highly charged atoms of N3 accepts two hydrogen bonds. Unfortunately, we do not have the resources to search for all reasonable configurations of N3 and N1 with nine waters to conclude that this proposed structure will show significant reduction in the N1 to N3 energy gap. With the addition of six water molecules, the difference in the DPEs of N1 and N3 has been halved from about 14 to about 7 kcal mol
1. One wonders if this gap can close to about nil with even more added waters, as suggested by the pKa experiments. To test an approximate limit of added water, we performed two polarized continuum model computations (see Table 4). First, using the IEFPCM33 approach with PBE1PBE/6-311þG(d,p), the geometries of N1 and N3 were reoptimized and their energy difference remains rather sizable: 4.3 kcal mol
1. (A nearly identical difference is obtained using the CPCM34 approach with the same computational level.) Additionally a previous PCM/B3LYP/6-31þG* study predicts the energy difference to be 5.6 kcal mol
1,2 though these authors did not remark on how this differs dramatically from the pKa experiment.1 If the hydrogen bonding is not being properly accounted for with the PCM approach, our second computation where we applied IEFPCM to the N1-6a and N3-6a structures, including all six waters, led to an energy difference of 3.0 kcal mol
1. While these are not definitive computations, they are suggestive that the pKa values of the two sites might, in fact, not be identical.

5. CONCLUSIONS The N1 and N3 protons are decidedly different in the gas phase, with loss of the N1 proton much easier than loss of the N3

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proton; the difference in their DPEs is about 14 kcal mol
1.2 However, in solution, the pKa values of the two sites are indistinguishable.1 This presents an excellent opportunity to test the microsolvation model, in particular, to get at the question of how many water molecules are needed to bring the two acidities in coincidence. While every added water molecule does stabilize both the N1 and N3 conjugate bases, the magnitude of the effect is not the same for the two anions and the decreases in their respective deprotonation energies with added water are not linear or systematic. For N1, increased stabilization of the anion is particularly seen with the fifth and sixth added water. In the best configurations with five and six waters (N1-5a and N1-6a), the waters form a cage structure that maximizes the hydrogen bond interactions (a) to N1 and O2 and (b) between the waters themselves. This is expected as cage water structures are a prominent motif in microsolvation situations generally.8,9,29
32 On the other hand, the largest decrease in the DPE leading to N3 occurs with the fourth added water, giving N3-4a. N3-4a exhibits a four-water ring that makes hydrogen bonds to O2 and O4 and two hydrogen bonds to N3. Adding one or two waters to this does not lead to good cage structures, unlike with N1, because the anion centers O2 and O4 are too far apart for a sixwater cage to effectively bridge. Thus, a plateau in the difference in energies between the N1 and N3 conjugate bases is seen with four to six water molecules. We suggest that it is not until nine water molecules are associated with N3 that an effective cage structure (see Figure 7) will again significantly reduce the gap between the two conjugate bases. The difference in the DPEs leading to N1 and N3 diminishes from 13 kcal mol
1 with no water molecules to about 7 kcal mol
1 with four
six water molecules. This reduction of onehalf suggests that many more water molecules will be needed to account for the bulk water, where experiments suggest the two pKa values are nearly equivalent. Future computations involving more water molecules and higher computational levels might confirm our findings of a significant difference in the N1 and N3 energies, or if this energy gap is predicted to be small. However, PCM computations suggest that the differences in energy between the N1 and N3 conjugate bases may be as large as 4 kcal mol
1, indicating that perhaps their acidities could be measurably different. Re-evaluation of uracil acidity, both experimentally and computationally, may therefore be of interest. Future computations involving more water molecules and higher computational levels (especially a composite method like G3) might confirm our findings of a significant difference in the N1 and N3 energies and truly warrant additional experiments. On the other hand, if large computations find a small N1
N3 energy gap, this would highlight the appropriate computational methods required to treat highly hydrated complexes.

’ ASSOCIATED CONTENT

bS

Supporting Information. Full citation of ref 27, Table S1, Figures S1 to S6, and PBE1PBE/6-311þG(d,p) optimized coordinates and energies of the ten lowest energy configurations of uracil and its N1 and N3 conjugate bases with zero to six associated water molecules. This material is available free of charge via the Internet at http://pubs.acs.org.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank the Welch Foundation (Grant W-0031) for financial assistance used to purchase the computers utilized in this study. ’ REFERENCES

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