3534
J. Phys. Chem. B 2007, 111, 3534-3542
Isomers of the Uracil Dimer: An ab Initio Benchmark Study Jann A. Frey,† Andreas Mu1 ller,‡ Martin Losada,§ and Samuel Leutwyler*,† Departement fu¨r Chemie und Biochemie, UniVersita¨t Bern, Freiestrasse 3, CH-3012 Bern, Switzerland ReceiVed: December 4, 2006; In Final Form: January 23, 2007
Benchmark ab initio calculations at the correlated level are reported for ten isomers of the uracil dimer (U‚U): six are doubly N-H‚‚‚O hydrogen bonded, three have a C-H‚‚‚O and an N-H‚‚‚O hydrogen bond, and one is doubly C-H‚‚‚O hydrogen bonded. Their structures were optimized at the correlated level by using second-order Møller-Plesset perturbation theory (MP2), resolution of identity MP2 (RIMP2), and the binding energies De calculated with the coupled-cluster method with singles, doubles, and iterative triples, CCSD(T). The MP2 and RIMP2 binding energies De are extrapolated to the complete basis set (CBS) limit, using the aug-cc-pVXZ (X ) D, T, Q) basis sets, giving binding energies accurate to (0.07 kcal/mol. With one exception, the correlation energy contributions at the CCSD(T) level increase the binding energies, although the changes are small, +0.03 to -0.27 kcal/mol (or 0.1% to 2.2%). The most stable isomer is the doubly N1-H‚‚‚O hydrogen-bonded HB4 form, with De[CCSD(T)]) -19.04 kcal/mol. The biologically relevant HB2 dimer has De[CCSD(T)] ) -12.64 kcal/mol, and the HB5 dimer that constitutes the main structural motif of the uracil crystal has -13.20 kcal/mol. The “Calcutta’’ dimer, which occurs in an RNA hexamer, is among the weakest isomers, with De[CCSD(T)] ) -9.81 kcal/mol. We compare to the binding energies calculated with the B3LYP, PBE, and PW91 density functionals; the PW91/6-311++G(d,p) binding energies agree with the CBS benchmark values, to within HB3sand the Calcutta, HB9, and HB10 dimers were not calculated. The ∆CCSD(T)/6-31+G(d,p) correction terms are compiled in Table 1. The absolute corrections are small, ranging from +0.03 kcal/mol (+0.22%) for the HB5 dimer to -0.27 kcal/ mol for the HB2 dimer. On average, the ∆CCSD(T) is slightly stabilizing, by -0.09 kcal/mol. The order of stability is not influenced by taking the ∆CCSD(T) correction into account. B. PW91, PBE, and B3LYP Density Functional Binding Energies. For the doubly N-H‚‚‚O hydrogen bonded formamide dimers, (FA)2 and the 2-pyridone dimer, (2PY)2, we have previously shown that the PW91 density functional combined with the 6-311++G(d,p) basis set gives binding energies very close to those of MP2 complete basis set (CBS) extrapolabinding tions.28,35-37 Here, we have calculated the De and DCPC e energies for the ten uracil dimers with the PW91, PBE, and B3LYP functionals and the 6-311++G(d,p) basis set. These are given in Table 2. As was previously observed, the BSSE of the DFT methods is small: 0.4-0.7 kcal/mol with B3LYP, 0.60.8 kcal/mol with PBE, and 0.7-0.9 kcal/mol with the PW91 method.28,35 For all density functionals, we find that the CPuncorrected binding energies are closer to the RIMP2 CBS extrapolated D∞e energies than the CP-corrected binding energies. For all three functionals the order of stability of the ten uracil dimers is identical with that calculated with the RIMP2 CBS
J. Phys. Chem. B, Vol. 111, No. 13, 2007 3537 method, cf. Table 2. The only exception is the HB8 isomer, which the B3LYP functional predicts to be more stable than HB5, in contrast to the other methods. A graphical comparison of the performance of the three density functionals with the ∆CCSD(T) corrected RIMP2 CBS extrapolated binding energies is given in Figure 5. We note the excellent agreement of the PW91 binding energies with the RIMP2 CBS binding energies, with an average absolute difference of only +0.33 kcal/mol. This confirms the quality of the PW91 functional for hydrogenbonded dimers, noted previously.28,36 There we also showed that systematic basis set increase along the aug-cc-pVXZ series decreases the PW91 binding energies by 0.5-0.7 kcal/mol.36 The PBE and B3LYP binding energies agree less well with the RIMP2 CBS limits. The PBE binding energies are systematically smaller by ∼0.7 kcal/mol and the B3LYP binding energies by ∼1.5 kcal/mol. This is in accord with previous results on the (formamide)2 and the (2-pyridone)2 selfdimers.28,36 We note that our PBE binding energies differ unsystematically by -0.2 to +1.0 kcal/mol from those published recently by Kelly and Kantorovich.7 Their computational method employs a much smaller DZP (double-ζ plus polarization) numerically defined basis set, norm-conserving pseudopotentials for the 1s core electrons, and periodic boundary conditions. C. Uracil Dimer Structures. All methods applied here (PW91, PBE, B3LYP, MP2, and RIMP2) predict planar hydrogen-bonded minimum-energy geometries for the U‚U dimers. The H-bond structural parameters are defined in Figure 6. The calculated RIMP2/aug-cc-pVTZ values are compiled in Table 3. The N‚‚‚O distances R1 and R′1 of the N-H‚‚‚OdC hydrogen bonds vary between 2.765 and 2.857 Å. These distances are considerably longer than that calculated for the 2-pyridone dimer, (2PY)2.35 The increases range from +0.04 Å for HB6 and HB4 up to +0.13 Å for the N-H‚‚‚OdC hydrogen bond of the Calcutta and the HB9 dimer. Even the strongest N-H‚‚‚OdC hydrogen bonds of U‚U are both weaker (see Figure 5) and longer than those of (2PY)2. This is surprising, since the types and local environments of the H-bonds are similar in the two systems, and since uracil is larger and more polarizable. The reason for the difference will be discussed in section IV. For the C-H‚‚‚OdC hydrogen-bonded Calcutta dimer, the RIMP2/aug-cc-pVTZ calculation give R(C‚‚‚O) ) 3.191 Å, which is identical with the calculated C-H‚‚‚O distance in the analogous (2PY)2 dimer and within the experimental error of the 3.3(1) Å distance measured by X-ray diffraction for the Calcutta dimer.5 Formation of the two hydrogen bonds leads to small changes in intramolecular bond lengths: In the doubly N-H‚‚‚OdC hydrogen-bonded dimers, the N-H single bond length typically increases by 0.02 Å and the CdO double bond by 0.01 Å. The changes in the “Calcutta’’ structure are 0.01 Å for both N-H and CdO bonds, and the C-H bond length changes only by 0.003 Å. The hydrogen bond angle φ in the different isomers of the U‚U dimer lies between 164° and 180°. However, it is only 158.9° for the Calcutta dimer; this value is close to the 156.0° reported by Wahl and co-workers.5 Rotational Constants. The rotational constants of the most stable uracil dimer HB4 (see below) are very different from those of all the other isomers. This should allow the unequivocal identification of this dimer and determination of its hydrogen bond lengths by high-resolution spectroscopy. However, due to the Ci symmetry and absence of dipole moment of this isomer, normal microwave spectroscopy is not feasible. High-resolution UV spectroscopy is not expected to be applicable, since uracil
3538 J. Phys. Chem. B, Vol. 111, No. 13, 2007
Frey et al.
TABLE 2: Calculated Binding Energies De (kcal/mol) of Ten Isomers of the Uracil Dimer, Optimized with the B3LYP, PBE, PW91, and MP2 Methods and the 6-311++G(d,p) Basis Set, and Comparison to the RIMP2+∆CCSD(T) Binding Energies of Table 1a Calcutta
HB2
HB3
B3LYP PBE PW91 RIMP2+∆CCSD(T)
-8.01 -8.95 -9.52 -9.81
-10.13 -11.02 -11.68 -12.65
-10.60 -11.66 -12.34 -12.90
B3LYP PBE PW91 MP2
0.41 0.55 0.67 2.33
0.71 0.82 0.90 2.97
0.60 0.78 0.92 2.96
a
HB4 De -16.91 -18.03 -18.76 -19.04 BSSEs 0.71 0.79 0.92 3.28
HB5
HB6
HB7
HB8
HB9
HB10
-11.07 -12.44 -13.10 -13.20
-14.11 -15.42 -16.11 -16.11
-12.96 -13.99 -14.68 -15.35
-11.43 -12.35 -12.93 -13.04
-7.45 -8.29 -8.84 -9.53
-5.66 -6.38 -6.83 -7.30
0.46 0.69 0.86 2.92
0.58 0.69 0.89 3.13
0.70 0.82 0.91 3.12
0.52 0.58 0.68 2.48
0.51 0.62 0.66 2.32
0.30 0.34 0.41 1.92
Also given are the counterpoise corrections for basis set superposition error (BSSE).
Figure 5. Calculated binding energies De of the ten isomers of (uracil)2 and of the (2-pyridone)2 dimer. The B3LYP, PBE, and PW91 density functional binding energies (open symbols) are compared to the RIMP2+∆CCSD(T) benchmark values (closed symbols, see also Table 2).
has an extremely short excited-state lifetime and hence very broad spectra.38 The HB6 dimer is next in stability and has a large dipole moment (7.61 D). It exhibits rotational constants that are very similar to those of HB7, which is the third most stable dimer. IV. Molecular Predictors of H-Bond Strengths A. Molecular Dipole Moment. The uracil monomer has a dipole moment of 4.33 D (RIMP2/aug-cc-pVTZ), so that the dipole-dipole (d-d) interactions between the two monomers are expected to be quite large at the typical H-bond distances. The ten isomers of (uracil)2 with their wide variation in mutual dipole orientations constitute an interesting system to study the influence of dipole-dipole interactions (as the leading term in multipole-multipole interactions) on the binding energy. Also,
Figure 6. The optimized structures of (a) the 2-pyridone dimer (C2h ), (b) the HB3 uracil dimer, and (c) the Calcutta uracil dimer. The definitions of structural parameters are those employed in Table 3 and in the text.
the mutual orientation of the two monomers in all of the isomers is well defined by the antiparallel hydrogen bonds. Figure 2 shows the dipole moment of the uracil moieties as well as the total dipole moments of the (uracil)2 isomers. The dipole-dipole interaction energy is given by
Vµ1µ2(R12,θ1,θ2) )
-µ1µ2 4π0R123
‚ 2(cos θ1 cos θ2 sin θ1 sin θ2) (1)
Isomers of the Uracil Dimer
J. Phys. Chem. B, Vol. 111, No. 13, 2007 3539
TABLE 3: Hydrogen Bond Distances (in Å), Rotational Constants, and Dipole Moments of the Ten Isomers of the Uracil Dimer, Calculated at the RIMP2/aug-cc-pVTZ Level Calcutta R(N1‚‚‚O) R(N3‚‚‚O) R(C5‚‚‚O) RN1(H‚‚‚O) RN3(H‚‚‚O) RC5(H‚‚‚O) rotational constants Ae (MHz) Be (MHz) Ce (MHz) dipole moment (D) a
2.856 3.191
HB2 2.834
HB3
HB4
2.821/2.824
2.766 -
HB5
HB6
HB7
HB8
HB9
2.781 2.820
2.809
2.857
2.812
2.765 2.811
1.755 1.792
3.208 1.787
1.784
1.736 1.780
1.735 1.827 2.159
1.816
1372.4 214.2 185.3 4.71
1148.5 259.5 211.7 0.0
1.796/1.801 1155.4 259.1 211.6 2.33
1889.1 199.6 180.5 0.0
1163.6 255.1 209.2 0.0
1403.3 228.8 196.7 7.61
1394.9 228.9 196.6 8.28
HB 10
exptl
3.206 1.828
3.955
2.864a/2.82b 2.865a/2.86b 3.319a/3.3c
2.156
2.176
2.186
1858.6 156.3 169.3 4.67
1365.7 214.6 185.5 6.50
1826.1 174.0 158.9 0.0
Crystal structure, ref 8. b Crystal structure, ref 9. c Crystal structure, ref 5.
TABLE 4: Dipole-Dipole Interactions Vdip-dip between the Uracil Moieties for the Ten (Uracil)2 Isomersa dimer
Vdip-dip [kcal/mol]
COM dist [Å]
θ1b [deg]
θ2b [deg]
Calcutta HB2 HB3 HB4 HB5 HB6 HB7 HB8 HB9 HB10
+0.62 -0.11 +2.38 -0.14 +3.36 -1.61 -0.20 -1.15 +1.52 -0.65
5.93 5.39 5.39 6.04 5.40 5.69 5.69 6.31 5.92 6.58
72 124 191 123 7 120 308 76 249 70
188 304 309 303 187 187 308 308 302 252
a Also given are distances between the uracil centers of mass (COM) [Å] and dipole angles θ1, θ2 relative to the interconnection vector. b See also Figure 2.
where 1 and 2 designate the uracil subunits and R12 is the distance between the respective centers of mass; the resulting values are given in Table 4. Depending on the mutual orientation of the monomers, these interaction distances vary from 5.4 to 6.6 Å, since the center of mass of uracil is not equidistant from the five hydrogen-bonding groups. Since the dipole moment of the uracil monomer points between the N1-H and C6-H groups and since the latter group never acts as an H donor, none of the uracil dimers exhibits a fully attractive d-d interaction. On the other hand, the monomer dipole moments are oriented exactly antiparallel in the HB5 dimer, resulting in a fully repulsive d-d interaction of +3.36 kcal/mol. The HB3, HB9, and Calcutta dimers also show repulsive d-d interactions. The optimally attractive d-d orientation that can be attained is for isomer HB6, with an interaction energy of -1.61 kcal/mol. This is followed by HB8 with a d-d interaction of -1.15 kcal/mol, while the HB2, HB4, and HB7 isomers show only weakly stabilizing d-d interactions in the range between -0.1 and -0.2 kcal/mol. Detailed comparison of the RIMP2+CCSD(T) binding energies (Table 4) with the dipole-dipole interaction energies in Table 4 fails to show any clear correlation between the two. Although it is clear that the d-d interaction gives partially stabilizing or destabilizing contributions to the total binding energy, it cannot be usefully employed as a predictor of the dimer stability. B. Molecular Electrostatic Potential and Gas-Phase Protonation/ Deprotonation Energies. A map of the molecular electrostatic potential (MEP) of uracil projected onto its van der Waals surface of the uracil monomer is shown in Figure 1a. This representation already reveals that the N1-H hydrogen bond donor site is more positive than the N3-H binding site; on the other hand, both O-atom acceptor sites show about the same negative potential on this picture. In Figure 1b we plot
TABLE 5: PW91/6-311++G(d,p) Calculated Gas-Phase Deprotonation Enthalpies ∆E0(A-H) and Protonation Enthalpies PA(B) of 2-Pyridone and Uracil (in kcal/mol, at T ) 0 K) molecule
bond, site a
∆E0(A-H)
2-pyridone
N-H, A
343.8
uracil
C5-H, A1 C6-H, A2 N3-H, A3 N1-H, A4
374.0 361.9 342.6 330.0
a
atom, site a O, B1 O, B2 O2, B1 O2, B2 O4, B3 O4, B4
PA0(B) 210.8 214.9 191.9 193.3 200.1 202.8
For site numbering, see Figure 7.
the electrostatic potential isosurface of uracil at a value of (40.8 kcal/mol. In this representation, the two lone pairs at the O2 and O4 H-bond acceptors are clearly apparent, each with a marked asymmetry. This implies that there are four different proton-acceptor sites, marked B1-B4, each of which is expected to show a slightly different interaction energy with a given H-donor. It also follows that the proton affinities of the CdO group lone pairs should be useful predictors of H-bond binding energies Using the B3LYP method, Zeegers-Huyskens and co-workers have previously shown that trends in the hydrogen bond energies of uracil‚H2O and analogous nucleobase‚H2O complexes can be rationalized based on the gas-phase acidities of the N-H groups and the proton affinities of the CdO groups of the monomers.15-19 We find their concept to be very useful for interpreting the binding energies of the isomeric uracil dimers. To do this, we extended their calculations to deprotonation at the C5-H bond and to the 2-pyridone molecule. Also, we employ the PW91 instead of the B3LYP functional, because of its greater accuracy in predicting the binding energies, as noted in section III. The gas-phase acidity is defined as the enthalpy of the gasphase deprotonation reaction AH f A - + H+ at 298.15 K.39,40 The gas-phase proton affinity PA is defined as the negative of the reaction enthalpy for the gas-phase protonation reaction B + H+ f BH+ at 298.15 K. For comparison with the De and D0 values, which are 0 K values, we calculate and discuss the gasphase acidity at 0 K, ∆E0(A-H), and the gas-phase proton affinity at 0 K, PA0. Both include the changes of vibrational zero-point energy, from B to BH+ or A-H to A-, respectively. Gas-Phase Acidities. The PW91/6-311++G(d,p) gas-phase acidities ∆E0(A-H) for the N1-H, N3-H, C5-H, and C6-H groups are listed in Table 5 and shown graphically in Figure 7. The most acidic group is the uracil N1-H with ∆E0(N1-H) ) 330.0 kcal/mol, which corresponds to the gas-phase acidity of the O-H group of phenol and the N-H group of indole.39 The N3-H group is 12.5 kcal/mol less acidic, ∆E0(N3-H) ) 342.6
3540 J. Phys. Chem. B, Vol. 111, No. 13, 2007
Frey et al. TABLE 6: N-H‚‚‚O and C-H‚‚‚O Binding Energies per Hydrogen Bond, De/H-Bond, and Corresponding Differences of the Deprotonation and Protonation Energies of the Hydrogen Bond Sites ∆E0(A-H) - PA0(B) (See Table 5)a isomer C2h dimers (2PY)2 HB4 HB5 HB2 HB10 Cs dimers HB8 HB6 HB7 Calcutta HB9 HB3 HB3 HB6 HB7 Calcutta HB9 HB8
H-bond sitessite type De/H-bond ∆E0(A-H) - PA0(B) N-H‚‚‚OdC N1-H‚‚‚OdC2 N3-H‚‚‚OdC4 N3-H‚‚‚OdC2 C5-H‚‚‚OdC4
-10.84b -9.38b -6.55b -5.84b -3.42b
128.9 138.0 142.4 149.2 171.2
N1-H‚‚‚OdC4 N1-H‚‚‚OdC4 N1-H‚‚‚OdC2 N3-H‚‚‚OdC4 N3-H‚‚‚OdC4 N3-H‚‚‚OdC4 N3-H‚‚‚OdC2 N3-H‚‚‚OdC2 N3-H‚‚‚OdC2 C5-H‚‚‚OdC4 C5-H‚‚‚OdC2 C5-H‚‚‚OdC2
-10.27c -10.27c -9.38b -6.55b -6.55b -6.55b -5.84b -5.84b -5.30c -2.97c -2.66c -2.66c
127.2 129.8 136.6 139.8 139.8 142.4 149.2 150.6 150.6 173.9 173.9 182.1
a All values in kcal/mol, at the PW91/6-311++G(d,p) level. b Determined as half of the binding energies of the symmetric U‚U dimers, see text. c Determined by assuming H-bond additivity, see text.
Figure 7. Protonation and deprotonation sites and the corresponding PW91/6-311++G(d,p) gas-phase acidities and basicities of the uracil hydrogen-bonding sites.
kcal/mol; only this group is an H-bond donor in biologically relevant complexes (see Figure 2). These calculated gas-phase acidities are comparable to those of Kurinovich and Lee (+333 kcal/mol for N1-H and +347 kcal/mol for N3-H).41 A reason for this rather strong acidity is the efficient delocalization of the negative charge over the π-electron system of the molecule in the deprotonated form. The acidity of the 2PY N-H bond is ∆E0(A-H) ) 343.8 kcal/mol; this is close to the 342.6 kcal/ mol calculated for the less acidic N3-H bond of uracil. Thus, 2-pyridone should be a good model for the H-bond-donating properties of uracil. The deprotonation energy of the C5-H bond of uracil, which forms a H-bond in the Calcutta dimer, is 374.0 kcal/mol, 31 kcal/mol higher than that of N3-H (see Table 5). The analogous C-H bond in 2-pyridone has ∆E0(A-H) ) 391.7 kcal/mol, which is 15 kcal/mol less acidic. This shows that the C5-H bond of uracil is a relatively acidic compared to other C-H bonds. Proton Affinities. Each carbonyl oxygen exhibits two protonation sites, apparent in Figure 1 and defined in Figure 7. The O atom protonation energies of 2-pyridone are large, PA0 ) 210.8 kcal/mol at the N-H side (B1) and 214.9 kcal/mol at the C-H side (B2). This is in the range of the PAs of strong gasphase bases such as di- and trialkylamines39,40 and provides the rationalization for the strong and short hydrogen bonds in the (2PY)2 dimer. For uracil, the largest protonation energy is PA0
) 202.8 kcal/mol for the B4 site of O4, which is about 10 kcal/ mol smaller than that for 2-pyridone. The biologically relevant B3 H-binding site has an even lower PA0 of 200.1 kcal/mol, close to the gas-phase proton affinity of ammonia. Finally, the B1 and B2 sites of the O2 atom exhibit protonation energies of 191.9 and 193.3 kcal/mol, about 21 kcal/mol smaller than that for the O atom of 2-pyridone. The considerably larger proton affinity of 2-pyridone may be interpreted in terms of the more extended π-conjugation in this molecule. The PW91/6-311+G(d,p) proton affinities of the O2 and O4 atoms are 1-2 kcal smaller and the deprotonation enthalpies of the N1-H and N3-H bonds are 0.3-1.2 kcal/mol larger than those calculated at the B3LYP/6-31++G(d,p) level by ZeegerHuyskens and co-workers.15 C. Correlation of Hydrogen Bond Strengths. The C2h symmetry of (2PY)2 and the HB2, HB4, HB5, and HB10 dimers allows binding energies to be derived for single hydrogen bonds, giving -10.85 kcal/mol per N-H‚‚‚OdC H-bond for (2PY)2, -9.38 kcal/mol for the N1-H‚‚‚OdC2 H-bond of HB4, -6.55 kcal/mol for the N3-H‚‚‚OdC4 H-bond of HB5, -5.84 kcal/ mol for the N3-H‚‚‚OdC2 H-bond of HB2, and -3.42 kcal/ mol for the C5-H‚‚‚O-N4 H-bond of HB10, cf. Table 6. We then assume (i) transferability of the binding energies of these H-bonds to the noncentrosymmetric U‚U dimers and (ii) additivity of individual H-bond strengths. As an example, the H-bond energies of HB3, which has an N3-H‚‚‚OdC4 (A3B3) and an N3-H‚‚‚OdC2 (A3-B2) H-bond, are assumed to be transferable from the HB5 (A3-B3) and HB2 (A3-B2) H-bonds and sites. These single H-bond binding energies of HB5 (N3-H‚‚‚OdC4) and HB2 (N3-H‚‚‚OdC2) sum up to -12.39 kcal/mol, in excellent agreement with the calculated HB3 binding energy of -12.34 kcal/mol. Assuming additivity, individual H-bond strengths are deduced for the H-bonds of the noncentrosymmetric dimers HB3, HB6, HB7, HB8, HB9, and Calcutta, as given in Table 6. The last column of Table 6 lists the differences of the gas-phase deprotonation and protonation energies, ∆E0(A-H) - PA0(B), for the various possible site-site combinations. The HB6 dimer with the second largest binding energy (-16.11 kcal/mol) exhibits quite different H-bond strengths,
Isomers of the Uracil Dimer
Figure 8. Correlation between the PW91 calculated hydrogen bond binding energies and ∆E0(A-H) - PA0(B).
namely -10.27 kcal/mol for the N1-H‚‚‚OdC4 and -5.84 kcal/mol for the N3-H‚‚‚OdC2 H-bond. Even more extreme is the HB8 dimer that combines the strongest (N1-H‚‚‚OdC4) and the weakest (C5-H‚‚‚OdC2) H-bond interactions of -10.27 and -2.66 kcal/mol, respectively. The HB7 dimer structure has an H-bond strength of -9.38 kcal/ mol for the HB4 type hydrogen bond. This results in an interaction energy of -5.30 kcal/mol for the N3-H‚‚‚OdC2 H-bond. The centrosymmetric HB2 isomer also has the latter H-bond type, but with the A3-B2 site-site combination, giving -5.84 kcal/mol per H-bond. The difference of 0.71 kcal/mol between the two site-site combinations is due to the inequivalence of the O2 oxygen lone pairs, see Figure 1. From the individual H-bond energies one sees that the binding energy difference between the HB8 and the “Calcutta’’ dimer is not due to the C5-H‚‚‚O hydrogen bonds (-2.47 vs -2.39 kcal/ mol) but due to a 3.5 kcal/mol difference in the strength of the N-H‚‚‚OdC hydrogen bonds. In Figure 8 we plot the single H-bond binding energies values (column 3) against the ∆E0(A-H) - PA(B) differences (column 4). A very good correlation is apparent, both for the N-H‚‚‚OdC and C-H‚‚‚OdC hydrogen bonds. This confirms the observation of Zeegers-Huyskens et al. that hydrogen bond interaction strengths can be effectively rationalized by combining the gas-phase acidity of the N-H or C-H proton donor group with the basicity of the H-bond acceptor sites.15-17 The results indicate that the stabilities of the different U‚U dimers can be qualitatively understood in terms of the various acidbase interactions of the monomer sites. For uracil, the variation of the N-H and C-H gas-phase acidities is larger than that of the basicities of CdO acceptor sites. V. Conclusions The intermolecular binding energies De of all ten doubly hydrogen-bonded (uracil)2 isomers were investigated by the
J. Phys. Chem. B, Vol. 111, No. 13, 2007 3541 correlated resolution-of-identity MP2 (RIMP2) method. All structures were optimized at the RIMP2/aug-cc-pVTZ level. Extrapolations to the complete basis set (CBS) binding energy limits were carried out by using the Dunning aug-cc-pVXZ (X ) 2, 3, 4) basis set series. The CBS limit binding energies, extrapolated separately for the counterpoise-corrected and uncorrected binding energies, were determined to accuracies within 0.07 kcal/mol. The contributions to the binding energies from higher order correlation energy terms were evaluated at the CCSD(T) level and added to the RIMP2 values by using the ∆CCSD(T) procedure. The combined CBS extrapolated RIMP2+∆CCSD(T) binding energies are the most accurate to date. In addition to the binding energies De, we report the structure parameters characterizing the H-bonds, the rotational constants, and dipole moments. (1) The doubly N-H‚‚‚OdC hydrogen-bonded dimers HB2, HB3, HB4, HB5, HB6, and HB7 exhibit binding energies in the range between -12.4 and -19.0 kcal/mol. With all theoretical methods, the global minimum of U‚U is the planar centrosymmetric HB4 isomer with two N1-H‚‚‚OdC2 hydrogen bonds. Its CBS extrapolated RIMP2+∆CCSD(T) binding energy is D∞e ) -19.04 kcal/mol. However, the structurally related (2-pyridone)2 dimer exhibits an RIMP2 CBS limit of D∞e ) -22.63 kcal/mol, and is more strongly bound than the HB4 dimer by 3.6 kcal/mol.35,36 (2) Surprisingly, the HB8 dimer with both an N-H‚‚‚O and a C-H‚‚‚O hydrogen bond is found to be the fifth most stable isomer. Its binding energy is larger than or close to those of the doubly N-H‚‚‚O bonded HB2, HB3, and HB5 dimers. The HB10 dimer, which has two C-H‚‚‚OdC hydrogen bonds, shows a remarkably large binding energy of -7.22 or -3.6 kcal/ mol per H-bond. (3) Interestingly, the uracil crystal is not built up from the most strongly bound isomers HB4, HB6, or HB7. Its basic structural motif is a combination of two uracil dimers with moderate binding energies, namely HB5, with an RIMP2+∆CCSD(T) binding energy of -13.20 kcal/mol and HB8 with -13.04 kcal/mol. Both dimers are almost 6 kcal/mol less strongly bound than HB4. (4) The two doubly H-bonded uracil dimers that have been observed in biological contexts also exhibit moderate to low binding energies: The HB3 “wobble” dimer, which is found in an RNA dodecamer, has an RIMP2+∆CCSD(T) binding energy of only -12.90 kcal/mol while the Calcutta dimer, observed in an RNA hexamer, is bound even more weakly, by -9.81 kcal/ mol. In the sequence from the most to the least stable dimer, the HB3 dimer is no. 6 and the Calcutta dimer no. 9. (5) The higher order correlation energy contribution to the binding energy, ∆CCSD(T), is relatively small for all (uracil)2 isomers. With the exception of HB5, where ∆CCSD(T) is destabilizing by +0.03 kcal/mol, the ∆CCSD(T) corrections lead to small increases of binding energy, by -0.03 to -0.27 kcal/ mol. These corrections are of the same size as that calculated for the HB4 dimer with the aug-cc-pVDZ basis set in ref 13 (-0.18 kcal/mol). We note that ∆CCSD(T) corrections calculated with basis sets that lack diffuse functions, such as 6-31G*(0.25) and 6-31G**, yield ∆CCSD(T) contributions that are unreliable,28 as can also be seen in Table 3 of ref 13. (6) Comparisons of the B3LYP, PBE, and PW91 density functional binding energies to the RIMP2+∆CCSD(T) benchmark results were made for all ten hydrogen-bonded dimers. The B3LYP functional predicts binding energies that are ∼2 kcal/mol or between 11% and 22% too small. The PBE binding energies are on average 1.1 kcal/mol (or 5-13%) too
3542 J. Phys. Chem. B, Vol. 111, No. 13, 2007 small. The PW91 functional yields excellent predictions of binding energies, with an average absolute difference of only 0.32 kcal/mol and an average relative difference of 2.9%. Excellent performance of the PW91 method for hydrogenbonded dimers was previously found for the binding energies of five different isomers of (formamide)2.28 We note, however, that for stacked structures most DFT methods do not give useful results and in many cases not even stable minima.13 (7) The contributions from dipole-dipole interactions to the binding energies vary from weakly attractive to moderately repulsive over the ten different (uracil)2 isomers. The dipoledipole interactions vary between -1.61 and +3.36 kcal/mol. However, no correlation between the dipole-dipole interaction energy and the total binding energy is apparent and the dipoledipole interaction cannot be used as a single-molecule predictor for binding energies. (8) In contrast, the H-bond interaction strengths show a clear connection to the gas-phase deprotonation energies of the N-H or C-H proton donor sites, ∆E0(A-H), and the protonation energies, PA(B), of the four CdO lone-pair sites. The differences of the gas-phase deprotonation and protonation energies, ∆E0(A-H) - PA0(B), for the various possible site-site combinations shows an excellent correlation with H-bond strength. This property can be calculated for bare uracil and be used as a molecular predictor for hydrogen bond strengths.15-17 Acknowledgment. This work was supported by the Schweiz. Nationalfonds (project no. 2000-61890) and by the Swiss supercomputer center CSCS in Manno. References and Notes (1) Leontis, N. B.; Stombaugh, J.; Westhof, E. Nucleic Acids Res. 2002, 30, 3479. (2) Crick, F. H. C. J. Mol. Biol. 1966, 19, 548. (3) Baeyends, K. J.; Bondt, H. L. D.; Holbrook, S. R. Nat. Struct. Biol. 1995, 2, 52. (4) Wahl, M. C.; Rao, S. T.; Sundaralingam, M. Nature Struct. Biol. 1996, 3, 24. (5) Wahl, C.; Sundaralingam, M. Trends Biochem. Sci. 1997, 22, 97. (6) Carter, A. P.; Clemons, W. M.; Brodersen, D. E.; Morgan-Warren, R. J.; Wimberley, B. T.; Ramakrishnan, V. Nature 2000, 407, 340. (7) Kelly, R. E. A.; Kantorovich, L. N. J. Phys. Chem. B 2006, 110, 2249. (8) Stewart, R. Acta Crystallogr. 1967, 23, 1102.
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