Can QTAIM Topological Parameters Be a Measure of Hydrogen

Article pubs.acs.org/JPCA

Can QTAIM Topological Parameters Be a Measure of Hydrogen Bonding Strength? Yirong Mo* Department of Chemistry, Western Michigan University, Kalamazoo, Michigan 49008, United States S Supporting Information *

ABSTRACT: The block-localized wave function (BLW) method, which is the simplest variant of ab initio valence bond (VB) theory, together with the quantum theory of atoms in molecules (QTAIM) approach, have been used to probe the intramolecular hydrogen bonding interactions in a series of representative systems of resonance-assisted hydrogen bonds (RAHBs). RAHB is characteristic of the cooperativity between the πelectron delocalization and hydrogen bonding interactions and is identified in many biological systems. While the deactivation of the π resonance in these RAHB systems by the use of the BLW method is expected to considerably weaken the hydrogen bonding strength, little change on the topological properties of electron densities at hydrogen bond critical points (HBCPs) is observed. This raises a question of whether the QTAIM topological parameters can be an effective measure of hydrogen bond strength.

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INTRODUCTION Hydrogen-bond (H-bond) refers to the X−H···Y type of through-space interactions that ubiquitously exist in chemical and biological systems and play a fundamental role not only in molecular properties and structures but also in chemical and biological processes. Over the years, a number of very strong and unconventional H-bonds, including charge-assisted hydrogen bonds (CAHBs),1 low barrier hydrogen bonds (LBHBs),2,3 dihydrogen bonds (DHBs),4,5 and resonance-assisted hydrogen bonds (RAHBs)6,7 have been recognized. This leads to the claim by Desiraju that H-bonding is an interaction without borders.8 However, an accurate definition for H-bond is elusive, as many factors may contribute to this seemingly simple kind of interaction, and the underlying physical origin of H-bonds is thus still very controversial.9−14 Often the identification of Hbonds is simply based on the short distance between X and Y, although the latter may result from certain structural constrains, and the H-bond alone is actually strained and unstable.12,15 Perrin clearly pointed out that there is no relationship between the shortness of H-bonds and strength.14 For instance, the very short heavy-atom distance in CAHBs actually results from the ion−dipole attraction. Some researchers also use the n(Y) → σXH* hyperconjugative interaction as a measure of the covalency and directionality of H-bonds,16 as well as a diagnosis for the presence of H-bonds.17 However, this stabilizing force increases with the shortening of the H-bond distance, as does the Pauli repulsion, which increases exponentially and faster than the hyperconjugative attraction. In other words, the n(Y) → σXH* hyperconjugation only reflects a small part of the hydrogen bonding strength, and its magnitude can be much smaller than the classical electrostatic interactions.18−20 The measure of bonding energy is the way to justify the existence of the H-bond, but there are difficulties in the proper evaluation of the strength of an intramolecular H-bond, in © 2012 American Chemical Society

contrast to intermolecular H-bonds whose strengths may be reasonably estimated through a supermolecular approach. As a consequence, various approximated approaches have been developed.21−25 Gilli et al. suggested that H-bond strengths can be reasonably predicted from acid−base molecular properties, or the pKa slide rule.26 Notably, Bader’s quantum theory of atoms in molecules (QTAIM) approach27−29 has been extensively applied to the study of H-bonds.24,30−33 It has been found that the electron density at H-bond critical points (HBCPs) is a good descriptor, as it correlates well with hydrogen bond strengths. 34−36 The typical topological parameters at H···Y BCP are 0.002−0.04 au for the electron density and 0.02−0.15 au for its Laplacian.37,38 Densities of local electronic energy Hh and its components (kinetic energy Gh and potential energy Vh; Hh = Gh + Vh) at BCPs are also indicators of the strength of H-bonds.39,40 Fuster and Grabowski compared the QTAIM method and the electron localization function (ELF) method and found that ELF and QTAIM parameters are well correlated and can be used as descriptors of the hydrogen bond strength.41 In this work, we conducted a computational study on a series of typical intramolecular RAHB systems (Scheme 1) whose strengths range from weak (4, 5), intermediate (1, 2, 8), to strong (3, 6, 7)40 with the block-localized wave function (BLW) method42,43 combined with QTAIM analysis27−29 in an attempt to critically examine the correlation between the electron density topological parameters and hydrogen bonding strengths. The concept of RAHB comes from the observation of the crystal structures of β-diketo enols (···OC−CC− OH···) by Gilli and co-workers in the late 1980s, who Received: March 28, 2012 Revised: May 8, 2012 Published: May 10, 2012 5240

dx.doi.org/10.1021/jp3029769 | J. Phys. Chem. A 2012, 116, 5240−5246

The Journal of Physical Chemistry A

Article

nonorthogonal doubly occupied fragment-localized orbitals (or group functions48).49−54 On the basis of the conventional VB ideas, we proposed the BLW method where a BLW corresponds to a unique electron-localized diabatic state (usually the most stable resonance state).42,43 The fundamental assumption is that the total electrons and primitive basis functions can be divided into k subgroups (blocks), and each MO is block-localized and expanded in only one block. Assuming that there are mi basis functions {χiμ, μ = 1,2,...mi} and ni electrons for block i, we can express block-localized MOs for this block as

Scheme 1

ϕji =

mi

∑ Cjiμχμi (3)

μ=1

The whole matrix of orbital coefficients in the BLW method is a direct sum of k submatrixes k

CBLW = C1 ⊕ C2 ⊕ ... ⊕ Ck = ⊕ Ci i=1

and at both the HF and Kohn−Sham DFT levels, the total electron density is a simple summation of individual blocks as

interpreted the enhanced intramolecular H-bonding interaction by the shortened H-bond distance (2.39−2.44 Å for O···O distances, compared with 2.7−3.0 Å in conventional H-bonds) in terms of resonance through π-conjugated double bonds.6 This shortening is also associated with a decrease of O−H vibrational frequencies and abnormal downfield 1H NMR chemical shifts.7 Theoretically, valence bond (VB) theory44−46 describes a molecule in terms of resonance structures where each pair of electrons is strictly localized on a chemical bond between two atoms or on an individual atom. Although significant progress in the development and application of ab initio VB methods has been observed in recent years,47 one computationally efficient approach is the BLW method,42,43 which can be regarded as the simplest variant of the ab initio VB theory. By using the BLW method, one can uniquely define an electron-localized state where the π resonance is “turned off”. The comparison between the geometries, energetics, and topological properties of electron/energy densities of the electron-delocalized (via a standard DFT method) and electron-localized (via BLW method) states is able to shed new light on the nature of RAHB as well as the correlation between the topological parameters and hydrogen bond strengths.

k

ρ BLW = ρ1 + ρ2 + ... + ρk =

(5)

Orbitals in the same subspace are subject to the orthogonality constraint, but orbitals belonging to different subspaces are nonorthogonal. Thus, the BLW method combines the advantages of both MO and VB theories. The BLW method is available at the DFT level with the geometry optimization and frequency computation capabilities.43,55 We reiterate that the electron density (ρBLW) corresponding to the BLW state is different from the density for the ground state (ρ), which can be obtained by standard MO or DFT calculations. For the most stable resonance structure of a planar conjugated system, each two-atomic π bond or a one-atomic lone pair forms a block, as does the whole σ. The energy difference between E[ρBLW] and E[ρ] is the resonance energy (RE). We note that, as in all other methods, there is an inherent basis set superposition error in the BLW method to be corrected.56,57 However, computations of the resonance energies of conjugated systems demonstrated that the BLW method, when employed with midsized basis sets, gives reasonably invariant values consistent with viable experimental evidence.56,58−60 Additionally, the reliability of the BLW method is documented by its computed structural parameters, vibrational frequencies, and NMR data.61−63 Khaliullin, HeadGordon, et al. recently proposed the “absolutely localized molecular orbitals” (ALMOs) method,64,65 which is actually identical to the BLW method. Thus we take the ALMO method as further support for the BLW method. Computational Strategy. We performed the BLWQTAIM combined computations on a series of representative systems of homonuclear O−H···O H-bonds including malonaldehyde with substitutions (1−4, Scheme 1), three ionic systems (6−8) whose H-bonds are both resonance- and charge-assisted, and 1,3-butadiene-1,4-diol (5). Their H-bond strengths range from weak (4, 5), intermediate (1, 2, 8), to strong (3, 6, 7).40 Standard B3LYP DFT calculations with the basis set of 6-311+G(d,p) were performed throughout the work, as this level of theory has been assessed for intramolecular H-bonds and shown to be comparable with MP2/6-

COMPUTATIONAL DETAILS BLW Method. Within the VB theory, a conjugated system is described by the number of resonance structures whose wave functions can be individually defined with the Heitler− London−Slater−Pauling (HLSP) functions as ΨL = MLA(̂ ϕ ϕ ... ϕ ) (1) 2n − 1,2n

where ML is the normalization constant, Â is the antisymmetrizer, and φ2i−1,2i is a bond function composed of nonorthogonal orbitals ϕ2i−1 and ϕ2i (or a lone pair if ϕ2i−1 = ϕ2i) ϕ2i − 1,2i = Â {φ2i − 1φ2i[α(i)β(j) − β(i)α(j)]}

∑ ρi i=1

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1,2 3,4

(4)

(2)

The overall many-electron wave function for an adiabatic state is a linear combination of several important VB functions, and the resonance energy is the energy difference between the most stable resonance structure and the adiabatic state. One way to significantly simplify the computational costs involved in eq 1 is to represent bond orbitals with 5241



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Table 1. Selected Optimal Bond Distances (Å), Od−H Stretching Vibrational Frequency (cm−1) and RE (kJ/mol) at the B3LYP/6-311+G(d,p) Level method

R(Od−H)

R(Oa···H)

R(Oa···Od)

νOd−H

νCO

VRE

DFT

0.997

1.697

2.586

1636

214.2

BLW

0.967

2.093

2.884

3079 3092 3622

311+G(d,p) results. The principal resonance structures with π electron pairs strictly localized on the CC or CO double bond or O atom (i.e., lone pair) are obtained with the BLW method at the same DFT level, which has been implemented in our inhouse version of the quantum mechanical software GAMESS.66 Vibrational frequencies are computed with a scaling factor of 0.9679.67 The comparison of the geometrical parameters, vibrational frequencies, and molecular energies computed with the standard B3LYP and the BLW methods manifests the impact of the resonance on both the structures and energetics of molecules with RAHBs. The subsequent QTAIM analyses were conducted with CheckDen.68

1762

ARE

157.7

the optimal delocalized and localized structures corresponds to the adiabatic resonance energy (ARE), which is 157.7 kJ/mol for malonaldehyde. Interestingly, we observed a clear weakening of the RAHB in malonaldehyde with the localization of π electrons, as shown in Table 1. Crystallographic and spectroscopic studies suggested that stronger H-bonds (X−H···Y) are associated with shorter H-bond distances including X···Y and H···Y.69,70 But this relationship between shortness of H-bonds and strength has been questioned.14 For the present case of malonaldehyde, the O−H bond shortens by 0.03 Å, while the Oa···Od notably increases by 0.30 Å from 2.586 to 2.884 Å! The comparison between the stretching vibrational frequencies in the delocalized and localized structures also presents clear evidence for the strength of the intramolecular H-bond, as it is believed that larger red-shifts correspond to stronger H-bonds.71 In malonaldehyde, there are two peaks corresponding to the stretching vibrations of the O−H bond. Our computed values are 3079 and 3092 cm−1, compared with the experimental values of 2856 and 2960 cm−1.72,73 If there were no π conjugation, only one O−H stretching vibration would be observed at 3622 cm −1 , which is comparable to the experimental data 3681 cm−1 for gaseous methanol.74 Thus, resonance significantly red-shifts the O−H frequency by 530− 543 cm−1. Similarly, a red-shifting for the carbonyl group by 126 cm−1 is anticipated, and the CO stretching frequency in the localized state (1762 cm−1) of malonaldehyde is very close to 1750 cm−1 in formaldehyde. All these results seemingly provide strong proof for the proposal of resonance-assisted Hbond. To visualize the migration of electron density due to resonance, we plotted the electron density difference map (EDD) in Figure 1b at the DFT optimal geometry of MA, where the red/blue surface represents an increase/decrease in electron density. In accord with the conventional view, the π electrons move away from the hydroxyl oxygen to the carbonyl oxygen through the CC double bond. Electron density depletion from the hydrogen atom can also be seen and verified by population analyses. For instance, the natural population analysis (NPA)75 shows that the populations on the hydroxyl hydrogen are 0.516 and 0.494 e in the localized (BLW) and delocalized (DFT) states. Thus, π electron resonance does reduce the hydrogen population by 0.022 e and makes the hydrogen carry more positive charge. However, π electron migration induces the polarization of the σ electron density, which tends to offset the effect of π resonance by moving in the reverse direction of π electron migration. In other words, the carbonyl oxygen actually loses σ electron density, as clearly exhibited in Figure 1b. While overall the carbonyl group gains electrons due to resonance, its σ orbitals, which form a H-bond with the hydroxyl hydrogen, lose electrons. The NPA populations show that the carbonyl oxygen loses 0.030 e in its σ orbitals, although it gains 0.119 e in total. Thus, resonance assists the hydrogen bonding in a similar way to CAHBs, namely, through the enhanced electrostatic

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RESULTS AND DISCUSSION Resonance Effect on Geometry and Energy. To begin, we studied the impact of π resonance on molecular structures and energetics. The BLW method has been extensively applied to the study of electron delocalization, notably in aromatic systems with both the energetic and structural results justified by experimental data.56,58−61 In malonaldehyde (1), there are six conjugated π electrons. The conjugation effect can be elucidated by the CC and CO bond lengths. Our major results related to the H-bonds are listed in Table 1, and more data are exhibited in Figure 1a. Similar to butadiene, the conjugation

Figure 1. (a) Comparison of the optimal geometries of malonaldehyde with the DFT and BLW methods. (b) EDD isosurface map with the isovalue of 0.003 au showing the polarization of electron density due to π conjugation in malonaldehyde at the DFT optimal geometry.

remarkably shortens the single bonds of C−C and C−O, but modestly lengthens both the double bonds of CC and C O. At the DFT optimal geometry, the strict localization of π electrons on double bonds and oxygen atoms changes the molecular energy by 214.2 kJ/mol, which is defined as the vertical resonance energy (VRE). The BLW optimization results in the optimal localized structure whose parameters are comparable to those in nonconjugated systems. For instance, the C−C bond stretches to 1.544 Å, comparable to the bond length in ethane, while the CC bond shortens to 1.320 Å, identical to the bond length in ethylene. Similarly, the C−O single and CO double bond lengths are 1.435 Å and 1.202 Å, respectively. These numbers can be justified by the values in methanol and formaldehyde. The energy difference between 5242



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proportional to R(O−H) but reversely proportional to R(O···H). This unique finding comes from the deactivation of the π conjugation in these systems. Much like the above discussion on malonaldehyde, BLW optimizations result in electron-localized optimal structures (complete geometries are presented in the Supporting Information) where the single (C−C and C−O) and double (CC and CO) bond lengths are very close to the values in ethane, ethanol, ethylene, and aldehyde. Similar to 1, significant changes are observed for the H-bonds in 2−4, where the O···H distances increase 0.32−0.58 Å with the shortening of the O−H bonds by 0.015−0.070 Å when the π resonance is deactivated. Apart from 5 where the H-bond is very weak, in 6-8, the H-bond distances change very little, highlighting the dominating role of ion−dipole interactions. Table 2 also shows that VRE ranges from 211.3 kJ/mol in 5 to 451.0 kJ/mol in 6. Due to the involvement of substituent groups, there is no obvious correlation between resonance energies and H-bond strengths. QTAIM Analysis. As there is no unambiguous way to measure the strength of intramolecular H-bonds, the QTAIM approach has become a major diagnostic tool in the elucidation of the bonding features in H-bonding systems.24,27,29−33 But we note that there have been controversies over the validation of the QTAIM analysis.28,31,76−79 QTAIM’s workhorse is the Laplacian (∇2ρ) of electron density of molecules, which is a sensitive probe for identifying spatial changes of electron concentrations rather than the electron density itself. On the basis of the sign of the Laplacian, chemical bonds are classified as shared or closed-shell interactions. However, more sophisticated classifications are based on both the Laplacian and the total energy density at bond critical points.40,80,81 The QTAIM properties for

attraction between the H-bond donor and acceptor resulting from the π resonance shortening the H-bond distance. Key optimal H-bond distances and resonance energies for the remaining molecules (2−7) are listed in Table 2. At the Table 2. Selected Optimal Bond Distances (Å) and RE (kJ/ mol) at the B3LYP/6-311+G(d,p) Level mol

method

R(O−H)

R(O···H)

R(O···O)

REa

2

DFT BLW DFT BLW DFT BLW DFT BLW DFT BLW DFT BLW DFT BLW

0.983 0.965 1.040 0.970 0.980 0.965 0.966 0.966 1.083 1.078 1.104 1.102 1.000 1.002

1.855 2.194 1.510 2.088 1.894 2.212 1.909 1.902 1.377 1.408 1.318 1.340 1.710 1.742

2.689 2.956 2.474 2.868 2.712 2.966 2.750 2.757 2.429 2.459 2.421 2.441 2.490 2.559

268.6 215.0 323.0 228.9 317.6 261.1 211.3 183.2 451.0 331.4 415.0 363.6 346.4 303.8

3 4 5 6 7 8 a

The DFT RE refers to the vertical resonance energy (VRE); the BLW RE refers to the adiabatic resonance energy (ARE).

ground state, the hydroxyl bond distance differs from 0.966 Å in 5 to 1.104 Å in 7, but more significant variations can be observed for the distance between carbonyl oxygen and hydroxyl hydrogen, which fluctuates from 1.909 Å in 5 to 1.318 Å in 7. A good linear correlation between the distances of O−H and O···H can be found, and thus both can serve as geometrical measures for the H-bond strengths, which are

Table 3. Topological Properties at the Ring (r) and H-Bond (h) Critical Points (au)a mol

method

ρr

∇2ρr

ρh

∇2ρh

Gh

Vh

Hh

1

DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW DFT BLW0 BLW

0.0198 0.0199 0.0125 0.0177 0.0177 0.0118 0.0237 0.0239 0.0130 0.0167 0.0168 0.0114 0.0136 0.0137 0.0125 0.0232 0.0235 0.0196 0.0126 0.0129 0.0107 0.0353 0.0364 0.0310

0.1250 0.1262 0.0696 0.1046 0.1056 0.0615 0.1528 0.1539 0.0711 0.0967 0.0977 0.0585 0.0816 0.0826 0.0735 0.1399 0.1406 0.1114 0.0727 0.0736 0.0586 0.2157 0.2132 0.1721

0.0492 0.0482 0.0197 0.0334 0.0329 0.0156 0.0789 0.0767 0.0202 0.0305 0.0301 0.0151 0.0259 0.0262 0.0264 0.1114 0.1111 0.1024 0.1269 0.1258 0.1188 0.0510 0.0518 0.0476

0.1351 0.1471 0.0688 0.1095 0.1162 0.0556 0.1394 0.1640 0.0686 0.1024 0.1080 0.0532 0.1053 0.1059 0.1070 0.1024 0.0984 0.1129 0.0506 0.0484 0.0708 0.1413 0.1388 0.1263

0.0404 0.0421 0.0157 0.0275 0.0285 0.0123 0.0602 0.0637 0.0158 0.0251 0.0259 0.0118 0.0240 0.0243 0.0245 0.0795 0.0783 0.0729 0.0875 0.0857 0.0818 0.0420 0.0419 0.0373

−0.0470 −0.0474 −0.0142 −0.0276 −0.0280 −0.0107 −0.0856 −0.0864 −0.0144 −0.0245 −0.0249 −0.0103 −0.0217 −0.0221 −0.0222 −0.1334 −0.1320 −0.1176 −0.1623 −0.1593 −0.1458 −0.0486 −0.0492 −0.0430

−0.0066 −0.0053 0.0015 −0.0001 0.0005 0.0016 −0.0254 −0.0227 0.0014 0.0006 0.0010 0.0015 0.0023 0.0022 0.0023 −0.0539 −0.0537 −0.0447 −0.0748 −0.0736 −0.0640 −0.0066 −0.0073 −0.0057

2

3

4

5

6

7

8

a

DFT and BLW0 refer to standard DFT and BLW computations at the DFT optimal geometries, and BLW refers to BLW computations at the BLW optimal geometries. 5243



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molecules 1−8 at both the ring and H-bond critical points (HBCPs) are tabulated in Table 3. Three kinds of electron densities were analyzed. The first (DFT) is the DFT electron densities at the DFT optimal geometries, followed by the second (BLW0) which is the BLW electron densities at the DFT optimal geometries. The last one (BLW) is the BLW electron densities at the BLW optimal geometries. QTAIM analysis on the DFT electron densities showed that at HBCPs the electron densities fall in the range of 0.026− 0.123 au, and the Laplacians vary from 0.102 to 0.141 au. Figure 2 shows that the electron densities at HBCPs also

Figure 3. Isodensity contours of the magnitude of the gradient of density |∇ρ| (left, A1 and B1, from 0 to 1 with the increment of 0.02 au) and Laplacian of density ∇2ρ (right, A2 and B2, from −1 to 1 with the increment of 0.04 au; magnate color refers to < −1, and gray refers to >1; dashed lines correspond to regions in which ∇2ρ < 0, and solid lines correspond to regions in which ∇2ρ > 0) based on the (A) standard DFT (delocalized) and (B) BLW (π-localized) densities for malonaldehyde.

Figure 2. Correlation between the electron density at the H-bond critical points and the H-bond distance.

correlate with the H-bond distances, with similar exponential correlations already shown by others.24,41,82 Relatively large fluctuations of densities at HBCPs can be observed; particularly, the |Vh|/Gh values seem consistent with the measure of the H-bond strengths by Mariam and Musin,40 who classified molecules 1, 2, and 8 as intermediate, molecules 4 and 5 as weak, and systems 3, 6, and 7 as strong. In general, our present structural, energetic, and topological analyses on the RAHB systems 1−8 are in agreement with the literature. Striking deviation from the fundamental assumption of RAHB, however, comes from the QTAIM analyses on the BLW densities, which failed to show consistent changes (i.e., reductions) in the electron density and its Laplacian as well as all local energy densities at the ring critical points and Hbond critical points (DFT and BLW0 in Table 3). For electron densities at HBCPs, we observe a slight reduction by up to 2.8% for all molecules except 5 and 8, where a slight increase to 1.6% is found with the deactivation of resonance. For the Laplacians, however, there are increases from 0.6% to 17.6% for molecules 1−5, but for 6−8 the Laplacians decrease by 1.8− 4.3%. As an example, Figure 3 shows the gradient and Laplacian of the electron density in the whole molecule of malonaldehyde at the electron-delocalized (DFT) state and electron-localized (BLW0) state, which exhibit little noticeable change. Figure 4 further compares the electron densities and their Laplacians at HBCPs in all investigated molecules where BLW0 means that the BLW computations were done at the DFT optimal geometries. Since the magnitudes of Vh and Hh reflect the capacity of the system to concentrate electrons at HBCPs,27 the energy densities have also been used to measure the H-bond strengths.40 However, Table 3 shows that the electronic kinetic energy density Gh, the electronic potential energy density Vh, and the total energy density Hh change little with the

Figure 4. Electron density (A) and its Laplacian (B) at the HBCPs in the studied molecules (1−8) from the standard DFT and BLW computations. DFT and BLW0 refer to the computations at the DFT optimal geometries, and BLW refers to the computations at the BLW optimal geometries.

deactivation of the π resonance at the same DFT optimal geometries. As topological properties have been extensively documented to be a measure of bond strengths, the small changes of the density and energetic topological parameters at HBCPs from electron-localized states (BLW0) to electron5244



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Notes

delocalized states (DFT) raise a question, namely, whether the topological properties are able to measure H-bond strengths. With the deactivation of the π resonance, the H-bonds in molecules 1−4 elongate considerably, accompanied by the reduction of the electron density and its Laplacian at HBCP by 50−74% and 51−58% respectively, suggesting that the short Hbond distances in RAHB is not constrained by the σ-frame, but must be related to the π resonance, or resonance-assisted. However, the similarity of the topological properties in resonance-assisted and resonance-disabled states at the same nuclear conformations implies that they cannot be used as a direct measure of H-bond strengths. In fact, if we focus on one H-bond (e.g., in a water dimer) and plot the change of topological properties at the HBCP along the change of Hbond distance, we will find that the topological properties change monotonously. This is much like the n(Y) → σXH* hyperconjugative interaction. Thus, we surmise that the Hbond strength in terms of the topological properties only refers to the degree of covalency (i.e., electron transfer), which is attractive, as well as the electrostatic interactions and “continuously increasing with the shortening of the bond itself”,83 but the Pauli repulsion, which increases exponentially, is not appropriately counted,31,76 as clearly shown in Figure 4. The true H-bond strength should be a combination of all attractive and repulsive forces.

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CONCLUSION

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ASSOCIATED CONTENT

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the U.S. National Science Foundation under Grant CHE-1055310 and Western Michigan University with the Faculty Research and Creative Activities Award (FRACAA).

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On one hand, comparisons of the geometries and topological properties of electron densities at the respectively optimized electron-delocalized and electron-localized states show that the deactivation of the π conjugation significantly increases the Hbond distances and reduces H-bond strengths at least in molecules 1−4. On the other hand, at the same geometries, DFT and BLW computations result in comparable electron densities, and their Laplacians at HBCPs, although population analyses (as well as energy decomposition analyses12) confirm the enhancement of the electrostatic attractions between Hbonding partners. It has been well recognized that electrostatic interaction plays the major role in H-bonds. To interpret the above findings from the combined QTAIM and BLW computations, we rationalize that the driving force for intramolecular RAHBs is the electrostatic attraction which is further enhanced by the π resonance and subsequently shortens the H-bonds. RAHBs are thus akin to CAHBs. As a consequence of the H-bond shortening, the covalency of RAHBs is passively increased, as is the Pauli repulsion. However, the Pauli repulsion seems not appropriately reflected in the topological parameters of electron density and energy at HBCPs, and as a consequence, the estimate of H-bond strengths based on the QTAIM topological properties is imperfect.

S Supporting Information *

Molecular geometries at the B3LYP/6-311+G(d,p) level. This material is available free of charge via the Internet at http:// pubs.acs.org.

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Can QTAIM Topological Parameters Be a Measure of Hydrogen

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