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Substituent effects on water-assisted proton transfer in [p-XC6H4OH–(H2O)1–3]+ clusters
Chemical Physics Letters 442 (2007) 451–459 www.elsevier.com/locate/cplett
Substituent effects on water-assisted proton transfer in [p-XC6H4OH–(H2O)1–3]+ clusters Hugo F.M.C. Martiniano a, Benedito J. Costa Cabral a
a,*
, Jose´ A. Martinho Simo˜es
b
Departamento de Quı´mica e Bioquı´mica, Faculdade de Cieˆncias, Universidade de Lisboa, 1749-016 Lisboa, Portugal, and Grupo de Fı´sica Matema´tica da Universidade de Lisboa, Av. Professor Gama Pinto 2, 1649-003 Lisboa, Portugal b Departamento de Quı´mica e Bioquı´mica, Faculdade de Cieˆncias, Universidade de Lisboa, 1749-016 Lisboa, Portugal Received 2 April 2007; in final form 17 May 2007 Available online 29 May 2007
Abstract Substituent effects on proton transfer (PT) from the phenolic moiety to water in [p-XC6H4OH–(H2O)n]+ (X = N(CH3)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters were investigated by density functional theory. Structural and electronic aspects related to substituent effects and hydrogen bonding were analysed. PT to water is inhibited (favored) by electron donating (withdrawing) substituents. The results indicate that para-substituents have a less important role in promoting proton transfer than the interactions with the water molecules. Anharmonic vibrational frequencies associated with the PT coordinate correlate with the rþ p Hammett parameters. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction The importance of substituent effects on the molecular properties of chemical and biochemical species is well recognized [1]. These effects have been extensively investigated for aromatic compounds, where a substituent may lead to a considerable reorganization of the r and p-electron densities and therefore to significant changes of the molecular properties. Solution-phase acidity, for example, will be determined by the ability of the substituent to induce charge transfer. Phenol is a widely used model system to probe substituent effects on several properties, such as bond dissociation enthalpies [2], gas-phase acidities [3], and proton affinities of phenoxyl radicals [4,5]. For instance, it is well known that electron donating para-substituents, such as N(CH3)2 or NH2, decrease the phenolic O–H bond dissociation enthalpy, whereas electron withdrawing para-substituents, such as NO2 and CN, strengthen that bond [2]. Opposite trends are observed for the gas-phase acidity and for the *
Corresponding author. E-mail address: [email protected] (B.J. Costa Cabral).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.05.083
proton affinity. Indeed electron donating para-substituents make the heterolysis of the O–H bond more endergonic than in the case of phenol [2]; similarly, the proton affinity of the radical (also called the O–H proton dissociation enthalpy of the phenol radical cation, PDE) increases with the donating character of the para-substituent [4,5]. Phenol has also been used to investigate, from a microscopic point of view, how proton transfer to water depends on the number of interacting water molecules. Several works provided evidence that proton transfer from phenol to water does not occur in the ground state of small phenol–water clusters [6–10]. However, certain aromatic molecules exhibit a dramatic change in their acidity upon excitation or ionization [11,12]. The explanation for this behavior is that excitations trigger intramolecular charge transfer in the ring system and modify the hydrogen bond interactions that set the stage for proton transfer [11]. The proton transfer step is strongly dependent on the number and specific structure of the solvent molecules in interaction with the phenolic moiety, i.e., the proton transfer is a process assisted by the solvent [11]. Several studies have discussed how proton transfer in ionized phenol–water clusters depends on the number of water
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molecules [8–10,12–16]. On the other hand, substituent effects on the phenol O–H bond dissociation enthalpies in neutral [XC6H4OH–(H2O)1–4] clusters have been discussed by different authors [17–20]. For ionized phenol–water clusters, the studies on substituent effects were apparently limited to the [p-XC6H4OH–(H2O)]+ complex [15]. However, in contrast with phenol–ammonia clusters, where proton transfer is observed in the [C6H5OH–(NH3)]+ complex [21,22], proton transfer to water in [C6H5OH–(H2O)n]+ clusters, only takes place when n P 3 [9,10]. Therefore, substituent effects on the proton transfer mechanism deserve further analysis. In this Letter, we report results for the structure, electronic, and vibrational properties of ionized [pXC6H4OH–(H2O)n]+ (X = N(CH3)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters. We also discuss the importance of taking into account the anharmonic nature of the potential energy curve associated with the proton transfer coordinate [14,16]. The structure and electronic properties of the clusters were investigated by density functional theory (DFT). Wavefunctions and anharmonic frequencies associated with the proton transfer coordinate were calculated by a transfer-matrix path-integral approach [23,24].
ferred (NT) and transferred (T) complexes, respectively. In ˚ . Anharmonic both cases, x was sampled from 0.6 to 1.9 A frequencies and wavefunctions associated with the proton transfer coordinate were calculated through a transfermatrix path-integral procedure [23,24]. We are also reporting binding energies for the phenol–water cationic complexes. For NT clusters the binding energy (Eb) is defined as: Eb = E[p-XC6H4OH]+ + E[(H2O)n] E[p-XC6H4OH– (H2O)n]+. For T clusters, Eb = E[p-XC6H4O] + E[H3O+– (H2O)n1] E[p-XC6H4OH–(H2O)n]+. Binding energies at 0 K were calculated at the BHandHLYP/aug-ccpVTZ//BHandHLYP/cc-pVDZ level and include zeropoint vibrational energies. 3. Results and discussion 3.1. Structure The structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) are shown in Fig. 1 and selected structural infor-
2. Computational details The structures of [p-XC6H4OH–(H2O)n]+ (X = N(Me)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters were optimized with the BHandHLYP functional as implemented in the GAUSSIAN 03 suite of programs [25]. The choice of this functional was driven by studies on hydrogen bonding [26] and ionized water clusters [27,28]. The Dunning’s cc-pVDZ basis set [29] was used in all the optimizations. Natural atomic charges (NAO) [30,31] for the optimized structures were evaluated with the aug-cc-pVDZ basis set [29,32]. An adiabatic approximation was used to generate the potential energy curve associated with the proton transfer coordinate. The potential energy curves were generated by stretching of the O–H distance along the O–H bond direction. This means that for a given structure of the cationic phenol–water complex, the quantum degree of freedom associated with the proton motion is assumed to be much faster than the reorganization of the molecular structure. The adiabatic approximation was also adopted by Jansen and Gerhards [14] who reported anharmonic vibrational frequencies associated with proton transfer coordinates in phenol–water and aminophenol–water clusters [14]. This kind of simplification also neglects the coupling between O–H stretching and bending modes in cationic phenol– water complexes that was investigated by Yamamoto [16]. For each [p-XC6H4OH–(H2O)n]+ complex (n = 1–3), a total number of 14 points were generated and the corresponding potential energy curves were fitted to a polynoP13 mial form i¼0 ai xi , where ai’s are fitting coefficients. The variable x represents either the phenolic O–H distance when no proton transfer has occurred, or the distance H–OH2 between the transferred proton and the nearest water molecule. These structures will henceforth be called non-trans-
Fig. 1. Optimized structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1– 3).
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
mation is reported in Table 1. In agreement with previous investigations [9,10], when X = H proton transfer to water occurs only for n = 3. This is indicated by a sharp increase of the O–H distance and a sharp decrease of the H O distance when n changes from 2 to 3. The same behavior is observed when X is an electron withdrawing group (X = CN, CF3, NO2), i.e., T complexes are formed when n = 3. Nevertheless, when X is an electron donating group (X = N(Me)2, NH2, OH), only NT complexes are formed. As expected, these results follow a similar trend to the one observed for the proton affinity of substituted phenoxyl radicals [4,5]. Our data for the optimized structure of the phenol– water cation complex can be compared with CASSCF/ccpVDZ results [14]. In general, a good agreement is observed. H O and O O distances from BHandH˚ shorter then LYP/cc-pVDZ calculations are ca. 0.09 A the CASSCF/cc-pVDZ predictions [14]. For NT complexes (n = 1, 2) the analysis of structural data can provide some information related to the role
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played by substituents in proton transfer. For example, taking phenol (X = H) as reference, O–H distances slightly increase for electron withdrawing groups (X = CN, CF3, NO2) and decrease for electron donating substituents (X = OH, NH2, N(CH3)2). Opposite patterns are observed for the H O and O O distances. Finally, C–O distances are not significantly changed for X = CN, CF3, NO2, ˚ when X = OH, NH2, although they increase by 0.01 A N(CH3)2. Data for the T complexes (n = 3) show that the H O ˚ when X = H, to 1.026 A ˚ distance decreases from 1.056 A when X = NO2. The O–H distance increases from ˚ when X = H to 1.471 A ˚ (X = NO2). A similar 1.390 A trend can be observed for the O O distance, which ˚ (X = H) to 2.497 A ˚ (X = NO2). increases from 2.446 A Note that for T complexes, what we call the H O distance should be regarded as the H–OH2 bond between the transferred phenolic proton and the water molecule. Concomitantly, the phenolic O–H distance is now better described as a hydrogen bond, O H.
Table 1 Data for BHandHLYP/cc-pVDZ optimized structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) X
n=1
n=2
n=3
N(CH3)2
O–H H O O O C–O
0.983 [1.006] 1.668 2.650 1.304
0.998 [1.027] 1.578 2.575 1.299
1.019 [1.060] 1.491 2.509 1.293
NH2
O–H H O O O C–O
0.987 [1.011] 1.644 2.630 1.299
1.004 [1.036] 1.553 2.555 1.294
1.030 [1.079] 1.458 2.486 1.288
OH
O–H H O O O C–O
0.994 [1.021] 1.606 2.599 1.291
1.017 [1.056] 1.503 2.518 1.285
1.061 [1.134] 1.380 2.440 1.278
H
O–H H O O O C–O
1.003; 1.568; 2.570; 1.282;
1.035 [1.086] 1.449 2.483 1.276
1.390 1.056 [1.123] 2.446 1.256
O Hb H–OH2b
CN
O–H H O O O C–O
1.007 [1.038] 1.553 2.559 1.278
1.045 [1.104] 1.422 2.466 1.271
1.443 1.035 [1.087] 2.478 1.250
O Hb H–OH2b
CF3
O–H H O O O C–O
1.008 [1.040] 1.548 2.556 1.278
1.047 [1.106] 1.418 2.464 1.272
1.439 1.037 [1.109] 2.476 1.253
O Hb H–OH2b
NO2
O–H H O O O C–O
1.012 [1.046] 1.532 2.544 1.276
1.061 [1.128] 1.385 2.445 1.269
1.471 1.026 [1.070] 2.497 1.251
O Hb H–OH2b
1.011a [1.033] 1.653a 2.664a 1.293a
˚ . Vibrationally averaged distances are shown in brackets. Data for transferred structures are in italic. Distances in A a CASSCF/cc-pVDZ calculation by Jansen and Gerhards [14]. b O–H is the distance between the phenolic oxygen and hydrogen; H O is the distance between the phenolic hydrogen and the oxygen of the nearest water molecule; O O is the distance between the phenolic and water oxygen atoms; C–O is the carbon–oxygen bond length in the phenolic moiety. Note that for proton transferred complexes, H O corresponds to the H–OH2 bond between the phenolic proton and a water molecule. Concomitantly, the phenolic O–H distance is now better described as a hydrogen bond, O H.
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Table 1 also reports vibrationally averaged distances associated with the proton transfer coordinate. They were estimated by using the vibrational wavefunctions determined through the transfer-matrix path-integral approach. Vibrationally averaged distances associated with the proton transfer coordinate show the same dependence on the substituent that was observed for the equilibrium distances. However, they may differ significantly from these distances. For example, the average O–H distance for X = H and ˚ ) is 0.05 A ˚ longer than the equilibrium disn = 2 (1.086 A ˚ tance (1.035 A). These differences are even more significant when X = CN, CF3, NO2. The averaged H O distances in the T complexes, which, as stated above, should now be regarded as the ˚ H–OH2 distance in H3O+, decrease from 1.123 A ˚ (X = H) to 1.070 A (X = NO2). The differences between vibrationally averaged and equilibrium distances reflect the quantum nature of the proton coordinate and are related to the specific shape of the potential energy curve for the different substituents. 3.2. Potential energy curves, proton probability densities, vibrational frequencies, and binding energies Potential energy curves for n = 1–3, together with the probability distributions describing the proton transfer coordinate are reported in Figs. 2–4, respectively. The shapes of the curves provide additional information concerning the specific role played by the different substituents on the proton transfer energetics. We will firstly discuss the potential energy curves of NT complexes.
As shown in Figs. 2 and 3, the potential energy curves in ˚ range for X = NMe2, NH2, OH are less attracthe 1–1.6 A tive than for X = H. In addition, the slopes of the curves near the minima are higher for those substituents than for X = H, indicating that electron donating substituents hinder the O–H elongation of the phenolic moiety as compared to phenol. This is also illustrated by the probability distribution of the O–H distance that is shifted to lower values for electron donating substituents. The potential energy curves of Figs. 2 and 3 exhibit an ˚ for n = 1 and 1.6 A ˚ for ‘inversion’ region, at about 1.7 A ˚ n = 2. For instance, at distances shorter than 1.6 A (Fig. 3), the potential energy increases with the electron donation of the substituents, whereas for longer distances an opposite trend is observed. Our explanation of these patterns is as follows. At longer distances the trend is consistent with the fact that the phenolic moiety XC6H4O is quite similar to a phenoxyl radical (see the discussion below on charge distribution). It is well known that electron donating substituents stabilize phenoxyl radicals and this stabilization is the main cause of the weakening of the O–H bond. On the other hand, at distances shorter than the inversion range, where the species [p-XC6H4OH]+ prevails, the trend is similar to the one observed for the proton affinities, viz. the potential energy of the O–H bond in the radical cation [p-XC6H4OH]+ is smaller when X is an electron withdrawing group than for X = H. Note also that the proton affinity trend is caused by a ‘ground state’ effect, i.e., it is determined by the stability of [pXC6H4OH]+ rather than by the stability of the p-XC6H4O radical.
30000
NMe2 NH2 OH H CN CF3 NO2
Potential energy (cm-1)
25000 20000 15000 10000
n=1
5000 0
Probability
n=1 0.02
0.01
0 0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
O-H(Å)
Fig. 2. Potential energy (cm1) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)1]+ clusters.
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
455
Potential energy (cm -1)
30000 25000
n=2
NMe2 NH2 OH H CN CF3 NO2
20000 15000 10000 5000 0
n=2
Probability
0.03
0.02
0.01
0
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
O-H (Å) 1
Potential energy (cm-1)
Fig. 3. Potential energy (cm ) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)2]+ clusters.
30000
30000
25000
n=3
20000
n=3
NMe2 NH2 OH
25000
H CN CF3 NO2
15000
20000 15000
10000
10000
5000
5000
Probability
0
0
0.02
0.02
0.01
0.01
0
0.8
1
1.2 1.4 O-H (Å)
1.6
0.8
1
1.2 1.4 H-OH2 (Å)
1.6
0
Fig. 4. Potential energy (cm1) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)3]+ clusters. Results for non-transferred complexes are shown in the left panel and results for transferred complexes are shown in the right panel.
The potential energy curves for n = 3 and the corresponding O–H probability distributions are presented in Fig. 4. In comparison to n = 2, the curves of the NT complexes (left panel) for n = 3 show broader probability distributions with a more significant difference between X = NH2 and X = OH. The curves for the T complexes are also shown in Fig. 4 (right panel). In comparison with
the potential energy curves for X = H, the curves corresponding to X = CN, CF3, NO2 are less attractive for dis˚ , leading to H–OH2 distance tances longer than 1.1 A probability distributions shifted to the left (lower values). This is in keeping with the smaller vibrationally averaged H–OH2 distances for CN, CF3, and NO2 reported in Table 1.
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Vibrational frequencies are related to the curvatures of the potential energy curves and are very dependent on the specific theoretical procedure. Therefore, it is important to compare experimental data with theoretical predictions so that an adequate approach can be selected. For cationic phenol–water complexes, experimental frequencies are available for the [C6H5OH–H2O]+ species [6]. Results for the infrared spectra of neutral phenol–water complexes were also reported [33]. Our BHandHLYP prediction for the anharmonic phenol O–H stretching frequency in [C6H5OH–H2O] is 3544 cm1, in good agreement with experiment (3524 cm1) [33]. For comparison, the B3LYP/cc-pVDZ result is 3311 cm1, i.e. 213 cm1 below the experimental value. BHandHLYP/cc-pVDZ vibrational frequencies for the [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) are reported in
Table 2. For cationic phenol–water complexes, our harmonic frequencies can be compared with B3LYP/DZP predictions of Re and Osamura [10]. Although for NT complexes our frequencies are higher (it appears that B3LYP frequencies are much too low), they exhibit a similar behavior when n varies (the frequency decreases by 582 cm1 from n = 1 to n = 2 in our calculations and by 717 cm1 in the study by Re and Osamura [10]). Anharmonic frequencies are significantly lower. For X = H and n = 1, the O–H frequency is 2605 cm1, which is only 25 cm1 above a CASSCF/cc-pVDZ value (2580 cm1) reported by Jansen and Gerhards [14]. Both predictions are in keeping with the experimental estimate (<2800 cm1) [6]. However, they are significantly higher than a recent theoretical prediction (2300 cm1), based on mixed quantum-classical calculations [34].
Table 2 O–H vibrational frequencies (cm1) in [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) from BHandHLYP/cc-pVDZ calculations X
rþ p
n=1
n=2
n=3
N(CH3)2 NH2 OH H CN CF3 NO2
1.7 1.3 0.92 0.0 0.66 0.61 0.79
3437 [3119] 3363 [3015] 3227 [2831] 3071; 2793a [2605]; [2580]b; [<2800]c 3004 [2516] 2983 [2496] 2907 [2378]
3131 [2704] 3024 [2538] 2788 [2177] 2489; 2076a [1770] 2314 [1589] 2294 [1577] 2084 [1455]
2727 [2507] 2542 [1796] 2050 [1416] 2147; 1896a [1489] 2079d 2472 [1734 ] 2443 [1708] 2621 [1937]
rþ p are Hammett parameters. Anharmonic frequencies are in brackets. Values in italic are for transferred structures. a B3LYP/DZP calculation by Re and Osamura [10]. b CASSCF/cc-pVDZ calculation by Jansen and Gerhards [14]. c Experimental result by Tanabe et al. [6]. d ROHF/6-31G(d,p) calculation by Kleinermanns et al. [13].
3000
ν
O-H
(cm-1 )
2700
n=2
2400 2100 1800 1500 1200 3200
NMe
2
(cm-1 )
2600
O-H
2800
ν
3000
NH 2
n=1
OH
CF H
CN
2400 2200 -2
3
-1.6
-1.2
-0.8
-0.4 σ p+
0
0.4
NO 2 0.8
+ Fig. 5. Correlation between the anharmonic frequencies (mO–H) and the rþ clusters p Hammett parameter in non-transferred [p-XC6H4OH–(H2O)n] 1 1 þ (n = 1, 2). The data was fitted to the expression mO–H ¼ a þ brp (dashed line). a = 2636 cm , b = 271.3 cm , with r = 0.988 (n = 1); a = 1845 cm1, b = 482.3 cm1, with r = 0.990 (n = 2).
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
As expected from the above discussion on structure, substituent effects on the vibrational frequencies are quite visible. For NT complexes and n = 1, 2, frequencies increase for X = OH, NH2, NMe2 and decrease for CN, CF3, NO2, relative to the phenol–water cation (X = H). Deviations from harmonicity increase from n = 1 to n = 2. These deviations can be significant (719 cm1 for X = H and n = 2). Therefore, our results confirm the conclusion by Jansen and Gerhards [14] that an harmonic analysis is not adequate for describing the proton transfer coordinate of cationic phenol–water clusters. A correlation between Hammett constants rp and hydrogen bonding interaction energies in the phenoxyl radical cation–water molecule complex was discussed by Feng et al. [15]. Our results in Table 2 show that hydrogen bond-
Table 3 Binding energies (kcal mol1) at 0 K for [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) n=1
NMe2 NH2 OH H CF3 CN NO2
n=2
n=3
Eb
DEb
Eb
DEb
Eb
DEb
12.37 13.94 15.83 17.58; 19.6a; 18.54 ± 0.11b 18.72 18.59 19.56
5.21 3.64 1.74 0.00
19.04 21.38 24.21 26.84
7.80 5.47 2.63 0.00
21.25 24.34 28.25 27.10
5.85 2.76 1.15 0.00
1.14 1.02 1.98
28.74 28.58 29.98
1.90 1.74 3.14
22.07 20.65 18.86
5.03 6.45 8.25
Results are from BHandHLYP/aug-cc-pVTZ//BHandHLYP/cc-pVDZ calculations and include zero-point vibrational energies. DEb for each complex is the difference between the binding energy of that complex and the binding energy of the complex with X = H. Values in italic are for proton transferred structures. a MP2/DZP value by Re and Osamura [10]. b Experimental value by Courty et al. [35].
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ing between the phenolic moiety and water in NT complexes will induce a significant red-shift of the O–H frequency associated with the proton transfer coordinate. Therefore, frequencies and Hammett parameters should correlate. This is confirmed in Fig. 5, where the dashed lines represent the least square plots of mO–H (anharmonic frequencies) vs. the Hammett parameters rþ p (Table 2). We have found that the correlations improve when rp is replaced by rþ p. Binding energies (Eb) for ionized phenol–water clusters are reported in Table 3, where DEb for each complex is the difference between the binding energy of that complex and the binding energy of the complex with X = H. For the phenol–water cationic complex, an experimental value for the binding energy (18.54 ± 0.11 kcal mol1) was reported [35]. Our prediction (17.58 kcal mol1) is in good agreement with experiment. It is also in reasonable agreement with a MP2 prediction by Re and Osamura (19.6 kcal mol1) [10]. For NT clusters, electron donating (withdrawing) substituents decrease (increase) the binding energy relative to the complex with X = H. This effect can be significant and for X = NMe2 and n = 2, DEb = 7.80 kcal mol1. For T complexes, electron withdrawing substituents can also induce a significant decrease of the binding energy relative to the non-substituted complex (DEb = 8.25 kcal mol1 for X = NO2 and n = 3). 3.3. Charge distribution We will focus the discussion of the charge distribution in phenol–water complexes on two fragments: p-XC6H4OH and (H2O)n (n = 1–3) for the NT complexes, and pXC6H4O and (H3O)+(H2O)2 for the T complexes. Natural atomic orbital (NAO) charges for these fragments are reported in Table 4. Here, DqX for each fragment was
Table 4 NAO charges (a.u.) for p-XC6H4OH, p-XC6H4O, (H2O)n, and H3O+–(H2O)n1 fragments in the optimized structures of [p-XC6H4OH–(H2O) n]+ clusters (n = 1–3) X
N(CH3)2
NH2
OH
H
CN
CF3
NO2
n=1 p-XC6H4OH DqX (H2O)n
0.946 0.021 0.054
0.942 0.017 0.058
0.933 0.008 0.067
0.925 0.0 0.075
0.920 0.005 0.080
0.919 0.006 0.081
0.915 0.010 0.085
n=2 p-XC6H4OH DqX (H2O)n
0.925 0.036 0.075
0.919 0.030 0.081
0.905 0.016 0.095
0.889 0.0 0.111
0.879 0.010 0.121
0.878 0.011 0.122
0.866 0.023 0.134
0.898 0.762 0.102
0.888 0.752 0.112
0.860 0.724 0.140 0.136 0.0 0.864
0.114 0.022 0.886
0.117 0.019 0.883
0.105 0.031 0.895
n=3 p-XC6H4OH DqX (H2O)n p-XC6H4O DqX H3O+–(H2O)n1
Results are from BHandHLYP/aug-cc-pVDZ//BHandHLYP/cc-pVDZ calculations. DqX for each fragment is the difference between the charge in that fragment and the charge in the fragment with X = H. Values in italic are for proton transferred complexes.
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defined as the difference between the charge in that fragment and the charge in the fragment with X = H. Our results show that when X = H and n = 1 the charge of the cationic complex (+1) is essentially localized in the phenolic moiety (0.925) and only a small fraction (0.075) is in the water fragment. For n = 2, the total charges of the phenolic and water fragments are 0.889 and 0.111, respectively, indicating that electron charge migration from water to the phenolic moiety is favored by increasing the number of water molecules. This trend (increase of the electron charge transfer from water with increasing n) is also observed for all the substituted NT complexes. For a given n, the charge reorganization induced by substitution in NT complexes follows a simple pattern. In comparison with X = H, electron-donating substituents (X = NMe2, NH2, OH) hinder the electron charge migration from water to the phenolic moiety. For X = NH2 and n = 1, the charge of the phenolic moiety is 0.942, leading to a relative charge (DqX) of 0.017. A similar trend can be observed for n = 2. Electron charge transfer from water decreases with the increasing donating character of the substituent (more negative rþ p values in Table 2). On the other hand, charge transfer from water to the phenolic fragment is enhanced by electron-withdrawing substituents (X = CN, CF3, NO2). For example, for X = NO2 and n = 2, the total charge of the phenolic fragment is 0.866 or DqX = 0.023. Electron charge transfer from water increases with the increasing withdrawing character of the substituent (more positive rþ p values in Table 2). For T complexes (X = H, CN, CF3, NO2; n = 3), a very small charge is observed in the phenolic moiety, suggesting that this fragment is similar to the phenoxyl radical. The positive charge of the phenolic moiety decreases with increasing withdrawing character of the substituent, e.g. from 0.136 (X = H) to 0.105 (X = NO2). This indicates that electron charge transfer from the phenoxyl radical to the hydronium–water cluster decreases with the increasing withdrawing character of the substituent. 4. Conclusions Density functional theory (DFT) and transfer-matrix path-integral calculations were made to investigate substituent effects on proton transfer assisted by water molecules in [p-XC6H4OH–(H2O)n]+ (X = NMe2, NH2, OH, H, CN, CF3, NO2) clusters (n = 1–3). DFT calculations were based on the BHandHLYP functional, which has been previously applied to the study of ionized water clusters [27,28]. Proton transfer from the phenolic moiety to water is favored by electron withdrawing substituents (X = CN, CF3, NO2). However, a minimum of three water molecules is required to transfer a proton from the phenolic moiety to water. Structural and electronic aspects related to substituent effects and hydrogen bond interactions were analysed. The results indicate that para-substituents have a less important role in promoting proton transfer than the interactions with
the water molecules. The calculated mO–H anharmonic frequencies are in good agreement with theoretical and experimental data for some of the complexes. Moreover, a correlation between these frequencies and rþ p Hammett parameters was established for those cationic phenol–water complexes where proton transfer did not occur. Ground state probability densities and vibrationally averaged distances were also calculated and illustrate the quantum nature of the proton transfer process in the clusters. Acknowledgments H.F.M.C.M. gratefully acknowledges FCT (Ph.D. Grant No. SFRH/BD/27577/2006). This work was partially supported by Fundac¸a˜o para a Cieˆncia e a Tecnologia (FCT), Portugal (Grant No. POCI/MAT/55977/2004). References [1] T.M. Krygowski, B.M. Stepien, Chem. Rev. 105 (2005) 3482. [2] R.M. Borges dos Santos, J.A. Martinho Simo˜es, J. Phys. Chem. Ref. Data 27 (1998) 707. [3] K.D. Wiberg, J. Org. Chem. 68 (2003) 875. [4] A.P. Vafiadis, E.G. Bakalbassis, Chem. Phys. 316 (2005) 195. [5] E. Klein, V. Lukes, J. Phys. Chem. A 110 (2006) 12312. [6] S. Tanabe, T. Ebata, M. Fujii, N. Mikami, Chem. Phys. Lett. 215 (1993) 347. [7] S. Sato, N. Mikami, J. Phys. Chem. 100 (1996) 4765. [8] T. Sawamura, A. Fujii, S. Sato, T. Ebata, N. Mikami, J. Phys. Chem. 100 (1996) 8131. [9] M. Sodupe, A. Oliva, J. Bertran, J. Phys. Chem. A 101 (1997) 9142. [10] S. Re, Y. Osamura, J. Phys. Chem. A 102 (1998) 3798. [11] N. Agmon, J. Phys. Chem. A 109 (2005) 13. [12] P. Hobza, R. Burcl, V. Spirko, O. Dopfer, K. Mullerdetlefs, E.W. Schlag, J. Chem. Phys. 101 (1994) 990. [13] K. Kleinermanns, Ch. Janzen, D. Spangenberg, M. Gerhards, J. Phys. Chem. A 103 (1999) 5232. [14] A. Jansen, M. Gerhards, J. Chem. Phys. 115 (2001) 5445. [15] Y. Feng, L. Liu, Y. Fang, Q.-X. Guo, J. Phys. Chem. A 106 (2002) 11518. [16] N. Yamamoto, N. Shida, E. Miyoshi, Chem. Phys. Lett. 371 (2003) 724. [17] M.M. Bizarro, B.J. Costa Cabral, R.M. Borges dos Santos, J.A. Martinho Simo˜es, Pure Appl. Chem. 71 (1999) 1249. [18] M. Guerra, R. Amorati, G.P. Pedulli, J. Org. Chem. 69 (2004) 5460. [19] Y. Fu, R. Liu, L. Liu, Q.-X. Guo, J. Phys. Org. Chem. 17 (2004) 282. [20] D.-S. Ahn, S.-W. Park, S. Lee, B. Kim, J. Phys. Chem. A 107 (2003) 131. [21] H.-T. Kim, R.J. Green, J. Qian, S.L. Anderson, J. Chem. Phys. 112 (2000) 5717. [22] M. Yi, S. Scheiner, Chem. Phys. Lett. 262 (1996) 567. [23] J.P.P. Ramalho, F.M.S. Fernandes, Z. Naturforsch A 45 (1990) 1193. [24] J.P.P. Ramalho, B.J. Costa Cabral, F.M.S. Fernandes, Chem. Phys. Lett. 184 (1991) 53. [25] M.J. Frisch et al., GAUSSIAN-03, Rev. C.02, Gaussian Inc., Pittsburgh, PA, 2003. [26] J.A. Anderson, G.S. Tschumper, J. Phys. Chem. A 110 (2006) 7268. [27] M. Sodupe, J. Bertran, L. Rodrigues-Santiago, E.J. Baerends, J. Phys. Chem. A 103 (1999) 166. [28] P. Cabral do Couto, B.J. Costa Cabral, J. Chem. Phys. 126 (2007) 014509. [29] D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358. [30] A.E. Reed, F. Weinhold, J. Chem. Phys. 78 (1983) 4066.
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[34] T. Yamashita, K. Takatsuka, J. Chem. Phys. 126 (2007) 074304. [35] A. Courty, M. Mons, I. Dimicoli, F. Piuzzi, V. Brenner, P. Millie, J. Phys. Chem. A 102 (1998) 4890.
Substituent effects on water-assisted proton transfer in [p-XC6H4OH–(H2O)1–3]+ clusters Hugo F.M.C. Martiniano a, Benedito J. Costa Cabral a
a,*
, Jose´ A. Martinho Simo˜es
b
Departamento de Quı´mica e Bioquı´mica, Faculdade de Cieˆncias, Universidade de Lisboa, 1749-016 Lisboa, Portugal, and Grupo de Fı´sica Matema´tica da Universidade de Lisboa, Av. Professor Gama Pinto 2, 1649-003 Lisboa, Portugal b Departamento de Quı´mica e Bioquı´mica, Faculdade de Cieˆncias, Universidade de Lisboa, 1749-016 Lisboa, Portugal Received 2 April 2007; in final form 17 May 2007 Available online 29 May 2007
Abstract Substituent effects on proton transfer (PT) from the phenolic moiety to water in [p-XC6H4OH–(H2O)n]+ (X = N(CH3)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters were investigated by density functional theory. Structural and electronic aspects related to substituent effects and hydrogen bonding were analysed. PT to water is inhibited (favored) by electron donating (withdrawing) substituents. The results indicate that para-substituents have a less important role in promoting proton transfer than the interactions with the water molecules. Anharmonic vibrational frequencies associated with the PT coordinate correlate with the rþ p Hammett parameters. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction The importance of substituent effects on the molecular properties of chemical and biochemical species is well recognized [1]. These effects have been extensively investigated for aromatic compounds, where a substituent may lead to a considerable reorganization of the r and p-electron densities and therefore to significant changes of the molecular properties. Solution-phase acidity, for example, will be determined by the ability of the substituent to induce charge transfer. Phenol is a widely used model system to probe substituent effects on several properties, such as bond dissociation enthalpies [2], gas-phase acidities [3], and proton affinities of phenoxyl radicals [4,5]. For instance, it is well known that electron donating para-substituents, such as N(CH3)2 or NH2, decrease the phenolic O–H bond dissociation enthalpy, whereas electron withdrawing para-substituents, such as NO2 and CN, strengthen that bond [2]. Opposite trends are observed for the gas-phase acidity and for the *
Corresponding author. E-mail address: [email protected] (B.J. Costa Cabral).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.05.083
proton affinity. Indeed electron donating para-substituents make the heterolysis of the O–H bond more endergonic than in the case of phenol [2]; similarly, the proton affinity of the radical (also called the O–H proton dissociation enthalpy of the phenol radical cation, PDE) increases with the donating character of the para-substituent [4,5]. Phenol has also been used to investigate, from a microscopic point of view, how proton transfer to water depends on the number of interacting water molecules. Several works provided evidence that proton transfer from phenol to water does not occur in the ground state of small phenol–water clusters [6–10]. However, certain aromatic molecules exhibit a dramatic change in their acidity upon excitation or ionization [11,12]. The explanation for this behavior is that excitations trigger intramolecular charge transfer in the ring system and modify the hydrogen bond interactions that set the stage for proton transfer [11]. The proton transfer step is strongly dependent on the number and specific structure of the solvent molecules in interaction with the phenolic moiety, i.e., the proton transfer is a process assisted by the solvent [11]. Several studies have discussed how proton transfer in ionized phenol–water clusters depends on the number of water
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molecules [8–10,12–16]. On the other hand, substituent effects on the phenol O–H bond dissociation enthalpies in neutral [XC6H4OH–(H2O)1–4] clusters have been discussed by different authors [17–20]. For ionized phenol–water clusters, the studies on substituent effects were apparently limited to the [p-XC6H4OH–(H2O)]+ complex [15]. However, in contrast with phenol–ammonia clusters, where proton transfer is observed in the [C6H5OH–(NH3)]+ complex [21,22], proton transfer to water in [C6H5OH–(H2O)n]+ clusters, only takes place when n P 3 [9,10]. Therefore, substituent effects on the proton transfer mechanism deserve further analysis. In this Letter, we report results for the structure, electronic, and vibrational properties of ionized [pXC6H4OH–(H2O)n]+ (X = N(CH3)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters. We also discuss the importance of taking into account the anharmonic nature of the potential energy curve associated with the proton transfer coordinate [14,16]. The structure and electronic properties of the clusters were investigated by density functional theory (DFT). Wavefunctions and anharmonic frequencies associated with the proton transfer coordinate were calculated by a transfer-matrix path-integral approach [23,24].
ferred (NT) and transferred (T) complexes, respectively. In ˚ . Anharmonic both cases, x was sampled from 0.6 to 1.9 A frequencies and wavefunctions associated with the proton transfer coordinate were calculated through a transfermatrix path-integral procedure [23,24]. We are also reporting binding energies for the phenol–water cationic complexes. For NT clusters the binding energy (Eb) is defined as: Eb = E[p-XC6H4OH]+ + E[(H2O)n] E[p-XC6H4OH– (H2O)n]+. For T clusters, Eb = E[p-XC6H4O] + E[H3O+– (H2O)n1] E[p-XC6H4OH–(H2O)n]+. Binding energies at 0 K were calculated at the BHandHLYP/aug-ccpVTZ//BHandHLYP/cc-pVDZ level and include zeropoint vibrational energies. 3. Results and discussion 3.1. Structure The structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) are shown in Fig. 1 and selected structural infor-
2. Computational details The structures of [p-XC6H4OH–(H2O)n]+ (X = N(Me)2, NH2, OH, H, CN, CF3, NO2; n = 1–3) clusters were optimized with the BHandHLYP functional as implemented in the GAUSSIAN 03 suite of programs [25]. The choice of this functional was driven by studies on hydrogen bonding [26] and ionized water clusters [27,28]. The Dunning’s cc-pVDZ basis set [29] was used in all the optimizations. Natural atomic charges (NAO) [30,31] for the optimized structures were evaluated with the aug-cc-pVDZ basis set [29,32]. An adiabatic approximation was used to generate the potential energy curve associated with the proton transfer coordinate. The potential energy curves were generated by stretching of the O–H distance along the O–H bond direction. This means that for a given structure of the cationic phenol–water complex, the quantum degree of freedom associated with the proton motion is assumed to be much faster than the reorganization of the molecular structure. The adiabatic approximation was also adopted by Jansen and Gerhards [14] who reported anharmonic vibrational frequencies associated with proton transfer coordinates in phenol–water and aminophenol–water clusters [14]. This kind of simplification also neglects the coupling between O–H stretching and bending modes in cationic phenol– water complexes that was investigated by Yamamoto [16]. For each [p-XC6H4OH–(H2O)n]+ complex (n = 1–3), a total number of 14 points were generated and the corresponding potential energy curves were fitted to a polynoP13 mial form i¼0 ai xi , where ai’s are fitting coefficients. The variable x represents either the phenolic O–H distance when no proton transfer has occurred, or the distance H–OH2 between the transferred proton and the nearest water molecule. These structures will henceforth be called non-trans-
Fig. 1. Optimized structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1– 3).
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
mation is reported in Table 1. In agreement with previous investigations [9,10], when X = H proton transfer to water occurs only for n = 3. This is indicated by a sharp increase of the O–H distance and a sharp decrease of the H O distance when n changes from 2 to 3. The same behavior is observed when X is an electron withdrawing group (X = CN, CF3, NO2), i.e., T complexes are formed when n = 3. Nevertheless, when X is an electron donating group (X = N(Me)2, NH2, OH), only NT complexes are formed. As expected, these results follow a similar trend to the one observed for the proton affinity of substituted phenoxyl radicals [4,5]. Our data for the optimized structure of the phenol– water cation complex can be compared with CASSCF/ccpVDZ results [14]. In general, a good agreement is observed. H O and O O distances from BHandH˚ shorter then LYP/cc-pVDZ calculations are ca. 0.09 A the CASSCF/cc-pVDZ predictions [14]. For NT complexes (n = 1, 2) the analysis of structural data can provide some information related to the role
453
played by substituents in proton transfer. For example, taking phenol (X = H) as reference, O–H distances slightly increase for electron withdrawing groups (X = CN, CF3, NO2) and decrease for electron donating substituents (X = OH, NH2, N(CH3)2). Opposite patterns are observed for the H O and O O distances. Finally, C–O distances are not significantly changed for X = CN, CF3, NO2, ˚ when X = OH, NH2, although they increase by 0.01 A N(CH3)2. Data for the T complexes (n = 3) show that the H O ˚ when X = H, to 1.026 A ˚ distance decreases from 1.056 A when X = NO2. The O–H distance increases from ˚ when X = H to 1.471 A ˚ (X = NO2). A similar 1.390 A trend can be observed for the O O distance, which ˚ (X = H) to 2.497 A ˚ (X = NO2). increases from 2.446 A Note that for T complexes, what we call the H O distance should be regarded as the H–OH2 bond between the transferred phenolic proton and the water molecule. Concomitantly, the phenolic O–H distance is now better described as a hydrogen bond, O H.
Table 1 Data for BHandHLYP/cc-pVDZ optimized structures of [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) X
n=1
n=2
n=3
N(CH3)2
O–H H O O O C–O
0.983 [1.006] 1.668 2.650 1.304
0.998 [1.027] 1.578 2.575 1.299
1.019 [1.060] 1.491 2.509 1.293
NH2
O–H H O O O C–O
0.987 [1.011] 1.644 2.630 1.299
1.004 [1.036] 1.553 2.555 1.294
1.030 [1.079] 1.458 2.486 1.288
OH
O–H H O O O C–O
0.994 [1.021] 1.606 2.599 1.291
1.017 [1.056] 1.503 2.518 1.285
1.061 [1.134] 1.380 2.440 1.278
H
O–H H O O O C–O
1.003; 1.568; 2.570; 1.282;
1.035 [1.086] 1.449 2.483 1.276
1.390 1.056 [1.123] 2.446 1.256
O Hb H–OH2b
CN
O–H H O O O C–O
1.007 [1.038] 1.553 2.559 1.278
1.045 [1.104] 1.422 2.466 1.271
1.443 1.035 [1.087] 2.478 1.250
O Hb H–OH2b
CF3
O–H H O O O C–O
1.008 [1.040] 1.548 2.556 1.278
1.047 [1.106] 1.418 2.464 1.272
1.439 1.037 [1.109] 2.476 1.253
O Hb H–OH2b
NO2
O–H H O O O C–O
1.012 [1.046] 1.532 2.544 1.276
1.061 [1.128] 1.385 2.445 1.269
1.471 1.026 [1.070] 2.497 1.251
O Hb H–OH2b
1.011a [1.033] 1.653a 2.664a 1.293a
˚ . Vibrationally averaged distances are shown in brackets. Data for transferred structures are in italic. Distances in A a CASSCF/cc-pVDZ calculation by Jansen and Gerhards [14]. b O–H is the distance between the phenolic oxygen and hydrogen; H O is the distance between the phenolic hydrogen and the oxygen of the nearest water molecule; O O is the distance between the phenolic and water oxygen atoms; C–O is the carbon–oxygen bond length in the phenolic moiety. Note that for proton transferred complexes, H O corresponds to the H–OH2 bond between the phenolic proton and a water molecule. Concomitantly, the phenolic O–H distance is now better described as a hydrogen bond, O H.
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Table 1 also reports vibrationally averaged distances associated with the proton transfer coordinate. They were estimated by using the vibrational wavefunctions determined through the transfer-matrix path-integral approach. Vibrationally averaged distances associated with the proton transfer coordinate show the same dependence on the substituent that was observed for the equilibrium distances. However, they may differ significantly from these distances. For example, the average O–H distance for X = H and ˚ ) is 0.05 A ˚ longer than the equilibrium disn = 2 (1.086 A ˚ tance (1.035 A). These differences are even more significant when X = CN, CF3, NO2. The averaged H O distances in the T complexes, which, as stated above, should now be regarded as the ˚ H–OH2 distance in H3O+, decrease from 1.123 A ˚ (X = H) to 1.070 A (X = NO2). The differences between vibrationally averaged and equilibrium distances reflect the quantum nature of the proton coordinate and are related to the specific shape of the potential energy curve for the different substituents. 3.2. Potential energy curves, proton probability densities, vibrational frequencies, and binding energies Potential energy curves for n = 1–3, together with the probability distributions describing the proton transfer coordinate are reported in Figs. 2–4, respectively. The shapes of the curves provide additional information concerning the specific role played by the different substituents on the proton transfer energetics. We will firstly discuss the potential energy curves of NT complexes.
As shown in Figs. 2 and 3, the potential energy curves in ˚ range for X = NMe2, NH2, OH are less attracthe 1–1.6 A tive than for X = H. In addition, the slopes of the curves near the minima are higher for those substituents than for X = H, indicating that electron donating substituents hinder the O–H elongation of the phenolic moiety as compared to phenol. This is also illustrated by the probability distribution of the O–H distance that is shifted to lower values for electron donating substituents. The potential energy curves of Figs. 2 and 3 exhibit an ˚ for n = 1 and 1.6 A ˚ for ‘inversion’ region, at about 1.7 A ˚ n = 2. For instance, at distances shorter than 1.6 A (Fig. 3), the potential energy increases with the electron donation of the substituents, whereas for longer distances an opposite trend is observed. Our explanation of these patterns is as follows. At longer distances the trend is consistent with the fact that the phenolic moiety XC6H4O is quite similar to a phenoxyl radical (see the discussion below on charge distribution). It is well known that electron donating substituents stabilize phenoxyl radicals and this stabilization is the main cause of the weakening of the O–H bond. On the other hand, at distances shorter than the inversion range, where the species [p-XC6H4OH]+ prevails, the trend is similar to the one observed for the proton affinities, viz. the potential energy of the O–H bond in the radical cation [p-XC6H4OH]+ is smaller when X is an electron withdrawing group than for X = H. Note also that the proton affinity trend is caused by a ‘ground state’ effect, i.e., it is determined by the stability of [pXC6H4OH]+ rather than by the stability of the p-XC6H4O radical.
30000
NMe2 NH2 OH H CN CF3 NO2
Potential energy (cm-1)
25000 20000 15000 10000
n=1
5000 0
Probability
n=1 0.02
0.01
0 0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
O-H(Å)
Fig. 2. Potential energy (cm1) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)1]+ clusters.
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
455
Potential energy (cm -1)
30000 25000
n=2
NMe2 NH2 OH H CN CF3 NO2
20000 15000 10000 5000 0
n=2
Probability
0.03
0.02
0.01
0
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
O-H (Å) 1
Potential energy (cm-1)
Fig. 3. Potential energy (cm ) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)2]+ clusters.
30000
30000
25000
n=3
20000
n=3
NMe2 NH2 OH
25000
H CN CF3 NO2
15000
20000 15000
10000
10000
5000
5000
Probability
0
0
0.02
0.02
0.01
0.01
0
0.8
1
1.2 1.4 O-H (Å)
1.6
0.8
1
1.2 1.4 H-OH2 (Å)
1.6
0
Fig. 4. Potential energy (cm1) and probability distribution associated with the proton transfer coordinate in [p-XC6H4OH–(H2O)3]+ clusters. Results for non-transferred complexes are shown in the left panel and results for transferred complexes are shown in the right panel.
The potential energy curves for n = 3 and the corresponding O–H probability distributions are presented in Fig. 4. In comparison to n = 2, the curves of the NT complexes (left panel) for n = 3 show broader probability distributions with a more significant difference between X = NH2 and X = OH. The curves for the T complexes are also shown in Fig. 4 (right panel). In comparison with
the potential energy curves for X = H, the curves corresponding to X = CN, CF3, NO2 are less attractive for dis˚ , leading to H–OH2 distance tances longer than 1.1 A probability distributions shifted to the left (lower values). This is in keeping with the smaller vibrationally averaged H–OH2 distances for CN, CF3, and NO2 reported in Table 1.
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Vibrational frequencies are related to the curvatures of the potential energy curves and are very dependent on the specific theoretical procedure. Therefore, it is important to compare experimental data with theoretical predictions so that an adequate approach can be selected. For cationic phenol–water complexes, experimental frequencies are available for the [C6H5OH–H2O]+ species [6]. Results for the infrared spectra of neutral phenol–water complexes were also reported [33]. Our BHandHLYP prediction for the anharmonic phenol O–H stretching frequency in [C6H5OH–H2O] is 3544 cm1, in good agreement with experiment (3524 cm1) [33]. For comparison, the B3LYP/cc-pVDZ result is 3311 cm1, i.e. 213 cm1 below the experimental value. BHandHLYP/cc-pVDZ vibrational frequencies for the [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) are reported in
Table 2. For cationic phenol–water complexes, our harmonic frequencies can be compared with B3LYP/DZP predictions of Re and Osamura [10]. Although for NT complexes our frequencies are higher (it appears that B3LYP frequencies are much too low), they exhibit a similar behavior when n varies (the frequency decreases by 582 cm1 from n = 1 to n = 2 in our calculations and by 717 cm1 in the study by Re and Osamura [10]). Anharmonic frequencies are significantly lower. For X = H and n = 1, the O–H frequency is 2605 cm1, which is only 25 cm1 above a CASSCF/cc-pVDZ value (2580 cm1) reported by Jansen and Gerhards [14]. Both predictions are in keeping with the experimental estimate (<2800 cm1) [6]. However, they are significantly higher than a recent theoretical prediction (2300 cm1), based on mixed quantum-classical calculations [34].
Table 2 O–H vibrational frequencies (cm1) in [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) from BHandHLYP/cc-pVDZ calculations X
rþ p
n=1
n=2
n=3
N(CH3)2 NH2 OH H CN CF3 NO2
1.7 1.3 0.92 0.0 0.66 0.61 0.79
3437 [3119] 3363 [3015] 3227 [2831] 3071; 2793a [2605]; [2580]b; [<2800]c 3004 [2516] 2983 [2496] 2907 [2378]
3131 [2704] 3024 [2538] 2788 [2177] 2489; 2076a [1770] 2314 [1589] 2294 [1577] 2084 [1455]
2727 [2507] 2542 [1796] 2050 [1416] 2147; 1896a [1489] 2079d 2472 [1734 ] 2443 [1708] 2621 [1937]
rþ p are Hammett parameters. Anharmonic frequencies are in brackets. Values in italic are for transferred structures. a B3LYP/DZP calculation by Re and Osamura [10]. b CASSCF/cc-pVDZ calculation by Jansen and Gerhards [14]. c Experimental result by Tanabe et al. [6]. d ROHF/6-31G(d,p) calculation by Kleinermanns et al. [13].
3000
ν
O-H
(cm-1 )
2700
n=2
2400 2100 1800 1500 1200 3200
NMe
2
(cm-1 )
2600
O-H
2800
ν
3000
NH 2
n=1
OH
CF H
CN
2400 2200 -2
3
-1.6
-1.2
-0.8
-0.4 σ p+
0
0.4
NO 2 0.8
+ Fig. 5. Correlation between the anharmonic frequencies (mO–H) and the rþ clusters p Hammett parameter in non-transferred [p-XC6H4OH–(H2O)n] 1 1 þ (n = 1, 2). The data was fitted to the expression mO–H ¼ a þ brp (dashed line). a = 2636 cm , b = 271.3 cm , with r = 0.988 (n = 1); a = 1845 cm1, b = 482.3 cm1, with r = 0.990 (n = 2).
H.F.M.C. Martiniano et al. / Chemical Physics Letters 442 (2007) 451–459
As expected from the above discussion on structure, substituent effects on the vibrational frequencies are quite visible. For NT complexes and n = 1, 2, frequencies increase for X = OH, NH2, NMe2 and decrease for CN, CF3, NO2, relative to the phenol–water cation (X = H). Deviations from harmonicity increase from n = 1 to n = 2. These deviations can be significant (719 cm1 for X = H and n = 2). Therefore, our results confirm the conclusion by Jansen and Gerhards [14] that an harmonic analysis is not adequate for describing the proton transfer coordinate of cationic phenol–water clusters. A correlation between Hammett constants rp and hydrogen bonding interaction energies in the phenoxyl radical cation–water molecule complex was discussed by Feng et al. [15]. Our results in Table 2 show that hydrogen bond-
Table 3 Binding energies (kcal mol1) at 0 K for [p-XC6H4OH–(H2O)n]+ clusters (n = 1–3) n=1
NMe2 NH2 OH H CF3 CN NO2
n=2
n=3
Eb
DEb
Eb
DEb
Eb
DEb
12.37 13.94 15.83 17.58; 19.6a; 18.54 ± 0.11b 18.72 18.59 19.56
5.21 3.64 1.74 0.00
19.04 21.38 24.21 26.84
7.80 5.47 2.63 0.00
21.25 24.34 28.25 27.10
5.85 2.76 1.15 0.00
1.14 1.02 1.98
28.74 28.58 29.98
1.90 1.74 3.14
22.07 20.65 18.86
5.03 6.45 8.25
Results are from BHandHLYP/aug-cc-pVTZ//BHandHLYP/cc-pVDZ calculations and include zero-point vibrational energies. DEb for each complex is the difference between the binding energy of that complex and the binding energy of the complex with X = H. Values in italic are for proton transferred structures. a MP2/DZP value by Re and Osamura [10]. b Experimental value by Courty et al. [35].
457
ing between the phenolic moiety and water in NT complexes will induce a significant red-shift of the O–H frequency associated with the proton transfer coordinate. Therefore, frequencies and Hammett parameters should correlate. This is confirmed in Fig. 5, where the dashed lines represent the least square plots of mO–H (anharmonic frequencies) vs. the Hammett parameters rþ p (Table 2). We have found that the correlations improve when rp is replaced by rþ p. Binding energies (Eb) for ionized phenol–water clusters are reported in Table 3, where DEb for each complex is the difference between the binding energy of that complex and the binding energy of the complex with X = H. For the phenol–water cationic complex, an experimental value for the binding energy (18.54 ± 0.11 kcal mol1) was reported [35]. Our prediction (17.58 kcal mol1) is in good agreement with experiment. It is also in reasonable agreement with a MP2 prediction by Re and Osamura (19.6 kcal mol1) [10]. For NT clusters, electron donating (withdrawing) substituents decrease (increase) the binding energy relative to the complex with X = H. This effect can be significant and for X = NMe2 and n = 2, DEb = 7.80 kcal mol1. For T complexes, electron withdrawing substituents can also induce a significant decrease of the binding energy relative to the non-substituted complex (DEb = 8.25 kcal mol1 for X = NO2 and n = 3). 3.3. Charge distribution We will focus the discussion of the charge distribution in phenol–water complexes on two fragments: p-XC6H4OH and (H2O)n (n = 1–3) for the NT complexes, and pXC6H4O and (H3O)+(H2O)2 for the T complexes. Natural atomic orbital (NAO) charges for these fragments are reported in Table 4. Here, DqX for each fragment was
Table 4 NAO charges (a.u.) for p-XC6H4OH, p-XC6H4O, (H2O)n, and H3O+–(H2O)n1 fragments in the optimized structures of [p-XC6H4OH–(H2O) n]+ clusters (n = 1–3) X
N(CH3)2
NH2
OH
H
CN
CF3
NO2
n=1 p-XC6H4OH DqX (H2O)n
0.946 0.021 0.054
0.942 0.017 0.058
0.933 0.008 0.067
0.925 0.0 0.075
0.920 0.005 0.080
0.919 0.006 0.081
0.915 0.010 0.085
n=2 p-XC6H4OH DqX (H2O)n
0.925 0.036 0.075
0.919 0.030 0.081
0.905 0.016 0.095
0.889 0.0 0.111
0.879 0.010 0.121
0.878 0.011 0.122
0.866 0.023 0.134
0.898 0.762 0.102
0.888 0.752 0.112
0.860 0.724 0.140 0.136 0.0 0.864
0.114 0.022 0.886
0.117 0.019 0.883
0.105 0.031 0.895
n=3 p-XC6H4OH DqX (H2O)n p-XC6H4O DqX H3O+–(H2O)n1
Results are from BHandHLYP/aug-cc-pVDZ//BHandHLYP/cc-pVDZ calculations. DqX for each fragment is the difference between the charge in that fragment and the charge in the fragment with X = H. Values in italic are for proton transferred complexes.
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defined as the difference between the charge in that fragment and the charge in the fragment with X = H. Our results show that when X = H and n = 1 the charge of the cationic complex (+1) is essentially localized in the phenolic moiety (0.925) and only a small fraction (0.075) is in the water fragment. For n = 2, the total charges of the phenolic and water fragments are 0.889 and 0.111, respectively, indicating that electron charge migration from water to the phenolic moiety is favored by increasing the number of water molecules. This trend (increase of the electron charge transfer from water with increasing n) is also observed for all the substituted NT complexes. For a given n, the charge reorganization induced by substitution in NT complexes follows a simple pattern. In comparison with X = H, electron-donating substituents (X = NMe2, NH2, OH) hinder the electron charge migration from water to the phenolic moiety. For X = NH2 and n = 1, the charge of the phenolic moiety is 0.942, leading to a relative charge (DqX) of 0.017. A similar trend can be observed for n = 2. Electron charge transfer from water decreases with the increasing donating character of the substituent (more negative rþ p values in Table 2). On the other hand, charge transfer from water to the phenolic fragment is enhanced by electron-withdrawing substituents (X = CN, CF3, NO2). For example, for X = NO2 and n = 2, the total charge of the phenolic fragment is 0.866 or DqX = 0.023. Electron charge transfer from water increases with the increasing withdrawing character of the substituent (more positive rþ p values in Table 2). For T complexes (X = H, CN, CF3, NO2; n = 3), a very small charge is observed in the phenolic moiety, suggesting that this fragment is similar to the phenoxyl radical. The positive charge of the phenolic moiety decreases with increasing withdrawing character of the substituent, e.g. from 0.136 (X = H) to 0.105 (X = NO2). This indicates that electron charge transfer from the phenoxyl radical to the hydronium–water cluster decreases with the increasing withdrawing character of the substituent. 4. Conclusions Density functional theory (DFT) and transfer-matrix path-integral calculations were made to investigate substituent effects on proton transfer assisted by water molecules in [p-XC6H4OH–(H2O)n]+ (X = NMe2, NH2, OH, H, CN, CF3, NO2) clusters (n = 1–3). DFT calculations were based on the BHandHLYP functional, which has been previously applied to the study of ionized water clusters [27,28]. Proton transfer from the phenolic moiety to water is favored by electron withdrawing substituents (X = CN, CF3, NO2). However, a minimum of three water molecules is required to transfer a proton from the phenolic moiety to water. Structural and electronic aspects related to substituent effects and hydrogen bond interactions were analysed. The results indicate that para-substituents have a less important role in promoting proton transfer than the interactions with
the water molecules. The calculated mO–H anharmonic frequencies are in good agreement with theoretical and experimental data for some of the complexes. Moreover, a correlation between these frequencies and rþ p Hammett parameters was established for those cationic phenol–water complexes where proton transfer did not occur. Ground state probability densities and vibrationally averaged distances were also calculated and illustrate the quantum nature of the proton transfer process in the clusters. Acknowledgments H.F.M.C.M. gratefully acknowledges FCT (Ph.D. Grant No. SFRH/BD/27577/2006). This work was partially supported by Fundac¸a˜o para a Cieˆncia e a Tecnologia (FCT), Portugal (Grant No. POCI/MAT/55977/2004). References [1] T.M. Krygowski, B.M. Stepien, Chem. Rev. 105 (2005) 3482. [2] R.M. Borges dos Santos, J.A. Martinho Simo˜es, J. Phys. Chem. Ref. Data 27 (1998) 707. [3] K.D. Wiberg, J. Org. Chem. 68 (2003) 875. [4] A.P. Vafiadis, E.G. Bakalbassis, Chem. Phys. 316 (2005) 195. [5] E. Klein, V. Lukes, J. Phys. Chem. A 110 (2006) 12312. [6] S. Tanabe, T. Ebata, M. Fujii, N. Mikami, Chem. Phys. Lett. 215 (1993) 347. [7] S. Sato, N. Mikami, J. Phys. Chem. 100 (1996) 4765. [8] T. Sawamura, A. Fujii, S. Sato, T. Ebata, N. Mikami, J. Phys. Chem. 100 (1996) 8131. [9] M. Sodupe, A. Oliva, J. Bertran, J. Phys. Chem. A 101 (1997) 9142. [10] S. Re, Y. Osamura, J. Phys. Chem. A 102 (1998) 3798. [11] N. Agmon, J. Phys. Chem. A 109 (2005) 13. [12] P. Hobza, R. Burcl, V. Spirko, O. Dopfer, K. Mullerdetlefs, E.W. Schlag, J. Chem. Phys. 101 (1994) 990. [13] K. Kleinermanns, Ch. Janzen, D. Spangenberg, M. Gerhards, J. Phys. Chem. A 103 (1999) 5232. [14] A. Jansen, M. Gerhards, J. Chem. Phys. 115 (2001) 5445. [15] Y. Feng, L. Liu, Y. Fang, Q.-X. Guo, J. Phys. Chem. A 106 (2002) 11518. [16] N. Yamamoto, N. Shida, E. Miyoshi, Chem. Phys. Lett. 371 (2003) 724. [17] M.M. Bizarro, B.J. Costa Cabral, R.M. Borges dos Santos, J.A. Martinho Simo˜es, Pure Appl. Chem. 71 (1999) 1249. [18] M. Guerra, R. Amorati, G.P. Pedulli, J. Org. Chem. 69 (2004) 5460. [19] Y. Fu, R. Liu, L. Liu, Q.-X. Guo, J. Phys. Org. Chem. 17 (2004) 282. [20] D.-S. Ahn, S.-W. Park, S. Lee, B. Kim, J. Phys. Chem. A 107 (2003) 131. [21] H.-T. Kim, R.J. Green, J. Qian, S.L. Anderson, J. Chem. Phys. 112 (2000) 5717. [22] M. Yi, S. Scheiner, Chem. Phys. Lett. 262 (1996) 567. [23] J.P.P. Ramalho, F.M.S. Fernandes, Z. Naturforsch A 45 (1990) 1193. [24] J.P.P. Ramalho, B.J. Costa Cabral, F.M.S. Fernandes, Chem. Phys. Lett. 184 (1991) 53. [25] M.J. Frisch et al., GAUSSIAN-03, Rev. C.02, Gaussian Inc., Pittsburgh, PA, 2003. [26] J.A. Anderson, G.S. Tschumper, J. Phys. Chem. A 110 (2006) 7268. [27] M. Sodupe, J. Bertran, L. Rodrigues-Santiago, E.J. Baerends, J. Phys. Chem. A 103 (1999) 166. [28] P. Cabral do Couto, B.J. Costa Cabral, J. Chem. Phys. 126 (2007) 014509. [29] D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358. [30] A.E. Reed, F. Weinhold, J. Chem. Phys. 78 (1983) 4066.
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