soft hydrogen bond interaction

Journal of Molecular Structure 615 (2002) 61–72 www.elsevier.com/locate/molstruc

On a hard/soft hydrogen bond interaction P. Huyskensa, L. Sobczykb,*, I. Majerzb a

b

Department of Chemistry, University of Leuven, B-3001, Heverlee, Belgium Faculty of Chemistry, University of Wrocław, F Joliot-Curie 14, 50-383, Wrocław, PL, Poland Received 6 September 2001; accepted 24 September 2001

Abstract Various physical properties of AH· · ·B hydrogen bonded complexes are analyzed from the point of view of possible proton transfer processes. As a general parameter of the proton-donor – acceptor ability of interacting components the normalized DpKN ¼ DpKa 2 DpKa ðcritÞ parameter was assumed, where DpKa ¼ pKa ðBþ HÞ 2 pKa ðAHÞ: DpKa(crit) refers to the range where the proton transfer degree reaches 50%. Two kinds of correlations between the given physical property and DpKN can be distinguished: of sigma and delta type. To the first one belong dipole moments, 15N NMR chemical shifts, NQR frequencies and the bond lengths in the solid state, while to the second one infra-red protonic band positions, their intensities and 1H NMR chemical shift. A general equation expressing the relationship between any physical property and DpKN was derived in which the central factor expð2:303jDpKN Þ describes the behavior in the critical region. It has been shown that the j parameter can be used for the expression of the hardness. The value of this parameter is the higher the harder is interaction its maximum being equal 1. This measure very well correlates with the polarizability in transition state of hydrogen bonds. The detailed analysis of data in literature collected so far shows a good agreement of estimated j values by using different physical properties. The influence of various factors on the j value is discussed. Most important are chemical properties of interacting components but it was clearly shown the importance of the environment. With increasing permittivity a marked augmentation of the j parameter is generally observed. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen bond; Proton transfer; Softness; Hardness

1. Introduction The concept of hard and soft acids and bases was well established in the scope of Lewis formulation [1, 2] and found reflection in rich literature (see selected critical reviews [3 – 14]). The softness of the electron donor – acceptor interaction was put together usually * Corresponding author. Tel.: þ48-71-375-7207; fax: þ 48-71328-2348. E-mail address: [email protected] (L. Sobczyk).

with the polarizability of directly interacting atoms. The relation to the Brønsted acids was only that protons were classified as a hardest acid as due to a lowest polarizability. The general outline of hardness/softness found, however, a common acceptance for any chemical system when it was formulated in density functional theory [15]. The acid –base systems in Brønsted – Lowry formulation can also be analyzed in terms of such an approach. In papers [16 – 18] it was clearly shown that proton-transfer (PT) processes can be well described by using the hardness (h ) softness (s )

0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 2 ) 0 0 2 0 7 - 7

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Fig. 1. Proton transfer degree, xPT, plotted versus DpKa for carboxylic acid–pyridine complexes. Experimental points according to Ref. [21]; solid curve calculated according to Eq. (2).

written as 1 1 h¼ ¼ s 2

›2 E ›N 2

!

  1 ›m ¼ 2 ›N VðrÞ VðrÞ

ð1Þ

where E is total energy, N is number of electrons, m is chemical potential and VðrÞ is the external potential. In the present review, we will show that there is in the literature a rich experimental material related to the acid –base interaction in the Brønsted –Lowry formulation which can be analyzed in terms of hardness/softness. From numerous literature data it follows that both the properties of hydrogen bonds and proton transfer equilibria substantially depend on atoms between which the proton is located and the environment. It seems that the hardness of interaction should depend also on the potential for the proton movement and the higher is the barrier to proton transfer, and more independent are the non-protontransfer (HB) and proton-transfer states, the harder is the interaction. Immediately one can postulate that the softness of interaction AH · · · B , A2 · · · HBþ HB

PT

should be characterized by a high polarizability of hydrogen bonds in agreement with the Zundel concept [19] for systems with the double minimum potential and low barrier (strong coupling of the HB and PT states). In such a case we are dealing with a splitting of vibrational levels due to a tunneling effect. The unusual polarizability is well reflected in the Rayleigh wings of elastic

light scattering [20] and broad (almost continuous) IR absorption. In the present article we will try to discuss first of all experimental manifestations of hardness and softness: dipole moments of acid –base systems in solution, nuclear quadrupole resonance spectra in the solid state, multinuclear magnetic resonance spectra, infra-red spectra of various systems and some scarce data on the geometrical correlations for hydrogen bonded systems. A long time ago Barrow studied by using IR spectra the proton transfer equilibria in complexes of carboxylic acids with pyridine in CHCl3 [21]. The results of the Barrow studies expressed as a plot of proton transfer degree against DpKa are presented in Fig. 1, and compared with calculated one by using simple thermodynamic approach [22]. In this approach the free enthalpy change related to the proton-transfer DGPT consists of three components: DG of the detachment of the proton from AH, its attachment to B and the effect connected with the interaction with environment. Because the two first components are related to pKa of the acid AH and the base B, logKPT ¼ DpKa þ const:

ð2Þ

In the critical point which is defined as corresponding to log KPT ¼ O the slope of the experimental curve is always smaller than expected from Eq. (1). Very good agreement is reached when one introduces the coefficient j , 1, so that logKPT ¼ jDpKa þ const:

ð3Þ

This parameters is of main importance in quantitative description of various physical properties of hydrogen bonded systems and can be associated with a softness of interaction. After introducing a normalized parameter DpKN ¼ DpKa 2 DpKa ðcritÞ where DpK a (crit) refers to KPT ¼ 1; logKPT ¼ jDpKN

ð4Þ

Defining DG1 PT (water) as a change of free enthalpy for the proton transfer at an infinite

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Fig. 2. Plot of polarity of hydrogen bond, Dm~ versus DpKa for complexes of phenol with triethylamine in benzene [23].

distance in water, we get

j¼

d logKPT dDG0PT ¼ dDpKa dDG1 PTðwaterÞ

ð5Þ

2. The charge distribution in hydrogen bonded systems The first systematic measurements of dipole moments were performed for complexes composed of triethylamine with phenols in benzene [23]. The plot of so called polarity of hydrogen bonding, i.e. the increase of the dipole moment along the hydrogen bond evoked by the charge deplacement versus DpKa is shown in Fig. 2. The dependence can be described formally in terms of the proton transfer equilibrium in the transition range of DpKa. For very small DpKa

Fig. 3. Dm~ for O –H· · ·N hydrogen bonds in various phenol–amine complexes. Solid curve according to Eq. (6).

63

values the polarity Dm~ does not exceed in most cases, reported so far [24], 0.5D that can be entirely ascribed to the inductive effect. For high values of DpKa we notice the full proton transfer states and Dm~ reaches values characteristic of ion pairs. The transition (intermediate) states correspond to the proton transfer equilibria which can be related to the DpKN value according to Eq. (4). This simplified approach needs, in the light of the results gathered over many years [25,26], a considerable revision. First of all the dipole moments of HB and PT states depend on DpKa, particularly when approaching a so called critical (inversion) range where the proton transfer equilibrium appears. Moreover the DpKa(crit) depends on the chemical nature of interacting components and environment. Assuming that the polarity of hydrogen bonding Dm in the precritical (HB) and postcritical (PT) ranges linearly depend on DpKN, the general expression of Dm versus DpKN gets a form [27] Dm~ ¼ DmHB þ bHB DpKN þ ðDmPT þ bPT DpKN Þexpð2:303jDpKN Þ 1 þ expð2:303jDpKN Þ

ð6Þ the fraction of the proton transfer state, xPT, being equal to xPT ¼

expð2:303jDpKN Þ 1 þ expð2:303jDpKN Þ

ð7Þ

The confrontation of such an approach with experimental data is shown in Fig. 3. The plot describing the experimental results corresponds to following values of parameters: DmHB ¼ 1:8D; bHB ¼ 0:1D; DmPT ¼ 7:8D; bPT ¼ 0:3D and j ¼ 0:65: Notice that for various systems different values of DpKa(crit) had to be assumed: for phenols – TEA complexes in benzene 5.2; for phenols – pyridines and imidazoles complexes in toluene 2.5; for pentabromophenol – amines complexes in CCl4 4.8, in CHCl3 3.0 and C2H4Cl2 1.5. To this group of complexes cannot be included those formed by derivatives of acetic acid. This problem will be discussed later. There is also gathered rich experimental material related to dipole moments of OH· · ·O hydrogen bonded complexes. This relates mainly complexes of phenols with oxygen bases such like dibutylether,

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Fig. 4. Dm~ for O –H· · ·O hydrogen bonds in various phenol– oxygen bases complexes. Solid curve according to Eq. (6).

Fig. 6. Enthalpy of O–H· · ·O hydrogen bonds formation, DH bond, plotted versus DpKN [30].

tetrahydrofurane, acetamide derivatives, amine oxides, phosphine oxides, sulphoxides, arsene oxides, tetramethylurea [28,29]. In Fig. 4 we compared experimental data of polarity of O – H· · ·O hydrogen bonds with theoretical curve obtained by assuming following values of parameters in Eq. (6): DmHB ¼ 1:5D; bHB ¼ 0:07D; DmPT ¼ 8:0D; bPT ¼ 0:7D; j ¼ 0:26; DpKa ðcritÞ ¼ 22:5: One can see a substantial difference between OH· · ·N and O – H· · ·O hydrogen bonds expressed in the values of the j parameter and the position of the critical point on the DpKa axis. Of particular interest is much smaller value of the j

parameter for the oxygen bases that can be attributed to a considerably softer interaction.

3. Enthalpy of H-bond formation In a similar way the results of measurements of molar formation enthalpies of hydrogen bonded complexes can be related to the DpKN values [30]. The plot of DH versus DpKN for O –H· · ·N complexes is shown in Fig. 5. It is fitted by the following equation DH ¼ DHHB þ bHB DpKN þ ðDHPT þ bPT DpKN Þexpð2:303jDpKN Þ 1 þ expð2:303jDpKN Þ

ð8Þ

Fig. 5. Enthalpy of O–H· · ·N hydrogen bonds formation, DH bond, plotted versus DpKN [30].

with following values of parameters: DHHB ¼ 240 kJmol21 ; bHB ¼ 1:7 kJ mol21 ;: DHPT ¼ 21 260 kJ mol ; bPT ¼ 8 kJ mol21 : j is exactly the same as in case of the hydrogen bond polarity equation, i.e. equal to 0.65. DH behaves critically in the same range of DpKa as the dipole moment. Analogous treatment of the O–H· · ·O hydrogen bonded complexes leads to results shown in Fig. 6. The plot of DH versus DpKN fits Eq. (8) with following values of parameters: DHHB ¼ 260 kJ mol21 ; bHB ¼ 3 kJ mol21 ;:DHPT ¼ 280 kJ mol21 ; bPT ¼ 6 kJ mol21 with the j parameter exactly the same as that obtained from the dipole moment correlation, i.e.

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65

Fig. 7. Comparison of plots Dm~ versus DH for three types of molecular complexes: (A) O– H· · ·O hydrogen bonded, (B) O–H· · ·N hydrogen bonded and (C) EDA complexes formed by I2 [32].

¼ 0.26. Again a substantial difference in behaviour of O–H· · ·N and O–H· · ·O bridges is visible. It would be interesting in this place the comparison of the behaviour of electron-donor – acceptor (EDA) interaction with that of hydrogen bonded complexes. Some similarities between them were postulated [31]. Let us try to express the dependence of Dm~ on formation enthalpy for three types of complexes: hydrogen bonded OH· · ·N and OH· · ·O and EDA complexes formed by I2 with various electron donors. The results of such comparison are shown in Fig. 7. The general equation, describing the dependence of Dm~ on DH gets a form [32]. Dm ¼

ð2DHÞ þ ðB þ Cð2DHÞexp½A1 þ B1 ð2DHÞ 1 þ exp½A1 þ B1 ð2DHÞ ð9Þ

The parameters of the equation for three groups of complexes are compared in Table 1. From these data clearly follows that the behaviour of EDA complexes differs substantially from that of H-bonded complexes. The comparison shows that in case of Table 1 The values of parameters in Eq. (7), for O –H· · ·O and O –H· · ·N hydrogen bonded complexes and I2 charge transfer EDA adducts, DH expressed in kJ mol21

A B C A1 B1

O –H· · ·O

O– H· · ·N

I2· · ·N

0.028 3.20 0.075 26.5 0.085

0.0074 4.64 0.045 27.70 0.172

0.097 0.00 0.097 0.00 0.00

hydrogen bonded complexes a critical region appears where a stepwise proton transfer takes place. The slope of the plot Dm~ versus DH in this range characterizes the hardness of interaction. In the case of EDA complexes a linear dependence is observed without any transition step.

4. NQR of hydrogen bonded complexes There are in literature numerous data related to hydrogen bonded complexes studied by using the NQR technique. This refers particularly to complexes formed by chloroderivatives of acetic acid, benzoic acids and phenol [33 –37]. The creation of a dipole moment along the O – H· · ·N hydrogen bonding generates an electric field strength in the place of the quadrupole nucleus   1 Dm~ 3ðDmrÞ~r E¼ 2 ð10Þ 4p10 1 r 3 r5 where 10 is the electric permittivity of vacuum, 1permittivity of a medium and ~r the vector linking the quadrupole nucleus with the centre of the dipole Dm~: Thus, the quadrupole nuclei can be treated as a probe of the electric field gradient (EFG). If the EFG tensor possesses the symmetry close to axial (h # 0.2) and the spin of the quadrupole nucleus equals to 3/2, the shift of the resonance frequency evoked by the dipole Dm~; Dn, can be expressed by Dn ¼

eQ R E 2h zzz z

ð11Þ

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P. Huyskens et al. / Journal of Molecular Structure 615 (2002) 61–72 J

Fig. 8. Average NQR 35Cl frequency plotted versus DpKa for complexes of pentachlorophenol with amines [37].

where Rzzz ¼ dnzz =dEz is a parameter dependent on the character of the chemical bond in which the Cl atom is participating [38], e-the elementary charge, Qthe quadrupole moment of the 35Cl nucleus, h-the Planck constant and Ez -the Z component (in the principal axes system of the EFG tensor) of the electric field strength vector created by the dipole moment Dm~: Because the information about dn=dEz can be obtained directly from the measurements of NQR frequencies in the external electric field it is convenient to express Eq. (11) in the form Dn ¼

dn E dEz z

ð12Þ

the creation of a dipole moment O – H · · · N leads always to a decrease of the 35Cl resonance frequency. Taking as an example the complexes of pentachlorophenol with N-bases, the correlation between the average 35Cl resonance frequency, n; and DpKa parameter gets a form shown in Fig. 8. As can be seen the experimental points are spread between the limiting values of n for phenol itself and TBA salt which corresponds to almost free phenolate anion. The plot in Fig. 8 resembles that obtained when correlated Dm~; obtained in solution, with DpKa. Formally we can treat the change of n as a measure of proton transfer degree. Therefore the formalism expressed in Eq. (7) can be applied in description of the correlation between n¯NQR and DpKN. However, we cannot forget some differences in the behavior of Hbonded complexes in solutions and solid state. Firstly, the scattering of experimental points in the solid state is much more pronounced than in solution. This is due to the packing effects. The electric field gradient at a given nucleus arises also from the orientation of dipole moments of neighboring molecules which is different for various complexes. Secondly the proton transfer equilibria are, most probably, not observed in the solid and usually there is a continuous shift of the proton with increasing DpKN. Nevertheless if the observed average NQR frequency reflects the change of H-bond polarity we can formally bring it into relationship with proton transfer degree xPT according to a simple equation

The analysis of all data reported so far [37] shows that

nNQR ¼ xPT nPT þ ð1 2 xPT ÞnHB

ð13Þ

Fig. 9. Proton transfer degree, xPT, deduced from NQR 35Cl data for amine complexes with (1) trichloroacetic acid, (2) dichloroacetic acid, (3) pentachlorophenol.

where nHB and nPT are extrapolated values of NQR frequencies for HB and PT states of a given type of complexes. Then xPT can be correlated with DpKN according to Eq. (7). The best fits of correlation xPT versus DpKN for three different types of O –H· · ·N complexes are shown in Fig. 9. For pentachlorophenol complexes DpKa ðcritÞ ¼ 1:2 and j ¼ 0:74; while for dichloroacetic acid and trichloroacetic complexes the corresponding numbers are 1.6; 0.42 and 2 0.4; 0.12. These data clearly show how pronounced is the influence of the chemical nature of interacting compounds on the DpKa(crit) and j values. The comparison of available data for solution and solid state shows that the DpKa(crit) values in solid state are markedly shifted to the left as compared with

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solutions. This can be predicted because the solid state stabilizes more polar forms. Generally, an increase of polarity of the environment favors a polar state. This problem will be discussed in Section 8.

5. NMR of hydrogen bonded systems

Fig. 10. Dd15N plotted versus DpKa: solid line-complexes of trifluoroacetic acid with pyridines in CH2Cl2 [41]; dashed linecomplexes of pyridine with carboxylic acids in freons at 130 K [42].

Nuclear magnetic resonance (NMR) method belongs to most sensitive techniques of determination of the hydrogen bond strength and proton transfer degree [39]. In the case of acid – base complexes with O –H· · ·N hydrogen bonds the interaction strength can be monitored by means of 15N or 1H chemical shifts. The plots of d15N and d1H versus DpKa are however different. The plot of d15N versus DpKa possesses, similarly to Dm or nNQR, a sigmoidal character. In the case of d1H one observes a plot of the delta type with a maximum for the critical range. Because, as known [40], the chemical shift of nitrogen is particularly sensitive in cases of aromatic amines, the data which we would like to analyze come from the studies of pyridines complexes [41,42]. In the first case the objects of studies were complexes of trifluoroacetic acid with various pyridine derivatives in CH2Cl2 at room temperature, while in the second case were complexes of 15N labeled pyridine with various acids in liquefied freons. In Fig. 10 there are presented the plots of Dd15N for both systems with curves of the best fit according to the function: Q¼

Fig. 11. d1H plotted versus DpKa for pyridine–carboxylic acids – liquid freons systems (A), correlation ace. Eq. (15) (B) [41].

QHB þ QPT expð2:303jDpKN Þ 1 þ expð2:303jDpKN Þ

ð14Þ

where Q is the value of Dd15N at a given DpKN and QHB and QPT correspond to extrapolated values for HB and PT states. The fitting leads to following values of DpKa(crit) and j: for CF3COOH complexes with various pyridines they are equal to 2.6 and 0.19; while for pyridine complexes with various acids 1.8 and 0.56. Notice that in CH2Cl2 at room temperature the j value is very low while in much more active solvent, liquefied freons, is markedly higher. On the other hand the DpKa(crit) in this active medium shifts to lower values. As shown [43] the electric permittivity of liquid freons reaches 20 units. Independently the activity of such solvent is due to a specific interaction of C – H bonds with oxygen atoms of carboxylic acids that stabilizes more polar states.

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Fig. 12. Evolution of broad protonic absorption in infra-red spectra for complexes of pentachlorophenol [51].

The analysis of the correlation plots exhibiting an extremum in the critical region, as can be seen for d1H and position as well intensity of the protonic bands in infra-red spectra, needs some modified approach. Thus, for the description of the dependence of a given physical property Q, showing an extremum, on DpKa it is necessary to employ the following simple procedure. The reference value of a given physical property Q is its extremum (critical)-maximum or minimum. In case of d1H for the systems composed of carboxylic acids and pyridine in liquid freons the maximum value equals to 21.5 ppm. Now we can transform the delta type correlation to the sigmoidal one by assuming that Q(crit) ¼ 0 while DQHB , 0 and DQPT . 0 as has been done in Fig. 11(B). Eq. (15) expresses the correlation between DQ and DpKN and enables the estimation of the j parameter DQ ¼

DQHB þ DQPT expð2:303jDpKN Þ 1 þ expð2:303jDpKN Þ

ð15Þ

The best fit of the results obtained with respect to d1H for pyridine– carboxylic acids complexes in liquid freons [41] according to Eq. (15) is shown in Fig. 11(B). The parameters for best fitting are DpKa ðcritÞ ¼ 1:8; QðmaxÞ ¼ 21:5 ppm; DQHB ¼ 28:3 ppm; DQPT ¼ 4:4 ppm: j equals to 0.46, i.e. it is a little lower as

Fig. 13. Center of gravity of broad absorption, ncg, plotted versus DpKa for benzoic acids– amine complexes in the solid state (A) compared with calculated curve acc to Eq. (15), (B) [52].

compared with that deduced from the correlation between Dd15N and DpKa. There are in literature several other data related to the 1H chemical shifts [44 –46] which, however could not be used in correlation versus DpKa tending towards determination of the j parameter. One should also mention a possibility to correlate 13C chemical shifts with DpKa [47].

6. Infra-red spectra Most information about the formation of acid – base complexes comes from the studies of infra-red spectra. The behavior of the stretching vibration band associated with n(AH) in the A –H· · ·B is commonly

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Table 2 DpKa(crit) and j parameters deduced from IR studies for various systems System

DpKa(crit)

j

Reference

Benzoic acids–amine complexes; ncg-solid state HCl2COOH–amine complexes; ncg-in CH2Cl2 HCl2COOH–amine N-oxides complexes; ncg-in CH2Cl2 Phosphinic acid N-base complexes; integrated absorbance in CHCl3 þ CH3CN Phosphinic acid N-oxides complexes; integrated absorbance in CHCl3 þ CH3CN

3.2 4.2 1.8 5.5 2.0

0.35 0.43 0.30 0.43 0.26

[52] [54–58] [54–58] [59] [60]

accepted criterion of hydrogen bond interaction. One should emphasize a particularly wide range of changes in n(AH) band. This relates not only to the position (first moment) but also to the width (second moment) as well as integrated intensity and in many cases to the band substructure [48 – 50]. The evolution of broad bands, ascribed to protonic vibrations, in the infra-red region, is exemplified in Fig. 12 by the pentachlorophenol complexes in the solid phase [51]. The picture shown in Fig. 12 was obtained after tentative separation of broad protonic absorption from narrow bands of internal vibrations. This picture shows that on increasing the DpKa value the broad absorption shifts towards lower frequencies with increasing width and intensity reaching at some critical region extreme values. Starting from the critical state the broad absorption comes back continuously to a primary shape which now corresponds to complete proton transfer with the n(NHþ· · ·O2) vibrator. The quantitative analysis of the IR behavior we would like to perform taking as an example the complexes of benzoic acids with amines. In this case numerous data are available [52]. In the literature there is collected plentiful number of data related to various systems [53–57] but only a few of them can be adapted for correlations. The plot of the centre of gravity of broad protonic absorption versus DpKa for benzoic acids complexes is shown in Fig. 13. Thus this is a correlation of delta type with a minimum instead of maximum as has been expressed in correlation between d1H and DpKa. Let us notice first of all a huge scattering of experimental points, similarly to the behavior of NQR data. The reasons in both cases are similar, i.e. the packing effects and some differences in chemical properties of interacting components. Let us notice also some difficulties in estimation of the minimum value of ncg in the critical point.

This is due to difficulties in quantitative determination of integrated intensities in the far IR region. Thus the values appearing at about 1000 cm21 can be burdened by high errors. The analysis of data presented in Fig. 13 leads after best fitting, to parameters of Eq. (15) listed in Table 2. In this table there are also included results of best fitting for complexes of dichloroactic acid with pyridines and pyridine N-oxides [54 –58]. Very important in IR studies was finding that in critical region the maximum of integrated absorbance takes place that was shown for the first time by Zundel. Simultaneously the maximum absorbance was associated with maximum polarizability of hydrogen bonds with a low barrier for the proton motion [19]. Let us remind that a maximum polarizability corresponds to a minimum of hardness and maximum of softness. Taking into account the data of integrated intensity from [59,60] we performed the analysis based on Eq. (15) for OH· · ·N and OH· · ·O complexes getting the results included in Table 2. As shown the DpKa(crit) for OH· · ·O is always shifted to lower values as compared with O – H· · ·N bridges. On the other hand the O – H· · ·O complexes are always characterized by lower value of j-parameter that can be associated with higher softness. Similar results were obtained for complexes of phenols with octylamine by Zundel who studied in this case the absorbance in the region of intense IR continuum [61]. They are shown in Fig. 14 and deserve a special comment because direct data related to the proton transfer degree are available here. The value of j parameter deduced from the correlation shown in Fig. 14(C) appeared to be close to that derived directly from the plot of %PT versus DpKa (Fig. 14(A)). The corresponding numbers are 0.56 and 0.58. This means that the change of polarizability expressed by the intensity of the IR

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Fig. 14. Phenols–octylamine systems. Percentage of the proton transfer (A), absorbance in a continuum (B) and the fitting curve according to Eq. (15) (C) plotted versus DpKa [61].

continuum quite well correlates with the proton transfer degree. The maximum polarizability is close to the critical point. These findings are in excellent agreement with the results of direct evaluation of the H-bond vibrational polarizability based on the studies of dielectric dispersion in the IR region [62].

7. Geometrical correlations Systematic studies of geometry of hydrogen bonded complexes composed of chemically defined components in relation to DpKa were performed so far only for amine phenolates [63]. The X-ray structures of 16 complexes of phenols with amines were determined in the critical region where the proton transfer is observed. In Fig. 15 there is shown the correlation between the C – O bond length and DpKa.

Fig. 15. C–O bond length, dCO, plotted versus DpKa for phenols– amine complexes [63].

This bond length is a good measure of the ionization of OH group and, therefore, the proton transfer, too.  For free phenols the C – O bond length dCO ¼ 1:33 A; while for isolated phenolate anion (in the adduct with  From the correproton sponge [64]) dCO ¼ 1:26 A: lation shown in Fig. 15, by a best fit, we get DpKa ðcritÞ ¼ 1:6 and j ¼ 0:76: Notice that from NQR measurement on pentachlorophenol complexes we obtained DpKa ðcritÞ ¼ 1:2 and j ¼ 0:74 so that very close values.

8. Factors affecting DpKa(crit) and j One can distinguish internal (chemical) and external parameters. The analysis of data gathered by using various techniques shows, without any doubts, that for complexes with oxygen bases both DpKa(crit) and j are lower as compared with nitrogen bases. There are also no doubts that in case of carboxylic acids, as proton donors, these parameters are lower as compared with phenolic proton donors. It seems also that the j value depends to a considerable extent whether we are dealing with aliphatic or aromatic acids and bases. It was very well seen when comparing the NQR results. But also the measurements of dipole moments seem to indicate univocally such a rule. Thus the complexes of aliphatic carboxylic acids with aliphatic amines are characterized in non-polar solvent by particularly low value of j [65]. A substantial influence on the behavior of acid – base complexes exerts the environment. As shown for the first time by Jadz˙yn and Małecki [66] the

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permittivity of the solvent exhibits substantial influence on the proton transfer equilibrium. This influence can be related to the Onsager reaction field effect expressed by the factor ð1 2 1Þ=ð21 þ 1Þ: On increasing the solvent activity the DpKa(crit) shifts towards lower values. But not only the DpKa(crit) value changes on increasing the solvent activity. As showed the studies of dipole moments of pentabromophenol complexes with amines in CCl4 (1 ¼ 2:24), CHCl3 ð1 ¼ 4:81Þ; CH2ClCH2Cl (10.36) the corresponding values of DpKa(crit) and j are equal to 4, 2.5, 1.5 and 0.65, 0.78, 0.96 [67]. In such an active solvent like 1.2-dichloroethane the critical value of DpKa is close to that found for the solid state. There are no doubts that in the solid state DpKa(crit) is shifted as a rule to lower values as compared with solutions. This is not valid, however, with respect to the j parameter. For instance if we would like to correlate the j parameter with polarizability which is reflected in the intensity of IR continuum, there are no differences for the behavior of solutions and solid states. The complexes from the critical region are characterized, as a rule, in the solid state by very intense broad absorption and j parameter markedly less than unity. The question arises in this place with respect to the extent of agreement of results obtained by using various techniques. From the data analyzed in this article, it follows that agreement is generally very good. Although various techniques observe different physical quantities their results can be resolved into the correlation with proton transfer degree and the slope of the plot of this quantity versus DpKa in the critical region. Thus, very good agreement is seen when comparing the behavior of dipole moments and enthalpies of interaction. Very good agreement is also seen in case of results obtained from NQR and infrared spectra in the solid state.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

[26]

[27] [28] [29] [30] [31]

Acknowledgments The studies were performed within a cooperation project between the Universities of Leuven and Wrocław. The financial support from the Polish Committee for Scientific Research (Grant KBN No 09A 03416) is acknowledged.

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