1. Introduction

2. Homoconjugated Hydrogen Bonds with Large Proton Polarizability

3. Heteroconjugated Hydrogen Bonds with Large Proton Polarizability

4. Proton Polarizability in Hydrogen-Bonded Chains due to
Collective Proton Motion

5. Theoretical Treatment of Such Chains with Large Proton
Polarizability due to Collective Proton Tunneling

6. Other Cation Bonds with Cation Polarizabilities

7. Cation Polarizability due to Tunneling of one Cation in
Multiminima Potentials

8. Electrochemistry: Hydrogen Bonds with Large Proton
Polarizability and the Molecular Understanding of Processes
in Acid and Base Solutions

9. Hydrogen Bonds with Large Proton Polarizability in Proteins
- Studies of Model Systems

10. Significance of Hydrogen Bonds with Large Proton Polarizability
in the Catalytic Mechanism of Serine and Aspartate Proteases

11. Importance of Hydrogen Bonds with Large Proton Polarizability
for the Catalytic Mechanism of Alcohol Dehydrogenases
and Maltodextrinphosphorylase

12. Importance of Hydrogen-Bonded Chains with Large Proton
Polarizability for the Proton Conduction in Biological Membranes

References

Subject Index

Hydrogen bonds with double minimum proton potential or with broad flat potential well show polarizabilities so-called proton polarizabilities which are about two orders of magnitude larger than the usual polarizabilities due to distortion of electron systems. Homoconjugated B⁺H...BB...H⁺B as well as heteroconjugated AH...B^-A...H⁺B bonds show this property. They cause continua in the infrared spectra and are indicated by those IR continua. A theoretical treatment of these polarizabilities is presented. Not only hydrogen bonds but also Li⁺ and Na⁺ bonds, i.e., for instance, N⁺Li...NN...Li⁺N bonds may show this property. They cause continua in the far infrared spectra. Polarizabilities due to tunneling of cations in multiminima potentials are studied with crown ethers.

Acid-water hydrogen bonds with proton polarizability are of large significance for the dissoziation process of acids. H₅O₂⁺ the most important hydrate structure of the excess proton is discussed. The interaction entropy term shifts the dissoziation equilibria to the left. is large due to the large order around the polar proton limiting structure A^-...H⁺B. H₅O₂⁺ contains a hydrogen bond with large proton polarizability. H₉O₄⁺ fluctuates between the
O atoms of H₅O₂⁺. The large proton conductivity is discussed. With P containing acids and arsenic acid the acid-acid hydrogen bonds show also large proton polarizability. With basic systems H₃O₂^- with easily polarizable hydrogen bond is of large significance.

Model systems for hydrogen bonds with large proton polarizability in biological systems are also studied by infrared spectroscopy. It is shown that in the active centers of serine and aspartate proteases as well as in alcohol dehydrogenases and in maltodextrinphosphorylase polarizable hydrogen bonds are present. Their importance for the catalytic mechanism is explained. Protons are conducted in biological membranes via hydrogen-bonded chains with large proton polarizability. The L₅₅₀ intermediate of bacteriorhodopsin as well as the F₀ submit of the ATP synthase are discussed.

Hydrogen bonds with double minima proton potential well or with broad flat potential show so-called proton polarizabilities. Particularly large proton polarizabilities are observed with hydrogen-bonded systems.¹ It is important that these proton polarizabilities are about two orders of magnitude larger than the usual polarizabilities arising by distortion of electron systems. These proton polarizabilities are indicated by intense continua in the infrared spectra. These proton polarizabilities of hydrogen bonds are important, for instance, for the dissoziation process of acids, for proton shifts in active centers of enzymes or for the proton conduction of biological membranes, respectively.

All B⁺H...BB..H⁺B or AH...A^--A...HA hydrogen bonds, respectively, i.e. bonds with which the donor and the acceptor is the same type of group, cause intense continua in the infrared spectra

These so-called homoconjugated hydrogen bonds are structurally symmetrical and thus, if they are considered in a completely symmetrical environment a symmetrical double minimum proton potential or a symmetrical broad flat potential is present within these hydrogen bonds

The presence of such hydrogen bonds is indicated by these continua in the infrared spectra.^2-6

Already 30 years ago we have shown that in aqueous solutions of strong acids the hydrogen bonds in H₅O₂⁺ groups cause these continua. The proton fluctuates with a frequency larger than 10¹³ sec^-1 within these bonds.^7,8

Now the question about the reason of these IR continua arises and which effects are indicated by them.

Already at the end of the sixties we performed the following analytical treatment⁷. If one considers such B⁺H...BB...H⁺B bonds in a completely symmetrical environment the potential of the proton within these hydrogen bonds is a symmetrical double minimum proton potential. We solved the Schrödinger equation for the proton motion in such a potential with an additional term - µ(x)F, whereby µ(x) is the dipole moment in hydrogen bond direction as a function of the position of the proton along the hydrogen bond axis and F is the electrical field strength. This term should simulate the local electrical fields of the environment. With these calculations we obtained the highly astonishing result that the polarizability due to shifts of the proton within such hydrogen bonds is about two orders of magnitude larger than polarizabilities caused by distortion of electron systems.

In a next step we performed ab initio SCF calculations of the H₅O₂⁺ group⁹ taking also into account the hydrogen bond vibration n _s. From these calculations we obtained the energy surface E(x,y) as well as the dipole moment surface µ(x,y). Herewith is x the proton coordinate and y the vibrational coordinate. With these surfaces we solved the Schrödinger equation for the proton motion using the energy surface E(x,y) and added a term -µ(x,y)F whereby µ(x,y) is the dipole moment surface and F the electrical field strength. Also these calculations have shown that such hydrogen bonds show so-called proton polarizabilities being two orders of magnitude larger than the usual polarizabilities due to distortion of electron systems.

From these calculations we obtained the infrared transitions as a function of the electrical field strength.⁹ These transitions are shown in Fig. 3. This Figure demonstrates that the transitions shift strongly as a function of the electrical field strength. Some transitions arise, some other ones vanish. In a solution a broad distribution of the strength of the local electrical fields at the hydrogen bonds with large proton polarizability is present and thus, an IR continuum arises.

Of course, there are also other interaction effects caused by the large proton polarizability, which are important for the observation of the IR continua, for instance, an interaction of the hydrogen bonds with the phonons and polaritons of the thermal bath.¹⁰

Not only homoconjugated hydrogen bonds but also AH...BA^-...H⁺B bonds - so-called heteroconjugated bonds - with double minimum proton potential cause such IR continua.^11,12 This fact is shown in Fig. 4. With pure perchloric acid, for instance, no IR continuum is observed. If, however, only one water molecule is present per perchloric acid molecule an IR continuum is found caused by the acid - water hydrogen bonds. The intense IR continuum demonstrates that the perchloric acid - water hydrogen bonds are hydrogen bonds with double minimum proton potential and show large proton polarizability.^13-15

In the meantime we studied hundreds of such heteroconjugated hydrogen bonds with double minimum proton potential showing large proton polarizability.¹⁵ Such hydrogen bonds are of very high significance for all proton transfer processes, especially in biology. The position of such proton transfer equilibria depends on the following parameters.

1. The pK_a of the protonated base and the pK_a of the acid. The D pK_a was defined in refs. 16 and 17 as pK_a of the protonated base minus pK_a of the acid, i.e. with decreasing pK_a of the acid the D pK_a increases. Figure 5 illustrates the connection between the % transfer of the proton in the OH...NO^-...H⁺N bonds formed between phenols and trimethylamine as a function of the D pK_a. Figure 5A shows that the proton transfers with increasing acidity to the phenol. Figure 5B shows that the intensity of the IR continuum is largest if the double minimum potential is most symmetrical.


2. The second parameter which determines the position of the AH...BA^-...H⁺B equilibria in hydrogen bonds is the interaction with their environments. With increasing non-specific as well as specific interactions of the hydrogen bonds with their environments the equilibria are shifted in favor of the polar structure.¹⁸

3. The third parameter is the temperature of the systems. With decreasing temperature the equilibria are shifted to the right hand side.^18-20

Huyskens gave the following definitions of families of systems with heteroconjugated hydrogen bonds:^16,17 1. All systems of a family have the same hydrogen bond donor AH, and all acceptors B are similar molecules. They differ only in the pK_a of B, or 2. the acceptor B is always the same, and the donors AH are similar molecules which differ only in their pK_a values.

The first family which we studied was the carboxylic acid - N base family with
OH...N^-O...H⁺N hydrogen bonds.¹¹ The percent proton transfer can be determined in these systems from bands of the carboxylic group (Fig. 6). The n (C=O) stretching vibration of the -COOH group is observed at about 1715 cm^-1, and the antisymmetrical stretching vibration of the -CO₂^- ion, n _as(CO₂^- ) at about 1570 cm^-1, and the symmetrical ones at about 1400 cm^-1, respectively.

The fact that in the IR spectrum one can distinguish between the non-polar and the polar structures shows that the fluctuation of the proton in these bonds is slightly slower than in the homoconjugated bonds. This fluctuation is still so fast that in the far infrared no separate bands of a hydrogen bond vibration of the non-polar and the polar structure can be observed.

All 1:1 carboxylic acid + N base mixtures were studied without solvent.¹¹ All these mixtures are liquids. Figure 7 shows the IR spectra of three extreme examples.

In the 1:1 acetic acid + 2-methylpyrazine system an intense n (C=O) vibration indicates that the proton is localized at the carboxylic acid group, i.e. only the non-polar structure of the OH...N^-O...H⁺N equilibrium has weight. In the acetic acid + n-propylamine system an intense n _as(CO₂^- ) band and a n _s(CO₂^- ) band indicate that the proton is localized at the amine molecule, i.e. only the polar proton limiting structure O^-...H⁺N has weight. In the acetic acid + imidazole system these three bands have comparable intensity. Thus, both proton limiting structures have comparable weight. An intense IR continuum demonstrates that the OH...N^-O...H⁺N bonds show large proton polarizability. A double minimum proton potential is present in these hydrogen bonds.

In Fig. 8 (dashed line) the % proton transfer are shown as a function of the D pK_a. The protons transfer from the acid to the base. For the systems with smaller D pK_a the deeper well of the double minimum is still at the acid. For the systems with D pK_a of about 2.3 both wells are comparably deep on the average, and for those of higher D pK_a the deeper well is already at the N base. The curve, drawn with the solid line, represents the absorbance of the IR continuum. In the region around 50% proton transfer the OH...N^-O...H⁺N bonds show large proton polarizability, since intense IR continua are observed for these systems.

These results show that 50% proton transfer is not observed at D pK_a = 0, but with this family of systems at = 2.3.

These values at which the systems are symmetrical are characteristic of the families of systems and depend on interaction effects influencing the symmetry.

I have summarized such values in Tab. 1. With these systems the values are found between 1.3 and 5.3. They have been measured by various authors with various methods.

Let us return to the carboxylic acid - N base systems¹¹. In Fig. 9 the curve, drawn as dashed line, is the proton transfer curve which we already know, and the curve, drawn as solid line, is the curve, for the case when no hydrogen bond donor groups are present at the respective N bases. Then, 50% proton transfer is only found at = 4.0, i.e. the transfer equilibrium is shifted in favor of the non-polar structure. The smaller value 2.3 for the systems with N bases with additional hydrogen bond donor groups can be understood as follows: To the second O atom of the carboxylic group an O...HN hydrogen bond is built up. Because of this additional hydrogen bond the carboxylic acid OH group becomes more acidic, favoring the transfer of the proton to the N base.

For few systems quantitative values of the proton polarizability of heteroconjugated hydrogen bonds were determined by Hawranek.^21-23

Particularly large proton polarizabilities are shown by hydrogen-bonded chains with almost symmetrical proton potentials. Hydrogen-bonded systems with such properties are also indicated by intense continua in the infrared spectra.⁴⁴

This result was first obtained with models for biological systems, with poly-a-aminoacid + dihydrogenphosphate systems [in (44) further refs. are given]. Figure 10A shows polylysine + dihydrogenphosphate systems. With increasing dihydrogenphosphate content a very intense continuum arises. The same is true with polyglutamic acid + dihydrogenphosphate systems, shown in Fig. 10B. In Fig. 11 the intensities of these continua are shown as a function of the dihydrogenphosphate to side chain ratio.

Figure 11a demonstrates that with the polylysine systems the intensity increases up to three dihydrogenphosphates per lysine residue if sodium or up to five if potassium ions are present, respectively. Figure 11b shows that in the case of the polyglutamic acid + dihydrogenphosphate systems the intensity of the IR continuum increases up to dihydrogenphosphate : glutamic acid residue ratios of 5:1, the highest dihydrogenphosphate content which could be measured.

These results demonstrate that the side chains form with the dihydrogenphosphates hydrogen-bonded chains with large proton polarizabilities which are caused by collective proton tunneling within these chains. Probably these chains are structurally symmetrical. Then with the polylysine + dihydrogenphosphate systems in the case of the Na⁺ system seven and with the K⁺ system eleven hydrogen bonds with large proton polarizability due to collective proton tunneling are built up, whereas in the polyglutamic acid + dihydrogenphosphate system hydrogen - bonded networks with this property are formed. The charge shift due to collective proton tunneling within such chains occurs within picoseconds and thus such chains are very effective pathways for protons (see sec. 12).

We studied in tight cooperation with Prof. Brzezinski from Poznan in Poland these proton polarizabilities of hydrogen-bonded chains more in detail with intramolecular hydrogen-bonded chains.

Two examples are given in the following:

The tetrabutylammonium mono-salt of a CH₂Cl₂ solution of 1,11,12,13,14 pentahydroxy-methylpentacene causes, as shown by Fig. 12 (solid line), an intense IR continuum.⁴⁷ It indicates that the chain of four hydrogen bonds shows very large proton polarizability due to collective proton tunneling.

Particularly interesting are monoperchlorates of 2,6-disubstituted MANNICH bases.⁴⁸ With these substances the acidity of the phenolic group can be changed by the substituents R₁ and R₂.

In Tab. 2 in the series of substituents from top to bottom, the acidity of the phenolic group increases. In the last column the absorbance of the continuum of the monoperchlorates is given. With increasing acidity of these groups the absorbance of the IR continuum increases. If the acidity increases further, the absorbance decreases again and finally instead of the IR continuum, NH⁺ stretching vibration bands are observed. Thus, the proton polarizability due to collective proton motion in these two hydrogen bonds first increases and if the acidity becomes still larger it decreases again and finally it vanishes.

How can this behaviour be understood? The proton limiting structures correspond to minima in the energy surface. With increasing acidity of the phenolic group the collective proton fluctuation between the two proton limiting structures (I) N⁺H...OH...NN...HO...H⁺N (II) of the system is favored, and thus, the proton polarizability due to collective proton tunneling increases. With further increasing acidity a third proton limiting structure, the structure N⁺H...O^-...H⁺N (III) obtains weight. The system must now be represented by the three proton limiting structures N⁺H...OH...NN⁺H...O^-...H⁺NN...HO...H⁺N. If the acidity of the phenolic O atom increases still further the weights of the limiting structure I and II decrease and thus, the proton polarizability of the system becomes smaller. Finally, only limiting structure III remains. The protons are now localized at the nitrogens and instead of an IR continuum, n (NH⁺) stretching vibration bands are observed. The system shows no longer noticeable proton polarizability.

All these experimental results can be justified by theoretical treatments. We calculated ab initio energy and dipole moment surfaces of the systems formic acid - water - formate and formic acid - water - water - formate.⁴⁹ With the first system one obtains the energy surface with three minima shown in Fig. 13. ⁴⁹

Each minimum corresponds to one of the three proton limiting structures. This energy surface shows that the collective proton transfer proceeds step by step. One proton shifts and the other follows delayed. In the case of the formic acid - water - water - formate system one obtains an energy surface with four minima.

Solving the Schrödinger equation for the proton motion with an additional term, dipole moment times electrical field strength, demonstrates the following⁴⁹: In the case of the formic acid - water - formate system the proton polarizability due to collective proton motion is largest at ± 0.6 x 10⁷ Volt/cm. It amounts then (150-250) x 10^-24 cm³, it increases with decreasing temperature. In the case of the formic acid - water - water - formate system the proton polarizability amounts to (500-900) x 10^-24 cm³, it increases with decreasing temperature.

Thus, going from the formic acid - water - formate to the formic acid - water - water - formate system the proton polarizability - due to collective proton motion - increases, i.e., the proton polarizability increases with increasing length of the hydrogen - bonded chains.

No longer chains can be calculated in this way ab initio. Therefore, we proceeded our calculations with model proton potentials.⁵⁰ Figure 14 shows the proton polarizability as a function of the number of minima. With increasing number of minima it becomes three to four orders of magnitude larger than the usual polarizabilities due to distortion of electron systems.

The charge shifts due to collective proton motion within such chains occur within picoseconds and thus such chains with large proton polarizability are very effective proton pathways, for instance, in biological membranes (see sec. 12).

Not only hydrogen bonds may show large polarizabilities but also other cation bonds, Li⁺, Na⁺ and Be²⁺ bonds may show this property. A review on these studies was given by Zundel et. al.²⁰

The formation of the Li⁺ bonds is indicated in Fig. 15 by the vanishing of the Li⁺ ion motion band at 400 cm^-1. The relatively long NLi⁺...NN...Li⁺N bonds give rise to IR continua which begin at 450 cm^-1 and extend toward smaller wavenumbers.⁵¹ The slightly shorter OLi⁺...OO...Li⁺O bonds formed by two alcoholate groups begin at 410 cm^-1 and show a band - like structure at about 100 cm^-1.^51,52

Short Li⁺ bonds formed between two carboxylate or two N oxide groups cause continua which begin at about 250 cm^-1 and have a distinct structure.^51,52 These IR continua indicate that all homoconjugated Li⁺ bonds show large Li⁺ polarizability. The decreasing integrated intensity of these continua shows that the Li⁺ polarizability decreases in the series of the studied compounds.

Heteroconjugated OLi⁺...ONO...Li⁺ON bonds were studied with three families of systems.^53-55

Figure 16 shows the carbonyl region of the compounds shown in the Scheme.⁵⁴ The decrease in the intensity of the n (C=O) band at higher wavenumbers and the increase of the intensity of the n _as(CO₂^-) band at lower wavenumbers demonstrate that within this series of compounds the weight of the Li⁺ limiting structure I decreases and that of structure II increases from R = -NO₂ to R = -OC₂H₅. Thus, the Li⁺ potential changes from a double minimum with deeper well at the carboxyl group via an almost symmetrical double minimum to a broad single minimum at the oxygen atom of the NO group.

Figure 17 shows the spectra in the FIR region. When R = -NO₂ an intense IR continuum is observed in the region 425-25 cm^-1, its intensity decreases strongly toward smaller wavenumbers (beginning at 150 cm^-1). This result confirms that the double minimum Li⁺ potential is still relatively asymmetrical. When R = -Br or R = -H, IR continua are observed which begin at about 350 cm^-1 and extend with high intensity to 25 cm^-1. These are the systems with, on average, symmetrical double minimum Li⁺ potentials. In the case of the compound with R = -OC₂H₅, only a broad band with a maximum at about 90 cm^-1 and a wing toward higher wavenumbers is observed. Thus, with all compounds, except for the compound with R = -OC₂H₅, the O^-Li⁺...ONO^-...Li⁺ON bonds show high Li⁺ polarizability. The Li⁺ ions can easily be shifted within these bonds by local electric fields.

Also homoconjugated ONa⁺...OO...Na⁺O bonds cause IR continua and show large Na⁺ polarizabilities.⁵⁶ The transfer equilibrium and the Na⁺ polarizability of heteroconjugated Na⁺ bonds was studied with intramolecular Na⁺ bonds formed between a carboxylate and N oxide group.⁵⁶

Also intramolecular systems with two Li⁺ or two Na⁺ bonds, respectively, show large cation polarizabilities due to collective cation motion.^57,58

The intensity of the IR continua and hence the cation polarizabilities decrease, however, in the series of H⁺,D⁺, Li⁺, Na⁺ and K⁺ bonds.^20,59

We studied the interaction of Be²⁺ with four carboxylate groups⁶⁰ with four NO groups⁶¹ and with the four oxygen atoms within the gossypol molecule.⁶² In all cases the Be²⁺ ions interact equally strong with all four acceptor groups. The molecular mass of Be²⁺ is comparable to that of Li⁺. As shown in Fig. 18 the IR continuum is found in the region 1300 - 500 cm^-1, i.e. strongly shifted toward higher wavenumbers.

Thus, due to the stronger interaction of the Be²⁺ ions with the acceptor O atoms, the Be²⁺ potential is much narrower and steeper. Hence, a four minima potential or a potential without barriers is present. The Be²⁺ polarizability due to the fluctuation of the Be²⁺ ions within this potential is, however, considerable as shown by the IR continuum.

Figure 19 shows that with the mono Li⁺- and mono Na⁺-salts of 1,11,12,13,14-pentahydroxypentacene intense continua are observed in the far infrared region.⁶³ Four minima cation potentials are present in theses systems. The IR continua demonstrate that due to the tunneling of the Li⁺ or Na⁺ ions in four minima potentials large cation polarizabilities arise.

Systems with fluctuating cations in multiminima potentials can be realized with crown ethers, adding HAuCl₄, LiClO₄ or NaClO₄ in the ratio 1:1 to their solutions.⁶⁰ Figure 20 shows that in the spectra of the 1:1 complexes 1 to 3 far infrared continua are observed, demonstrating that Li⁺ ions fluctuate in five or six minima Li⁺ potentials.

The systems show large Li⁺ polarizabilities. With the ring with eight O atoms the Li⁺ ion remains localized. With the Na⁺ complexes only the system with six O atoms in the ring shows Na⁺ polarizability.

The molecular processes with the dissoziation of acids are discussed in ref. 65 (see also ref 1).

The dissoziation equilibria are determined^1,65 by

where and are intrinsic quantities of the system, i.e. they describe the properties of the system in gas phase, whereas and are extrinsic quantities, i.e. they describe the influence of the environment.^1,65 and are determined by non-specific and specific interactions of the hydrogen-bonded molecules with their environments. As a result of both kinds of interactions takes great negative values, shifting the equilibria to the right. The term is negative, since the solvate molecules around the groups with the hydrogen bond, causing the reaction field, are much ordered. These negative values, caused by the ordering of solvate molecules around the hydrogen bonds, are responsible for a shift of these equilibria to the left.

When we discuss the behaviour of acid and base solutions we have to keep in mind the following: Due to the term in gas phase the transfer equilibria are usually completely shifted to the left hand side. In solutions the term is negative due to the order in the solvent environment of the hydrogen bonds. It shifts these equilibria also to the left hand side. When proton transfer in these hydrogen bonds with large proton polarizability occurs, these two terms are overcompensated by the interaction enthalpy term , which is negative and may be very large, owing to the non-specific and specific interaction effects. On the basis of these considerations I shall discuss the molecular process with the dissociation of acids.

The following molecular processes are responsible for the dissoziation of acids in solutions.^14,15,66

1. The formation of AH...BA^-...H⁺B bonds with large proton polarizability between the acid and the solvent.

2. The shift of the AH...BA^-...H⁺B equilibria to the right hand side increases due to the increasing polarity of the environments of these easily polarizable hydrogen bonds. Hence, the addition of more polar molecules favors this shift, since the amount of the negative increases.

3. The transfer of the positive charge from acid solvent into solvent - H⁺ - solvent hydrogen bonds. These B⁺H...BB...H⁺B bonds are structurally symmetrical and show considerable proton polarizability. Thus, the strong interaction of these hydrogen bonds with their environments also favors the transfer of the positive charge into these hydrogen bonds.

We know that the H₅O₂⁺ group with the hydrogen bond with large proton polarizability plays the most important role.^14,67-71 It is, however, also well-known from various experiments that H₉O₄⁺ is of significance.^72-89 Also, our studies with polystyrene sulfonic acid suggested a H₉O₄⁺ group.²

This result is not in contradiction to the fact that the H₅O₂⁺ group plays the most important role, as shown by the following consideration:¹⁵ When the proton fluctuates in H₅O₂⁺ all electrons follow instantaneously. Thus, the center of gravity of H₉O₄⁺ fluctuates between the two O atoms of H₅O₂⁺, as illustrated in Fig. 21. Thus, one has a fluctuating H₉O₄⁺. H₉O₄⁺ is a group which fluctuates with the tunneling frequency of the proton in H₅O₂⁺.

Let us now consider the importance of the proton polarizability for the high conductivity of acid solutions.⁷

Figure 22 shows both proton limiting structures of H₅O₂⁺ before and after a structure diffusion step. Such a step occurs when the excess proton changes its role as excess proton with one of the hydrogen atoms of the two water molecules of the H₅O₂⁺ groups. In this way, the H₅O₂⁺ group shifts within the hydrate structure network. When an external electrical field is present, this structure diffusion occurs more frequently in the direction of the electrical field.

Because of the large proton polarizability of the hydrogen bond in H₅O₂⁺, the proton limiting structure in which the proton is shifted in field direction obtains a somewhat larger weight. This favors the structure diffusion in the direction of the electrical field.⁷

This structure diffusion is, however, a much slower process when compared to the fluctuation of the proton in the polarizable hydrogen bonds. This structure diffusion was studied, for instance, in the dielectric frequency region by Careri.⁹⁰

Let us now consider acids with pK_a values > 0.⁹¹ Table 3 shows the number of water molecules n, necessary to observe spectroscopically dissociated species. Much more water molecules are necessary for the dissociation of these acids. Thus, is considerably larger than with acids of smaller pK_a values. The AH...OH₂A^-...H⁺OH₂ equilibria are still largely on the left-hand side. However, as shown in Fig. 23A, in the case of chromic acid intense IR continua are observed also with the highly concentrated solutions. The acid-water hydrogen bonds formed by these acids show a still relatively large proton polarizability, although the non-polar structure predominates strongly⁹¹ (Fig. 23B).

The at first surprising result, that the AH...OH₂A^-...H⁺OH₂ bonds show already large proton polarizability, although these equilibria are almost completely on the left hand side, becomes understandable if one considers the term .

It is very important to notice that the shape of the proton potential is essentially determined by the enthalpy term . The smaller , the larger the degree of the symmetry of the proton potential and the larger the proton polarizability. The position of the proton transfer equilibria is, however, determined by the free enthalpy and thus, also by the term . Around the polar structure A^-...H⁺B the environment is strongly ordered. Thus, is negative and high for such proton transfer equilibria. Because of this term the equilibria are shifted to the left. Thus, the acid-water hydrogen bonds show already large proton polarizability, although the equilibria are almost completely on the left hand side.

Figure 24 shows that the degree of dissociation decreases in this series of acids from the trifluoroacetic acid to the formic acid system.

A particularly interesting behavior is shown by acids, containing phosphorus, as well as by arsenic acid.⁹² If one considers the above series of acids the hydrogen bond donor strength of the OH groups decreases in this series. The hydrogen bond acceptor strength of the O atoms in these acids increases.

Thus, in the region of the acid molecules in which the donor and acceptor strengths are comparable, the hydrogen bonds formed between these acid molecules should show large proton polarizability. This is indeed true for acids containing phosphorus or for arsenic acid⁹², respectively. In the case of H₃PO₄ Fig. 25 shows that the IR continuum is very intense already in the almost water-free H₃PO₄ system.

I will now discuss strong bases. Figure 26 shows the IR spectrum of a strongly basic polyelectrolyte of quarternated poly-p-dimethylaminostyrene and for comparison, the IR spectrum of the corresponding iodide.^93,94

For this basic polyelectrolyte an intense IR continuum indicates the presence of hydrogen bonds with large proton polarizability. One can show that this IR continuum is caused by the hydrogen bond in H₃O₂^-. This bond is represented by these two proton limiting structures.

At 3640 cm^-1 a weak shoulder is observed. It appears due to the free (OH)_- groups of H₃O₂^-. These groups are free since, due to the negative charge of H₃O₂^-, they are only very weak hydrogen bond donors.

For all aqueous solutions of strong bases, as for instance KOH, intense IR continua are observed.^2,95 Their intensity increases with increasing base concentration. These IR continua are also caused by H₃O₂^-. In this case one has a fluctuating H₇O₄^-. Its center fluctuates between the two O atoms of its central H₃O₂^-. ^2,95

We observed intense continua not only for aqueous solutions but also for solutions of bases in other solvents.⁹⁵ An intense IR continuum is found, for instance, with potassium alcoholate solutions in methanol. It is due to the hydrogen bond in H₃COH...O^-CH₃ H₃C^-O...HOCH₃ groups. Thus, also in aqueous and non-aqueous solutions of strong bases hydrogen bonds of large proton polarizability are present. As for solutions of strong acids the behavior of strong bases can be discussed, considering these hydrogen bonds with large proton polarizabilities.

The following model systems have been studied¹:

1. Poly-a-amino acids, polymers, consisting of only one amino acid.
2. Copolymers, consisting of two amino acids.
3. Mixtures of two kinds of amino acids.
4. Mixtures of amino acids, having protecting groups at the a-amino and at the a-carboxylic acid groups.

We studied the following systems with homoconjugated bonds: semi-deprotonated glutamic acid⁹⁶, semi-protonated histidine^97,98, semi-deprotonated tyrosine, semi-protonated lysine and semi-deprotonated cysteine.⁹⁶ The IR continua demonstrates that the following homoconjugated hydrogen bonds show large proton polarizability: (Asp-Asp)^-, (Glu-Glu)^-, (His-His)⁺, (Tyr-Tyr)^-, (Lys-Lys)⁺ and (Cys-Cys)^-.

Also heteroconjugated AH...B^-A...H⁺B bonds between side chains may show large proton polarizability. The studied systems^99-103 are summarized in Tab. 4. We investigated homopolymer poly-a-amino acids with monomers to determine at which DpK_a values one can expect hydrogen bonds which are on the average largely symmetrical and, thus showing large proton polarizability.

The proton transfer curves of two systems are shown in Fig. 27. The weights of the polar limiting structures are given in Tab. 5. The following heteroconjugated hydrogen bonds between side chains show large proton polarizability: Tyr-Arg, Cys-Lys, Tyr-Lys, Glu-His and Asp-His hydrogen bonds. The protons in all these bonds can easily be shifted by changes of the local electrical fields and by specific interactions.

Does hydration cause a shift of the proton transfer equilibria?

Figure 28A shows results for carboxylic acid - N base systems¹¹. The dotted curve shows the proton transfer in percent as a function of the D pK_a, the dashed-dotted curve shows the analogous dependence for the same systems when four water molecules are present per acid-base pair. In the presence of water molecules the proton transfer curve is shifted toward a larger transfer.¹⁰²

Figure 28B shows that for the polyhistidine + carboxylic acid systems the position of the proton transfer equilibria is much more sensitive to the degree of hydration. The OH...N bonds are asymmetric in the water-free polyhistidine + acetic acid system. The protons are localized at the acetic acid molecules in the water-free system, but even one water molecule per residue increases very strongly the weight of the polar proton limiting structure O^-...H⁺N. These hydrogen bonds acquire large proton polarizability.¹⁰⁰

Thus, hydration water - more generally polar environments - favor the transfer of the proton, i.e. as far as the hydrogen bonds are not broken, polar environments increase the weight of the polar proton limiting structure B₁^-...H⁺B₂. With regard to the stability of these bonds if hydration water is present see ref. 1.

Figure 28C demonstrates¹⁰⁰ that conformational changes and proton transfer may be strongly correlated.

We can state that the proton transfer processes in hydrogen bonds between side chains in proteins with large proton polarizability the degree of hydration of the systems and the conformation of the backbone are strongly interdependent, as illustrated in Scheme 7. The coupling of these processes is probably of great significance for the functions of proteins, involving proton transfer processes via easily polarizable hydrogen bonds.

In the following the poly-a -aminoacid - dihydrogenphosphate systems are discussed⁴⁴ (further refs. are given there). We have already seen in sec. 4.1 that such systems may show large proton polarizability.

It is very important that the behavior of these hydrogen - bonded systems strongly depends on the type of cations present. 1. The cations influence the position of the proton transfer equilibria in the side chains - P_i bonds. 2. They influence the size of the proton polarizability, as shown by the different intensities as a function of the cations present. 3. The length of the chains is determined by the cations, as indicated by the limiting value of the intensity of the IR continua as a function of the ratio P_i : side chain.

These cation dependencies are summarized in Tab. 6. In conclusion we can state⁴⁴ that a large number of hydrogen bonds and hydrogen-bonded systems which may be present in biological systems show large proton polarizabilities. The behavior of such systems can easily be controlled by the cations present.

Easily polarizable hydrogen bonds between dihydrogenphosphates: Long ago we could prove that POH...O^-PP^-O...HOP bonds formed between orthophosphate molecules show proton polarizability.¹⁰⁹ Also in aqueous solutions of hydrolyzed adenosintriphosphate such bonds have been observed.^110,111 Furthermore, it was shown that also a pyridoxalphosphate Schiffbase complex shows large proton polarizability due to collective proton motion in a hydrogen-bonded chain.¹¹² Such a system is present in the active center of maltodextrinephosphorylase.¹¹³

Two hydrogen bonds are present in the active center of serine proteases.

In the literature two different catalytic mechanisms are discussed. The first mechanism, a proton relay system.^114,115 It was suggested that both protons in the hydrogen-bonded system are shifted simultaneously, and in this way Ser 195 should become negatively charged and thus, catalytically active.^114-119

The second suggested mechanism is an acid catalysis with a tetrahedral intermediate in which the protonated His 57 residue is the acid.^120-126

We have taken FT-IR difference spectra of the (serine protease trypsin) minus (anhydrotrypsin).¹²⁷ In anhydrotrysin the serine residue is modified. Instead of the -CH₂OH group a C=CH₂ group is present.

Figure 29 shows the FT-IR difference spectra of the two samples at pH 7 and at pH 3. At pH 3 the bands of Ser 195 are found as positive bands at 1084, 1058 and 1033 cm^-1. These bands demonstrate that no reaction occurs at pH 3.

Drastic changes have occurred in the difference spectra of the samples at pH 7. The positive bands, characteristic of serine have vanished to a large extend. Positive bands are found at 1161 and at 1096 cm^-1. They demonstrate that His 57 is protonated in the tetrahedral intermediate.

In the following I shall discuss why the OH...N^-O...H⁺N equilibrium between Asp and His is shifted to the right in the tetrahedral intermediate. Two viewpoints are decisive for this shift: 1. I have already shown with model systems that this equilibrium is shifted to the right by specific interactions of the second O atom of the carboxyl group with polar groups¹¹ (see Figs. 28A and B and sec. 9). 2. It is well known that in the neighborhood of Asp 102 a second serine residue, Ser 214 is present as well as a lot of structural water, building up a channel from the active side to the external surface of the enzyme.^128-133

Caused by the interaction of these polar groups with the carbonyl O atom of the C=O group, the proton in the Asp-His hydrogen bond, being a bond with large proton polarizability¹⁰⁰, is shifted from Asp to His and remains localized at this residue.

The fact that the histidine residue is protonated in the tetrahedral intermediate is decisive for the catalytic mechanism. The protonated histidine residue can now act as acid and protonate the N atom of the peptide group. In this way the peptide bond is destabilized and can be split by a water molecule.

The second family of proteases which I shall discuss are the aspartate proteases. Many X-ray studies have been performed already for these enzymes.^134-149 These enzymes have two Asp residues in their active center. One of the most important representative of these enzymes is pepsin. Therefore, we performed our studies with this
enzyme.^150-152

A base catalysis mechanism is discussed in the literature.^143,153,154 With this mechanism a proton relay system with large proton polarizability is present in the active center. This mechanism could be proved by our FT-IR studies.^150-152

Two Asp residues Asp 32 and Asp 215 are present in the active center. These residues can selectively be modified. We have taken difference spectra (native) minus (modified enzyme) with the result that in the native enzyme Asp 215 is protonated and Asp 32 is present as anion. With the modified enzyme, Asp 32 becomes protonated. If the inhibitor pepstatin is present Asp 32 becomes also protonated and Asp 215 deprotonated. The same is true if substrate is added.

Hence, such an arrangement, as discussed in sec. 5, is realized in the active side of pepsin. We know that such a system shows very large proton polarizability due to collective proton motion.^44,49 Thus, if the substrate is attached, the positive charge can easily be shifted due to changes of the local electrical fields or specific interactions, resulting in a protonation of Asp 32 and a deprotonation of Asp 215.

At first, I will discuss alcohol dehydrogenases. They catalyze the oxidation of alcohols to aldehydes. They contain as coenzyme nicotinamid adenin dinucleotide (NAD⁺). NAD⁺ is composed of the nicotinamide rest, a ribose, two phosphates, a second ribose and an adenine rest.

In the active center of all alcohol dehydrogenases there is a Zn²⁺ ion present. This Zn²⁺ ion is complexed with two cysteins and one histidine. A water molecule is bound as the fourth ligand. Thus, the Zn²⁺ ion is in a tetrahedral arrangement. NAD⁺ is attached to the alcohol dehydrogenase in such a way that the positively charged nicotinamide rest is near the Zn²⁺ ion, whereas the adenine rest is far from the Zn²⁺ ion.

Two different mechanisms are discussed with regard to the deprotonation of the alcohol. Brändén et al.¹⁵⁵ suggested that the Zn²⁺ bound water dissociates when the coenzyme nicotinadenine dinucleotide, NAD⁺, is added. The remaining (OH)^- deprotonates afterwards the alcohol which is then bound to the Zn²⁺ ion as the fourth ligand.

In contrast, Cook and Cleland¹⁵⁶ assumed that the Zn²⁺ bound water is substituted by the alcohol. The alcohol becomes deprotonated and then the alcoholate is bound to the Zn²⁺ ion.

In both mechanisms a proton relay system is important to shift the positive charge away from the Zn²⁺ ion.

We studied NAD⁺ complexes of yeast and of liver alcohol dehydrogenase by FT-IR spectroscopy.^157,158 We could show that the proton arising by water splitting at the Zn²⁺ ion is conducted to the N₁ atom of the adenine ring.

The question is how the positive charge is conducted to the N₁ atom of the adenine rest. It was already postulated that a hydrogen-bonded chain Zn²⁺ bound water - ribose OH - Ser 48 - His 51 is present. Let us first consider why the proton can be conducted in this chain. We have already seen in sec. 5 that a proton can be conducted in such a chain if the whole proton potential is largely symmetrical. The positive charge can also be conducted if the proton affinity of groups within the chain is much higher or lower than that of the endstanding groups since, due to the strong coupling of the proton motion, the potentials of the protons are energetically equilibrated.

The proton potential in the above mentioned hydrogen-bonded pathway becomes largely symmetrical due to the strong covalent interaction of the Zn²⁺ ion with the water
molecule.^159-162 It was already shown a long time ago that such a strong interaction occurs if the Zn²⁺ ion is present in a tetrahedral environment. Thus, by the interaction with the Zn²⁺ ion the acidity of the water proton becomes comparable to the acidity of the protonated His 51.

Consequently, the proton potential in the hydrogen-bonded chain is largely symmetrical. Hence, the chain shows large proton polarizability due to collective proton motion. Thus, the strong field of the positively charged nicotinamide can shift the positive charge to His 51. Recently, we published results¹⁶² for a model system with a spectrum which shows an intense IR continuum indicating that this part of the chain is easily polarizable.

Let us now analyze the question how the positive charge can be conducted in the second part of the pathway, i.e. from His 51 to the N₁ atom of the adenine rest of NAD⁺. To find out how symmetrical the proton potential in a histidine-adenine hydrogen bond is, we studied the system protonated 1-methylimidazole - 9-ethyladenine as a function of the degree of hydration.^1,158 In the spectrum of the dry complex an intense IR continuum is observed. It indicates that the proton potential in this hydrogen bond is on the average largely symmetrical. Furthermore, as indicated by the IR continuum, this hydrogen bond shows large proton polarizability.

The distance between His 51 and the N₁ atom of the adenine rest is about 6-7 Å . Thus, a direct contact between these groups is not possible. We have, however, already seen in sec. 5 that, if structural water is inserted between a donor and an acceptor of an easily polarizable hydrogen bond, the whole system shows large proton polarizability due to collective proton motion.⁴⁹ Thus, along this pathway the positive charge can easily be shifted to N₁.

Now, I would like to discuss the conduction of protons in the maltodextrinphosphorylase (MDP).¹¹³ This enzyme catalyzes the degradation and in vitro the elongation of polysaccharides.^113,163-173

We could show in ref. 113 that at least one hydrogen-bonded chain with large proton polarizability is present in this enzyme. One chain connects lys 533, pyridoxal phosphate (PLP) and the substrate phosphate (Glc).

We know already (see sec. 9) that hydrogen bonds in lys-dihydrogenphosphate chains show very large proton polarizability.¹⁰⁵

Furthermore, POH...^-OPPO^-...HOP bonds formed between phosphates show large proton polarizability, too. ¹⁰⁹ We could prove in ref. 113 that the lys-PLP-glc chain shows large proton polarizability. Thus, the positive charge can easily be conducted from lys 533 to the substrate phosphate.

All these studies of enzymes demonstrate that hydrogen bonds and hydrogen-bonded systems play an important role with charge shifts in active centers of enzymes.

The proton pathway in the bacteriorhodopsin molecule: The bacteriorhodopsin molecule is present in the purple membrane of halobacteria in a seven helical arrangement. It absorbs light at a retinal rest, bonded as Schiffbase to the lys residue 216. Due to this light absorption a cis-trans isomerization of the retinal rest occurs. Using this free enthalpy a proton is pumped from the active side at the Schiffbase to the outside of the purple membrane and afterwards the Schiffbase is reprotonated from the inside of the membrane. This proton pumping and conduction process occurs during a photocycle. The intermediates of this cycle can be stabilized.

We have taken FT-IR difference spectra from the initial state BR₅₇₀ minus the respective intermediate.^176,177 Hence, the bands of the initial state BR₅₇₀ appear as positive bands and those of the intermediates as negative bands.

Figure 30A shows the difference spectrum of BR₅₇₀ minus that of the L₅₅₀ intermediate. Positive are the bands of the intermediate BR₅₇₀, and negative those of the intermediate L₅₅₀. In this IR spectrum, caused by the L₅₅₀ intermediate, a pronounced IR continuum is observed, beginning at about 2800 cm^-1 and extending over the whole region. This result demonstrates that in the L₅₅₀ intermediate a proton pathway with large proton polarizability is present.

Figure 30B shows the respective difference spectrum of a bacteriorhodopsin molecule in which the retinal rest is modified in such a way that the photocycle is interrupted before the L₅₅₀ intermediate is formed. No IR continuum due to a L₅₅₀ intermediate is found, demonstrating that with this modified bacteriorhodopsin no such proton pathway is formed.

Thus in the L₅₅₀ intermediate the proton is conducted from the active side to the external surface by the hydrogen-bonded system with large proton polarizabilities shown in the Scheme.

By a FT-IR study of the model system 7-methyl-1,5,7-triazabicyclo[4,4,0]dec-5-ene with 4-tert-butyl-phenol in chloroform we confirmed that such systems show large proton polarizability.¹⁷⁸

The ATP synthase^179-187 consists of the two protein complexes F₀ and F₁. F₀ conducts the protons through the membranes to F₁, which is the catalytic center.

With E.Coli bacteria F₀ consists of the subunits a, b and c with a stoichiometry 1:2:12.^188-190 Herewith, the subunits a and c are directly involved in the proton conduction.^182,184,188 Due to chemical modification of Asp 61 by dicarbodiimide (DCCD) in only one of the subunits c, the proton conduction, and hence, the ATP synthesis is blocked completely.^189,190

We prepared F₀ subunits of E.Coli and embedded them in phospholipid vesicles.¹⁹¹

Figure 31A shows the IR spectra of vesicles with native F₀ and that one of vesicles with DCCD-blocked Asp 61. In the spectrum with the native F₀ an intense IR continuum is found, beginning at 3000 cm^-1 and extending toward smaller wavenumbers. In the spectrum of the DCCD blocked F₀ no IR continuum is observed.

Figure 31B shows the spectrum of dehydrated vesicles with native F₀ and the spectrum of dehydrated vesicles with DCCD-blocked F₀. With dehydration the IR continuum also vanishes completely.

These results demonstrate that in the hydrated native F₀ subunit a proton pathway with large proton polarizability is present, which conducts protons by collective proton tunneling within less than picoseconds.¹⁹¹

The nature of this channel is discussed in detail in ref. 191.

1. G. Zundel, Advances in Chemical Physics, 1999.

3. G. Zundel, H. Noller and G.-M. Schwab,

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J. Menon Ed., Publ. Res. Trends Trivandrum 3, 129 (1992).

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9. R. Janoschek, E.G. Weidemann and G. Zundel,

J. Chem. Soc. Faraday Trans. II 69 505 (1973).

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and W.J. Orville-Thomas Eds., Vol. II, Wiley, New York, (1981).

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J. Chem. Soc. Faraday Trans. 88, 1659 (1992).

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Fig. 1 IR spectra: (^{_____________}), polystyrene sulfonic acid membrane, (thickness 5 m m); (- - - - - - -), Na⁺ salt of this membrane, for comparison [Taken from ref. 2]

Fig. 2 Double minimum proton potential and wave functions y _o+ and y _o-, of the two lowest states [Taken from ref. 7].

Fig. 3 Relative absorption intensities of the transitions of H₅O₂⁺ (O-O distance 2.6 Å) as a function of the electrical field strength F in the hydrogen bond direction.

Temperatures: l , 0; n , 100; D , 200; -, 300; x, 400 K. The length of the lines is equal to the relative absorption intensities, for negative electrical fields I_ij (-F) = I_ij (+F)

[Taken from ref. 9].

Fig. 4 IR spectra of aqueous HClO₄ solutions; (^____________), 17.6 M (n = 0.0); ( ), 16.1 M (0.51); (- - - - - - -), 14.2 M (1.3); (^{__ __ __ __}), 11.5 M (2.4) [Taken from ref. 13].

Fig. 5 (A) % proton transfer of octylamine + substituted phenols plotted as a function of the D pK_a, (B) absorbance of the continuum for the same systems plotted as function of D pK_a: (1) 4-chlorophenol, (2) 3-chlorophenol, (3) 3,4-dichlorophenol, (4) 3,5-dichlorophenol,(5) 2,4-dichlorophenol (6) 2,3 dichlorophenol, (7) 2,3,4-trichlorophenol, (8) 2,4,5-trichlorophenol, (9) 2,3,5-trichlorophenol, (10) 2,4,6-trichlorophenol, (11) pentachlorophenol. [Taken from ref. 12].

Fig. 6 IR spectra: (^{_____________}), acetic acid + imidazole; (- - - - - - -), acetic acid + n-propylamine; (...............), acetic acid + 2-methylpyrazine [Taken from ref. 11].

Fig. 7 IR spectra: (^{_____________}), acetic acid + imidazole; (- - - - - - -), acetic acid + n-propylamine; (...............), acetic acid + 2-methylpyrazine [Taken from ref. 11].

Fig. 8 Carboxylic acid - N base systems with N bases with additional hydrogen bond donor group; (- - - - - - -), degree of transfer of the proton to the N base in %; (^{_____________}), absorbance of the IR continuum in the region of higher wavenumbers; (b) acetic acid + pyrazole, (c) acetic acid + 2-methanolpyridine, (e) acetic acid + 3-aminopyridine, (f) acetic acid + imidazole, (k) acetic acid + 2-ethylimidazole, (m) formic acid + 2-ethylimidazole, (o) acetic acid + n-propylamine, (p) formic acid + n-propylamine [Taken from ref. 11].

Fig. 9 Carboxylic acid - N base systems, degree of proton transfer to the N base in %; (^____________), systems with N bases without additional hydrogen bond donor groups;

(- - - - - -), systems with N bases with additional hydrogen bond donor groups, for comparison. (d) acetic acid + pyridine, (g) acetic acid + N-methylimidazole, (h) acetic acid + 2,4,6-trimethylpyridine, (i) formic acid + N-methylimidazole, (l) monochloroacetic acid + N-methylimidazole, (n) dichloroacetic acid + N-methylimidazole [Taken from ref. 11].

Fig. 10A) IR spectra of (L-Lys)_n^_KH₂PO₄ systems: ( ), pure (L-Lys)_n; (^{_____________}), Lys: KH₂PO₄ = 3:1; (- - - - - - -), Lys: KH₂PO₄ = 1:1; (...............), Lys: KH₂PO₄ = 1:2.
B) IR spectra of (L-Glu)_n^_KH₂PO₄ systems: ( ), pure (Glu)_n; (^{_____________}), Glu:KH₂PO₄ = 2:1; (- - - - - - -), Glu: KH₂PO₄ = 1:1; (...............), Glu: KH₂PO₄ = 1:3
[Taken from refs. 45 and 46].

Fig. 11 Absorbance of the IR continuum at 1900 cm^-1 as a function of the P_i:residue ratio;

a) (L-Lys)_n^_MH₂PO₄ systems, b) (L-Glu)_n^_MH₂PO₄ systems [Taken from refs. 45 and 46].

Fig. 12 FT-IR spectra of 0.1 mol dm^-3 CH₂Cl₂ solutions of: (- - - - - - - -), 1,11,12,13,14^__pentahydroxymethylpentacene; and (^{_____________}), of its tetrabutylammonium mono-salt [Taken from ref. 47].

Fig. 13 Energy surface of the formic acid - water - formate system. R₁ and R₂ are the coordinates of the two protons. The zero point for these coordinates is the central O atom. The distances between the lines in the level diagram are 300 cm^-1 [Taken from ref. 49].

Fig. 14 Proton polarizability as a function of the minima of the multiminima potential

[Taken from ref. 50].

Fig. 15 FT-IR spectra of 0.1 mol dm^-3 chloroform solutions of the dialcoholate at 298 K:
(- - - - - - -), (Bu)₄ N⁺ 2:1 complex; (^{_____________}), Li⁺ 1:1 complex. The spectrum of the pure LiClO₄ solutions is given for comparison ( ) [Taken from ref. 51].

Fig. 16 Carbonyl region of the FT-IR spectra of acetonitrile solutions of the Li⁺ salts of ((4R)-2-pyridyl-N-oxide) acetic acids, (^{_____________}), ^_NO₂; (- - - - - - -), ^_Br; ( ), ^_H; (...............), ^_CH₃ ; (^{_____________}), ^_OC₂H₅ [Taken from ref. 54].

Fig.17 FT-IR spectra of chloroform solutions of the Li⁺ salts of ((4R)-2-pyridyl-N-oxide) acetic acids (^{_____________}), and for comparison, the tetrabutylammonium salts (- - - - - - -): A) -NO₂; B) -Br; C) -H; D) -CH₃; E) -OC₂H₅ [Taken from ref. 54].

Fig. 18 FT-IR spectra (region 1300-1500 cm^-1) of 0.2 mol dm^-3 acetonitrile solutions.

(- - - - - - -), di-N-oxide; (^{_____________}), 2:1 di-N-oxide: Be(AuCl₄)₂ complex;
(- · - · - · -), pure Be(AuCl₄)₂ solution [Taken from ref. 61].

Fig. 19 FT-IR spectra of 1:4 mixtures of the pentacene tetrakisbutylammonium salt of 1,11,12,13,14-pentahydroxypentacene A) with LiAuCl₄ (^____________), and (- - - - - - -), pure LiAuCl₄ solution; B) with NaAuCl₄ (^{_____________}), and (- - - - - - -), pure NaAuCl₄ solution

[Taken from ref. 63].

Fig. 20 FT-IR spectra of (...............), crown ethers and (^{_____________}), their 1:1 LiClO₄ complexes. For comparison, the spectrum of pure LiClO₄ solution (- - - - - - - -), is given:
a) crown ether 1; b) crown ether 2; c) crown ether 3; d) crown ether 4 [Taken from ref. 64].

Fig. 21 The fluctuating H₉O₄⁺ [Taken from ref. 15].

Fig. 22 Structure diffusion of H₅O₂⁺ in the hydration structure network [Taken from ref. 7].

Fig. 23A) IR spectra of aqueous H₂CrO₄ solutions: (^{_____________}), 10.3 M (n = 2.6);
( ), 2.9 M (n = 16.5); (...............), 1.0 M (n = 53); ( ^{__ __ __ __} ), H₂O;
( ), KHCrO₄ solution [Taken from ref. 91].

Fig. 23B) Degree of dissociation from the IR spectra of H₂CrO₄ [Taken from ref. 91].

Fig. 24 Change of the degree of dissociation within the series,
from trifluoroacetic acid to formic acid [Taken from ref. 91].

Fig. 25 IR spectra of aqueous H₃PO₄ solutions; (^{_____________}), 18.6 M (n = 0.1);
( ), 14.7 M (1.0); ( ^{__ __ __ __ __}), 12.2. M (1.8) [Taken from ref. 92].

Fig. 26 (^{______________}), poly(p-trimethylammonium)styrene hydroxide (10 m m thick membrane, H₂O-hydrated, 90% relative atmospheric humidity); (...............), poly-(p-trimethylammonium styrene) iodide (10 m m thick membrane, H₂O-hydrated,
90% relative atmospheric humidity) [Taken from ref. 94].

Fig. 27 Percent of proton transfer as a function of the D pK_a . D -D (Glu)_n - N base systems.
o-o (His)_n - carboxylic acid systems [Taken from refs. 99,100].

Fig. 28A) Carboxylic acid ^_ N base systems (N bases with additional hydrogen bond donor group, systems b,c,e..... see ref. 11). Proton transfer to the N base in %: (...............), pure systems; ( ), systems with four water molecules per acid - N base pair

[Taken from ref. 11].

B) (His)_n - acetic acid system. Position of the proton transfer equilibrium as a function of H₂O-molecules/histidine residue. o results for a film; x results for suspensions.

[Taken from ref. 100].

C) (His)_n + carboxylic acid systems (^{_____________}), relative integral absorbance of the sharp amide A band; (- - - - - - -), % proton transfer as function of the D pK_a [Taken from ref. 100].

Fig. 29 FT-IR difference spectra of (trypsin + SBTI) minus (anhydrotrypsin + SBTI). Aqueous solutions (0.001 mol dm^-3), A) samples a pH=3; B) samples at pH=7

[Taken from ref. 127].

Fig. 30A) FT-IR difference spectrum. BR₅₇₀ positive bands; L₅₅₀ negative bands

[Taken from ref. 176].

30B) FT-IR difference spectrum. Modified BR_as (under the same conditions as in A)

[Taken from ref. 176].

Fig. 31A) FT-IR spectra in the region 4000-800 cm^-1 of films of the F₀ complex, embedded in cardiolipin liposomes. (^{_____________}), native, hydrated; (- - - - - - -), DCCD-blocked, hydrated

B) FT-IR spectra of films of the F₀ complex, embedded into cardiolipin liposomes in the region 4000-800 cm^-1. (^{_____________}), native, dried; (- - - - - - -), DCCD-blocked, dried
[Taken from ref. 191]

.

system family
donor	acceptor		solvent			method	ref.
subst.phenols	n-propylamine	3.25	CD3CN			IR	24
subst.phenols	octylamine	3.6	CCl4			IR	25
pentachlorophenol	subst.pyridines	1.6	CCl4			IR	25
3,4-dichloro-thiophenol	subst.pyridines	2.4	none			IR	26
subst.phenols	triethylamine	5.3	C6H6			dipole	27
subst.phenols	subst.pyridines	3.5	C6H6			dipole	28
subst.phenols	(L-lys)n	2.2				IR	29
carboxylic acids	pyridine	3.5	CHCl3			IR	30
subst. benzoic acids	pyridine	3.7	C6H6			dipole	31
carboxylic acids	pyridine	4.5	C6H6			dipole	32
carboxylic acids	aromatic N bases (no self-solvation)	4	none			IR	11
carboxylic acids	aromatic N bases (self-solvation possible)	2.3	none			IR	11
carboxylic acids	subst.pyridines	2.6	CH3CN			IR	33
carboxylic acids	(CH3)3NO	2.76	CH3CN			IR	34
CF3COOH	subst.pyridine N oxides	1.68	C6H6, C6H5Cl C2H4Cl2 CHCl3			IR, NMR	35
CF3COOH	subst.quinoline N oxides	1.62	C6H6,C6H5Cl C2H4Cl2 CHCl3			IR, NMR	36
CF3COOH	subst.pyridines	5.2	C6H6, C6H5Cl CH2Cl2 C2H4Cl2 CH3CN			NMR, IR	37-39
CF3COOH	subst.pyridine N oxides	1.32	CH2Cl2			NMR, IR	40
(L-glu)n	aromatic N bases	2.0				IR	41
carboxylic acids	(L-his)n	2.8				IR	42
(L-cys)n	N bases	2.0				IR	43

Tab. 1 Proton transfer equilibria of heteroconjugated hydrogen bonds [Taken from ref. 1]

		absorbance of the continuum [ ln (I0/I ) ]
compound				monoperchlorate
R1	R2	monobase		of the dibase
H	OBU	0.000		0.000
H	F	0.011		0.213
H	Ph	0.040		0.264
H	Cl	0.047		0.284
Cl	Cl	0.065		0.261
H	COOCH3	0.085		0.178
H	COOC2H5	0.089		0.088
H	NO2	0.105		0.037
NO2	NO2			Bands at 3283 and 3120 cm-1

Tab. 2 Absorbance ln I₀/I of the IR continuum at 1900 cm^-1 [Taken from ref. 48).

acid	degree of dissociation determined from band at cm-1		dissociated species begin to appear
			M	n	pKa
CF3COOH	n sCO2-	1440	7.4	3.6	0.22
H2CrO4	n sCrO3-	880	6.5	5.5	0.74
NaHSO4	n asSO42-	1100	5.7	8.4	1.9
H3PO2	n sPO2	1040	4.1	11.0	1.1
H3PO3	n sPO2	1065	5.0	8.3	1.8
H3PO4	n sPO2	1065	2.5	19.4	2.1
CF2HCOOH	CF2HCOO-	1320	6.0	5.8	1.3

Tab. 3 Number of water molecules n per acid molecule necessary that dissociated species is spectroscopically observed. Refs. of the pK_a values see ref. 66 [Taken from ref. 66]

system		D pKa in proteins
(L-Glu)n + N bases (L-His)n + carboxylic acids	2.0 2.8		Glu-His	1.8
(L-Tyr)n + N bases (L-Lys)n + phenols	0.6 1.9		Tyr-Lys	0.5
(L-Cys)n + N bases	2.0		Cys-Lys	2.2
(L-Arg)n + phenols	2.3		Arg-Tyr	2.4
Tab. 4 D pKa50% with model systems [Taken from refs. 99-103] and D pKa of the side chains in proteins (literature data).

substance	hydrogen bonds	weight of the polar proton limiting structure (%)
		dry	hydrated at 90% humidity of the air
(L-Tyr)n + (L-Arg)n	OH...N -O...H+N	73	73
(L-Cys)n + (L-Lys)n	SH...N -S...H+N	50	(80-90)*
(L-Tyr)n + (L-Lys)n	OH...N -O...H+N	10	10
Glu+ His	OH...N -O...H+N	71
Asp + His	OH...N -O...H+N	87

Tab. 5 Weights of the polar proton limiting structure of heteroconjugated hydrogen bonds between side chains [Taken from ref. 99-103].

* The hydrogen bonds are broken to a large extent in the hydrated system

System	Hydrogen bond	Cation	% Proton transfer	Chains formed	Dihydrogenphosphates in the chain Ref.
R HN N + H2PO4		Li+ Na+ K+	55 41 to His 32	• • • • • • H H O O N H • • • OPOH • • • OPO • • • O2 O • • • • • •	No chains 104 No chains 2
	N• • • HOP N H • • • -OP
R(CH2)4NH2 + H2PO4		Li+ Na+ K+	100 85-95 to Lys 75-85	H H H O O -N H • • • OPOH • • • OPO • • • H O2 O • • • • • •	> 4 105 3 5
OH + HPO4 R		Li+ Na+ K+	0 5 to Pi 10	• • • • • • O O O • • • HOPO • • • HOPOH • • • O2 O • • • • • •	No chains 106 2 4
	OH• • • OP O • • • HOP
R(CH2)2CO2H + HPO4		Li+ Na+ K+	< 5 75 to Pi 95	No chains	No chains 107
R(CH2)2CO2H + H2PO4		Li+ Na+ K+	> 0 to Pi	O H H -C O O OH • • • OPOH • • • OPOH • • • O O • • • • • •	> 5 108

Tab. 6 Hydrogen bonds with large proton polarizability formed between side chains of proteins and dihydrogenphosphates [Taken from ref.44].

ab initio calculations

acid-water hydrogen bonds

acid solutions

active side

alcohol-alcoholate bonds

alcohol dehydrogenase

amino acids

analytical treatment

anhydrotrypsin

arsenic acid

aspargine

aspartate proteases

ATP sythase

bacteriorhodopsin

base solutions

basic polyelectrolytes

Be²⁺ bonds

Be²⁺ polarizability

calixarenes

carboxylic acid - N base family

catalytic mechanisms

cation dependencies

collective proton motion

conformation

cysteine

D pK_a

dissoziation equilibrium of acids

double minimum potential

electrical fields local

enthalpy

entropy

enzymes

F₀ subunit

families of system

FIR

fluctuating H₉O₄⁺

formic acid - water - formate systems

formic acid - water - water - formate systems

glutamine

H₃O₂^-

H₅O₂⁺

H₉O₄⁺

histidine

hydration water

hydrogen bond

hydrogen-bonded systems

IR continuum

L₅₅₀ intermediate of bacteriorhodopsin

Li⁺ bonds

Li⁺ polarizability

lysine

maltodextrinphosphorylase

Mannich bases

mitochondria

molecular processes with dissoziation of acids

Na⁺ bonds

Na⁺ polarizability

nicotinamid adenin dinucleotid

nicotinamide rest

non-polar structure

non-specific interactions

ortho phosphates

P containing acids

pathways for protons

pepsin

pepstatin

phonons

pK_a

polar structure

polaritons

polarizability

poly-a-aminoacids

poly-a-aminoacids-dihydrogenphosphate systems

polyelectrolyte

polyglutamic acid

polyhistidine

polylysine

polysaccharides

potential

proteases

proton channels

proton conduction

proton pathway

proton polarizability

proton potential

proton transfer

proton tunneling

pyridoxalphosphate

serine proteases

SCF treatment

shift of AH...BA^-...H⁺B equilibria

solvent-H⁺-solvent hydrogen bonds

specific interactions

structure water

structure diffusion

trypsin

tyrosine

Zn²⁺ ion