Effects of “excessive” exciton interactions in polarized IR spectra of the hydrogen bond in 2-butynoic acid crystals: Proton transfer induced by dynamical co-operative interactions involving hydrogen bonds

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Chemical Physics 345 (2008) 49–64 www.elsevier.com/locate/chemphys

Effects of ‘‘excessive” exciton interactions in polarized IR spectra of the hydrogen bond in 2-butynoic acid crystals: Proton transfer induced by dynamical co-operative interactions involving hydrogen bonds Henryk T. Flakus *, Barbara Hachuła Institute of Chemistry, University of Silesia, 9 Szkolna Street, Pl-40-006 Katowice, Poland Received 12 November 2007; accepted 21 January 2008 Available online 30 January 2008

Abstract In this article, we present the results of our study of polarized IR spectra of the hydrogen bond in crystals of 2-butynoic acid (CH3C„CCOOH) as well as in crystals of its deuterium derivative (CH3C„CCOOD). 2-Butynoic acid can exist in two polymorphous crystalline forms: in the ‘‘a” form, based on a classic dimer motif and in the ‘‘b” form, based on the catamer pattern of the hydrogen bond arrangement. By cooling the melted substance crystals of the ‘‘b” phase were obtained selectively. The polarized IR spectra of the hydrogen bond in the ‘‘b” form of 2-butynoic acid crystals were measured at room temperature and at the temperature of liquid nitrogen in the mO–H and mO–D band frequency ranges. In terms of the ‘‘strong-coupling” theory the fine structure patterns of the mO–H and mO–D polarized bands were quantitatively explained along with the dichroic and the H/D isotopic effects in the spectra. To interpret the main properties of the spectra the existence of a non-conventional effect concerning a self-stimulated concerted proton position rearrangements in the neighboring cells in the lattice had to be assumed. On the basis of the spectra of isotopically diluted crystalline samples of 2-butynoic acid it was suggested that a random distribution of protons and deuterons occurred in the open chains of the hydrogen bonded molecules. However, coordination in the mutual arrangement of protons and deuterons in the neighboring hydrogen bonds from the closely spaced molecular chains was found to be non-random. This fact was ascribed to dynamical co-operative interactions, most strongly involving hydrogen bonds from different chains in the modified lattice. These non-conventional interactions were responsible for appearance of the so-called H/D ‘‘self-organization” isotopic effects in the spectra. Ó 2008 Elsevier B.V. All rights reserved. Keywords: Hydrogen bond; Molecular crystals; Polarized IR spectra; H/D isotopic effects; Linear dichroic effects; Temperature effects; Isotopic dilution; H/D isotopic ‘‘self-organization” effects

1. Introduction For over six decades the IR spectroscopy has been considered to be a powerful tool in the area of hydrogen bond research. The main spectral effects in IR concerning hydrogen bonds are connected with the mX–H proton stretching

*

Corresponding author. Fax: +48 32 2599 978. E-mail address: fl[email protected] (H.T. Flakus).

0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.01.035

vibrations in the X–H


Y hydrogen bridges (where X and Y denote heavy atoms like: O, N, S, etc.). They occur in the highest frequency range of the middle IR. These effects comprise: a considerable decrease of the mX–H band frequencies, a strong increase of their band integral intensities and a considerable widening of the band contours [1– 5]. Quantitative theoretical models of the hydrogen bonded system IR spectra, subsequently developed over the last four decades aimed to reconstitute the intensity

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distribution patterns in the spectra of single hydrogen bonds, as well as in the spectra of more complex hydrogen bond systems. At first centrosymmetric hydrogen bond dimers were assumed. Despite the doubtless success achieved in this area, when interpreting the dimeric system spectra in terms of the ‘‘strong-coupling” theory [6–8] and recently, with the use of the so-called ‘‘relaxation” theory [9–11], it seems that a number of serious theoretical problems still remain unsolved. IR spectra of hydrogen bonded molecular crystals measured in polarized light seem to open new prospects in the area of hydrogen bond research. This kind of experimental study, aided by suitable model calculations of the mX–H band contour shapes, performed within the limits of the quantitative theory of hydrogen bond IR spectra for diverse systems of hydrogen bonds allowed us to reveal new non-conventional phenomena in this area. These new effects include the breaking of the vibrational dipole selection rules in IR for centrosymmetric hydrogen bond dimers [12] and the so-called H/D ‘‘self-organization” isotopic effects [13,14]. The H/D ‘‘self-organization” isotopic effects result from a non-random distribution of protons and deuterons between the hydrogen bridges in crystalline lattices for samples with a mixed H/D isotopic content. The consequence of these effects is the invariability of mX–H bands contour fine structure patterns in these circumstances. The so-called ‘‘residual” mX–H bands are the attribute of the residual protons, which remained non-replaced by deuterons in the sample after the isotopic exchange. This phenomenon may occur independent of the increasing H/D isotopic exchange rates for the samples [13,14]. The latter discovery seems to be of a potential biological importance. The H/D ‘‘self-organization” spectral effects are the result of dynamical co-operative interactions in diverse hydrogen bond systems, i.e. in such small systems of hydrogen bonds as dimers, trimers or tetramers, as well as in lattices of molecular crystals. Most probably, these non-conventional mechanisms are also co-responsible for the dramatic changes in the rates of metabolic processes in biological systems occurring in the environment of heavy water [15]. In our recent studies the conditions of the appearance of the H/D ‘‘self-organization” isotopic effects were established by investigating the independence effect of the ‘‘residual” mX–H band contours in relation to the increasing isotopic dilution rates [16–18]. The circumstances, in which the ‘‘self-organization” effects did not appear, were also established [19–21]. It turned out that the electronic structure of the associating molecules, affecting the magnitude of the dynamical co-operative interaction energies, was the dominant factor responsible for such behavior [16–21]. The problem of the dynamical co-operative interactions in crystal lattices, formed of infinitely long chains of hydrogen bonds, seems to be especially interesting. From our initial studies of the problem it follows that the phenomenon of the H/D isotopic ‘‘self-organization”, provided it occurs

for several molecular crystals, can take place in two different ways. In the first case the mechanism involves the neighboring hydrogen bonds belonging to each individual chain of the associating molecules. In these circumstances no coordination in the hydrogen isotope distribution between the hydrogen bridges of two neighboring chains in the unit cell appears [16–18,22]. In the other case, this phenomenon refers exclusively to the closely spaced hydrogen bonds, where each hydrogen bond in the mutually coupled system belongs to a different translationally nonequivalent chain penetrating a unit cell [23,24]. In crystals characterized by infinite chain systems of hydrogen bonds in their lattices, both ways in which the H/D ‘self-organization’ isotopic effect is generated may visibly influence the spectral properties of the so-called ‘‘residual” mX–H bands. This remark concerns the intensity distribution, the temperature and the linear dichroic effects, measured in the crystal spectra, within the frequency range of the mX–H band contours [16–18,22–24]. This spectral behavior allows us to distinguish both ways of the occurrence of this process with the use of spectral studies performed on diverse hydrogen bonded crystalline systems. The way the H/D ‘‘self-organization” proceeds in chain systems of the hydrogen bond lattices in isotopically diluted crystals determines the shapes of the domains occupied by identical hydrogen isotope atoms, i.e. by protons or deuterons. In the first case, the longitudinal domains are extended over several fragments of the hydrogen bond chains [16–18,22], whereas in the second case, the domains containing identical hydrogen isotope atoms, have the form of plain, disc-shaped structures, oriented perpendicularly to the chain direction in the crystal lattices [23,24]. Since the start of spectral IR studies of hydrogen bond systems, (accompanied by the spectra theory development), associated carboxylic acid have been treated as the most popular model systems for testing the adequacy of the subsequently proposed theoretical models introduced for spectra interpretation [6,10,11,25–30]. Carboxylic acid crystals basically form two kinds of lattices. For the vast majority of carboxylic acids the crystal lattices were composed of centrosymmetric cyclic hydrogen bond dimers [31,32]. However, in rare cases, infinitively long chains of the associated molecules exist in the crystal lattices [31,32]. In this case, it is of particular interest to investigate the problem of the inter-hydrogen bond vibrational exciton couplings and of dynamical co-operative interactions involving hydrogen bonds. All these crystal structures were characterized by at least four translationally non-equivalent hydrogen bonds in their unit cells (Z = 4). This made complex the problem of the inter-hydrogen bond interactions and led to the fact that the conclusions drawn had a relatively high uncertainty level. The main aim of the reported project was to investigate the H/D ‘‘self-organization” in model carboxylic acid crystals with the chain arrangement of hydrogen bonds for a

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system with an extremely simple structure of the lattice, i.e. by a system with Z = 2. We initially also assumed that the electronic properties of the selected model molecular system, for instance the p-electronic system existing in the molecular skeleton, should prefer the latter type of H/D isotopic ‘‘self-organization” mechanism, involving hydrogen bonds from one chain. Hence we selected the 2-butynoic acid, which seemed to have the proper molecular system satisfying the demands of the project. For instance, in the solid-state its molecules associate forming the so-called ‘‘b” phase characterized by infinite molecular chains in the lattice and by Z = 2 [33,34]. From our recent study of H/D isotopic ‘‘self-organization” effects it results that the energy magnitude of the dynamical co-operative interactions correlates with that of vibrational exciton coupling energy values. These values govern the interactions between the pairs of translationally non-equivalent hydrogen bonds in the unit cells, for the crystal lattices with Z = 4, 8, etc. [16–18,22–24]. Complete information about the energies of exciton coupling can be obtained from the IR solid spectra, measured by using polarized light. In case of 2-butynoic crystals of the ‘‘b” form, characterized by such a simple X-ray structure, the crystal IR spectra of the hydrogen bond should be devoid of any Davydow-splitting effects attributed to the interchain exciton couplings [35,36]. For the selected system the H/D isotopic ‘‘self-organization” can only occur in one way when it takes place in each chain in the lattice. This can happen since no other translationally nonequivalent chains with respect to the reference chain are present. For the ‘‘b” phase of 2-butynoic acid crystals the energy of the dynamical co-operative interactions should correlate exclusively with only one type of the exciton coupling energy magnitude, i.e. the one related to the interaction involving the adjacent hydrogen bonds in the ‘‘zig-zag” type chain. It may be expected that such a simple but rare internal structure of 2-butynoic acid crystals should influence the IR spectra of the hydrogen bonds in the system in a predictable way. One might also expect that these spectra should resemble the corresponding spectra of formic acid crystals with regard to their intensity distribution pattern and their linear dichroic properties [22]. Any discrepancies from this scheme would prove the existence of some other unknown hidden interaction mechanisms involving the hydrogen bonds, not considered previously in the theoretical models. In the spectra of other more complex crystalline hydrogen bonded systems, e.g. for crystals with Z = 4, the spectral effects attributed to these hypothetical hidden interaction mechanisms, may be probably masked by more complex exciton inter-hydrogen bond coupling effects. 2. 2-Butynoic acid crystal The crystal structure of 2-butynoic acid was determined from X-ray diffraction data by Benghiat and Leiserowitz

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[33]. There are two polymorphic forms of 2-butynoic acid: the ‘‘a” and the ‘‘b” one. The molecules of the ‘‘a” modification form hydrogen bonded cyclic dimers whereas the crystals of the ‘‘b” form consist of chains of 2-butynoic acid molecules bound together by hydrogen bonds. The ‘‘a” phase crystals are triclinic and the space symmetry group is P1. The unit cell contains two translationally non-equivalent molecules. The unit cell parameters are: ˚ , b = 5.099 A ˚ , c = 7.226 A ˚ , a = 83.91(1)°, b = a = 7.320 A 117.46° and c = 112.00(1)°. The ‘‘b” phase 2-butynoic acid crystals are monoclinic and belong to the space group P21. The unit cell also contains two translationally non-equivalent molecules. The ˚ , b = 7.121 A ˚ , c = 3.937 A ˚, unit cell constants: a = 7.887 A a = 90.00°, b = 100.18(1)° and c = 90.00°. It was found that, the ‘‘a” form could be obtained by evaporation of chloroform solution while the ‘‘b” form crystallizes from ethanol solution [33,34]. This latter phase can also be obtained by crystallization of the melted 2-butynoic acid. Its melting point is 78 °C. 3. Experimental 2-Butynoic acid, CH3C„CCOOH, used for our studies was a commercial substance (Sigma–Aldrich). The substance was investigated without further purification. First, the two different solid-state phases of 2-butynoic acid were obtained selectively. The deuterium derivative of the 2-butynoic acid was obtained by evaporation of D2O solution of the compound at room temperature and under reduced pressure. The single crystals of the ‘‘b” form of 2-butynoic acid and of its deuterium derivative were obtained by crystallization from melt, occurring between two closely spaced CaF2 windows. In this way thin enough crystals were prepared, which exhibited their maximum absorbance at the mO–H band frequency range, close to 0.5 at the mO–H band frequency range. Next suitable monocrystalline fragments were selected from the crystalline mosaic and then spatially oriented by using a polarization microscope. These selected single crystals were exposed for the experiment with the use of a metal plate diaphragm with a 1.5 mm diameter hole. The crystals of tetrolic acid most frequently developed the ‘‘bc” crystalline face. The IR spectra were recorded with the FT-IR Nicolet Magna 560 spectrometer by the transmission method with 2 cm 1 resolution. The polarized spectra were measured at 298 K and at 77 K, for two different orientations of the electric field vector ‘E’ with respect to the lattice. In one case the spectra were measured for the ‘E’ vector parallel to the ‘‘b” axis of the lattice, and in the second case, perpendicular to it, i.e. parallel to the ‘‘c” identity period. For each 2-butynoic acid isotopomer case, the measurements were repeated for ca. 10 single crystals. The Raman spectra were measured at room temperature for polycrystalline samples of tetrolic acid by using the Raman Accessory for the Nicolet Magna 560 spectrometer.

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4. Results of the spectral studies and discussion 4.1. IR spectra of two polycrystalline phases of 2-butynoic acid The IR spectra of 2-butynoic acid dissolved in the CCl4 solution recorded in the mO–H band frequency range are shown in Fig. 1. The IR spectra of the polycrystalline samples of the two solid-state phases of 2-butynoic acid: i.e. of the ‘‘a” and ‘‘b” phase, measured at two different temperatures, 293 and 77 K, are given in Fig. 2. The Raman spectrum of the polycrystalline samples is also plotted in order to indicate the influence of the mC–H band on the mO–H band contour shape. The IR spectra measured for both crystal forms of 2-butynoic acid were used for identification of the two different crystalline phases. The spectra of the commercial substance appeared to be identical with the spectra of the ‘‘a” form whereas the spectra of polycrystalline samples obtained by crystallization of melt were identical with the spectra of the ‘‘b” form. Fortunately, the ‘‘b” form crystals characterized by the chain arrangement of hydrogen bonds in the lattice and by Z = 2 belonged to the system of special interest in our project. Single crystals of the ‘‘b”-form could, therefore, be relatively easily obtained by crystallization of the melted substance. The observed differences between the spectra of ‘‘a” and ‘‘b” forms are undoubtedly connected with the essential differences in the crystalline phase structures. However, the spectral property differences appeared to be considerably smaller than preliminarily expected. This fact seems to be particularly surprising since the X-ray struc-

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tures of the two solid-state phases do not justify such behavior. In the case of the CCl4 solution of the compound we dealt with single, isolated hydrogen bond dimers, created in the cyclic dimers of 2-butynoic acid. The IR spectra of both forms of 2-butynoic acid having the mO–H band contour shapes significantly resembled the analogous spectra of the substance dissolved in CCl4. The fair similarity of the three compared IR spectra is highly puzzling and requires explanation. The spectra of polycrystalline samples of both phases represent the two-branch structure of their mO–H bands, similar to the band shapes measured for the spectra of other centrosymmetric hydrogen bond dimeric systems. In the shorter-wave range of each mO–H band an intense and diffused spectral branch appeared, whereas in the longer-wave range less intense spectral lines, forming a well-developed, regular spectral progression of a low frequency was observed. This fact is rather puzzling since the shape of the IR spectra of the ‘‘b” phase crystal structure would be expected to form the fine structure pattern typical for the chain-type associated hydrogen bond structures. For the hydrogen bond chain system the expected mO–H bands, with their characteristic spectral branch shapes, appeared in the reversal sequence in comparison with the corresponding spectra of cyclic hydrogen bond dimeric systems [16,18,22]. The mO–H bands of both forms are widespread in an almost identical frequency range, i.e. from ca. 2300 cm 1 up to 3300 cm 1. At room temperature, in the ‘‘a” and ‘‘b” phase spectra in their shorter-wave range there exists the diffused band, whereas in the longer-wave range the branch band consists of two well-separated intense lines.

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Fig. 1. (I) The IR spectra of 2-butynoic acid in the CCl4 solution, recorded in the mO–H and mC„C band frequency ranges. (II) The mO–H band intensity is multiplied by 3.6 and the mC„C band is blanked.

H.T. Flakus, B. Hachuła / Chemical Physics 345 (2008) 49–64

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Fig. 2. The IR spectra of polycrystalline samples of two polymorphous forms of 2-butynoic acid: ‘‘a” and ‘‘b”, dispersed in KBr pellets, measured at 293 K and at 77 K in the mO–H band frequency range. Full scale. The Raman spectrum of the ‘‘a” phase polycrystalline samples is also plotted in order to indicate the influence of the mC–H bands on the spectra.

It must be emphasized that the spectra of polycrystalline samples of both phases differ from each other mainly in the intensity ratio of their two-branches. In the ‘‘a” phase spectra the broad sub-band in the shorter-wave range is the most intense, whereas in the spectra ‘‘b” form both branches of the mO–H band are of almost equal intensities. It should also be mentioned that the narrow, intense line appearing in the spectra of the ‘‘a” as well as of the ‘‘b” form, measured at the frequency of ca. 2250 cm 1, is the attribute of the stretching vibrations of the –C„C– triple bond in 2-butynoic acid molecules. In the spectra of the deuterium derivative of 2-butynoic acid, this band is located within the mO–D band frequency range and, therefore, considerably disturbs the band fine structure pattern.

4.2. Polarized IR spectra of the ‘‘b” phase 2-butynoic acid crystals 4.2.1. Linear dichroic effects in the mO–H bands Fig. 3 shows the polarized IR spectra of single crystals of 2-butynoic acid ‘‘b” form measured at 293 and at 77 K in the mO–H band frequency range. The spectra from Fig. 3 exhibit the basic linear dichroic effects connected with the orientation of the ‘‘E” electric vector of the polarized beam with respect to the hydrogen bond lattice in experimental conditions. The two-branches of the mO–H polarized components bands, the shorter- and the longer-wave, measured for different orientations of the electric field vector ‘‘E”, only insignificantly differ from each other by their relative intensity distribution. The mO–H

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Fig. 3. Polarized IR spectra of the ‘‘b” form 2-butynoic acid crystals measured at 293 and 77 K in the mO–H band frequency range for the two polarizations of the electric field vector E: (I) E parallel to ‘‘c” identity period and (II) E parallel to ‘‘b” axis. Common scale: (a) 293 K and (b) 77 K.

band intensity in the whole band frequency range, measured for the ‘‘E” vector polarized along the hydrogen bond chains (i.e. parallel to the ‘‘b” identity period), is almost ideally proportional to the band intensity measured for the perpendicular ‘‘E” vector polarization (i.e. parallel to the ‘‘c” identity period). The temperature decrease does not significantly change the dichroic properties of the spectra in the mO–H band frequency range. The described dichroic effects in the crystal spectra are surprising enough, since 2-butynoic acid molecules in the ‘‘b” phase form infinite, zig-zag-type open hydrogen bond chains. As the result of the exciton in chain interactions, the obtained polarized spectra should exhibit a strong linear dichroic effect in the mO–H band frequency range, differentiating the spectral properties of the two spectral branches placed on the opposite wings of the band.

For the chain system the two vibrational transitions contributing to the mO–H band generation differ from each other in their transition moment direction. The transition moment for the totally symmetric proton stretching vibrations in the chain system are polarized parallel to the chain direction while for the non-totally symmetric vibrations is polarized perpendicularly to it [16–18]. This kind of linear dichroic effect should differentiate the spectral properties of the two opposite branches of the band. The absence of the above mentioned polarization effects in the experimental polarized spectra of ‘‘b” form 2-butynoic acid crystals contradicts these predictions. Similar qualitative predictions should also be valid for the crystalline spectra of the deuterium derivative of the compound measured in the mO–D band frequency range. For this band there are also no considerable differences

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in the polarization properties of the opposite spectral branches. 4.2.2. Linear dichroic effects in the mO–D bands Fig. 4 presents the polarized IR spectra of deuterium bonded 2-butynoic acid crystals measured at 293 K and at 77 K in the mO–D and the ‘‘residual” mO–H band frequency range. The mO–D band in the spectra of the ‘‘b” solid-state phase of the 2-butynoic acid deuterium derivative extends over the frequency range of 1900–2500 cm 1. Unfortunately, the intense line attributed to the –C„C– bond stretching vibrations also appears in this area. Therefore, this line interferes the mO–D band shape by overlapping it, which makes the quantitative analysis of this band uncertain.

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Nevertheless, the mO–D band exhibits qualitatively similar spectral properties to the ones of the mO–H band. It also has the two-branch fine structure pattern with qualitatively similar polarization and temperature effects characteristic for the mO–H band properties. 4.2.3. Impact of temperature on to the mO–H and mO–D bands The impact of temperature on the more intense polarized component mO–H band contour shape from the crystalline spectra of 2-butynoic acid is presented in Fig. 5. The temperature impact taken from the crystalline spectra of partially deuterated 2-butynoic acid samples on the more intense polarized component of the ‘‘residual” mO–H and the mO–D band contour shape is shown in Fig. 6.

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Fig. 4. Polarized IR spectra of deuterium bonded the ‘‘b” form 2-butynoic acid crystals measured at 293 and 77 K in the mO–D and the ‘‘residual” mO–H band frequency range. Common scale. The spectra were measured for the normal incidence of the IR beam with respect to the ‘‘bc” crystallographic plane. (I) E parallel to ‘‘c” and (II) E parallel to ‘‘b”. (a) 293 K and (b) 77 K.

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0.6 0.5

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Wavenumbers (cm-1) Fig. 5. Temperature impact on to the most intense polarized component band contour shape of the mO–H band from the crystalline spectra of 2-butynoic acid. Common scale.

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Fig. 6. Temperature impact on to the most intense polarized component band contour shapes of the mO–D and the ‘‘residual” mO–H bands from the crystalline spectra of the deuterium bonded ‘‘b” form 2-butynoic acid. Common scale.

On analyzing Figs. 5 and 6 one can see that the temperature effect accompanying the reduction of temperature to 77 K, depended on the almost proportional intensity growth of the both branches of the mO–H band. The temperature decrease also caused a slight narrowing of the shorter-wave branch of the mO–H and mO–D bands. At room temperature the two-branches of the mO–H band had comparable intensities whereas the longer-wave branch became the most intense at the liquid nitrogen temperature. From the spectra it can be estimated that the impact of temperature on the dichroic spectral properties of the mO–H and

mO–D bands is relatively weak. The temperature change caused no noticeable change in the intensity ratios of the mO–H and mO–D band branches. 4.3. Isotopic dilution effects in the crystalline spectra The IR spectra of the ‘‘b” form crystals measured for samples characterized by considerably high deuterium contents (see Fig. 4) have proved that the isotopic dilution did not essentially influence either the position, the band shape or the branch intensity ratio of the ‘‘residual” mO–H band.

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This ‘‘residual” mO–H band exhibited almost identical linear dichroic and temperature effects as the mO–H band of the isotopically neat crystalline samples. A similar conclusion is also valid for the comparison of the ‘‘residual” mO–D band measured for deuterated samples with a low deuterium content (i.e. below 20% D) and for the mO–D band recorded for samples with an over 80% content of deuterons. The latter bands can be formally treated as the ones measured for approximately neat deuterium derivative samples since they exhibit a full system of exciton splitting effects in their IR spectra. 4.4. Model calculations of the mO–H band and mO–D band contour shapes 4.4.1. Choice of model A quantitative analysis of the spectral properties of the ‘‘b” form of 2-butynoic acid crystals was performed by employing the model calculations of the mO–H and mO–D band contour shapes in terms of the ‘‘strong-coupling” theory [6,7,37]. It was be expected that the results of the model calculations would shed light on the problem of the vibrational exciton interactions, involving the hydrogen bonds of a unit cell, which most strongly influenced the IR spectra of the hydrogen and deuterium bonds in the 2-butynoic acid crystals. A careful quantitative study of the crystalline spectra should allow for the identification of the nature of the exciton interaction mechanisms. This indicates which hydrogen bonds in the lattice are most strongly excitoncoupled. From our recent studies it resulted that these hydrogen bond pairs also effectively interacted via the dynamical co-operative interactions. This is reflected in the H/D isotopic ‘‘self-organization” effects in the IR crystalline spectra of the isotopically diluted crystalline samples [13,14]. In terms of the ‘‘strong-coupling” theory [7,8,37] the mO–H band shape depends on the following coupling parameters: (i) on the distortion parameter ‘‘bH” and (ii) on the resonance interaction parameters ‘‘Co” and ‘‘C1”. The ‘‘bH” parameter describes the change in the equilibrium geometry of the low-energy hydrogen bond stretching vibrations, accompanying to excitation of the protonic stretching motion in hydrogen bonds. The ‘‘Co” and ‘‘C1” parameters are responsible for the exciton interactions between the hydrogen bonds in the model hydrogen bond dimer. However, the spectral properties of the model hydrogen bond dimers strongly depend on their geometry. A detailed analysis of the relation between the crystalline mO–H band shapes and their dichroic properties may be helpful in determining of the hypothetical hydrogen bond aggregate geometry responsible for the spectra generation. 4.4.2. Linear dimer approximation Our initial approach to the theoretical quantitative treatment of the problem, performed with the use of the ‘‘strong-coupling” model [7,8,37], assumed that the linear dimeric hydrogen bond model was responsible for the

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basic spectral properties of this crystalline system. In this case, the hydrogen bonds in the model dimer were considered to be linked in the form of the ‘‘tail-to-head” chain system, similarly as in the crystal lattice. Within this model, the mO–H and the mO–D band structures were treated as a superposition of two component bands, each of a different origin. The lower frequency branch of each analyzed band should be connected with the totally symmetric ‘‘inphase” proton stretching vibration in a linear, quasi-axial hydrogen bond dimer [16,18]. This branch is generated by the symmetry-allowed dipole transition. The higher frequency band branch relates to the ‘‘out-of-phase” proton stretching vibration in the dimeric system. Such vibrational transition in IR should be symmetry-forbidden for the ideally axial, linear hydrogen bond dimer. The two component spectra should differ from each other by the polarization properties of their transition moment vectors, which are expected to be mutually perpendicular. Nevertheless, it must be emphasized that the shapes of the analyzed crystalline spectra, along with their dichroic properties, cannot be quantitative reproduced within the initial assumption of the model. On the other hand, considering to the crystal space symmetry it seemed to be the most reasonable one to employ. 4.4.3. A ‘‘side-to-side” type dimer model Another, approach to solve the problem based on the unusual assumption that the structural unit of crystal lattice, being the bearer of the basic spectral properties of a crystal, was a quasi-centrosymmetric dimer, with the approximately anti-parallel arrangement of the bonds in a ‘‘side-to-side” type system. Its geometry resembled fairly well the one for associated carboxyl groups in carboxylic acid cyclic dimers. Moreover, in this approach the mO–H and the mO–D bands were treated as a superposition of the two component bands, each of a different origin. From this particular model it results that the lower frequency branch of each analyzed band corresponds with the dipole-forbidden transition to the excited state of the totally symmetric proton stretching vibration in the centrosymmetric hydrogen bond dimer. This part of the spectrum was satisfactorily reproduced by the so-called ‘‘minus” band from the ‘‘strong-coupling” theory [12,37]. The forbidden transition in the IR may, however, become spectrally activated via the vibronic promotion mechanism, which is a reversion of the familiar Herzberg–Teller mechanism [12,38] from the electronic spectroscopy of aromatic hydrocarbon molecules. Therefore, the sub-band connected with the forbidden vibrational transition may appear in the spectra of centrosymmetric hydrogen bond dimers [12]. The higher frequency branch of each considered band corresponds with the symmetry-allowed transition ascribed to the non-totally symmetric proton vibrations in the centrosymmetric hydrogen bond dimer. It was successfully reproduced quantitatively by the so-called ‘‘plus” band [6,7,37].

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In Fig. 7 the results of the model calculation are shown aiming at a qualitative reconstruction of the mO–H band contour shape of 2-butynoic acid crystals. The ‘‘minus” and ‘‘plus” bands contributed proportionally to their respective statistical weight parameters F and F+. The parameter values used for calculation of the theoretical spectrum were: bH = 1.3, C0 = 1.0, C1 = 0.0, F = 1.0, F+ = 0.8, XO


O = 100 cm 1. The corresponding experimental spectrum is given in insert. The results of the qualitative reconstitution of the mO–D band contour shape of the ‘‘b” form 2-butynoic acid crystals are shown in Fig. 8. The parameter values used for reconstitution of the experimental spectrum were: bD = 0.2, C0 = 1.0, C1 = 0.0, F = 1.0, F+ = 0.7, XO


O = 100 cm 1. In this case both component transitions participating in the generation of each of the analyzed bands should be characterized by identical polarization properties [12]. Unexpectedly, this latter model, although seemingly contradictory to the crystal structure, appeared successful in the quantitative description of the crystalline spectra of the 2-butynoic acid ‘‘b” form. It allowed for a reasonably good reproduction of the mO–H as well as mO–D band shapes from the crystal spectra. It also correlates fairly well with

the dichroic properties of the experimental spectra, measured in the mO–H and mO–D frequency ranges. 4.5. Abnormal exciton interaction effects in the crystalline spectra On analyzing the polarized IR spectra of diverse carboxylic acids crystals, with their lattice structures composed of cyclic centrosymmetric hydrogen bond dimers, it resulted that in each case the mO–H and mO–D bands were characterized by a two-branch fine structure pattern. Both branches of each analyzed band, of different branch intensity ratios, exhibited almost identical polarization properties in the whole band frequency ranges [12,39, 40]. To understand the spectra of 2-butynoic acid crystals it is necessary to explain the striking similarity of the spectra of the ‘‘b” phase crystals to the corresponding spectra of other molecular systems forming cyclic hydrogen bond dimers in their crystal lattices. The mO–H and mO–D band characteristics of the previously investigated dimeric systems is the key property attributed to the nature of the inter-hydrogen bond exciton interactions in the crystal and the approximate geometry of the hydrogen bond aggregate responsible for generation of the crystal

12.00

III 8.00 2000

Intensity

3000

II

4.00

I

0.00 4.00

0.00

-4.00

ωo — o Fig. 7. Theoretical reconstitution of the most intense mO–H band component from the low-temperature polarized spectra of 2-butynoic acid crystals. (I) The ‘‘minus” band reconstituting the higher-energy transition branch of the mO–H band, (II) the ‘‘plus” band reproducing the lower-energy transition branch and (III) the superposition of the ‘‘minus” and ‘‘plus” bands contributing proportionally to their respective statistical weight parameters F and F+. The corresponding experimental spectrum is given in insert.

H.T. Flakus, B. Hachuła / Chemical Physics 345 (2008) 49–64

59

12.00

III 2400

2200

II

2000

8.00

Intensity

III I

4.00

I II

0.00 4.00

2.00

0.00

-2.00

- 4.00

ωo — o Fig. 8. Theoretical reconstitution of the most intense mO–D band component from the low-temperature spectra of deuterated 2-butynoic acid crystals. (I) The ‘‘minus” band reconstituting the higher-energy transition branch of the mO–D band, (II) the ‘‘plus” band reproducing the lower-energy transition branch and (III) the superposition of the ‘‘minus” and ‘‘plus” bands contributing proportionally to their respective statistical weight parameters F and F+. The corresponding experimental spectrum is given in insert.

spectra. In these cases the band properties are determined by the hydrogen bond dimers with an anti-parallel arrangement of the component moieties. To solve the problem of the 2-butynoic acid crystal spectra generation mechanism it is necessary to accept an unusual assumption that also in this case the centrosymmetric hydrogen bond dimers are practically the effective bearers of the spectral properties of the ‘‘b” form of 2-butynoic acid crystals. However, this assumption remains in basic conflict with the crystal space symmetry described by the P21 space group, which contains no symmetry center operation. Basing on the molecular exciton theory [35,36] for the space group P21 and for Z = 2, it would be natural to expect that the exciton couplings in the lattice of 2-butynoic acid crystal should exclusively involve the hydrogen bonds, located within each individual chain of the associated molecules. In this way only the adjacent, exciton-coupled translationally non-equivalent hydrogen bonds in a unit cell of the lattice should be the exclusive bearers of

the crystal spectral properties. Consequently a strong linear dichroic effect in the IR spectra should appear, differentiating the dichroic properties of the two opposite spectral branches of the mO–H and mO–D bands. Nevertheless, it has to be emphasized that the crystal spectral properties contradict the formerly estimated X-ray structure of 2-butynoic acid crystal given by the P21 space symmetry group and by Z = 2 [33,34]. From our model calculations and from the analysis of the dichroic effects in crystalline spectra it may be concluded that the exciton interactions involve hydrogen bonds of an approximately parallel mutual arrangement in the lattice. Paradoxically, the strongest exciton interactions seem to be of the ‘‘side-to-side” type, i.e. that which apparently involves the parallel oriented hydrogen bonds belonging to the different, although closely spaced translationally equivalent chains. On the other hand, from the exciton theory it also results that the translationally equivalent molecules cannot generate the exciton splitting effects in the crystalline spectra [35,36].

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4.6. A possible source of the dimeric character of the 2butynoic crystal spectra In terms of the molecular exciton theory, a unit cell is the source of the basic spectral properties of a molecular crystal [36,41]. In the case of the ‘‘b” form 2-butynoic acid crystals, the two translationally non-equivalent hydrogen bonds from a unit cell, belonging to one chain, should be exclusively responsible for the main crystal spectral properties. However, experimental facts show convincingly that some irregular effects in the spectra can be observed which should definitively not appear in this lattice type. A larger effective unit cell seems to be responsible for the observed spectral effects. This results from the comparison with unit cell characteristics determined by the X-ray [33,34], i.e. an effective unit cell containing more than two molecules. It seems, therefore, that the only possible explanation of this paradox is to assume that the particular proton position system in an individual unit cell stimulates other protons, namely those belonging to the neighboring chains, to take the concerted jump in their hydrogen bonds towards the acceptor oxygen atoms. As the result of this process the neighboring hydrogen bond chains, a special attention paid to the proton positions, are no longer translationally equivalent. Consequently, the effective unit cells, matching the description of the spectral properties, are twice as big as the unit cell size resulting from the X-ray data [33,34]. The effectively enlarged unit cell would therefore contain four hydrogen bonds, divided into two centrosymmetric hydrogen bond pairs, which in the doubled unit cells are only weakly mutually exciton-coupled. The idea of the postulated rearrangement in the crystal lattice structure is schematically presented in Fig. 9. This figure was prepared on the basis of the structural data concerning the ‘‘b” form crystal, available from [41]. The proposed idea of the spectra generation mechanism is at least partly supported by the newly revealed, dynam-

ical co-operative interaction mechanism involving hydrogen bonds. These non-conventional interactions in the hydrogen bond lattice of 2-butynoic acid crystals may lead to the formation of a more thermodynamically stable structure following the proton replacement processes in the lattice [13]. According to the consequences of the dynamical co-operative interaction mechanism theory, the proton position rearrangement may effectively reduce the lattice energy in relation to the energy value corresponding to the formerly estimated crystal X-ray structure [33,34]. The postulated mechanism does not basically contradict the formerly published results of the crystal structure determination. With the standard X-ray diffraction methods the proton positions in the hydrogen bond bridges cannot be precisely established since the X-ray diffraction occurs on the electrons of atoms in the crystal lattice. This is due to the fact that hydrogen bond protons are practically devoid of the electron charge. Hence their positions cannot be precisely determined by the X-ray method since ‘‘bare” protons cannot effectively participate in X-ray diffraction. Therefore, the modified proton positions due to proton replacement phenomenon should not influence significantly the molecular structure in the crystal and the crystal lattice parameters, since it is the structure of the lattice determined by positions of the heavy atoms. Therefore, it seems rather difficult to identify the postulated effect of the self-stimulated proton position rearrangement, occurring in the neighborhood of an individual hydrogen bond chain, without making preliminary assumptions concerning this effect in the crystal structure refinement routine. An additional suggestion in support of the existence of this phenomenon is also the fact that the X-ray structure researchers of the ‘‘b” form 2-butynoic acid crystals reported some problems in the precise determination of the crystal structure [33,34]. Perhaps, this was connected with the postulated effects of the structural transformation occurring in the lattice, which were not taken into account previously.

Fig. 9. A schematic presentation of the idea of the proton position rearrangement in the crystalline lattice of 2-butynoic acid crystal of the ‘‘b” form stimulated by dynamical co-operative interactions: (a) the X-ray structure of the P21 symmetry and Z = 2 and (b) the lattice structure after the replacement of protons.

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4.7. The spectra generation mechanism in the scope of isotopic dilution effects On analyzing the IR spectra of 2-butynoic acid crystals, measured even at the highest isotopic dilution rates, it can be noticed that the spectral properties of the ‘‘residual” mO–H band did not noticeably change on comparison with the analogous mO–H band properties, characterizing isotopically neat crystals. Also the ‘‘residual” mO–D bands, recorded for low concentrations of deuterons, exhibited the polarization and temperature effects qualitatively similar to the corresponding properties of the mO–D bands, measured at the highest deuterium contents in the crystalline samples. The ‘‘residual” mO–H bands still retained the polarization effects and the intensity distribution typical for the spectra of centrosymmetric dimers of hydrogen bonds in the isotopically neat crystalline samples. This means that the ‘‘residual” mO–H bands remain affected by the same exciton interactions, which determined the main spectral properties of the mO–H bands from the spectra of the isotopically neat crystals. Therefore, in the case of a considerable proton deficiency the residual protons belonging to the closely spaced hydrogen bonds are held together by some non-conventional forces. However, the ‘‘residual” mO–D bands, in relation to the mO–D bands, exhibited fairly similar spectral properties. The isotopic dilution effects in the spectra strongly support the assumption that the strongest exciton interactions are restricted to pairs of hydrogen bonds only. In the case of a high deficiency of protons, the spectral properties of such pairs of coupled hydrogen bonds still resemble those of centrosymmetric hydrogen bond dimers, of the ‘‘sideto-side” type arrangement of hydrogen bonds. Owe to this ‘‘side-to-side” type exciton coupling of hydrogen bonds only very slight differences in the polarization properties may appear, differentiating the spectral properties of the two opposite branches of the mO–H and mO–D bands. This is a typical property of the IR spectra of centrosymmetric hydrogen bond dimeric systems found in molecular crystals [12,39,40]. To explain all the discussed isotopic dilution effects some newly revealed mechanisms need to be recalled, i.e. (i) the breaking of the dipole selection rules for dipole transitions in IR spectra of centrosymmetric hydrogen bond dimers [12] and (ii) the dynamical co-operative interactions mechanisms involving hydrogen bonds in crystal lattices [13,14]. The band two mO–H and mO–D branch fine structure patterns is determined by the selection rule breaking mechanism for centrosymmetric hydrogen bond dimers [12]. The same mechanism is responsible for the generation of the ‘‘residual” bands. The dynamical co-operative interaction mechanism was considered to be responsible for the so-called the H/D isotopic ‘‘self-organization” effects in IR spectra of isotopically diluted crystals [13,14]. These effects depend on the invariability of the mO–H band contour shapes in the spectra

61

of hydrogen bonded crystals, regardless of the increasing deuterium substitution rates. They result from a non-random distribution of protons and deuterons between the hydrogen bridges in the lattices of isotopically diluted crystals. This effect was interpreted as a result of the dynamical co-operative interactions involving hydrogen bond in crystals [13,14]. On the basis of the results of our recent systematic study of the dynamical co-operative interactions in diverse solidstate systems with lattices formed by hydrogen bond chains, the crystalline systems can be divided into two main groups. The first group comprises the systems where the H/D isotopic ‘‘self-organization” concerns the neighboring hydrogen bonds within domains placed in fragments of each single hydrogen bond chain (pyrazole [17], imidazole [18], 4-thiopirydone [16] and formic acid [22]). The second group comprises crystals in which the H/D isotopic ‘‘selforganization” mechanism involves the neighboring hydrogen bonds belonging to different, closely spaced chains (N-methylthioacetamide [23] and acetic acid [24]). From our recent estimations it also follows that if the H/D isotopic ‘‘self-organization” in chain systems takes place, the strongest dynamical co-operative interactions involve these hydrogen bond aggregates which are most strongly exciton-coupled. In our case, the H/D isotopic ‘‘self-organization” involving hydrogen bond pairs, belonging to two different chains penetrating a unit cell occurs and the strongest exciton interactions also involve the same hydrogen bond systems [23,24]. From the analysis of the 2-butynoic acid crystal spectra it results that in this particular case a highly abnormal H/D isotopic ‘‘self-organization” phenomenon takes place. The problem is the way in which the H/D isotopic ‘‘self-organization” phenomenon occurs in the ‘‘b” form crystals of 2-butynoic acid. On the basis of the above reported experimental facts it seems justified to assume that for describing the spectral properties of the ‘‘b” form 2-butynoic acid crystals a model centrosymmetric hydrogen bond dimeric system should be considered. However, this model dimer appears as the result of the preceding proton replacements, occurring in the hydrogen bridges of the neighboring chains with respect to the reference chain. It leads to the alternate proton position arrangements in the closely spaced chains. This is the way to optimize the hydrogen bond lattice energy. The centrosymmetric hydrogen bond dimeric systems with the hydrogen bond mutual arrangement in the centrosymmetric pairs also derive their stability from the dynamical co-operative interactions between the hydrogen bonds [13]. Such hydrogen anti-parallel arrangement of the closely spaced hydrogen bonds in the lattice is the prerequisite for these interactions to occur. For the transformed lattice, the dynamical co-operative interactions hold identical hydrogen isotope atoms, protons or deuterons together, in the hydrogen bond pairs. Therefore, are responsible for the observed exciton interaction effects in the spectra. The excess stabilization energy of the dimers, achieved via the dynamical co-operative

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interactions takes place only in the case of the co-existence of identical hydrogen isotopes in the coupled centrosymmetric hydrogen bond pairs. The mechanism of this phenomenon is of vibronic nature, strongly depending on the electronic properties of the associating molecules [13]. Therefore, in the ‘‘b” form crystals, the H/D isotopic ‘‘self-organization” phenomenon does not concern the hydrogen bonds in each single chain. This is due to the fact that they are only weakly exciton-coupled owing to the not easily polarizable chemical bonds linking the adjacent hydrogen bridges in a chain. The coupling involves the hydrogen bonds of two different chains, from two neighboring unit cells. This may happen, if the preceding selfstimulated proton replacements induced by the dynamical co-operative interaction mechanisms involved the hydrogen bonds from the neighboring chains. The discussed effect may be considered as a highly nonconventional natural phenomenon, having no equivalent counterpart in the behavior of other crystalline systems, investigated so far. We found that a similar phenomenon also occurred in the case of other hydrogen bond systems in molecular crystals, e.g. in crystals with chain structures of their lattices resembling the X-ray structure of the ‘‘b” form 2-butynoic acid crystals (e.g. 2-nitrocinnamic acid). These crystal structures are related to each other by their similar lattice properties (i.e. by the P21 space group and Z = 2). 4.8. Electronic structure of 2-butynoic acid molecules and the crystal spectral properties The electronic structure of 2-butynoic acid molecules apparently determines the spectral properties of the ‘‘b” form crystals. In the case of associating molecular systems, forming hydrogen bond chains in the crystal lattice, there are two ways in which the dynamical co-operative interactions responsible for the H/D isotopic ‘‘self-organization” processes may occur. In the first case these processes involve the neighboring hydrogen bonds in a single chain. Crystals, in which lattices are formed by molecules with the delocalized p-bond systems like in pyrazole [17], imidazole [18], 4-thiopirydone [16] and formic acid [22] exhibit such behavior. In the other case the associating molecules, with no aromatic rings in their structures, but only containing carbonyl or thiocarbonyl groups, participate in a different type of co-operative interactions. These interactions involve hydrogen bonds belonging to neighboring chains. Crystals of N-methylthioacetamide [23] and also of acetic acid [24] exhibit such behavior. Carboxylic acid crystals, characterized by the chain structure in their lattices, e.g. formic and acetic acid crystals, may strongly differ in their spectral properties [22,24]. This depends on the way in which the H/D ‘‘selforganization” processes occur, regardless of the fact that their very similar crystal X-ray structures are governed by the same space group. This is undoubtedly connected with

the influence of the methyl groups, effectively withdrawing electronic charge from the hydrogen bonds in acetic acid crystals. In this way the vibronic mechanisms of the inter-chain co-operative interactions for the acetic crystal are stronger than the intra-chain interactions. A very similar influence on the electronic properties of associated carboxylic groups seems to be exerted by the CH3C„Cgroups in the molecular structure of 2-butynoic acid, withdrawing the electronic charge from the hydrogen bonds. Hence, the spectral properties of 2-butynoic acid crystals are closely related to the properties of the second group systems for which the inter-hydrogen bond dynamical cooperative interactions involve hydrogen bonds from different chains. However, they remain in contradiction to the crystal X-ray structure.

5. Conclusion The unusual spectral behavior of the ‘‘b” form 2-butynoic acid crystals was the subject of our main research interest. Instead of the vibrational exciton interactions, involving the adjacent hydrogen bonds from each individual chain, which resulted from the space symmetry of the crystal, we detected some substantial effects of exciton splitting in the spectra, which should not appear for the P21 space-symmetry of the crystal and Z = 2 [33,34]. They were interpreted as ascribed to the ‘‘side-to-side” type exciton interactions, involving the translationally equivalent, closely spaced hydrogen bonds (the ‘‘c” identity period is ˚ ). Such spectral behavior remains in only equal to 3.937 A contrast to the crystal spectral properties predicted by the theory of molecular excitons [35,36]. At this point it seems also noteworthy to add that for some crystals of the similar symmetry and structure, e.g. the naproxene (2-(6-methoxy2-naphthyl) propionic acid) crystal, the spectra behave regularly, exhibiting the mX–H band intensity distribution and dichroic properties typical for hydrogen bond chain structure of their lattices [42]. In this case the inter-molecular layer distance is longer than for 2-butynoic acid crystal ˚ [43]. and is equal to ca. 5.8 A The analysis of the polarized IR spectra of 2-butynoic acid crystals allowed us to reveal a new natural phenomenon which is co-responsible for the generation of the mO–H and mO–D band fine structure patterns. From the linear-dichroic, temperature and isotopic dilution effects it follows that the main reason of the unusual spectral behavior of 2-butynoic acid crystals is, most probably, the selfstimulated concerted jump of the protons occurring between the oxygen atoms of the hydrogen bridges in the associated molecule chain systems. The vibrational exciton interaction effects observed in the spectra, involving hydrogen bonds from two different chains, belonging to neighboring unit cells, were the simple consequences of the postulated proton replacements. The hydrogen bond pairs, formed in this way, were treated as the source of the basic spectral properties of 2-butynoic acid crystals, determining

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the two-branched structure of the analyzed mO–H and mO–D bands in the IR crystalline spectra. From the analysis of the IR spectra of partially deuterated crystalline samples of 2-butynoic acid it could it resulted that the ‘‘residual” mO–H bands show identical polarization and temperature effects as the mO–H bands of isotopically neat crystals. The isotopic dilution effects in the spectra of ‘‘b” form crystals have proved the existence of a specific H/D isotopic ‘‘self-organization” phenomenon in the hydrogen bond systems in the crystal lattices. This means that the protons and deuterons were non-randomly distributed between the hydrogen bridges in the crystal lattice. However, in this particular case the H/D isotopic ‘‘self-organization” mechanisms involves the closely spaced hydrogen bonds from the neighboring chains. The lattice composed of dimers, originating from the protonic replacement phenomenon, were thermodynamically more stable due to the dynamical co-operative interactions than the hydrogen bond pair system taken without the structural rearrangement in the lattice. Moreover, these interactions were able to hold the identical hydrogen isotope atoms in the hydrogen bond pairs together [13]. As the result of the described processes in the hydrogen bond chain systems, the distribution of protons and deuterons is non-random, whereas the H/D isotopic ‘‘self-organization” mechanisms involve hydrogen bonds with identical hydrogen isotope atoms from the neighboring chains. In this way plain domains in the crystal lattice, approximately perpendicular to the chain directions, in which the hydrogen bonds have identical hydrogen isotopes, i.e. so-called, ‘‘domains”, were formed. This may be the reason why the hydrogen bond IR spectra, measured in the mO–H band frequency range for the ‘‘b” phase, are fairly similar to the corresponding spectra of the ‘‘a” phase. This difference occurs regardless of the substantial difference between the lattice structures of the two phases of 2-butynoic acid crystals. The mechanism of the dynamical co-operative interactions involving hydrogen bonds essentially differs from the formerly proposed mechanism of static co-operative interactions. This latter mechanism was considered as responsible for a considerable hydrogen bond strengthening in the infinitely long hydrogen bonded molecular chains [44–46]. It acts within the limits of the Born–Oppenheimer approximation. The phenomenon of the proton position disorder in the hydrogen bond crystalline systems appears not to be an exception in the nature. Although the positions of the hydrogen bond protons in crystals are difficult to determine by use of the X-ray diffraction methods, the rearrangement of the proton positions is reflected in measurable changes of the geometry of the associated molecules. This fact indirectly proves the occurrence of the rearrangement process [47,48]. However, the natural source of this phenomenon has remained so far unclear. The above discussed phenomenon of the self-stimulated proton replacements in the hydrogen bond lattice of the

63

‘‘b” form 2-butynoic acid crystals, induced by the dynamical co-operative interactions, may be considered as a new natural phenomenon in the area of molecular interactions. It strongly supports the idea concerning the existence of dynamical co-operative interactions in hydrogen bond systems. The reported study seems to be the first case discussed in literature, in which the dynamical cooperative interactions optimize the lattice total energy by causing changes in the crystal internal structure. References [1] G.C. Pimentel, A.L. McClellan, The Hydrogen Bond, W.H. Freeman, San Francisco, 1960. [2] P. Schuster, G. Zundel, C. Sandorfy (Eds.), The Hydrogen Bond, Recent Developments in the Theory and Experiment, Parts I, II and III, North-Holland, Amsterdam, 1976. [3] G.L. Hofacker, Y. Marechal, M.A. Ratner, The dynamical aspects of hydrogen bonds, in: P. Schuster, G. Zundel, C. Sandorfy (Eds.), The Hydrogen Bond, Recent Developments in Theory and Experiment, Part I, North-Holland, Amsterdam, 1976, p. 295. [4] D. Had_zi (Ed.), Theoretical Treatments of Hydrogen Bonding, Wiley, New York, 1997. [5] Y. Marechal, The Hydrogen Bond and the Water Molecule, The Physics and Chemistry of Water, Aqueous and Bio Media, Elsevier, Amsterdam, Oxford, 2006. [6] A. Witkowski, J. Chem. Phys. 47 (1967) 3645. [7] Y. Marechal, A. Witkowski, J. Chem. Phys. 48 (1968) 3697. [8] S.F. Fisher, G.L. Hofacker, M.A. Ratner, J. Chem. Phys. 52 (1970) 1934. [9] O. Henri-Rousseau, P. Blaise, The infrared density of weak hydrogen bonds within the linear response theory, in: I. Prigogine, S.A. Rice (Eds.), Advances in Chemical Physics, vol. 103, John Wiley & Sons, Inc., 1998. [10] O. Henri-Rousseau, P. Blaise, The mX–H lineshapes for centrosymmetric cyclic dimers involving weak hydrogen bonds, Advances in Chemical Physics, vol. 139, in press. [11] P. Blaise, M.J. Wo´jcik, O. Henri-Rousseau, J. Chem. Phys. 122 (2005) 064306. [12] H.T. Flakus, J. Mol. Struct. (Theochem.) 187 (1989) 35. [13] H.T. Flakus, J. Mol. Struct. 646 (2003) 15. [14] H.T. Flakus, A. Pyzik, Chem. Phys. 323 (2006) 479. [15] A. Kohen, H.H. Limbach, Isotope Effects in Chemistry and Biology, CRC Press, New York, 2006. [16] H.T. Flakus, A. Tyl, P.G. Jones, Spectrochim. Acta A 58 (2002) 299. [17] H.T. Flakus, A. Machelska, Spectrochim. Acta A 58 (2002) 555. [18] H.T. Flakus, A. Michta, J. Mol. Struct. 707 (2004) 17. [19] R.J. Jakobsen, J.W. Brasch, Y. Mikawa, J. Mol. Struct. 1 (1967) 309. [20] I.D. Mikhailov, V.A. Savelev, N.D. Sokolov, N.G. Bokh, Phys. Status Solidi 57 (1973) 719. [21] H.T. Flakus, A. Michta, Vibrat. Spectr. 33 (2003) 177. [22] H.T. Flakus, B. Stachowska, Chem. Phys. 330 (2006) 231. [23] H.T. Flakus, W. S´miszek-Lindert, K. Stadnicka, Chem. Phys. 335 (2007) 221. [24] H.T. Flakus, A. Tyl, Chem. Phys. 336 (2007) 36. [25] J.L. Leviel, Y. Marechal, J. Chem. Phys. 54 (1971) 1104. [26] J. Bournay, Y. Marechal, J. Chem. Phys. 55 (1971) 1230. [27] P. Excoffon, Y. Marechal, Spectrochim. Acta, Part A 28 (1972) 269. [28] P. Blaise, M. El-Amine Benmalti, O. Henri-Rousseau, J. Chem. Phys. 124 (2006) 024514. [29] A.M. Yaremko, H. Ratajczak, J. Baran, A.J. Barnes, E.V. Mozdor, B. Sylvi, Chem. Phys. 306 (2004) 57. [30] M. Boczar, Ł. Boda, M. Wo´jcik, J. Chem. Phys. 124 (2006) 084306. [31] R.W.G. Wyckoff, Crystal Structures, vol. 5, Wiley, New York, 1972. [32] Z. Berkovitch-Yellin, L. Leiserowitz, J. Am. Chem. Soc. 104 (1982) 4042.

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