D Isotopic âSelf-Organizationâ Effects in the IR

Article pubs.acs.org/JPCA

Temperature and H/D Isotopic “Self-Organization” Effects in the IR Spectra of the Hydrogen Bond Tetramer Systems in 3,5Diphenylpyrazole and 4‑Methyl-1,2,4-triazolethione Crystals Henryk T. Flakus,* Barbara Hachuła,* and Aleksandra Majchrowska Institute of Chemistry, University of Silesia, 9 Szkolna Street, Pl-40-006 Katowice, Poland ABSTRACT: Polarized IR spectra of hydrogen-bonded 3,5-diphenylpyrazole and of 4-methyl-1,2,4-triazolethione crystals were measured at 293 and 77 K in the νN−H and νN−D band frequency ranges. These crystals contain molecular tetramers in their lattices. The individual crystal spectral properties remain in close relation with the electronic structure of the two different molecular systems. We show that a vibronic coupling mechanism involving the hydrogen bond protons and the electrons on the π-electronic systems in the molecules determines the way in which the vibrational exciton coupling between the hydrogen bonds in the tetramers occurs. A strong coupling in 3,5-diphenylpyrazole tetramers prefers a “tail-to-head”-type Davydov coupling widespread via the π-electrons. A weak through-space exciton coupling in 4methyl-1,2,4-triazolethione tetramers involves two opposite hydrogen bonds in the cycles. The relative contributions of each exciton coupling mechanism in the tetramer spectra generation are temperature and the molecular electronic structure dependence. This explains the observed difference in the temperatureinduced evolution of the compared spectra. The mechanism of the H/D isotopic ‘‘self-organization’’ processes in the crystal hydrogen bonds was also analyzed. The two types of hydrogen bond tetramers differ by the way in which the processes occur. In 3,5-diphenylpyrazole tetramers, identical hydrogen isotope atoms exist in the entire hydrogen bond system, whereas in the case of 4-methyl-1,2,4-triazolethione crystals, the H/D isotopic self-organization mechanism involves the opposite hydrogen bonds in a tetramer.

1. INTRODUCTION Infrared spectroscopy still constitutes a basic tool in the research of the hydrogen bond dynamics. The νX−H bands measured in the highest-frequency range of the mid-infrared that attributed to the proton stretching vibrations in X−H···Y hydrogen bonds are a source of wealth for data systems in this matter. Complex fine structure patterns of these bands are considered as the result of anharmonical coupling mechanisms involving the proton stretching vibrations and other normal vibrations occurring in associated molecular systems, mainly the low-frequency X···Y hydrogen bridge stretching vibrational motions.1−5 The band contour shapes are extremely susceptible to the influences exerted by diverse physical factors, such as changes of temperature, changes in the matter state of condensation, pressure, solvents, and so forth.1−5 Among the contemporary theories of the IR spectra of the hydrogen bond formed in molecular systems, quantitative theoretical models that elaborated on the description of the νX−H band generation mechanisms are of particular importance. There are two quantitative theoretical models, namely, the “strong-coupling” theory6−8 (the elder theory) and the socalled “relaxation” (linear response) theory, the novel model.9,10 Both theoretical models are of a purely vibrational nature. Over the last 4 decades, by using of these theories, IR spectra of diverse hydrogen bond systems have been © 2012 American Chemical Society

reproduced satisfactorily. The model calculations involved quantitative interpretation of spectra of single, isolated hydrogen bonds,7,11 spectra of cyclic dimeric hydrogen bond systems,7,12−14 and the IR spectra of hydrogen-bonded molecular crystals.15 Simultaneously, the H/D isotopic effects observed in the spectra of the deuterium-bonded corresponding systems have been interpreted.7−15 Nevertheless, despite the doubtless successes achieved in this area when interpreting the hydrogen bond system spectra, it seems that a number of basic theoretical problems still remain unsolved. It also seems that the main source in the understanding of many spectral phenomena characterizing systems consisting of a number of mutually coupled hydrogen bonds, in terms of the two different quantitative approaches, is in the early history of these studies. In practice, up to the beginning of the 1990s, these studies were restricted to the interpretation of spectra of a number very simple hydrogen bond systems, mainly to the spectra of cyclic acetic acid dimers formed in the gaseous phase.7,12−14 The extension of this research over other, more diversified and complex hydrogen bond aggregates allowed us to recognize numerous puzzling Received: April 12, 2012 Revised: June 14, 2012 Published: July 8, 2012 7848

dx.doi.org/10.1021/jp303541m | J. Phys. Chem. A 2012, 116, 7848−7861

The Journal of Physical Chemistry A

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C2/c ≡ C62h. There are 32 molecules in a unit cell (Z = 32). The lattice constants at 298 K are a = 16.948(4) Å, b = 17.163(4) Å, c = 17.677(6) Å, and β = 109.59(2)°. The asymmetric unit consists of a hydrogen-bonded dimer of 3,5-Ph2Pz, which is further hydrogen-bonded to form four discrete tetrameric aggregates per unit cell. Each tetrameric unit forms a 12membered (N−N−H)4 heterocycle. Two of the bridging H atoms form symmetrical hydrogen bonds, N−H 1.443(5) and 1.456(4) Å, while the other two bridge asymmetrically, N−H 1.12(4) and 1.74(4) Å. The distances between N atoms bridged symmetrically by a H atom average 2.90(2) Å, while between the asymmetrically bridged ones, the distances average 2.83(2) Å. These distances are, respectively, 6 and 9% shorter than the sum of the van der Waals radii for two N atoms, with the two symmetrically bridging H atoms almost linearly bound to two pyrazoles, N−H···N 176(4)°. The projection of the 3,5-Ph2Pz crystal lattice onto the ab plane is shown in Figure 1.

spectral effects attributed to these systems. Interpretation of these effects seemed to be beyond the contemporary quantitative theoretical models of the hydrogen bond IR spectra without assuming that some not yet revealed mechanism codecide in the spectra generation. Spectroscopy in polarized light of hydrogen-bonded molecular crystals has provided key experimental data in this area. By measuring the polarized IR spectra of spatially oriented molecular crystals, characterized by a rich diversity of hydrogen bond arrangements met in their lattices, the most complete information has been obtained about the coupling mechanisms involving hydrogen bonds in these systems. It appeared that the investigation of spectra of even so simple mutually interacting hydrogen bond aggregates like cyclic dimers (e.g., carboxylic acid dimers) allowed one to reveal new H/D isotopic effects, namely, the H/D isotopic “self-organization” effects. They depend on a nonrandom distribution of protons and deuterons in the crystal lattices of isotopically diluted hydrogen bond systems. These spectral effects may be considered as the manifestation of a new kind of cooperative interaction involving hydrogen bonds, that is, the so-called dynamical cooperative interactions.16−18 This revelation has emphasized the role of the vibronic coupling between the electronic and the proton vibrational motions taking place in hydrogen bond aggregates in the generation of the very nature of the hydrogen bond as the natural phenomenon.17,18 In this paper, we present our investigation results concerning the IR crystalline spectra of hydrogen-bonded 3,5-diphenylpyrazole and 4-methyl-1,2,4-triazolethione. These two crystals contain cyclic hydrogen bond tetramers in their lattices. The two molecular systems differ, one from the other, by their electronic properties. They also differ by their spectral properties attributed to the hydrogen bonds in each individual crystal. This was the basic criterion for the choice of these systems as the subjects of our studies. The aim of this work was to perform comprehensive studies of the H/D isotopic and temperature effects in polarized IR spectra of the two model crystalline systems. The results of these investigations should provide new arguments in order to elucidate the nature of the cooperative interaction mechanisms involving hydrogen bonds in oligomeric hydrogen bond systems like cyclic tetramers via a quantitative interpretation of the crystalline system spectra. The problem with the quantitative theoretical treatment of the spectral properties of systems composed of mutually interacting hydrogen bonds still constitutes a real challenge in the area of hydrogen bond research. Despite spectacular achievements in the quantitative description of the intensity distribution in the νX−H bands and of the very complex spectral H/D isotopic effects, the understanding of temperature effects in the spectra of hydrogen-bonded systems seems to be insufficient. Solving of the theoretical problems connected with the IR spectra interpretation should illuminate mechanisms of interhydrogen bond couplings in the ground and in the first excited state of the proton and deuteron stretching vibrations. This should allow for a better understanding of the mechanisms of cooperative interactions involving hydrogen bonds that strongly influence molecular properties in biological systems. A. X-ray Structures of 3,5-Diphenylpyrazole and 4Methyl-1,2,4-triazolethione. The crystal structure of 3,5diphenylpyrazole (3,5-Ph2Pz in abbreviated notation) was already measured and published in 1992 by Aguilar-Parrilla et al.19 and redetermined by Raptis et al. in 1993.20 Crystals of 3,5-Ph2Pz are monoclinic, and the space symmetry group is

Figure 1. X-ray structure of the 3,5-Ph2Pz crystal. Projection of the lattice on to the ab plane.

The crystal structure of 4-methyl-1,2,4-triazolethione (4MeTAS in abbreviated notation) was determined by El Hajji et al. in 1998.21 4-MeTAS crystallizes in the monoclinic system with the space group P21/n. The unit ce1l parameters are a = 7.946(2) Å, b = 6.295(1) Å, c = 20.901(7) Å, β = 100.47(7)°, and Z = 8. The main structural units are cyclic tetramers of 4MeTAS molecules, linked by four complementary strong hydrogen bonds N−H···N. The hydrogen bond geometry has RH···N = 2.04 and 2.10 Å, RN···N = 2.91 and 2.93 Å, and ∠N−H···N = 161.3 and 159.5°. Among the two possible tautomeric forms, only the thione form is present in the crystal structure. The projection of the 4-MeTAS crystal lattice on to the ab plane is presented in Figure 2.

2. EXPERIMENTAL DETAILS 3,5-Ph2Pz and 4-MeTAS, used for our studies, were commercial substances (Sigma-Aldrich). The substances were investigated without further purification. The deuterium-bonded 3,5-Ph2Pz and 4-MeTAS were obtained by evaporation of a D2O solution of each compound at room temperature and under reduced pressure. It was found that the deuterium exchange rate for the NH groups varied from 50 to 90% for 3,5-Ph2Pz and from 50 to 90% for 4-MeTAS, respectively. 7849



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Figure 2. X-ray structure of the 4-MeTAS crystal. Projection on to the ab plane.

Crystals of 3,5-Ph2Pz and 4-MeTAS, suitable for further spectral studies, were obtained by melt crystallization, that is, by cooling of the molten samples occurring between two closely placed CaF2 plates. By that means, reasonably thin crystals could be received and characterized by their maximum absorbance at the νN−H and νN−D band frequency ranges near 0.5 at room temperature. From the crystalline mosaic, adequate monocrystalline fragments, having dimensions of at least 2 × 2 mm, were selected and then spatially oriented with the help of a polarization microscope. These crystals were selected for the experiment by use of a thin tin plate diaphragm with a 1.5 mm diameter hole. It was found that 3,5-Ph2Pz crystals developed most frequently in the ab plane of the lattice, whereas 4MeTAS crystals also developed in the ab plane. In each measurement, two different, mutually perpendicular orientations of the electric field vector E of the incident beam were applied with respect to the crystal lattice. The IR spectra of liquid- and solid-state samples of 3,5-Ph2Pz and 4-MeTAS were recorded with the use of a FT-IR Nicolet Magna 560 spectrometer by the transmission method with 2 cm−1 resolution at two temperatures, 293 and 77 K. The measurements were repeated for ∼10 different single crystals of each isotopomer. The Raman spectra of polycrystalline samples of 3,5-Ph2Pz and 4-MeTAS were measured at room temperature with the use of the Bio-Rad FTS-175C FT-IR spectrometer at the 1 cm−1 resolution.

Figure 3. The νN−H band in the IR spectra of (top) 3,5-Ph2Pz and (bottom) 4-MeTAS in the CCl4 solution.

proton stretching vibration region (see Figures 3 and 4), shows a substantial difference between the two compared band contours that is, the shapes of these two compared spectra. They are related to one another by an approximate mirror reflection operation. The shorter-wave branch of the νN−H band in the 3,5-Ph2Pz spectrum, measured in the CCl4 solution, is of higher intensity than that in the longer-wave range. In the case of KBr pellet spectra, one can observe a different situation. The intensity of the longer-wave spectral branch is higher than the intensity of the shorter-wave branch. These differences in the band intensity distribution patterns can be intuitively ascribed to different structural units of the molecular associates found in each individual phase. Cyclic hydrogen-bonded tetramers of the molecules exist in the 3,5-Ph2Pz crystal lattice.19,20 We assume that in the CCl4 solution, 3,5-Ph2Pz molecules associate, forming cyclic hydrogen-bonded trimers because it was experimentally evidenced that for molecular geometry reasons, hydrogen-bonded cyclic trimers are the most privileged oligomers of diverse pyrazole derivative molecules found in nonpolar solvent solutions.22−24 When comparing the 4-MeTAS spectra measured in the frequency range of the νN−H band in the CCl4 solution, with the spectra of polycrystalline samples in KBr pellets, one can notice a striking similarity of the corresponding band contour shapes. The similarity concerns the two-branch fine structure of the νN−H band, where the shorter-wave branch (3200−2900 cm−1) is more intense when compared with the longer-wave band branch (2900−2500 cm−1). This effect seems rather surprising, owing to the fact that in the CCl4 solution and in the crystal, different structural units are the sources of the analyzed spectral properties. The structural units in solid 4-MeTAS are cyclic hydrogen bond tetramers, and in the liquid phase, cyclic, centrosymmetric dimers are the basic associated complexes. The similarity of the compared band contour shapes is most likely not accidental.

3. RESULTS The preliminary experimental studies of spectral properties of 3,5-Ph2Pz and 4-MeTAS depended on the measurements in CCl4 solution in the frequency range of the vN−H proton stretching vibration bands. The spectra are shown in Figure 3. In Figure 4 are shown the νN−H and νN−D bands from the IR spectra of polycrystalline 3,5-Ph2Pz and 4-MeTAS samples in KBr pellets, measured at 293 and 77 K. Polarized IR spectra of the two crystalline systems measured at 77 K in the νN−H and νN−D band frequency ranges are presented in Figure 5. The temperature effect in the crystalline spectra in the most intense polarized components of the νN−H and the νN−D bands is given in Figure 6. The IR spectra of hydrogen bonds in 3,5-Ph2Pz, measured in CCl4 solution, consist of two spectral branches, the shorterwave branch placed in the 3400−3000 cm−1 frequency range and the lower-wave branch in the 3000−2500 cm−1 frequency range. The spectral peak at 3452 cm−1 corresponds to the stretching vibrations of free, not associated, N−H groups. Comparison of the IR spectra of 3,5-Ph2Pz in the CCl4 solution, with the KBr pellet spectra, recorded in the νN−H 7850



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Figure 4. The νN−H and νN−D bands in the IR spectra of polycrystalline samples of (top) 3,5-Ph2Pz and (bottom) 4-MeTAS, dispersed in KBr pellets. Temperature effects are shown in the spectra.

Figure 5. Polarized IR spectra of (top) 3,5-Ph2Pz and (bottom) 4-MeTAS crystals measured at 77 K in the νN−H and νN−D band frequency ranges. (top, I) The electric field vector E parallel to the a-axis; (II) the E vector parallel to the b-axis. (bottom, I) The electric field vector E parallel to the baxis; (II) the E vector parallel to the a-axis.

4. THE “STATE-OF-THE-ART” IN THE RESEARCH OF IR SPECTRA OF HYDROGEN- BONDED CRYSTALS

similar to one another due to the similar structural units, in which four hydrogen bonds exist, forming hydrogen bond tetramers. However, upon comparison of the crystalline spectra of diverse tetrameric systems existing in crystal lattices, a considerable variation degree of the analyzed band contour shapes can be found. Up to our previous estimations, this fact remains in close connection with differences in the electronic

A. Electronic Structure of Cyclic Tetramers of Hydrogen Bonds versus the Temperature Effects in Their IR Spectra. One could expect that the hydrogen bond IR spectra of diverse hydrogen-bonded tetramers, measured in the νX−H and νX−D band frequency ranges, should be qualitatively fairly 7851



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Figure 6. The νN−H and νN−D bands in the IR spectra of monocrystalline samples of (top) 3,5-Ph2Pz and (bottom) 4-MeTAS. Temperature effects are shown in the spectra.

azaindole,31 4-MeTAS,21 3- and 4-benzaldehyde,32 indole-3carboxaldehyde, and 3-acetylindole.33 A similar property also characterizes spectra of acetic acid crystals.34 The νX−H bands in the room-temperature spectra of the hydrogen bond of the tetramer systems from the (a) group are characterized by a relatively low intensity of the higherfrequency branch of each band in comparison with the lowerfrequency band branch intensity. Upon the decrease of temperature to 77 K, a noticeable growth of the relative intensity of the lower-frequency branch of each band can be observed. Nevertheless, the higher-frequency band branches still remain the less intense ones. In the case (b), the νX−H bands even in room-temperature spectra exhibit a relatively high intensity of their higherfrequency branches in relation to the corresponding lowerfrequency branches. Upon the temperature decrease up to 77 K, a considerable growth of the relative intensity of each higherfrequency branch of each analyzed band can be observed. As the result of the thermal evolution of the νX−H band contours, in the low-temperature spectra of tetrameric systems of this group, the higher-frequency branch is of dominant intensity in the bands. According to the state-of-the-art in our contemporary knowledge about the quantitative description of the IR spectra of the hydrogen bond in crystals with a chain arrangement of hydrogen bonds in their lattices, the following interpretation of the tetrameric νX−H band generation mechanisms seems to be valid. The lower-frequency spectral branch of the band corresponds to the symmetry-allowed transition to the A state of the totally symmetric “in-phase” proton vibrations in a linear quasi-axial hydrogen bond dimer. Therefore, the lowerfrequency branch of the νX−H band, attributed to the allowed transition, should be more intense than the other band branch related to the forbidden transition. On the basis of these intuitive predictions, the spectral properties of the chain systems from the (b) group seem to be highly surprising,

structures of diverse hydrogen-bonded molecules. The basic experimental facts supporting the hypothesis given above are presented below. On the basis of our state-of-the-art knowledge concerning IR spectra of hydrogen-bonded systems, at this point, let us summarize the basic properties of the νX−H bands in the IR spectra of the cyclic tetramers of hydrogen bonds in relation to their molecular electronic structures. (a) In the case of molecules that contain large delocalized πelectronic systems coupled directly with the hydrogen bonds (e.g., 3,5-Ph2Pz), the νX−H bands are fairly similar to the corresponding spectra of a group of crystals with open hydrogen bond chains (e.g., pyrazole,22 imidazole,25 and 4thiopyridone26). These bands are characterized by different intensity distribution patterns when compared with the corresponding band properties in the IR spectra of different amides or thioamides.18,27−29 In the first case, the lowerfrequency branch of the νX−H band is more intense in relation to the intensity of the higher-frequency band branch. Moreover, the characteristic linear dichroic effects, differentiating the spectral properties of the two opposite branches of the νX−H bands in the polarized IR spectra, can be observed. Surprisingly, a similar property characterizes the crystalline spectra of the simplest carboxylic acid, that is, formic acid.30 (b) In the case of crystalline systems that contain only small π-electronic systems (i.e., carbonyl or thiocarbonyl groups) in their molecular structures (e.g., crystals diverse amides and thioamides18,27−29) coupled directly with hydrogen bonds, the νX−H bands are fairly similar to the corresponding spectra of other groups of crystals with open hydrogen bond chains in their lattices. In this case, the νX−H band contours can be treated as a “mirror reflection” of the corresponding band shapes of systems from the point (a). In this case, the higherfrequency branch of the band is the most intense fragment one, and no essential differences in the dichroic properties between the opposite νX−H band branches can be seen. Crystals formed by molecules with larger π-electronic systems may also exhibit similar spectral properties. To this group belong crystals of 77852



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spectral properties of hydrogen bond dimers. The analysis of the interhydrogen bond coupling in the case of cyclic centrosymmetric dimers and in linear dimers requires taking into consideration two situations of the vibrational transition moment directions for dimer hydrogen bonds. For the parallel arrangement of the dipole transition moments, the exciton interaction energy for the “side-to-side” (SS) interhydrogen bond coupling is of positive sign. The vibrational transition corresponding to such an arrangement of the vibrational dipole moments is responsible for generation of the intense, symmetry-allowed, shorter-wave branch of the dimeric spectra. In contrast, when the dipole transition moments are of the antiparallel arrangement, the energy value is negative; therefore, the band generated by this situation is placed at the lower frequency, and it corresponds to the symmetry-forbidden excitation of the totally symmetric proton vibrations. Such a sequence of the spectral branches in the hydrogen bond stretching bands is typical for cyclic, centrosymmetric hydrogen bond dimers. When the vibrating transition moment dipoles are oriented axially in a linear dimer as “tail-to-head” (TH), the sign of the energy value of the dipole−dipole exciton interaction is negative; therefore, the intense branch corresponding to the symmetry-allowed transition is placed at a lower frequency. On the contrary, the spectral branch forbidden by the symmetry rules, situated at the higher frequency, is generated by the antiparallel orientation of the vibrating dipoles. In this case, the exciton coupling energy is of positive sign. The sequence and the properties of the branches in the proton stretching vibration bands in the discussed case are reverse to those observed in the IR spectra of hydrogen bond cyclic dimeric systems. Therefore, the following problem demands explanation: Why do the majority of crystals with hydrogen-bonded molecular chains in their lattices, from the (b) group, (e.g., acetic acid,34 N-methylthioacetamide,27 or acetanilide18 crystals), surprisingly exhibit spectral properties similar to the analogous properties of cyclic hydrogen bond dimer spectra. Undoubtedly, this property remains in close connection with the π-electronic properties of the associating molecules. In these associated molecular systems, vibrational exciton couplings are of the SStype and involve the closely spaced hydrogen bonds where each moiety belongs to a different chain. In molecules of this group, large π-electronic systems are absent. Only carbonyl and thiocarbonyl groups, each with a small π-electronic system, are present in these molecules. In the associated molecular systems from the (a) group, vibrational exciton couplings are of the THtype. They involve the adjacent hydrogen bonds within each individual chain in the lattice. The electronic structure of molecules of this group is most probably the key factor governing these interhydrogen bond interactions. Thus, in the case of IR spectra of cyclic tetramers of hydrogen bonds, two different extreme behaviors can be observed. For tetramers formed by molecules containing large π-electronic systems coupled directly with the hydrogen bonds (3,5-Ph2Pz), the adjacent hydrogen bonds in a chain couple as TH via the π-electrons of the associating molecules with their spectra typical for chain hydrogen bond systems. In tetramers of 3,5-Ph2Pz, hydrogen bond no. 1 couples with the neighboring hydrogen bond no. 2, and hydrogen bond no. 2 couples with the moiety no. 3, and so forth. This is the main reason for the similarity of the corresponding spectra of 3,5Ph2Pz, measured in the crystals and in CCl4 solution. Although dissolved in CCl4 solution, the molecules form cyclic trimers,

contradicting the interpretation of the spectra of chain hydrogen bond systems belonging to the (a) group. The higher-frequency branch of the νX−H band is generated by the transition occurring to the B symmetry excited state of the nontotally symmetric “out-of-phase” proton stretching vibrations in the chains. Similarly as in the case of cyclic centrosymmetric hydrogen bond dimeric systems, this transition, which is forbidden by the symmetry rules, becomes allowed via a vibronic mechanism. The promotion mechanism is a kind of reverse of the familiar Herzberg−Teller mechanism originally responsible for the promotion of forbidden electronic transitions in UV spectra of aromatic hydrocarbons.35 Within this approach, electronic properties of single hydrogen bonds themselves, as well as electronic properties of the whole associated molecules and the proton vibration anharmonicity, are responsible for the magnitude of the forbidden transition promotion effects in the dimeric spectra.29,36−38 This nonconventional mechanism determines unique properties of linear hydrogen bond dimeric systems. It finds no counterpart in the vibrational spectroscopy of centrosymmetric single molecular systems. Also declining from the linear arrangements of hydrogen bonds in a chain causes the increase of the higherfrequency branch intensity. In order to propose a reliable explanation of this paradox in our analysis, one should also recall the hydrogen bond IR spectra of other chain hydrogen bond systems, including spectra of hydrogen-bonded amides and thioamides. Upon comparison of the IR spectra of diverse crystalline systems containing chains of associated molecules as the structural units of their lattices, the following general conclusions can be made: Most of the chain hydrogen bond systems exhibit an abnormal, that is, a “reverse” intensity distribution pattern, in their contours. In this case, the νX−H bands have the lower-frequency (i.e., the “allowed”) branch of a lower intensity, even in their low-temperature spectra. However, in some rare cases, for example, formic acid,30 imidazole,25 and pyrazole,22 the νO−H and νN−H bands are characterized by regular enough spectral properties characterizing their hydrogen bond spectra. In the latest cases, the lower-frequency branch of each band is more intense when compared with the higher-frequency band intensity. Most of chain hydrogen bond systems resemble the properties of the spectral properties at 77 K of chain systems of the (b) group. In the case of the spectra of the reverse intensity distribution patterns in the bands, for example, N-methylacetamide28 and N-methylthioacetamide,27 this effect was ascribed previously to the strong exciton couplings involving hydrogen bonds from the different closely spaced molecular chains in the crystal lattices. B. IR Spectra of Tetrameric Hydrogen Bond Systems. It is surprising that crystalline spectra of hydrogen bond chains in different aldehydes,32 amides,18,28,29 and thioamides27 fairly resemble one another by their intensity distribution patterns and by the linear dichroic effects characterizing the νX−H bands in the spectra of cyclic dimeric hydrogen bond systems in a particular group of molecular crystals. In the hydrogen bond spectra of another group of crystals (e.g., pyrazole22 and 4thiopyridone26), with hydrogen-bonded molecules forming infinitely long chains in their lattices, strong linear dichroic effects can be observed, which prove to have a considerable influence on the exciton interactions involving the adjacent hydrogen bonds in each chain. We start our considerations on the spectra of cyclic tetramer hydrogen bond systems from the discussion of the analogous 7853



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coupling of the SS-type, without the generation of the ring electric current in the cyclic tetramer. This behavior characterizes the associated molecular systems with no large π-electronic systems in their structures, where only small π-electronic systems are present in carbonyl and thiocarbonyl groups. In these circumstances, the tetramer spectra are of a standard form, resembling by shapes the spectra of carboxylic acid cyclic dimers, with a low intensity of the lower-frequency νX−H band branch. For the quantitative description of the exciton interactions involving hydrogen bonds influencing the dimer spectra, the dipole−dipole model was sufficiently adequate. The νX−H band shapes in the two types of tetramer spectra are related to one another by the approximate mirror reflection symmetry. In case (1), the lower-intensity spectral branch appears in the higher-frequency range and is generated by the quasi-forbidden vibrational transition in a linear dimer, occurring to the excited state of the nontotally symmetric proton stretching vibrations. In case (2), the lower-intensity spectral branch appears in the lower- frequency range. It corresponds to the allowed vibrational transition in a linear dimer. The above- presented spectral properties of diverse hydrogen bond linear dimers may allow for explanation of the thermal evolution effects in the hydrogen bond IR spectra of tetramer systems. It seems that in order to explain the temperature effects in the IR spectra of cyclic hydrogen bond tetramers, the following hypothesis concerning the mechanisms of the spectra generation should be accepted. Let us assume that two competing mechanisms of vibrational exciton interactions involving hydrogen bonds in cyclic tetramers are simultaneously responsible for the formation of the νX−H band contour shapes. The contribution of each individual mechanism depends on the electronic structure of the associating molecules, on the electronic properties of the heavy atoms forming the hydrogen bridges, as well as on temperature. (A) The first mechanism depends on the SS vibrational exciton coupling between the hydrogen bonds in cyclic tetramers. In this case, the tetramer hydrogen bonds interact with one another as through-space, 1 with 3 and 2 with 4. (B) The other mechanism assumes a TH-type exciton coupling involving the hydrogen bonds in the cyclic tetramers. These interactions occur around the cycles via electrons. The (B) mechanism seems to be privileged in the case of the associated molecules, in which hydrogen bonds couple with large π-electronic systems, for example, for pyrazole-associated molecules in crystals. The (A) mechanism seems to dominate in the case of molecular systems with small π-electronic systems, for example, for amide- and thioamide-associated molecules. It seems obvious that for an individual hydrogen-bonded tetramer system, the contribution of each mechanism should be strongly temperature-dependent. At very low temperatures, the (B) mechanism should be privileged, particularly in the case of the advantageous electronic structure of the associating molecules, that is, for molecules with large π-electronic systems directly coupled with the hydrogen bonds. Temperature growth, influencing the increase of atomic vibration amplitudes, the hydrogen atom vibrations included, should annihilate the electric current induced by the totally symmetric proton vibrations in the cycles. Under these circumstances, the role of the (A) mechanism increases, namely, of the through-space vibrational exciton coupling between the hydrogen bonds in a tetramer. This should therefore result in a particularly strong

not tetramers (similarly like pyrazole derivative molecules22−24), this way of the interhydrogen bond coupling guarantees the practical independence of the band shapes upon the molecular cycle dimensions. In other cases (4-MeTAS), the hydrogen bond tetramer spectra are similar to the crystalline spectra of chain systems (N-methylthioacetamide27 or acetanilide18). In the case of these latter molecular systems, the hydrogen bonds couple in the crystals via a SS interaction mechanism. In tetramers of 4MeTAS and 7-azaindole,31 hydrogen bond no. 1 couples with the other, opposite hydrogen bond no. 3, and hydrogen bond no. 2 couples with the moiety no. 4. The hydrogen bond spectra of this group of cyclic tetramers, therefore, resemble the corresponding spectra of cyclic centrosymmetric hydrogen bond dimers due to the almost identical interhydrogen bond coupling mechanism in both cases. From the above-presented data, it results that realization of the vibrational exciton interactions in tetrameric hydrogen bond aggregates, affecting the νN−H and νN−D band fine structures, is determined by the electronic structure of the associating molecules.

5. THEORETICAL APPROACH PROPOSED The dipole−dipole interaction model, widely used for a simplified description of the exciton interactions between hydrogen bonds, seems to be nonadequate in the explanation of the wide diversity of the spectra of cyclic tetramers of hydrogen bonds. There is some experimental data indicating that these couplings do not always occur as “through-space”, and they are also widespread by the hydrogen bond electrons as well as by electrons of the molecular skeletons. Therefore, in terms of the theory of molecular vibrational excitons,39,40 the exciton interaction integrals in some cases may also considerably strongly depend on the electronic coordinates. In advantageous circumstances, resulting from the particular electronic structure of the associating molecules, the proton stretching vibrations can induce electric current oscillating around a cyclic hydrogen bond dimer or, in the case of other crystalline systems, oscillating along a hydrogen bond chain. However, only the totally symmetric proton vibrations are able to effectively induce the electric current in the ring or in the chain, while the nontotally symmetric vibrations are inactive in this mechanism because currents induced in each individual hydrogen bond dimer are annihilated in these circumstances. The formalism for the model assuming the electric current generated by oscillating protons in cyclic hydrogen bond dimers was proposed by Nafie 3 decades ago.41 In the scope of the considerations given above, it seems justified to treat formally a cyclic hydrogen bond tetramer by the two following different methods, taking into account the way in which the interhydrogen bond exciton interactions are widespread in the systems. (1) As a closed chain in which the adjacent hydrogen bonds in a cycle are strongly exciton- coupled, similarly as in the chain associated in pyrazole22 and 4-thiopyridone26 crystals. This is the coupling of the TH-type occurring around the molecular cycle. This method of coupling realization can possibly occur via the easy-polarizable electrons on the π-orbitals. Therefore, the linear dimer spectrum is similar to the spectrum of a chain system, with a low intensity of the higher-frequency band branch. (2) As a pair of partially independent hydrogen bonds, which remain only through-space exciton-coupled. It would be a 7854



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temperature-induced evolution of the νX−H bands. Even when the lower-frequency branch of the band is less intense when compared with the intensity of the higher-frequency one, the temperature decrease until 77 K causes its considerable intensity growth. The lower-frequency branch becomes more intense than the higher-frequency band branch. In the spectra of cyclic tetramers, with only small π-electronic systems in the associating molecules, the temperature decrease does not cause a considerable intensity growth of the lowerfrequency band branch. It still remains less intense when compared with the higher-frequency branch of the band. It means that due to the molecular electronic properties of this group of tetramers, the (B) mechanism cannot be activated effectively enough even at low temperatures.

used for the PAB A (T) an exponential temperature dependence according to the formula ⎛ α AB ⎞ PAAB(T ) = 1 − exp⎜ − ⎟ ⎝ kBT ⎠

(1)

where is αAB the activation energy parameter when the SS state is dominant and kB is the Boltzmann constant. Under such circumstances, PAB B (T) takes the following expression: ⎛ α AB ⎞ PBAB(T ) = exp⎜ − ⎟ ⎝ kBT ⎠

(2)

It is interesting to note that in the case of (A), for very low temperatures, the statistical weight PAB A (T) parameter is close to 1.0, and PBAB(T) is almost equal to 0.0. Under these circumstances, the SS-type interaction is the basic type of the exciton coupling involving the dimer hydrogen bonds. For high temperatures, the PAB B (T) parameter values are different from 0.0, and they are intermediate between 0.0 and 1.0 (rather closer to 0.5), and PAAB(T) approaches 0.5. When the temperature increases, PAB B (T) also increases. It means that the TH coupling, occurring via the electric current in the ring, is activated in higher temperatures at a magnitude depending on the energy gap between these two states of the vibrationally excited dimer. From our experimental estimations, the energy gap for some dimeric system cases is relatively large, and in another cases, it may be relatively low. In case (B), where the SS state is of a higher energy value, we assume the same formula, but the energy barrier αBA height is relatively low. Under such a circumstance, the statistical weight parameters, PA(T) and PB(T) may be written as follows:

6. SPECTRAL CONSEQUENCES OF THE MODEL FOR 3,5-PH2PZ AND 4-METAS From the above assumptions, a way of performing model calculations of the νX−H and νX−D band contours in IR spectra of hydrogen bond tetramers results. In the proposed approach, a theoretical spectrum of the model system can be derived, formally treated as a superposition of two component spectra, where each individual spectrum corresponds with a different mechanism of the vibrational exciton interactions involving two hydrogen bonds in the tetramer, treated as a dimeric system. In terms of the strong-coupling theory,6−8 in each exciton interaction mechanism case, the νX−H band in the dimeric spectrum is the superposition of two component bands, “plus” and “minus”, each of a different origin. In the case of a linear dimer approximation, with the THtype coupling, the plus band is generated by the dipole-allowed transition to the excited state of the totally symmetric proton stretching vibrations in a dimer, belonging to the A representation. On the other hand, the minus band is connected with the symmetry-forbidden transition to the B symmetry state of the nontotally symmetric proton vibrations in the linear dimers. In the case, when the mechanism (A) exclusively decides about the dimer spectra generation mechanism, the minus band appears in the higher-frequency range in relation to the plus band location. In the other case, when the (B) mechanism governs the dimer spectra generation, with the SS-type coupling, the two component bands appear in the reverse sequence than in case (A). It means that the minus band representing the forbidden transition appears in the lower-frequency range than the plus band connected with the allowed transition.

⎛ α BA ⎞ PABA(T ) = exp⎜ − ⎟ ⎝ kBT ⎠

(3)

⎛ α BA ⎞ PBBA(T ) = 1 − exp⎜ − ⎟ ⎝ kBT ⎠

(4)

As we can see, for very low temperatures, PBA B (T) may be practically equal to 1.0. For this kind of dimeric system, the TH-type exciton coupling is the basic natural way in which the interhydrogen bond interactions occur. The growth in temperature annihilates this way of coupling due to the vanishing of the electronic current induced in the cycles, accompanied by large-amplitude thermal motions of atoms in the dimers. For high temperatures, PBA B (T) decreases and becomes of an intermediate value between 0.0 and 1.0 (rather closer to 0.5), while the statistical weight PBA A (T) grows, declining from 0.0 up to 0.5. The energy gap between the two states in some molecular cases is usually relatively large, and in other cases, it may be relatively small. It depends on the electronic properties of the associating molecules forming the dimers. From our experimental data, it can be concluded that cases (A) and (B) represent the extreme cases of the interhydrogen bond coupling in cyclic hydrogen bond dimers. There are also many systems exhibiting an intermediate behavior. For a relatively small magnitude of the absolute values of the energy barrier height, the two cases (A) and (B) are practically nondistinguishable.

7. GENERATION MECHANISM OF THE TEMPERATURE EFFECTS IN THE SPECTRA In the two cases, (A) and (B), the theoretical spectra are calculated within the “strong anharmonic coupling” theory.6−8,42 Here, we consider different anharmonic coupling parameters for the two individual mechanism cases (A) and (B), and we assume that the contribution of each mechanism as governed by a Boltzmann-type relation. In addition, for the statistical weight parameters, PA(T) and PB(T), one must distinguish which state is dominant, that is, when the SS (A) state is of the lower energy and the TH (B) state is of a higher energy and vice versa. In order to reproduce the temperature dependence of experimental spectra of the systems belonging to the A case, we 7855



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8. SPECTRA OF 3,5-PH2PZ AND 4-METAS CRYSTALS The analyzed crystalline spectra of 4-MeTAS seem to fully belong to case (A). On the other hand, the crystalline spectra of 3,5-Ph2Pz seem to satisfy the demands of case (B). The analyzed difference between the spectral properties of 4MeTAS tetramers and the 3,5-Ph2Pz tetramers most probably results from the influences exerted onto the hydrogen bond tetramers, present in the (N−H···N)4 cycles, by the two different five-membered ring systems. The direct contact between the pyrazole ring with the hydrogen bridge (3,5Ph2Pz) most likely influences the electric charge density in the (N−H···N)4 cycles. This in turn strengthens the vibronic mechanism of the electronic current generation in the hydrogen bond cycles.41 Partial loss of aromatic character of the triazole rings due to the tautomeric rearrangement and forming of thiocarbonyl groups (4-MeTAS) effectively weakens the vibronic coupling mechanism. Therefore, these latter systems belong to the (A) case. The analyzed spectral properties of the two different crystalline systems, 4-MeTAS and 3,5-Ph2Pz, are in a good agreement with the above-described vibrational exciton interaction mechanisms of the spectra generation for cyclic tetramers of hydrogen bonds. This remains in close relation to the electronic properties of the chain molecules. For 4-MeTAS tetramers, the exciton interactions involving the dimer hydrogen bonds of the SS-type are only weakly temperaturedependent. In the case of 3,5-Ph2Pz tetramers, due to their electronic structure, the interhydrogen bond exciton coupling mechanism changes its character along with the changes in temperature. At very low temperatures, the TH-type interactions, transferred in the (N−H···N)4 cycles via electrons, dominate. When the temperature increases, this mechanism becomes less privileged as being annihilated by the hydrogen bond atom thermal vibrational motions. It is replaced by the other mechanism depending on the SS-type interactions. Each individual mechanism generates its own spectrum characterized by its unique intensity distribution pattern. Therefore, the νN−H and νN−D bands in the spectra of 3,5-Ph2Pz crystals exhibit more complex fine structure patterns because they are a superposition of two different spectra, where each component spectrum is of a different origin. Each component spectrum contributing to the νN−H and νN−D band formation, with its statistical weight dependence on temperature, corresponds with another exciton interaction mechanism in the linear hydrogen bond dimers in the lattice. From the comparison of the spectra of the two different crystalline systems, 4-MeTAS and 3,5-Ph2Pz, it results that the electronic structure of the associating molecules is the main factor determining the crystal spectral properties in IR, differentiating the spectral properties of the two groups of hydrogen-bonded systems. Namely, the temperature effects registered in IR spectra of the hydrogen bond in the two different crystals with cyclic tetramers of hydrogen bonds remain in close connection with the electronic-level systems of the associating molecules forming hydrogen-bonded associate units in the lattices.

in the spectra, basically result from the spectral properties of dimeric units composed of two N−H···N hydrogen bonds. It can be also shown that the above-presented qualitative interpretation of the 4-MeTAS and 3,5-Ph2Pz crystal spectra is in general agreement with model calculations of the νN−H and νN−D band contour shapes, performed in terms of the strongcoupling theory6,7,42 for model hydrogen bond pairs (dimers). For 3,5-Ph2Pz crystals, we assumes that the linear dimeric hydrogen bond model is responsible for the basic spectral properties of this crystalline system. In this case, the hydrogen bonds in the model dimer are considered to be a TH-linked chain system. Within this model, the νN−H and the νN−D band structures are 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 in-phase proton stretching vibration in a linear, quasi-axial hydrogen bond dimer.22,25,26 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. Thus, the shapes of the analyzed crystalline spectra, along with their dichroic properties, can be quantitatively reproduced within the initial assumption of the model. The quantitative analysis of the spectral properties of 4MeTAS crystals employed the model calculations of the νN−H and νN−D band contour shapes based on the assumption that the bearer of the basic spectral properties of a crystal was a centrosymmetric hydrogen bond dimer of the SS-type. Within the centrosymmetric model, the N−H···N bond dimeric system spectra, the higher-frequency branch of each analyzed νN−H band corresponds to the dipole-forbidden transition occurring to the excited state of the totally symmetric proton stretching vibration in the centrosymmetric dimer. This part of the spectrum can be satisfactorily reproduced by the so-called minus band from the strong-coupling theory.6−8,42 The forbidden transition in the IR may, however, become spectrally activated via the vibronic promotion mechanism, which is a reverse of the familiar Herzberg−Teller mechanism,35 originally known from the electronic spectroscopy of aromatic hydrocarbon molecules. In this case, the coupling of the proton stretching vibrations with electronic motions in centrosymmetric hydrogen bond dimeric systems activates the symmetryforbidden vibrational transition in IR. The formalism of the coupling mechanism is beyond the Born−Oppenheimer approximation.35 Therefore, the sub-band connected with the forbidden transition contributing to the νN−H band may appear in the IR spectra of the crystals. On the other hand, the lowerfrequency branch of each considered band corresponds to the symmetry-allowed transition ascribed to the nontotally symmetric proton vibrations in the centrosymmetric dimers. It was successfully reproduced quantitatively by the so-called plus band.6,7,42 Within the strong-coupling theory, the νX−H band shape for a dimer, composed of two X−H···Y hydrogen bonds, depends basically on the following system of coupling parameters: (i) the distortion parameter bH and (ii) the resonance interaction parameters C0 and C1.6,7,42 Each parameter has a precisely defined physical meaning. The bH parameter describes the

9. MODEL CALCULATION OF THE BAND CONTOUR SHAPES We will show that the main spectral properties of 4-MeTAS and 3,5-Ph2Pz crystals, namely, the two-branch νN−H band fine structure pattern and the extremely strong H/D isotopic effect 7856



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Figure 7. Theoretically derived νN−H band contours calculated in terms of the strong-coupling theory in the limits of the two different vibrational exciton coupling mechanisms involving the cyclic dimer hydrogen bonds, that is, SS and the TH. (left) The SS coupling mechanism. (right) The TH coupling mechanism. (I) The “minus” band. (II) The “plus” band. (III) Superposition of the I and II spectra, each taken with its appropriate individual statistical weight parameter, F− and F+. In both mechanism cases, the same coupling parameter value system was used for calculations. For the 4-MeTAS crystal, bH = 1.2, C0 = 1.3, C1 = 0.2, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. For the 3,5-Ph2Pz crystal, bH = 1.4, C0 = 1.5, C1 = 0.2, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. The transition frequencies are in the ωN···N vibrational quantum units, and the transition frequencies are expressed with respect to the gravity center of the hypothetical spectrum of a monomeric hydrogen bond in the cyclic hydrogen bond dimer. Transition intensities are in arbitrary units.

change in the equilibrium geometry for the low-energy hydrogen bond stretching vibrations, accompanied by the excitation of the high-frequency proton stretching vibrations νN−H. The C0 and C1 parameters are responsible for the mutual interactions between the hydrogen bonds in a dimer in its vibrationally excited state. They denote subsequent expansion coefficients in the series upon developing the resonance interaction integral C with respect to the normal coordinates of the low-frequency hydrogen bond stretching vibrations νN···N

bH =

2 bD

For the C0 and C1 resonance interaction parameters, the simplest version of the theory predicts the H/D isotopic effect expressed by diminution by 1.0 to √2 times the parameter values. The details of these calculations were described previously.6,7,42 The results of the model calculation are shown in an attempt to qualitatively reconstruct the two-branch νN−H band contour shape of 4-MeTAS and 3,5-Ph2Pz crystals in terms of the centrosymmetric dimer and linear dimer approximation, respectively. The minus and plus bands contributed proportionally to their respective statistical weight parameters F− and F+. The theoretical spectra reconstituting the νN−H band contours were calculated for the following coupling parameter values: For the 4-MeTAS crystal spectrum, bH = 1.2, C0 = 1.3, C1 = 0.2, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. For the 3,5-Ph2Pz crystal, bH = 1.4, C0 = 1.5, C1 = 0.2, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. The coupling parameter values used for calculation of the νN−D band contour shapes were as follows:

C = C0 + C1Q 1

where Q1 represents the totally symmetric normal coordinate for the low-frequency stretching vibration in the dimer. These parameter values remain in close relation to the intensity distribution in the dimeric νN−H band. The bH and C1 parameters are directly connected with the dimeric νN−H bandwidth. The C0 parameter determines the splitting of the component bands of the dimeric spectrum, corresponding to the excitation of the proton vibrational motions of different symmetry.6,7,42 In its original version, the strong-coupling model predicts diminution of the distortion parameter value for deuterium bond systems, according to the relation 7857



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Figure 8. Theoretically derived νN−D band contours calculated in terms of the strong-coupling theory in the limits of the two different vibrational exciton coupling mechanisms involving the cyclic dimer hydrogen bonds, that is, SS and the TH. (left) The SS coupling mechanism. (right) The TH coupling mechanism. (I) The minus band. (II) The plus band. (III) Superposition of the I and II spectra, each taken with its appropriate individual statistical weight parameter, F− and F+. In both mechanism cases, the same coupling parameter value system was used for calculations. For the D-4MeTAS crystal, bD = 0.4, C0 = 0.5, C1 = 0.0, F+ = 1.0, F− = 0.0, ΩN···N = 85 cm−1. For the D-3,5-Ph2Pz crystal, bD = 0.4, C0 = 0.2, C1 = 0.0, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. The transition frequencies are in the ωN···N vibrational quantum units, and the transition frequencies are expressed with respect to the gravity center of the hypothetical spectrum of a monomeric hydrogen bond in the cyclic hydrogen bond dimer. Transition intensities are in arbitrary units.

In Figure 8, we present the theoretical νN−H and νN−D band contours calculated in terms of the two individual mechanisms of the vibrational exciton interactions involving the dimer hydrogen bonds, SS and TH. In Figure 9, the evolution of the νN−H and νN−D band contour shapes accompanying the variation in the relative contribution of the TH- and SS-type coupling mechanisms in the generation of the tetramer system spectra is shown. Similar band shape evolution accompanies temperature changes during the spectral experiments.

For the D-4-MeTAS crystal spectrum, bD = 0.4, C0 = 0.5, C1 = 0.0, F+ = 1.0, F− = 0.0, ΩN···N = 85 cm−1. For the D-3,5-Ph2Pz crystal, bD = 0.4, C0 = 0.2, C1 = 0.0, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. For the isotopically neat and deuterated 4-MeTAS crystal spectra, the statistical weight parameter ratios for the SS and TH mechanisms were estimated as equal to 0.95:0.05 in the case of the room-temperature spectrum reconstitution. For the low-temperature spectrum case, this ratio value is very similar and practically equal to 1.0:0.0. For the isotopically neat and deuterium diluted 3,5-Ph2Pz crystal spectra the statistical weight parameter ratio for the SS and TH mechanisms were estimated as 0.5: 0.5 in the case of the room temperature spectrum reconstitution. For the lowtemperature spectrum case this ratio value was equal to 0.25: 0.75. In Figure 7, the model calculation results are shown, aiming to at least semiquantitatively reproduce the νN−H band fine structure patterns in the IR spectra of 4-MeTAS and 3,5-Ph2Pz crystals in the limits of the two opposite exciton coupling mechanisms, SS and TH. The calculations were performed upon assuming that hydrogen bond dimeric systems, not the hydrogen bond tetramers, were the sufficiently effective bearers of the crystal spectral properties.

10. H/D ISOTOPIC “SELF-ORGANIZATION” MECHANISM IN THE TETRAMERS From the analysis of the isotopic dilution and temperature effects in IR spectra of the hydrogen bond in the two different tetramer systems, it was found that in both crystal cases, the spectra are affected by the “dynamical cooperative interactions” involving hydrogen bonds.17,18 Comparison of the νN−H band shapes, measured for the isotopically neat compounds, with the “residual” νN−H band contour shapes of the isotopically diluted samples allows one to find their considerable similarity. The fine structure pattern of νN−H and νN−D bands appear independent upon the increasing rate of isotopic H/D exchange in the crystal hydrogen bonds. Moreover, in each 7858



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Figure 9. Temperature-induced evolution of the νN−H and νN−D band contour shapes accompanying to the variation in the contribution rate of the two different exciton coupling mechanisms, that is, SS and TH. Numerical reproduction of the temperature effect in the spectra of hydrogen-bonded (bottom) the 4-MeTAS crystal and (top) the 3,5-Ph2Pz crystal. The relative contribution ratios of the SS and TH mechanisms in the generation of the νN−H bands are as follows: for the 4-MeTAS crystal, 0.95:0.05 at 293 K and 1.0:0.0 at 77 K; for the 3,5-Ph2Pz crystal, 0.5:0.5 at 293 K and 0.25:0.75 at 77 K. For the deuterium-bonded crystals, the relative contribution ratios of the SS and TH mechanisms in the generation of the νN−D bands are as follows: for the D-4-MeTAS crystal, 0.95:0.05 at 293 K and 1.0:0.0 at 77 K; for the D-3,5-Ph2Pz crystal, 0.5:0.5 at 293 K and 0.25:0.75 at 77 K.

the second case, only the independent pairs of opposite, closely spaced hydrogen bonds in a cycle participate in the mechanism. In the case of cyclic hydrogen bond tetramers existing in crystals of 3,5-Ph2Pz, from the analysis of the crystalline spectra, it is found that the H/D isotopic self-organization mechanism involves the four adjacent isotopically identical hydrogen or deuterium bonds in the cyclic tetramers of 3,5-Ph2Pz. This is the property of molecular systems with aromatic π-electronic systems attached to hydrogen bonds.16−18,22,25,26 Thus, in isotopically diluted samples of 3,5-Ph2Pz, all cycles contain identical hydrogen isotope atoms in the hydrogen bridge systems because all of the vibrational exciton interactions are retained in isotopically diluted sample cases. Therefore, the fine structure of the crystal spectra remains practically unchanged along with the increase of the isotopic dilution rates. A vibronic coupling mechanism, depending on the dynamical interaction of the proton stretching vibrations with the electron movements in the cyclic systems of hydrogen bonds, as cyclic dimers or cyclic trimers, is the source of this effect.16−18,43 In the case of 4-MeTAS, the H/D isotopic recognition mechanism only involves the independent pairs of the moieties composed of the opposite hydrogen bonds in a tetramer cycle. In one individual cycle, two hydrogen bond pairs, differing one from the other by the hydrogen isotope contents, may exist, whereas an individual pair is occupied by identical hydrogen isotope atoms. In one individual cycle, the adjacency of the HH−HH-, HH−DD-, and DD−DD-type pairs is equally statistically privileged, as governed by a statistically random distribution. The relative content of each individual pair in a sample depends on the H/D isotopic exchange rates.

individual compound case, the compared bands also exhibit fairly identical temperature effects. The shapes and the spectral properties of the residual νN−H bands still exhibit effects of vibrational exciton interactions, which can only take place between the closely spaced hydrogen bonds containing identical hydrogen isotope atoms. In terms of the vibronic model of the H/D isotopic self-organization effects, originally proposed for interpretation of IR spectra of hydrogen bond dimeric systems, this is the main reason for the nonrandom proton and deuteron distributions between hydrogen bonds in the isotopically diluted crystals.16−18 From the analysis of 3,5-Ph2Pz and 4-MeTAS crystalline spectra, it is found that a nonrandom distribution of protons and deuterons also occurs for cyclic tetramers of hydrogen bonds. Even at the highest deuterium substitution rates in the hydrogen bonds, the expected evolution of the residual νN−H band shape, toward the band shape, characteristic for the monomeric hydrogen bond spectrum and corresponding to a nonrandom distribution of the hydrogen isotope atoms, did not appear. The same remarks concern the evolution of the νN−D band contours accompanying the isotopic dilution. These effects prove the existence of the so-called H/D isotopic selforganization in the tetramer hydrogen bond systems, which, on the other hand, can be understood as a kind of the H/D isotopic recognition mechanism acting on the hydrogen bond aggregates. However, from the presented investigations, it is shown that there is a differentiation in the tetramer system behavior with respect to the way in which these nonconventional interactions occur. In the first way, it may involve the adjacent hydrogen bonds in each individual tetramer cycle. In 7859



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(5) Each individual mechanism, that is, the TH and SS ones, generates its own spectrum characterized by its unique intensity distribution pattern. As we can see, the νN−H and νN−D bands in the spectra of 3,5-Ph2Pz crystals exhibit more complex fine structure patterns because they are a superposition of two different spectra, where each component spectrum is of a different origin. Each component spectrum contributing to the νN−H and νN−D band formation, with its temperature-dependent statistical weight, corresponds o another exciton interaction mechanism in the linear hydrogen bond dimers in the lattice. This explains the observed difference in the temperatureinduced evolution effects in the compared spectra. (6) The hydrogen bond tetramer systems in the crystals differ, one from the other, by the way in which the H/D isotopic self-organization phenomenon occurs in the cycles. In the 3,5-Ph2Pz-type tetramers, identical hydrogen isotope atoms, protons, or deuterons occupy all of the four-membered hydrogen bond rings. For the 4-MeTAS-type tetramers, this mechanism only involves pairs of opposite hydrogen bonds in a cycle. In one cycle, two hydrogen bond pairs, differing one from the other by hydrogen isotopes, may exist, whereas an individual pair is occupied by identical hydrogen isotope atoms. This specific nonconventional H/D isotopic recognition mechanism is molecular electronic structure dependent.

Therefore, the spectra measured in CCl4 solution resemble by shape the spectra of this group of tetramer systems, also measured in isotopic dilution. This effect, known as the H/D isotopic self-organization effect, has been intensively studied, both experimentally and theoretically, in recent years. This effect is similar to the corresponding effects identified for dimeric systems of hydrogen bonds16−18 and also in the case of some open-chain hydrogen bonds systems.18,27,28 The mechanism proposed for the interpretation of the temperature effects in the IR spectra of hydrogen bond tetramer systems is fairly similar to the corresponding mechanism explaining the temperature effects in IR spectra of the hydrogen bond of cyclic dimeric systems found in carboxylic acid crystals.44

11. CONCLUSIONS The results presented in this paper, concerning the 3,5-Ph2Pz and 4-MeTAS crystalline IR spectra interpretation, allow for the formulation of the following conclusions: (1) Cyclic tetramers of hydrogen bonds exhibit generally similar spectral properties in IR as infinite chains of hydrogen bonds in molecular crystals. The hydrogen bond tetramers in crystals of 3,5-Ph2Pz exhibit qualitatively similar spectral properties as pyrazole,22 formic acid,30 or 4-thiopyridone26 crystals. Spectral properties of 4-MeTAS crystals are fairly similar to the corresponding properties of amide and thioamide crystals.18,27,29,34 (2) The crystal IR spectral properties remain in close relation with the electronic structure of the two different molecular systems. The vibronic coupling mechanism involving the hydrogen bond protons and the electrons in the molecules determines the way in which the vibrational exciton coupling between the hydrogen bonds in tetramers occurs. The coupling of hydrogen bonds with large π-electronic systems of aromatic rings determines the similar spectral properties of 3,5-Ph2Pz tetramers in the crystals and infinitely long hydrogen bond chains in crystals of pyrazole22 or 4-thiopirydone.26 The direct coupling of the protons with small π-electronic systems found in carbonyl or thiocarbonyl groups in open-chain molecular associate systems (amide or thioamide crystals18,27,29,34) generates spectra similar to the corresponding spectra of 4MeTAS crystals. (3) The analyzed spectral properties of the two different crystalline systems, 3,5-Ph2Pz and 4-MeTAS, remain in good agreement with the vibrational exciton interaction mechanisms of the spectra generation for chain hydrogen bond systems. For 4-MeTAS tetramers, the exciton interaction mechanism of SStype that involves the opposite dimer hydrogen bonds in the tetramer cycles is only weakly temperature-dependent. A weak through-space coupling of a van der Waals-type in 4-MeTAS tetramers is responsible for the SS-type Davydov coupling domination regardless of temperature. (4) In the case of 3,5-Ph2Pz tetramers, due to their electronic molecular structure, the interhydrogen bond exciton coupling mechanism strongly changes its character along with the changes in temperature. Strong coupling in 3,5-Ph2Pz tetramers prefers a TH-type Davydov coupling. At very low temperatures, the TH-type interactions, transferred in the (N−H···N)4 cycles, dominate. This mechanism becomes less privileged at higher temperatures as it is annihilated by thermally activated largeamplitude vibrational motions of the hydrogen-bond-forming atoms.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: fl[email protected] (H.T.F); barbara.hachula@us. edu.pl (B.H.). Phone: +48-32-359-15-98. Fax: +48-32-259-9978. Notes

The authors declare no competing financial interest.

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REFERENCES

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