D Isotopic and Temperature Effects in the Polarized IR Spectra of

Article pubs.acs.org/JPCA

H/D Isotopic and Temperature Effects in the Polarized IR Spectra of Hydrogen-Bond Cyclic Trimers in the Crystal Lattices of Acetone Oxime and 3,5-Dimethylpyrazole Henryk T. Flakus,* Barbara Hachuła,* and Aleksandra Garbacz Institute of Chemistry, University of Silesia, 9 Szkolna Street, Pl-40-006 Katowice, Poland

ABSTRACT: Polarized IR spectra of hydrogen-bonded acetone oxime and 3,5-dimethylpyrazole crystals were measured at 293 and 77 K in the νX−H and νX−D band frequency ranges. These crystals contain molecular trimers in their lattices. The individual crystal spectral properties remain in a 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 trimers occurs. A strong coupling in 3,5-dimethylpyrazole trimers prefers a “tail-to-head”-type Davydov coupling widespread via the π-electrons. A weak through-space exciton coupling in acetone oxime trimers involves three adjacent hydrogen bonds in each cycle. The relative contribution of each exciton coupling mechanism in the trimer spectra generation is temperature and the molecular electronic structure-dependent. This explains the observed difference in the temperature-induced 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 the hydrogen-bond trimers exhibit the same way, in which the H/D isotopic recognition mechanism occurs. In acetone oxime and 3,5-dimethylpyrazole trimers, identical hydrogen isotope atoms exist in these entire hydrogen-bond systems.

1. INTRODUCTION

on the influences exerted by diverse physical factors, such as changes of temperature, changes in the matter state of condensation, pressure, solvents, etc.1−5 There are two quantitative theoretical models, namely, the “strong-coupling” theory6−8 (the elder theory) and the so-called “relaxation” (linear response) theory, the novel model, elaborated for the description of the νX−H band generation mechanisms.9,10 The both theoretical models are of a purely

Infrared spectroscopy still constitutes a basic tool in the research of the hydrogen-bond dynamics. The νX−H bands measured in the high frequency range of the mid-infrared attributed to the proton stretching vibrations in X−H···Y hydrogen bonds constitute a wealth data system 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 lowfrequency X···Y hydrogen bridge stretching vibrational motions.1−5 The band contour shapes are extremely susceptible © 2012 American Chemical Society

Received: August 23, 2012 Revised: October 29, 2012 Published: October 29, 2012 11553

dx.doi.org/10.1021/jp308375z | J. Phys. Chem. A 2012, 116, 11553−11567

The Journal of Physical Chemistry A

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bond research. Despite spectacular achievements in the quantitative description of the intensity distribution in the νX−H bands and of the H/D isotopic effects, the understanding of temperature effects in the spectra seems to be highly incomplete. 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 arguments in order to elucidate the nature of the interaction mechanisms involving hydrogen bonds in oligomeric hydrogenbond systems like cyclic trimers. A. X-ray Structures of Acetone Oxime and 3,5Dimethylpyrazole. The crystal structure of acetone oxime (AceOxm in abbreviated notation) was already measured and published in 1951 by Bierlein and Lingafelter 19 and redetermined by Parsons et al. in 2004.20,21 Crystals of AceOxm are triclinic, and the space-symmetry group is P1̅ ≡ Ci. There are six molecules in a unit cell (Z = 6). The lattice constants at 220 K: a = 7.006(2) Å; b = 10.482(3) Å; c = 10.580(5) Å, α = 60.49(1)°, β = 79.61(3)°, and γ = 83.45(1)°.20 The three independent molecules of AceOxm are linked by intermolecular hydrogen bonds O−H···N into a trimeric structure. Therefore, the oxime O atoms act as hydrogen-bond donors and the N atoms as acceptors, thus generating the R33(9) graph set.22 The hydrogen-bond geometry is as follows: RH···N = 1.966, 1.968, and 1.974 Å, RO···N = 2.794, 2.795, and 2.798 Å, ∠O−H···N = 170.13, 176.34, and 178.55°. The projection of the AceOxm crystal lattice onto the ac plane is shown in Figure 1. The Hbonding structural motifs for oximes in the solid state were reported by Infantes and Motherwell.23 The crystal structure of 3,5-dimethylpyrazole (3,5-Met2Pz in abbreviated notation) was determined by Baldy et al. in 198524 and redetermined by Smith et al. in 1989.25 3,5-Met2Pz

vibrational nature. Over the last four decades, by use of these theories, IR spectra of diverse hydrogen-bond systems have been reproduced satisfactorily. The model calculations concerned quantitative interpretation of spectra of single, isolated hydrogen bonds,7,11 spectra of cyclic dimeric hydrogenbond 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 satisfactorily interpreted.7−15 However, despite the doubtless achievements 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 of troubles in the understanding of many spectral phenomena characterizing systems consisting with 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 of 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 found in molecular crystal lattices allowed us to recognize numerous puzzling spectral effects attributed to these systems. Without assuming that some not revealed yet mechanisms interfere with the spectra generation mechanism, the understanding of these effects appears to be beyond the scope of the contemporary quantitative theoretical models proposed for the hydrogen-bond IR spectra interpretation. Spectroscopy in polarized light of hydrogen-bonded molecular crystals has provided key experimental data in this area. By measuring polarized IR spectra of spatially oriented molecular crystals, characterized by a rich diversity of hydrogenbond 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 new H/D isotopic effects to be revealed, 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 co-operative interactions involving hydrogen bonds, i.e., the so- called dynamical co-operative interactions.16−18 This revealing has emphasized the role of the vibronic coupling between the electronic and proton vibrational motions, taking place in hydrogen-bond aggregates, in the generation of the very nature of the hydrogen bond.17,18 In this paper, we present our investigation results concerning the IR crystalline spectra of hydrogen-bonded 3,5-dimethylpyrazole and acetone oxime. The two crystals contain cyclic hydrogen-bond trimers in their lattice sites. The two molecular systems differ, one from the other, by their individual electronic properties. They also differ by their spectral properties attributed to the hydrogen bonds in each individual crystalline system, namely, by the temperature effects characterizing the compared spectra. This was the basic criterion for the choice of these systems as the subjects of our studies. The problem of the theoretical treatment of the spectral properties of cyclic systems, composed with mutually interacting hydrogen bonds, still constitutes a real challenge in the area of the hydrogen-

Figure 1. X-ray structures of (top) AceOxm and (bottom) 3,5-Met2Pz crystals. Projection of the lattice onto the ac plane of the AceOxm crystal and the ab plane of the 3,5-Met2Pz crystal. 11554



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crystallizes in the trigonal system with the space group R3c ≡ D63d. The unit cell parameters at 295 K are a = 11.775(2) Å, b = 11.775(2) Å, c = 20.991(4) Å, and Z = 18. The main structural units are planar trimers of 3,5-dimethylpyrazole molecules, linked by three complementary strong hydrogen bonds N− H···N. The hydrogen-bond geometry is RH···N = 2.103 Å, RN···N = 2.978 Å, and ∠N−H···N = 172.05°. The projection of the 3,5-Met2Pz crystal lattice onto the ab plane is presented in Figure 1. The H-bonding structural motifs for pyrazoles in the crystalline state were also discussed in the past.23

2. EXPERIMENTAL DETAILS AceOxm and 3,5-Met2Pz, used for our studies, were the commercial substances (Sigma-Aldrich). The substances were investigated without further purification. The deuteriumbonded AceOxm and 3,5-Met2Pz were obtained by evaporation from CH3OD (AceOxm) and D2O (3,5-Met2Pz) solution of the compounds, respectively (at room temperature and under reduced pressure). It was found that the deuterium exchange rate for the −X−H groups varied from 50 to 90% for AceOxm and from 50 to 90% for 3,5-Met2Pz, respectively. Crystals of AceOxm and 3,5-Met2Pz, suitable for further spectral studies, were obtained by cooling of the molten samples, occurring between two closely placed CaF2 plates. By that means, reasonably thin crystals could be received, characterized by their maximum absorbance at the νX−H and νX−D band frequency ranges lower than 0.8 at room temperature. From the crystalline mosaic, adequate monocrystalline fragments, having dimensions at least 2 × 2 mm, were selected and then spatially oriented with the help of a polarization microscope. These crystals were selected to the experiment by use of a thin, tin plate diaphragm with a 1.5 mm diameter hole. It was found that AceOxm crystals developed most frequently the “ac” plane of the lattice, whereas 3,5Met2Pz crystals developed 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 AceOxm and 3,5-Met2Pz 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 ca. 10 different single crystals of each isotopomer. The normal vibration calculations for 3,5Met2Pz have been performed in the past.26 The Raman spectra of polycrystalline samples of AceOxm and 3,5-Met2Pz were measured at room temperature with the use of the Bio-Rad FTS-175C FT-IR spectrometer at the 1 cm−1 resolution.

Figure 2. The νX−H band in the IR spectra of (top) AceOxm and (bottom) 3,5-Met2Pz in the CCl4 solution.

Figure 4. Figure 5 shows the corresponding low- temperature crystalline spectra. The temperature effect in the crystalline spectra in the most intense polarized components of the νX−H and the νX−D bands from Figures 4 and 5 is given in Figure 6. The IR spectra of the hydrogen bond in AceOxm, measured in CCl4 solution, consist of two spectral branches: the shorterwave branch is placed in the 3500−3000 cm−1 frequency range, and the lower-wave branch is located in the 3000−2500 cm−1 frequency range. The spectral peak at 3607 cm−1 corresponds to the stretching vibrations of free, not associated O−H groups. Comparison of the IR spectra of AceOxm in the CCl4 solution, with the KBr pellet spectra, recorded in the νO−H proton stretching vibration region (see Figures 3 and 4), shows an insignificant difference between the two compared band contours, i.e., the shapes of these two compared spectra. The longer-wave branch of the νO−H band in the AceOxm spectrum, measured in the CCl4 solution, is slightly narrower and of a lower intensity than that of the spectral branch from the spectra of the polycrystalline sample. These differences in the band intensity distribution patterns can be intuitively ascribed to similar structural units of the molecular associates found in each individual phase. From literature data, we know that AceOxm molecules associate, forming cyclic hydrogen-bonded dimers and trimers in inert solvent solutions,27−30 whereas in the AceOxm crystal lattice cyclic hydrogen-bonded trimers of the molecules exist.19,20 When comparing the 3,5-Met2Pz 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 relation concerns the two-branch fine structure of the νN−H band (the shorter-wave branch placed in the 3400− 3000 cm−1 frequency range and the longer-wave band branch in the 3000−2500 cm−1 frequency range). In the CCl4 solution

3. RESULTS The preliminary experimental studies of spectral properties of AceOxm and 3,5-Met2Pz depended on the measurements in CCl4 solution in the frequency range of the νX−H proton stretching vibration bands. The spectra are shown in Figure 2. In Figure 3 are shown the νX−H and νX−D bands from the IR spectra of isotopically neat and isotopically diluted, polycrystalline AceOxm and 3,5-Met2Pz samples in KBr pellets, measured at 293 and 77 K. Polarized IR spectra of the two crystalline systems, isotopically neat and isotopically diluted, measured at 293 K in the νX−H and νX−D band frequency ranges, are presented in 11555



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Figure 3. The νX−H and νX−D bands in the IR spectra of polycrystalline samples of isotopically neat and isotopically diluted (top) AceOxm and (bottom) 3,5-Met2Pz, dispersed in KBr pellets. Temperature effects are shown in the spectra. The Raman spectra are also shown.

Figure 4. Polarized IR spectra of isotopically neat and isotopically diluted crystals of (top) AceOxm and (bottom) 3,5-Met2Pz measured at 293 K in the νX−H and νX−D band frequency ranges. (top, I) The electric field vector E parallel to the a*-axis (the asterisk denotes the vector in the reciprocal lattice); (II) the E vector parallel to the c-axis. (bottom, I) The electric field vector E parallel to the b-axis; (II) the E vector parallel to the a*-axis (the asterisk denotes the vector in the reciprocal lattice).

spectra, the two components of the νN−H proton stretching vibration band, the longer and the shorter-wave ones, are of similar intensities. The spectral peak placed at 3475 cm−1 in the CCl4 solution spectra corresponds to the stretching vibrations

of non-associated N−H groups. In the band contour of the spectra of the polycrystalline sample, we can see that the longer-wave branch is more intense, when compared with the shorter-wave band branch. These similarities in the band 11556



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Figure 5. Polarized IR spectra of isotopically neat and isotopically diluted crystals of (top) AceOxm and (bottom) 3,5-Met2Pz measured at 77 K in the νX−H and νX−D band frequency ranges. (top, I) The electric field vector E parallel to the a*-axis (the asterisk denotes the vector in the reciprocal lattice); (II) the E vector parallel to the c-axis. (bottom, I) The electric field vector E parallel to the b-axis; (II) the E vector parallel to the a*-axis (the asterisk denotes the vector in the reciprocal lattice).

Figure 6. Temperature effect in the νX−H and νX−D bands in the IR spectra of isotopically neat and isotopically diluted monocrystalline samples of (top) AceOxm and (bottom) 3,5-Met2Pz. Comparison of the most intense polarized component bands from Figures 4 and 5.

solution.24,26,31 It was experimentally evidenced that for the molecular geometry reasons hydrogen-bond cyclic trimers are the most privileged oligomers of diverse pyrazole derivative molecules found in nonpolar solvent solutions.32

intensity distribution patterns can be ascribed to identical structural units of the molecular associates found in each individual phase. Hydrogen-bonded cyclic trimers of the molecules exist in the 3,5-Met2Pz crystal lattice and in CCl4 11557



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• hydrogen-bonded dimers, e.g., arylacetic acids33−35 and styrylacetic acid47 • hydrogen-bonded trimers, e.g., AceOxm20,21 • hydrogen-bonded tetramers, e.g., 7-azaindole48 and 4methyl-1,2,4-triazole-thione49 the νX−H bands are fairly similar to the corresponding spectra of the other group of crystals, i.e., those with open hydrogen-bond chains in their lattices (e.g., crystals diverse amides and thioamides,43−45 3- and 4-benzaldehyde,50 indole-3-carboxaldehyde and 3-acetylindole,51 acetic acid crystals52). In this case, the νX−H band contours can be treated as a “mirror ref lection” of the corresponding band shapes of systems from point “a”. In this case, the higher-frequency 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. In the “b” case, the νX−H bands, even at room temperature spectra, exhibit a relatively high intensity of their higherfrequency branches in relation to the corresponding lowerfrequency branch intensities. On the temperature decrease up to 77 K, only a light growth of the relative intensity of each lower-frequency branch of each analyzed band can be observed. As a result of the νX−H band contour thermal evolution, in the low temperature spectra of the dimeric and tetrameric systems of this group, the higher-frequency branch is of the dominant intensity in the bands. B. Spectra of Crystals with the Chain Arrangement of Hydrogen Bonds. We will start our interpretation of the IR spectra of the hydrogen bond in cyclic trimers based on the “state-of-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. For selected molecular crystalline systems from the “a”group, a characteristic intensity distribution pattern is the property of the νX−H band contours. The lower-frequency spectral branch of the band corresponds to the transition to excited state belonging to the A-irreducible representation of the totally symmetric “in-phase” proton vibrations in a chain system. The higher-frequency branch of the νX−H band is generated by the transition occurring to the B-symmetry excited state of the non-totally 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, may be allowed via a vibronic mechanism. In terms of the vibronic model of the vibrational selection rule breaking, the promotion mechanism of the forbidden transition is a kind of reverse of the familiar Herzberg−Teller mechanism, from the UV spectroscopy of aromatic hydrocarbons.53,54 Within this approach, the electronic properties of single hydrogen bonds themselves, as well as electronic properties of the associated molecules, along with the proton vibration anharmonicity, are responsible for the magnitude of the forbidden transition promotion effects in the dimeric spectra.45,54 This nonconventional mechanism determines unique properties of systems with the chain arrangement of hydrogen bonds. Also declining from the linear arrangement of hydrogen bonds in a chain causes the increase of the higher-frequency branch intensity. Therefore, the lowerfrequency branch of the νX−H band, attributed to the totally symmetric vibrations, is more intense than the other band

4. THE IR SPECTRA OF HYDROGEN-BONDED CRYSTALS A. Electronic Structure of the Molecules versus the Temperature Effects in Their Crystalline Spectra. Before considering the mechanisms of the spectra generation for cyclic hydrogen-bond trimers, let us remind the corresponding spectra of molecular crystals with other diverse hydrogenbond aggregates in their lattices. One could expect that the hydrogen-bond IR spectra of diverse hydrogen-bonded systems, measured in the νX−H or νX−D band frequency ranges, should be fairly similar, one to another. This statement is supported by the fact that similar structural units composed with a given number of hydrogen bonds exist in the crystal lattices, i.e., cyclic dimers, trimers, tetramers, etc. However, on comparison of the IR spectra of diverse crystalline systems, with the precisely defined number of moieties in the cycles existing in each individual crystal lattice, a considerable variation degree of the analyzed νX−H band contour shapes can be found. Up to our previous estimations, this fact remains in a close connection with differences in the electronic 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 systems of hydrogen bonds, in relation to their molecular electronic structures: (a) In the case of cyclic hydrogen-bond systems, in which molecules contain large delocalized π-electronic systems coupled directly with the hydrogen bonds, e.g., • hydrogen-bonded cyclic dimers, e.g., arylacetic acids33−36 and arylacrylic acids37 • hydrogen-bonded cyclic trimers, e.g., 4-bromopyrazole32 and 3,5-Met2Pz24,25 • hydrogen-bonded cyclic tetramers, e.g., 3,5-Ph2Pz38,39 the νX−H bands are fairly similar to the corresponding spectra of a group of crystals with open hydrogen-bond chains in their lattices (e.g., pyrazole,40 imidazole,41 and 4-thiopyridone42). These bands are characterized by substantially different intensity distribution patterns, when compared with the corresponding band properties in the IR spectra of diverse amides and thioamides.43−45 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 of crystals with chain arrangement of hydrogen bonds in their lattices, can be observed. Surprisingly, a similar property characterizes the crystalline spectra of the simplest carboxylic acid, i.e., formic acid.46 The νX−H bands in the room temperature spectra of the hydrogen bond of the cyclic 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. On 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. (b) In other cases of cyclic crystalline systems, e.g., 11558



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Figure 7. The (left) “through-space” (TS) exciton coupling involving the proton stretching vibrations of different symmetry in a cyclic model hydrogen-bond trimer. The relations between the vibrational exciton energy levels of the cyclic trimer in the limits of the dipole−dipole model approximation. The (right) “head-to-tail” (TH) exciton coupling involving the proton stretching vibrations of different symmetry in a chain system of associated hydrogen bonds. The relations between the exciton energy levels of a model linear trimer in the limits of the dipole−dipole approximation.

branch related to the transition to the B-representation attributed to the non-totally symmetric vibrations of the protons, which generate the higher-frequency band branch. For the analysis of the cyclic trimer spectral properties, one should also recall the hydrogen-bond IR spectra of other chain hydrogen-bond systems, including spectra of hydrogen-bonded amides and thioamides.43−45 On 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 also be made: Most of the chain hydrogen-bond systems exhibit an abnormal, i.e., a “reverse”, intensity distribution pattern in their contours. In this case, the νX−H bands have the lower-frequency branch of a lower intensity, even in their low-temperature spectra. However, only in some rare cases, e.g., formic acid,46 imidazole,41 and pyrazole,40 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. These spectra belong to the “a”-group of hydrogen-bonded systems. However, most of the

chain hydrogen-bond systems exhibit 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, e.g., acetic acid,52 N-methylacetamide,44 N-methylthioacetamide,43 and acetanilide,55 this effect was ascribed previously to the strong exciton couplings involving the opposite hydrogen bonds from the different closely spaced molecular chains in the crystal lattices.

5. THEORETICAL APPROACH PROPOSED A. Exciton Coupling Mechanism versus the Electronic Properties of the Molecules. We start our considerations on the IR spectra of cyclic trimer hydrogen-bond systems from recalling the interpretation of the analogous spectral properties of two and in the other case four mutually coupled hydrogenbond systems, i.e., hydrogen-bond cyclic dimers and tetramers. The interpretation of the analogous spectral properties of openchain systems of hydrogen bonds ought to be also reminded. The mechanism of the cyclic dimer and cyclic tetramer spectra generation was considered only recently.49,56 Similarly to the case of the cyclic dimers, tetramers, and the open-chain 11559



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Coulomb repulsion between the electric charges placed at the ends of the dipoles dominates. The vibrational transitions corresponding to such arrangements of the vibration dipole moments are responsible for the generation of the intense, higher-frequency branch of the νX−H band in the trimeric spectra. This spectral branch of the band is attributed to the symmetry-allowed transition.53 In contrast, when the dipole transition moments are of the arrangement corresponding to the totally symmetric proton vibration (see Figure 7), the energy exciton interaction energy value EAg is negative, since the Coulomb attraction between the transition moment dipoles dominates. In consequence, the subband generated by this situation is placed at the lower frequency and it corresponds to the symmetry-forbidden vibrational transition in IR. In the case of the totally symmetric proton vibrations, when the transition moment dipoles are oriented axially in a linear hydrogen-bond trimer as “tail-to-head” (TH), the sign of the exciton interaction energy value E+ is negative. Therefore, the intense branch corresponding to the symmetry-allowed transition is placed at the lower frequency range. On the contrary, the forbidden by the symmetry rules spectral branch, situated at the higher frequency, is generated by the anti-parallel orientations of the vibrating dipoles (see Figure 7). In this case, the exciton coupling energy E− is of the positive sign. Therefore, the spectral branch of a relatively low intensity appears at the higher-frequency range of the νX−H band. The sequence and the properties of the branches in the proton stretching vibration bands in the discussed case of the chain hydrogen-bond oligomer system is reverse to those observed in the IR spectra of hydrogen-bond cyclic trimeric systems. Therefore, the following problem demands explanation: Why do some individual cyclic hydrogen-bond trimeric systems exhibit similar spectral properties to the corresponding properties of a particular group of crystals, with chain structures of hydrogen-bonded associates (formic acid,46 pyrazole,40 and 4-thiopyridone42 crystals). Undoubtedly, this property remains in a close connection with the π-electronic properties of the associating molecules. In the associated molecular systems, vibrational exciton couplings are of the “tail-to-head” (TH) type. 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 factors governing these inter-hydrogen-bond interactions, since in this case the hydrogen bonds couple via electrons. Nevertheless, crystals, with hydrogen-bonded cyclic trimers in their lattices, surprisingly exhibit spectral properties similar to the analogous properties of the crystalline spectra of acetic acid,52 N-methylthioacetamide,43 or acetanilide.55 In the latest case, the exciton interactions of the “through-space” (TS) type involve the closely spaced hydrogen bonds where each moiety belongs to a different chain. In molecules of this group, large πelectronic systems are absent. Only the CO, CS, or CN groups, each with a small π-electronic system, are present in these molecules. The inter-hydrogen-bond interactions occur mainly “through-space” by the dipole−dipole interaction mechanism. From the above-presented data, it results that the way of realization of the vibrational exciton interactions in various hydrogen-bond aggregates (cyclic dimers, infinite chains), affecting the νX−H and νX−D band fine structures, does not directly depend on the geometry of a hydrogen-bond system. It

hydrogen-bond systems, the spectral properties of the cyclic hydrogen-bond trimers undoubtedly also remain in the closest correspondence with the electronic structure of the associating molecules. This is the key factor governing the spectral properties of the hydrogen-bond trimeric systems. In the case of IR spectra cyclic trimers of hydrogen bonds, similarly as in the case of the open chain hydrogen-bond systems, the two different extreme behaviors can be observed. For the hydrogen-bond cyclic trimers formed by molecules containing large π-electronic systems, coupled directly with the hydrogen bonds (3,5-Met2Pz), the adjacent hydrogen bonds in a cycle couple mainly as “tail-to-head” (TH), via the π-electrons, with their spectra typical for the “a”-group. In the 3,5-Met2Pz trimers, the hydrogen-bond proton vibrations strongly couple with the electronic motions on the π-orbitals of the pyrazole aromatic rings. Therefore, the 3,5-Met2Pz trimer spectral properties fairly resemble the analogous properties of cyclic dimers, tetramers, and open-chain hydrogen-bond systems from the “a”-group of crystals (see section 4A). On the other hand, the spectral properties of the AceOxm cyclic trimers with regard to the νO−H band shape thermal evolution fairly belong to the “b”-group of crystals (see section 4B). This is because in this case no large π-electronic systems couple with the protonic motions in the hydrogen bonds of these trimers. In AceOxm cyclic trimers, large π-electronic systems are absent. Only the CN bonds exist in these molecules, each with a small πelectronic system. In these associated molecular systems, the hydrogen bonds are mainly “through-space” (TS)-coupled and their mutual interaction is basically of the dipole−dipole character. B. Molecular Vibrational Exciton Approach. The dependence of the inter-hydrogen-bond coupling mechanism, which involves the hydrogen bonds in the cyclic trimers, upon the electronic properties of the associated molecules, strongly influences the energetic relations characterizing the trimeric vibrational exciton levels. As a consequence, the electronic properties of hydrogen-bond trimers determine their spectral properties in IR. The analysis of this inter-hydrogen-bond coupling in the case of cyclic trimers requires taking into consideration three different situations of the vibrational transition moment arrangement. Let us introduce the following symmetry coordinates for the proton stretching vibrations in the model cyclic hydrogen-bond trimer of the C3 symmetry, defined as Q1 =

1 (q + qB + qC) 3 A

Q2 =

1 (2qA − qB − qC) 6

Q3 =

1 (q − qC) 2 B

(1)

The A, B, and C indexes label the hydrogen bonds in the cycles. The Q1 symmetry coordinate belongs to the totally symmetric irreducible representation A, whereas the non-totally symmetric Q2 and Q3 symmetry coordinates belong to the E double degenerated representation of the C3 point group.57 For cyclic model trimers, the mutual orientation of the dipole transition moments of the exciton interaction energy values for the degenerated proton vibrational motions of the lower symmetry are positive within the “through-space” (TS) coupling approach. In this case, the dipole−dipole approximation in the 11560



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case 2, the lower intensity spectral branch appears in the lowerfrequency range. It corresponds with the quasi-forbidden vibrational transition in the closed chain, corresponding with the totally symmetric proton vibrations, whereas the higherfrequency branch of the band is attributed to the non-totally symmetric proton vibrations in the trimer. As it was shown in our recent papers, the relative position of the quasi-forbidden transition spectral branch in the νX−H bands depends of the way in which the inter-hydrogen-bond vibrational Davydov coupling occurs in hydrogen-bond systems. The “through-space” (TS) coupling generates the low-intensity spectral branch at the lower-frequency band region, while the “tail-to-head” (TH) coupling involving the trimer hydrogen bonds, occurring via electrons, is responsible for the appearance of the lowerintensity branch at the higher-frequency region of the band.48,49 D. Temperature Effects in the Spectra versus the Vibrational Exciton Model. It seems justified that in order to explain the temperature effects in the IR spectra of cyclic hydrogen-bond trimers 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 trimers 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 “through-space” (TS) vibrational exciton coupling involving the hydrogen bonds in cyclic trimers. In this case, the trimer hydrogen bonds interact one with the other as “side-to-side”. (B) The other mechanism assumes a “tail-to-head” (TH)type exciton coupling involving the hydrogen bonds in the cyclic trimers. These interactions occur around the trimeric 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, e.g., for pyrazole associated molecules in crystals. The “A” mechanism seems to dominate in the case of molecular systems with small π-electronic systems, e.g., for amide and thioamide associated molecules. It seems obvious that for an individual hydrogen-bonded trimer 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, i.e., 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. In these circumstances, the role of the “A” mechanism increases, namely, of the “through-space” vibrational exciton coupling between the hydrogen bonds in a trimer. This should therefore result in a particularly strong 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.

is rather determined by the electronic structure of the associating molecules. C. Two Mechanisms of the Inter-Hydrogen-Bond Exciton Coupling in the Trimers. The dipole−dipole interaction model, widely used for a simplified description of the exciton interactions between hydrogen bonds, seems to be inadequate in the explanation of the wide diversity of the spectra of cyclic trimers of hydrogen bonds. There is some experimental data indicating that these couplings do not always occur as “through-space” (TS), when the dipole−dipole model is adequate, and they are also widespread by the hydrogen-bond electrons as well as by electrons belonging to the molecular skeletons. Therefore, in terms of the theory of molecular vibrational excitons,58,59 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 trimer. In the case of other crystalline system cases, the electric current induced by the protonic motions oscillates along a hydrogenbond 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 non-totally symmetric vibrations are inactive in this mechanism, since currents induced in each individual hydrogen-bond trimer are annihilated in these circumstances. The model assuming the electric current generated by oscillating protons in cyclic hydrogen-bond dimers was proposed by Naf ie three decades ago.60 This idea seems to also be useful in our consideration of the inter-hydrogen-bond exciton coupling in the case of cyclic trimeric systems of hydrogen bonds. In the scope of the considerations given above, it seems justified to treat formally a cyclic hydrogen-bond trimer by the two following different ways, taking into account the way in which the inter-hydrogen-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 associates in pyrazole40 and 4-thiopyridone42 crystals. This is the coupling of the “tail-to-head” (TH) type occurring around the molecular cycle. This way of the coupling occurs via the easy-polarizable electrons on the π-orbitals. In this case, the trimer spectrum is similar to the spectrum of a chain system, with a low intensity of the higher-frequency band branch. (2) As three pairs of partially independent hydrogen bonds, which are mainly “through-space” (TS) exciton-coupled. 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 trimer spectra are basically of a standard form, with a relatively low intensity of the lowerfrequency νX−H band branch. For the quantitative description of the exciton interactions involving hydrogen bonds, influencing the trimer spectra, the dipole−dipole model seems to be adequate. The νX−H band shapes in the two types of the trimer spectra are related one with the other 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, occurring to the excited state of the non-totally symmetric proton stretching vibrations, occurring in the closed hydrogen-bond chain.48 In 11561



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In the spectra of cyclic trimers, 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 trimers, the “B” mechanism cannot be activated effectively enough even at low temperatures, since in this case the B-level can be formally treated as located considerably higher than the A-level. We assume further that a Boltzmann-type relation governs the contribution of each inter-hydrogen-bond coupling mechanism. In addition, for the statistical weight parameters of each individual mechanism, PA(T) and PB(T), one must distinguish which state is dominant, i.e., when the TS (A) state is of the lower energy and the TH (B) state is of a higher energy value and vice versa. In order to reproduce the temperature dependence of experimental spectra particularly for its width and the position of its first moment, we used for the PAB A (T) exponential temperature dependence according to ⎛ α AB ⎞ PAAB(T ) = 1 − exp⎜ − ⎟ ⎝ kBT ⎠

accompanied by large-amplitude thermal motions of atoms in the trimers. 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 trimers. From our experimental data, it can be concluded that the cases A and B represent the extreme mechanisms of the inter-hydrogen-bond exciton coupling in cyclic hydrogen-bond trimers. 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 non-distinguishable. E. Model Calculation of the Temperature Effects in the Spectra. In the two cases, A and B, model calculations, aiming at reconstituting of the “residual” νX−H and νX−D band shapes, were performed within the limits of the “strong-coupling” theory, for a model X−H···Y hydrogen-bond dimeric system.6−8,61 We assumed that the main νX−H and νX−D band shaping mechanism involved strongly anharmonically coupled, high-frequency proton (or deuteron) stretching vibrations and low-frequency X···Y hydrogen bridge stretching vibrational motions. Calculation of the hydrogen-bond system IR spectra in terms of the “strong-coupling” model allow one to obtain results fairly comparable with the results of the spectra calculation performed using the novel and more sophisticated “relaxation” theory.9,10,35,36,62 According to the formalism of the “strong-coupling” theory,6−8,61 the νX−H band shape depends on the following system of dimensionless coupling parameters: (i) on the distortion parameter, “bH”, and (ii) on the resonance interaction parameters, “C0” and “C1”. The “bH” parameter describes the change in the equilibrium geometry for the lowenergy hydrogen-bond stretching vibrations, accompanying the excitation of the high-frequency proton stretching vibrations νX−H. The “C0” and “C1” parameters are responsible for the effective exciton interactions between the hydrogen bonds in a trimer. They denote the subsequent expansion coefficients in the series on developing the resonance interaction integral “C” with respect to the normal coordinates of the νX···N low frequency stretching vibrations of the hydrogen bond. This is in accordance with the formula

(2)

where α is the activation energy parameter when the TS state is dominant and kB is the Boltzmann constant. In such a circumstance, PAB A (T) takes the following expression: AB

⎛ α AB ⎞ PBAB(T ) = exp⎜ − ⎟ ⎝ kBT ⎠

(3)

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 PAB A (T) is almost equal 0.0. In these circumstances, the TS-type interaction is the basic type of the exciton coupling involving the trimer hydrogen bonds. For high temperatures, the PAB A (T) parameter values are different from 0.0 and they are intermediate between 0.0 and 1.0 (rather closer to 0.5) and PAB A (T) approaches 0.5. When the temperature increases, the PAB A (T) value also increases. It means that the TH coupling, occurring via the electric current in the ring, is activated in higher temperatures in a magnitude depending on the energy gap between these two states of the vibrationally excited trimer. From our experimental estimations, the energy gap for some trimeric system cases is relatively large and in other cases it may be relatively low. In case B, where the TH state is of a lower energy value, we assume the same formula but the energy barrier αBA height is relatively low. In such a circumstance, the statistical weight parameters, PA(T) and PB(T), may be written as follows: ⎛ α BA ⎞ PABA(T ) = exp⎜ − ⎟ ⎝ kBT ⎠

(4)

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

(5)

C = C0 + C1Q 1

where Q1 represents the totally symmetric normal coordinate for the low-frequency X···N hydrogen bridge stretching. This parameter system is closely related to the intensity distribution pattern in the νX−H band. The “bH” and “C1” parameters are directly related to the νX−H component bandwidth. The “C0” parameter defines the splitting of the component bands of the spectrum corresponding to the excitation of the proton vibrational motions of different symmetries. In its simplest, original version, the “strong-coupling” model predicts reduction of the distortion parameter value for the deuterium bond systems according to the relation

As we can see, for very low temperatures, PBA B (T) may be practically equal to 1.0. For this kind of trimeric systems, the TH-type exciton coupling is the basic natural way in which the inter-hydrogen-bond interactions occur. The growth in temperature annihilates this way of the coupling, due to the vanishing of the electronic current induced in the cycles,

bH =

2 bD

For the “C0” and “C1” resonance interaction parameters, the theory predicts the isotopic effect expressed by the 1.0 to √2fold reduction of the parameter values for D-bonded systems. 11562



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Figure 8. Theoretically derived νX−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 trimer of hydrogen bonds, that is, the TS and the TH. (left) The TS 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 AceOxm crystal, bH = 1.2, C0 = 1.5, C1 = −0.1, F+ = 1.0, F− = 0.8, ΩO···N = 85 cm−1. For the 3,5-Met2Pz crystal, bH = 1.5, C0 = 1.6, C1 = −0.3, F+ = 1.0, F− = 0.7, and ΩN···N = 85 cm−1. The transition frequencies are in the ωX···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 trimers. Transition intensities are in arbitrary units.

The F+ and F− symbols denote the statistical weight parameters for the “plus” and “minus” theoretically derived subspectra contributing to the band formation. The coupling parameter values used for calculation of the νX−D band contour shapes were as follows: For the AceOxm crystal spectrum, bD = 0.4, C0 = 0.5, C1 = 0.0, F+ = 1.0, F− = 0.2, ΩO···N = 85 cm−1, and for the 3,5-Met2Pz crystal spectrum, bD = 0.4, C0 = 0.2, C1 = 0.0, F+ = 1.0, F− = 0.2, ΩN···N = 85 cm−1. For the AceOxm crystal spectra, the statistical weight parameter ratio, PA(T):PB(T), for the TS and TH mechanisms were estimated as equal to 0.9:0.1 in the case of the room temperature spectrum reconstitution. For the low-temperature spectrum case, this parameter ratio value is very similar and approximately equal to 1.0:0.0. Among various parameter ratio values for the TS and TH mechanisms contributing to the band generation, this parameter ratio value allowed for the most adequate reproduction of the temperature effect in the crystal spectra. For the 3,5-Met2Pz crystal spectra, the statistical weight parameter ratio, PA(T):PB(T), for the TS and TH mechanisms was estimated as equal to 0.50:0.50 in the case of the room temperature spectrum reconstitution. For the low-temperature spectrum case, this parameter ratio value is equal to 0.0:1.0. In Figure 8, we present the theoretical νX−H band contours calculated in terms of the two individual mechanisms of the vibrational exciton interactions involving the trimer hydrogen bonds, TS and TH. The corresponding calculation results for the νX−D band contours are shown in Figure 9.

As a consequence of the “strong-coupling” model, the νX−H and νX−D band contour fine structures were treated as a superposition of two component bands. They correspond to the excitation of the two kinds of proton stretching vibrations, each exhibiting a different symmetry. In the case of the A exciton coupling mechanism and for the C3 point symmetry group of the model trimer, the excitation of the vibrations of the A-symmetry generates the lower-frequency branch of the νX−H band. The E vibrations are responsible for the higherfrequency band branch. In the case of the B mechanism, the component sub-bands, plus and minus, appear in reverse sequence. Here, we consider an identical anharmonic coupling parameter system for the two individual mechanism cases, A and B, although diversification of the coupling parameter value systems seems to be better justified. The theoretical spectra reconstituting the νX−H band contours measured at the two different temperatures, 293 and 77 K, were calculated in terms of the two different individual coupling mechanisms, TS and TH, which generate the two component bands, “plus” and “minus” in a different sequence. The following coupling parameter values, identical in both molecular system cases, were used: For the AceOxm crystal spectra calculated in the limits of the coupling mechanisms, TS and TH: bH = 1.2, C0 = 1.5, C1 = −0.1, F+ = 1.0, F− = 0.8, ΩO···N = 85 cm−1 For calculation of the 3,5-Met2Pz crystal spectra, the TS and TH coupling models were assumed: bH = 1.5, C0 = 1.6, C1 = −0.3, F+ = 1.0, F− = 0.7, ΩN···N = 85 cm−1. 11563



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Figure 9. Theoretically derived νX−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 trimer of hydrogen bonds, that is, the TS and the TH. (left) The TS 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-AceOxm crystal, bD = 0.4, C0 = 0.5, C1 = 0.0, F+ = 1.0, F− = 0.2, and ΩO···N = 55 cm−1. For the D-3,5-Met2Pz crystal, bD = 0.4, C0 = 0.2, C1 = 0.0, F+ = 1.0, F− = 0.2, and ΩN···N = 55 cm−1. The transition frequencies are in the ωX···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 trimers. Transition intensities are in arbitrary units.

In Figure 10, evolution of the νX−H and νX−D band contour shapes accompanying the variation in the relative contribution of the TS and TH coupling mechanisms in generation of the trimer system spectra is shown. Similar band shape evolution accompanies temperature changes during the spectral experiments. From the comparison of the corresponding calculated and experimental spectra, it results that the intensity distribution patterns and the temperature effects in the spectra of the two different crystalline systems have been at least semiquantitatively reproduced via the model calculations.

pyrazole ring with the hydrogen bridge (3,5-Met2Pz) most likely effectively influences the electric charge density in the (N−H···N)3 cycles. This in turn strengthens the vibronic mechanism of the electronic current generation in the hydrogen-bond cycles.60 Small π-electronic systems, present in carbonyl groups of AceOxm, effectively weaken the vibronic coupling mechanism. Therefore, this latter system in a good approximation belongs to the A case. The analyzed spectral properties of the two different crystalline systems, AceOxm and 3,5-Met2Pz, are in good agreement with the above-described vibrational exciton interaction mechanisms of the spectra generation for cyclic trimers of hydrogen bonds. This in turn remains in close relation to the electronic properties of the chain molecules. For AceOxm trimers, the exciton interaction mechanisms involving the hydrogen bonds of the TS type are only weakly temperature-dependent. In the case of 3,5-Met2Pz tetramers, due to their electronic structure, the inter-hydrogen-bond exciton coupling mechanism changes its character along with the changes in temperature. At very low temperatures, the THtype interactions, transferred in the (N−H···N)3 cycles via electrons, are dominating. When temperature increases, this mechanism becomes less privileged as being annihilated by the hydrogen-bond atom thermal vibrational motions. It is replaced

6. IR SPECTRA OF ACEOXM AND 3,5-MET2PZ CRYSTALS The analyzed crystalline spectra of AceOxm seem to sufficiently well belong to case A. On the other hand, the crystalline spectra of 3,5-Met2Pz seem to satisfy the demands of case B. This classification results from the qualitative analysis of the temperature effects characterizing these spectra. The analyzed difference between the spectral properties of AceOxm trimers and the 3,5-Met2Pz trimers most probably results from the influences exerted onto the hydrogen-bond trimers, present in the (N−H···N)3 cycles, by the π-electronic molecular structure of the two different systems. The direct contact between the 11564



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Figure 10. Temperature-induced evolution of (left) νX−H and (right) νX−D band contour shapes accompanying the variation in the contribution rate of the two different exciton coupling mechanisms, that is, TS and TH. Numerical reproduction of the temperature effect in the spectra of hydrogenbonded (top) AceOxm crystal and (bottom) 3,5-Met2Pz crystal. The relative contribution ratios of the TS and TH mechanisms in the generation of the νX−H bands are as follows: for the AceOxm crystal, 0.9:0.1 at 293 K and 1.0:0.0 at 77 K; for the 3,5-Met2Pz crystal, 0.5:0.5 at 293 K and 0.0:1.0 at 77 K. For the deuterium-bonded crystals, the relative contribution ratios of the TS and TH mechanisms in the generation of the νX−D bands are as follows: for the D-AceOxm crystal, 0.9:0.1 at 293 K and 1.0:0.0 at 77 K; for the D-3,5-Met2Pz crystal, 0.5:0.5 at 293 K and 0.0:1.0 at 77 K. The experimental spectra are shown in the insets.

In our approach, the dependency of the hydrogen-bond system geometry upon the electronic structure of the associating molecules was treated as a regular and familiar effect in the hydrogen-bond research. This problem is mainly the domain of the conventional quantum chemistry calculations, and it was out of the scope of our project. From our studies, it results that for cyclic trimeric hydrogen-bonded systems a considerable diversity of the spectral properties in IR can be observed (including the way in which the band shape thermal evolution occurs). We have ascribed these effects to nonconventional vibronic coupling mechanisms in the hydrogen-bond cyclic trimers which are also strongly molecular electronic structure dependent.

by the other mechanism depending of the TS-type interactions. Each individual mechanism generates its own spectrum characterized by its unique intensity distribution pattern. From the comparison of the spectra of the two different crystalline systems, AceOxm and 3,5-Met2Pz, 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 trimers of hydrogen bonds remain in a close connection with the electronic level system schemes of the associating molecules forming hydrogen-bonded associate units in the lattices. The PED analysis of normal modes based on the spectra calculation for 3,5-Met2Pz on the RHF/6-31G* level was insufficient to explain the nonconventional spectral effects in the crystalline spectra, since these quantum chemical calculations have been performed assuming the harmonic oscillator model for the description of molecular normal vibrations.26 Our experimental studies and theoretical considerations, however, were restricted to the proton and the deuteron stretching vibration spectral regions, since the most spectacular spectral effects attributed to the hydrogen bonds in the two different crystalline systems have been measured in these frequency ranges. In our approach, we assumed the coupling of the proton and deuteron vibrational motions with the electronic movement in the trimers. No contemporary commercial quantum chemical program (e.g., Gaussian) is able to treat such a coupling.

7. THE H/D ISOTOPIC “SELF-ORGANIZATION” MECHANISM IN THE TRIMERS From the analysis of the isotopic dilution and temperature effects IR spectra of the hydrogen bond in the two different trimer system, it results that in both crystal cases the spectra are affected by the “dynamical co-operative interactions” involving hydrogen bonds.17,55 Comparison of the νX−H band shapes, measured for the isotopically neat compounds, with the “residual” νX−H band contour shapes of the isotopically diluted samples, allows finding their fair similarity. The fine structure pattern of νX−H and νX−D bands appeared independent upon the increasing rate of isotopic H/D exchange in the crystal hydrogen bonds. Moreover, in each individual compound case, the compared bands also exhibit fairly identical temperature effects. The shapes and the spectral properties of the “residual” ν X−H bands still exhibit effects of vibrational exciton interactions, which can only take place between the closely 11565



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crystals of 3,5-dimethylpyrazole (3,5-Met2Pz) exhibit qualitatively similar spectral properties as pyrazole,40 formic acid,46 or 4-thiopyridone42 crystals. Spectral properties of acetone oxime (AceOxm) crystals are fairly similar to the corresponding properties of diverse amide and thioamide crystals.43−45,55 (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 trimers occurs. The coupling of hydrogen bonds with large π-electronic systems of aromatic rings in the molecules determines the similar spectral properties of 3,5-dimethylpyrazole (3,5-Met2Pz) trimers in the crystals and infinitely long hydrogen-bond chains in crystals of pyrazole40 or 4-thiopirydone.42 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 crystals18,43−45,55) generates the spectra similar to the corresponding spectra of acetone oxime (AceOxm) crystals. (3) The analyzed spectral properties of the two different crystalline systems, 3,5-Met2Pz and AceOxm, remain in good agreement with the vibrational exciton interaction mechanisms of the spectra generation for chain hydrogen-bond systems. For AceOxm trimers, the exciton interaction mechanism of the TS type involving the adjacent hydrogen bonds in the trimer cycles is only weakly temperature-dependent. A weak “through-space” coupling of a van der Waals type in AceOxm trimers is responsible for the TS-type Davydov coupling. It dominates regardless of temperature. (4) In the case of 3,5-Met2Pz trimers, due to their electronic molecular structure, the inter-hydrogen-bond exciton coupling mechanism strongly changes its character along with the changes in temperature. Strong coupling in 3,5-Met2Pz tetramers prefers a TH-type Davydov coupling. At very low temperatures, the TH-type interactions, transferred in the (N−H···N)3 cycles, dominate. This mechanism becomes less privileged at higher temperatures as annihilated by thermally activated large-amplitude vibrational motions of the hydrogenbond-forming atoms. (5) Each individual mechanism, i.e., the TH and TS ones, generates its own spectrum characterized by its unique intensity distribution pattern. The νX−H and νX−D bands are a superposition of two different spectra, where each component spectrum is of a different origin. Each component spectrum contributing to the νX−H and νX−D band formation, with its temperature-dependent statistical weight, corresponds with another exciton interaction mechanism in the cyclic hydrogen-bond trimers in the crystal lattices, TH or TS. This explains the observed difference in the temperature-induced evolution effects in the compared spectra. (6) The hydrogen-bond trimer systems in the crystals exhibit the same way in which the H/D isotopic “self-organization” phenomenon occurs in the cycles. In both systems, identical hydrogen isotope atoms, protons, or deuterons occupy the entire three-membered hydrogen-bond rings in the isotopically diluted crystals.

spaced hydrogen bonds, containing identical hydrogen isotope atoms. It is possible only in this particular case when, in the isotopically diluted crystals, only the identical hydrogen isotope atoms, protons, or deuterons are present in each hydrogenbond trimer. It was proved that such a symmetric distribution of the hydrogen isotope atoms is energetically privileged. In terms of the vibronic model of the H/D isotopic “selforganization” effects, originally proposed for the interpretation of IR spectra of hydrogen-bond dimeric systems, this is the main reason of the nonrandom proton and deuteron distributions between hydrogen bonds in the isotopically diluted crystals.17,55,57 From the analysis of AceOxm and 3,5-Met2Pz crystalline spectra, it results that a nonrandom distribution of protons and deuterons also occurs for cyclic trimers of hydrogen bonds. Even at the highest deuterium substitution rates in the hydrogen bonds, the expected evolution of the “residual” νX−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 νX−D band contours accompanying the isotopic dilution. These effects prove the existence of the so-called H/D isotopic “selforganization” phenomenon in the trimer hydrogen-bond systems which, on the other hand, can be understood as a kind of the H/D isotopic recognition mechanism acting in the hydrogen-bond aggregates. In a cyclic trimer, each individual hydrogen bond interacts with the other two hydrogen bonds in the cycle; therefore, the H/D isotopic “self-organization” mechanism involves the three isotopically identical hydrogen or deuterium bonds in the cyclic trimers of AceOxm and 3,5-Met2Pz. Thus, in isotopically diluted samples of AceOxm and 3,5-Met2Pz, the whole cycles contain identical hydrogen isotope atoms in the hydrogen bridge systems, since all the vibrational exciton interactions are retained in isotopically diluted sample cases. Therefore, the complex fine structure patterns of the crystal spectra remain practically unchanged along the increase of the isotopic dilution rates. A vibronic coupling mechanism, depending on the dynamical co-operative interaction of the proton stretching vibrations with the electron movements in the cyclic systems of hydrogen bonds, as cyclic dimers, trimers, and tetramers, is the source of this effect.16−18,49,56 The H/D isotopic “selforganization” effect has been intensively studied, both experimentally and theoretically, in the recent years. This effect observed in trimeric systems is similar to the corresponding effects identified for dimeric and tetrameric systems of hydrogen bonds,16−18,47,54 and also in the case of some open chain hydrogen-bond systems.18,41−46,52 The mechanism proposed for the interpretation of the temperature effects in the IR spectra of hydrogen-bond trimer systems is fairly similar to the corresponding mechanism explaining the temperature effects in IR spectra of the hydrogen bond of other cyclic, dimeric, and tetrameric systems.16−18,49,56

8. CONCLUSIONS The results presented in this paper, concerning the acetone oxime (AceOxm) and of 3,5-dimethylpyrazole (3,5-Met2Pz) crystalline IR spectra interpretation, allow for the formulation of the following conclusions: (1) Cyclic trimers of hydrogen bonds exhibit generally similar spectral properties in IR as infinite chains of hydrogen bonds in molecular crystals. The hydrogen-bond trimers in 11566



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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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