Polarized IR Spectra of the Hydrogen Bond in Two ... - ACS Publications

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Polarized IR Spectra of the Hydrogen Bond in Two Different Oxindole Polymorphs with Cyclic Dimers in Their Lattices Henryk T. Flakus* and Barbara Hachuza Institute of Chemistry, University of Silesia, 9 Szkolna Street, Pl-40 006 Katowice, Poland ABSTRACT: This article focuses on the problem of remarkably strong changes in the fine structure patterns of the νN
H and νN
D bands attributed to the hydrogen and deuterium bonds accompanying the phase transition, which occurs between two polymorphic forms of oxindole. The lattices of these two different crystals contain hydrogen-bonded cyclic dimers differ in their geometry parameters. The source of these differences in the polymorph spectral properties results from the geometry relations concerning the dimers constituting the lattice structural units. In the case of the “alpha” phase, the hydrogen bond lengths of the dimers differ by 0.18 Å. This leads to the “off-resonance exciton coupling” weakly involving the dimer hydrogen bonds. For the “beta” phase, with practically symmetric dimers in the lattice, the spectra become typical for centrosymmetric hydrogen bond systems due to the full resonance of the proton or deuteron vibrations.

I. INTRODUCTION Intermolecular hydrogen bonding constitutes a very important problem in natural sciences because this interaction decides about many phenomena in biology, chemistry, and physics.1
5 Hydrogen bonds seldom exist as single isolated systems. Mutual interactions involving hydrogen bonds in aggregates strongly influence properties of biological molecules. In the majority of cases, hydrogen bonds form larger aggregates, including cyclic dimers, small cyclic oligomers, and infinitive large hydrogen bond systems in diverse biological molecules like polypeptides and nucleic acids. They also determine the lattice structures of molecular crystals. In an assembly, hydrogen bonds exhibit different properties when compared with the corresponding properties of single isolated hydrogen bonds. Intermolecular interactions via hydrogen bonds in the excited state of the proton vibrations, that is, the vibrational exciton couplings (or the Davydov couplings),6
8 can be successfully studied by means of the IR spectroscopy methods. This is due to the fact that IR spectra of hydrogen bond aggregates, measured in the frequency range of the νX
H proton stretching vibration bands attributed to the X
H 3 3 3 Y hydrogen bonds, differ considerably from the analogous spectra characterizing monomer hydrogen bonds. Frequently, the νX
H bands exhibit welldeveloped fine structures that are susceptible to the influence of temperature, condensation state of the matter, the hydrogen bond aggregate structures, and so on. For almost five decades, quantitative theoretical interpretation of the IR spectra of hydrogen bonds formed in associated molecular systems has been treated as a great challenge for the theory of molecular interactions. Though great progress has been made in this field, there still remain problems to be solved. In this area, even simple systems composed of mutually coupled hydrogen r 2011 American Chemical Society

bonds exhibit their spectral properties in nontotally understood terms of the formalism given by the contemporary quantitative theories of IR spectra of the hydrogen bond system. For five decades two theoretical models, the so-called “strong-coupling” theory,9
11 and “relaxation” theory,12,13 have been used while interpreting the spectral properties of the hydrogen-bonded dimeric systems formed in the gaseous phase between carboxylic acid molecules.10,14
16 In numerous cases, these theoretical models facilitated the quantitative interpretation of IR spectra of molecular crystals containing cyclic hydrogen-bonded dimers in the sites of their lattices, for example, carboxylic acids,17
21 and also of some heterocyclic molecular systems.22 In terms of both quantitative theoretical models, the formalism of the mechanism responsible for the spectra generation of cyclic centrosymmetric hydrogen-bonded dimers takes into account the vibrational Davydov coupling involving the two closely spaced hydrogen bonds in a dimer.9,10,12
22 This interaction is considered to be one of the main factors influencing the νX
H and νX
D band fine structure patterns in the IR spectra of the dimers. In spite of great achievements of the quantitative theories in the hydrogen bond dimer spectra interpretation, including the H/D isotopic effects in the spectra, an older qualitative approach with respect to the quantitative theories is still being used. This competitive model considers Fermi resonance of the hydrogen bond atom vibrations as the main mechanism determining the fine structure of the spectra. The oldest versions of the theoretical approach based on the Fermi resonance considered Received: June 28, 2011 Revised: September 6, 2011 Published: September 23, 2011 12150

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The Journal of Physical Chemistry A no Davydov-coupling effects in the dimer spectra.23 In the novel theoretical approaches the Fermi resonance mechanism has been incorporated into the “strong-coupling”24
29 and the “relaxation” theory of hydrogen bond dimer IR spectra.30
32 In each of the theoretical approaches, the hypothetical Fermi resonance mechanism is treated as the property of an individual hydrogen bond. Despite the lack of convincing evidence supporting the influence of this mechanism on the hydrogen bond dimeric spectra, it is still considered by some authors to be the essential factor responsible for band shaping.25
29 However, the results of the most recent studies of hydrogen-bonded crystal polarized IR spectra have proved that the role of the hypothetical Fermi resonance mechanism in the fine structure generation of spectra, provided it takes place, is undoubtedly highly overestimated.33,34 One might expect that the key information about the role of the Davydov
coupling involving hydrogen bonds in cyclic dimers might be obtained from polarized IR spectra of molecular crystals with cyclic centrosymmetric hydrogen-bonded dimers in the sites of their lattices. The hypothetically observed differentiation of the linear dichroic properties of the opposite branches of the νX
H and the νX
D bands, that is, the higher- and lowerfrequency ones, might constitute strong evidence in the verification of this idea. Then, however, the bands should be characterized by homogeneous dichroic properties in the whole individual band contour frequency range.35 Therefore, basing solely on the polarized IR spectra of cyclic, centrosymmetric hydrogen bond dimers in molecular crystals, we do not obtain any crucial evidence in support of the role of the vibrational Davydovcoupling in the mechanism of spectra generation. It seems, however, that the potential solving of this problem is feasible, because we can obtain some essential evidence in this matter provided the polarized IR crystalline spectra is of a proper molecular system. This system should satisfy the following conditions: 1 It should crystallize in two different polymorph forms containing cyclic hydrogen-bonded dimers in each individual lattice. 2 In each polymorph case, its own individual geometry and symmetry of dimers constituting the lattice, different from the dimer geometry and from the symmetry characterizing the other solid-state phase, should characterize both types of the hydrogen-bond dimers. A thorough perusal of the available crystallographic database has shown that molecular systems fulfilling our expectations are extremely rare in nature. However, we have managed to find a relatively simple molecular system, which fully satisfies our requirements. Oxindole (or 2-indolinone) seems to be the exact molecular system we have been seeking for. Oxindole crystallizes in two different polymorphic phases, each with cyclic hydrogen- bonded dimers in its crystal lattice. In one phase the dimers are practically symmetric, with hydrogen bonds of almost identical lengths. In the other polymorph phase the dimers are nonsymmetric with hydrogen bonds considerably differing in their lengths, i.e. by ca. 0.18 Å. In this article, we have focused on the experimental as well as the theoretical studies of polarized IR spectra of the hydrogen bond in crystals of two different polymorph forms of oxindole, each with cyclic hydrogen-bonded dimers in their lattices. The differences in the polymorph spectral properties seem to originate from the differences in the dimer geometry characterizing the two different

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Scheme 1. Relation between Two Polymorphs of Oxindole Containing Cyclic Dimers in Their Crystalline Lattices

phases. Interpretation of the obtained results provides strong arguments in support of the role of the Davydov-coupling in the spectra generation of cyclic dimers of hydrogen bonds. A. Crystal Structures of Oxindole Polymorphs. The crystal structure of commercial oxindole (namely, the “alpha” form) was previously measured and described by Lipkowski et al.36 in 1995 and then reconsidered by Hachuza et al. in 2011.37 The crystal structures of the two new polymorph forms of oxindole (the “beta” and the “gamma” forms) were determined from X-ray diffraction data by Hachuza et al. in 2011.37,38 Crystals of the “alpha” and “beta” forms belong to the monoclinic system. The space-symmetry group of both forms is P21/c  C52h. There are eight molecules in a unit cell (Z = 8). The lattice constants of the “alpha” polymorph at 100 K: a = 12.8234(3) Å, b = 8.0674(2) Å, c = 13.4505(3) Å, β = 111.531(2)0, V = 1294.38(5) Å3; and of the “beta” form: a = 14.2644(9) Å, b = 12.9569(8)Å, c = 6.9931(4)Å, β = 100.393(6)0, V = 1271.28(13)Å3. The “gamma” form crystals are triclinic and belong to the space group P1. The crystal unit cell contains six molecules (Z = 6) and the unit cell constants at 100 K: a = 5.6075(1) Å, b = 13.0331(3) Å, c = 14.8275(3) Å, α = 114.825(2)0, β = 114.825(2)0, γ = 91.664(2)0, V = 960.32(3) Å3. The structures of the “alpha” and “beta” form crystals are stabilized by the presence of intermolecular N
H 3 3 3 O hydrogen bonds resulting in the formation of dimers between pairs of symmetry-dependent molecules. Molecules of the “gamma” form are linked by the N
H 3 3 3 O hydrogen bonds forming chains in the a-axis direction, which are additionally connected via the C
H 3 3 3 O hydrogen bonds into a three-dimensional network. Moreover the hydrogen bonds of the “alpha” form dimers are nonequivalent and differ in their lengths by 0.182 Å (2.797(1) Å and 2.979(1) Å), whereas the N 3 3 3 O distances in the hydrogen bonds of the “beta” form are almost identical and differ by only 0.023 Å (2.834(2) Å and 2.857(2) Å). It was found that the “alpha” form can be obtained by evaporation of commercial oxindole dissolved in a 1:1 mixture of acetone and water while the “beta” form crystallizes from acetone solution.37,38 This latter form can also be obtained by crystallization of melted oxindole. The relation between the two polymorphs is presented in Scheme 1. Projection of the lattice of the “alpha” and “beta” form crystal on to the “bc” plane (a view along the “a” axis) and projection of the lattices on to the “ac*” plane (a view along the “b*” axis), 12151

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Figure 1. ORTEP view of molecular structure of polymorphic forms of oxindole (the upper part). Projection of two polymorphous forms of oxindole crystal lattice on to the “bc” and “ac*” planes, respectively (the lower part). Dashed lines indicate the hydrogen-bonding interactions. For the sake of clarity, all H atoms bonded to C atoms are omitted.

respectively, are shown in Figure 1. The “b*” symbol denotes the vector in the reciprocal lattice.

II. EXPERIMENTAL DETAILS Oxindole used for our studies was the commercial substance (Sigma-Aldrich) and was investigated without further purification. The three different solid-state phases of oxindole were obtained selectively by evaporation of the solution of the commercial substance, dissolved in proper solvents. Then the polymorphs were characterized by FT-IR spectroscopy measurements. The deuterium-bonded oxindole was obtained by evaporation of the D2O solution of the commercial substance under reduced pressure at room temperature. The IR spectra of oxindole were measured in CCl4 solution, KBr pellets and in single crystals. By cooling the molten commercial substance, between two closely placed CaF2 plates, we obtained the crystals of the “alpha” or “beta” form with the probability ratio 1:5. The crystals of the “beta” form, prepared in this way, appeared to be stable for about three weeks. After this period the “beta” form crystals underwent a phase transition in the solid state. As a result of this transformation we obtained “alpha” phase crystals, which were stable at room temperature. In this way, we were able to receive sufficiently thin crystals, exhibiting their maximum absorbance at the νN
H band frequency range close to 0.5. The IR spectra of the oxindole polymorphs were recorded with the FT-IR Nicolet Magna 560 spectrometer by the transmission method with a 2 cm
1 resolution, at two temperatures, that is, 293 and 77 K, respectively. Monocrystalline fragments were selected from the crystalline mosaic and spatially oriented,

using a polarization microscope. Next, these selected single crystals were exposed for the experiment on a metal plate diaphragm with a 1.5 mm diameter hole. The “alpha” form crystals developed most often the “bc” plane of the lattice, whereas the crystals of the “beta” polymorph developed the “ac*” plane in most cases. Measurements of the spectra of monocrystalline fragments were performed for two different orientations of the electric field vector “E”. For “alpha” form crystals with the developed “bc” face, the spectra were recorded for the “E” vector parallel to the “b” axis of the lattice, and next for the vector perpendicular to it, that is, parallel to the “c” identity period. For the “beta” crystal form developing the “ac*” plane of the lattice, the spectra were measured similarly that is first for the “E” vector parallel to the “a” axis and then for the one perpendicular to it, that is, parallel to the “c” identity period. The measurements were repeated for about 10 different single crystals. The Raman spectra of polycrystalline samples of oxindole were measured at room temperature with the use of the Bio-Rad FTS-175C FT-IR spectrometer.

III. RESULTS A. IR Spectra of Two Polycrystalline Phases of Oxindole. The IR spectra of the polycrystalline samples of two oxindole polymorphs exhibiting either the “alpha” or the “beta” phase, measured at two different temperatures i.e. 293 and 77 K and in the frequency ranges of the νN
H and the νN
D proton stretching vibration bands, are shown in Figure 2. The Raman spectrum of the “alpha” phase polycrystalline sample is also plotted to indicate the influence of the νC
H band on the νN
H band contour shape. 12152

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Figure 2. IR spectra of polycrystalline samples of two polymorphous forms of oxindole, “alpha” and “beta”, measured at 293 and at 77 K by the KBr pellet technique, in the νN
H and the νN
D band frequency ranges. The Raman spectrum of the “alpha” phase polycrystalline sample allows for identification of the C
H bond vibration lines. Common scale.

Figure 3. Comparison of the νN
H and the νN
D band shapes from the polycrystalline spectra of the two solid-state phases of oxindole, measured at 77 K. Full scale.

Figure 3 presents the νN
H and the νN
D band shapes, measured at 77 K, for samples of the “alpha” and the “beta” phase crystals. The presented spectra illustrate the changes in the hydrogen bond spectra of oxindole accompanying the phase transition. The spectra of polycrystalline samples of both phases show a similar, two-branch structure of their νN
H bands, which resemble the band shapes found in spectra of other cyclic hydrogen bond dimeric systems.17
22 In the shorter-wave range of each νN
H band an intense and diffused spectral branch appears, whereas in the longer-wave range less intense spectral lines, forming a well-developed, regular spectral progression of a low frequency, are observed (Figure 2). The νN
H bands attributed to the two polymorphs differ considerably in their higher-frequency ranges, that is, from about 3000 cm
1 up to 3500 cm
1. The higher-frequency branch of the νN
H band in the “beta” phase sample spectrum, composed of

three intense component lines, is significantly narrower and shifted toward the lower frequencies by about 120 cm
1 with respect to the corresponding band position of the “alpha” phase spectrum. The “alpha” phase νN
H band is wide and of a complex fine structure pattern with a distinguishing, diffused band at 3192 cm
1 (see Figure 3). A completely different effect can be observed in the crystalline spectra of deuterium- bonded oxindole polymorphs in the frequency range of the νN‑D deuteron stretching vibration bands. In the case of the solid-state the “alpha” and the “beta” phases of their νN
D bands exhibit a totally unexpected effect of the band frequency change: the “alpha” phase band is of a doublet structure, composed of two separated and narrow bands of almost identical intensities whereas the “beta” phase νN
D band is narrow with a singlet structure. Furthermore, the “beta” phase band appears at the central part of the frequency range in which the νN
D band doublet appears in the spectrum of the “alpha” 12153

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Figure 4. IR spectra of oxindole in the CCl4 solution compared with the spectra of polycrystalline samples of two solid-state phases of oxindole in KBr pellets, measured at 293 K in the νN
H and the νN
D band frequency ranges.

phase (see Figure 2). This fact seems to be particularly surprising since the X-ray structures of the two solid-state phases are very much alike. In the “beta” phase spectra the temperature effects, accompanying the reduction of temperature to 77 K, depends on the almost proportional intensity growth of both branches of the νN
H and the νN
D bands. The temperature decrease also causes a slight narrowing of the higher-frequency branch of the νN
H bands. At room and at liquid nitrogen temperature the higherfrequency branch of the νN
H and the νN
D bands is more intense than the lower-frequency branch. After lowering the temperature the two separated and narrow bands of the doublet structure of the “alpha” phase became even more separated from each other, that is, by about 30% in comparison with the mutual separation of these bands observed on spectra at room temperature. From the spectra it can also be estimated that the temperature change did not cause any noticeable changes in the relative intensity ratios of the νN
H and νN
D band branches. The spectra of oxindole dissolved in CCl4, measured at the frequency ranges of the νN
H and the νN
D stretching vibration bands, are presented in Figure 4. The corresponding spectra of polycrystalline samples of the two solid-state phases of oxindole, measured in KBr pellets at room temperature, are also shown. The νN
H and the νN
D bands for CCl4 solution of oxindole are fairly similar in shape to the corresponding bands registered for different centrosymmetric dimeric systems, that is, carboxylic acids. From literature data we know that oxindole also forms cyclic dimers in nonpolar solvents.39 The IR spectra of the “beta” polymorph of oxindole, measured in the νN
H and the νN
D band contour frequency ranges, significantly resemble the spectra of observed for this substance when dissolved in CCl4. The “beta” phase νN
H and νN
D bands are slightly shifted toward the lower frequencies (by ca. 50 cm
1 νN
H and ca. 10 cm
1 νN
D) in relation to the CCl4 solution band location. The discussed band frequency shift effect is only an attribute of the

crystalline phase of hydrogen- and deuterium-bonded oxindole obtained from the commercial substance. The fair similarity of the compared IR spectra indicates that identical structural units, that is, centrosymmetric cyclic hydrogen-bonded dimers, are responsible for the basic spectral properties observed in both cases (see Figure 4). A comparison of the band shapes from the CCl4 spectra of oxindole with the spectra of the “alpha” form measured for KBr pellets reveals some substantial differences. For instance, the “alpha” phase νN
H band is considerably wider and of a more complex fine structure pattern than the νN
H band of the CCl4 solution. Moreover, the “alpha” phase νN
D band exhibits quite different spectral properties than the νN
D band of CCl4 solution as far as the intensity distribution, the band contour shape, and the band location are concerned. Thus, from the spectral results presented above, it can be concluded that there is a close correspondence between the CCl4 solution spectra and the “beta” phase spectra, whereas the commercial sample spectra measured in the KBr pellet differ considerably from the “beta” phase spectrum as well as the CCl4 solution. B. Polarized IR Spectra of the “alpha” and “beta” Phase Oxindole Crystals. 1. Linear Dichroic Effects in the νN
H and the νN
D Bands. Polarized IR spectra of the “alpha” and the “beta” phase crystals measured at 77 K in the frequency range of the νN
H band are given in Figure 5. In this case, each component spectrum corresponds with the orientation of the electric field vector “E” parallel to one individual axis of the crystal indicatrix. It is noteworthy that the contours of the two component polarized bands in the spectrum are mutually proportional, although the integral component band intensities differ considerably one from the other. Analogous spectra of the isotopically diluted “alpha” and “beta” phase crystals of oxindole measured at 77 K in the frequency range of the “residual” νN
H and the νN
D bands 12154

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)

are shown in Figure 6. The “residual” νN
H band is the attribute of the hydrogen-bond protons, nonreplaced by deuterons in the crystals. The spectra presented in Figures 5 and 6 exhibit typical linear dichroic effects for the hydrogen-bonded dimeric systems, related to the orientation of the “E” electric vector of the polarized beam with respect to the hydrogen bond lattice in experimental conditions. The two branches of the νN
H polarized components bands, the shorter- and the longer-wave ones, measured for two different orientations of the electric field vector “E”, differ only insignificantly from each other in their relative intensity distribution. For both oxindole polymorph spectra the νN
H band intensity distribution, no changes in the relative intensities of the opposite band branches are observed. This refers to the whole band frequency range, measured for the two different orientations of the “E” vector with respect to the crystal lattices. As can be seen, also, the temperature decrease does not affect significantly the dichroic properties of the spectra in the νN
H band frequency range. Similar qualitative predictions should also be valid for the crystalline spectra of the deuterium derivatives of both solid-state oxindole forms measured in the νN
D band frequency ranges. Also for these bands no considerable differences in the polarization properties of the opposite spectral branches are observed. 2. Isotopic Dilution Effects in the Crystalline Spectra of Two Solid-State Phases. The IR spectra of the “alpha” and “beta” phase crystals measured for samples characterized by considerably high deuterium contents have proved that the isotopic dilution are not essentially affected by either the position, the band shape, or the branch intensity ratio of the “residual”

)

)

Figure 6. Polarized spectra of the “alpha” and the “beta” phase single crystal of isotopically diluted oxindole, measured at 77 K in the frequency range of the “residual” νN
H band and of the νN
D band for the sample with a relatively high content of deuterons (ca. 20%H and 80%D). The spectra were measured for the normal incidence of the IR beam with respect to the “bc” and “ac*” crystal planes and for two polarizations of the electric field vector E: “bc” plane, E “b”, E ”c”; “ac*” plane, E “a”, E ”c”. )

)

)

)

)

Figure 5. Polarized spectra of the “alpha” and the “beta” phase single crystal of oxindole measured at 77 K in the νN
H band frequency range. The spectra were measured for the normal incidence of the IR beam with respect to the “bc” and “ac*” crystalline faces and for two polarizations of the electric field vector E: “bc” plane, E “b”, E ”c”; “ac*” plane, E “a”, E ”c”.

νN
H bands (see Figure 6). These “residual” νN
H bands exhibit almost identical linear dichroic and temperature effects as the νN
H bands of the isotopically neat crystalline samples. This means that the “residual” νN
H bands remain affected by the same exciton interactions, which determine the main spectral properties of the νN
H bands from the spectra of the isotopically neat crystals. Therefore, in the case of a considerable proton deficiency, the residual protons belonging to the closely spaced hydrogen bonds are held together by some nonconventional forces, that is, by the so-called dynamical co-operative interaction forces.40,41 The presented spectral properties of the isotopically diluted crystals may appear when the vibrational exciton interactions occurring in mixed systems of hydrogen and deuterium bonds involve the moieties containing the same hydrogen isotope atoms, protons or deuterons. This means that the distribution of protons and deuterons in the lattices of the solid-state phases of oxindole isotopically diluted crystals is not random. This effect (i.e., the H/D isotopic “self-organization” effect) in the spectra allows for the identification of those crystal structure units (i.e., centrosymmetric hydrogen bond or deuterium bond cyclic dimers), which are the bearers of the discussed spectral properties.40
43 They comprise the νN
H and νN
D band shapes as well as the linear dichroic and temperature effects in the crystalline IR spectra. The physical phenomenon of the H/D isotopic “self-organization” in this case concerns cyclic dimers of hydrogen bonds, involving identical hydrogen isotope atoms, belonging to the two mutually 12155

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labeled by the A and B indices (Figure 7). The symbols qA and qB label the normal coordinates of the X
H bond high-frequency proton stretching vibrations in each individual X
H 3 3 3 Y hydrogen bond, A and B. The symbols QA and QB label the normal coordinates of X 3 3 3 Y low-frequency stretching vibrations in each individual hydrogen bond. For this system, we assume that only the coupling between the high-frequency proton stretching motions occurring in the two closely spaced hydrogen bonds is responsible for the discussed basic spectral properties of the dimer. At this stage, we neglect the anharmonic coupling involving the high-frequency proton stretching vibration and the low-frequency hydrogen bond vibrations. Figure 7. Hydrogen-bonded cyclic oxindole dimer formed in the solidstate phase. The symbols qA and qB denote the normal coordinates of the X
H bond high-frequency proton stretching vibrations in each individual X
H 3 3 3 Y hydrogen bond, A and B. The symbols QA and QB denote the normal coordinates of X 3 3 3 Y low-frequency stretching vibrations in each individual hydrogen bond.

coupled identical hydrogen bonds (or deuterium bonds) in one cycle. This pattern of distribution of hydrogen isotopes allows us to retain the vibrational exciton interactions involving hydrogen and deuterium bonds in the crystals of mixed H/D contents unchanged. The nonrandom distribution of protons and deuterons in the lattice of the isotopically diluted “alpha” and “beta” phase crystals of oxindole is the result of the so-called dynamical cooperative interactions involving hydrogen bonds, which are responsible for the H/D isotopic “self-organization” effects in the crystalline spectra. These nonconventional interaction mechanisms are of a vibronic nature, involving the anharmonicity of the proton or deuteron vibrations as well as the electronic motions in the hydrogen-bonded molecules. The appearance of the H/D isotopic “self-organization” in the spectra is possible when the dynamical co-operative interaction energy is approximately equal to 1.5 kcal/mol of hydrogen bond pairs from a chain.40
43 The most probable source of these interactions is the vibronic coupling mechanism of the Herzberg
Teller type,44 which also involves the anharmonicity of the proton and deuteron stretching vibrational movement.40,41 On the basis of the crystalline spectra of isotopically neat and isotopically diluted polymorphs, it can be deduced that the H/D isotopic “self-organization” processes occur in the “beta” phase crystals. This is evidenced by the comparison of the corresponding spectra, which are fairly identical. Isotopic dilution allows us to retain the νN
H and νN
D band shapes with the spectral effects of the mutual hydrogen bond couplings unchanged. In the case of the “alpha” phase crystal, this effect may be uncertain because similar effects to the ones observed in the compared spectra may also characterize individual uncoupled hydrogen or deuterium bonds of different geometry in nonsymmetric dimers.

IV. EVOLUTION OF SPECTRA DUE TO PHASE TRANSITION A. Model of a Single Dimer in an Oxindole Crystal. To explain the band shape evolution, accompanying the phase transition, the following model describing the Davydov-coupling6,7 involving hydrogen bonds in the hydrogen-bonded dimers of different symmetry should be analyzed. Let us consider a cyclic dimeric system formed by two nonequivalent hydrogen bonds

HA ðqA Þ ¼ TðqA Þ þ UðqA Þ

ð1Þ

HB ðqB Þ ¼ TðqB Þ þ UðqB Þ

ð2Þ

where the symbols used denote the following: qA and qB, the proton stretching coordinates (at this stage, we assume that these coordinates differ only insignificantly from the analogous normal coordinates of a single isolated molecule); T(qA) and T(qB), the kinetic energy operators of the proton vibrations; and U(qA) and U(qB), the proton vibrational potential energy operators of the hydrogen-bonded oxindole molecule. The vibrational wave functions of the model system satisfies the Schr€odinger equations for the harmonic or anharmonic oscillator: HA ðqA Þϕn ðqA Þ ¼ EAn ϕn ðqA Þ

ð3Þ

HB ðqB Þϕn ðqB Þ ¼ EBn ϕn ðqB Þ

ð4Þ

EAn

EBn

and are the energy eigenvalues of the individual where hydrogen bond vibrations and ϕn(qA) and ϕn(qB) are the eigenfunctions of the Hamiltonians HA and HB, respectively. For a nonsymmetric dimer, the EAn and EBn energies differ one from the other according to the familiar relation between the hydrogen bond length and the proton vibration frequency.1
5 This assumption also finds its justification in the quantum chemical and the molecular dynamics calculations.45
47 B. Resonance of the Proton Vibrations in the Dimer. The vibrational Hamiltonian of the dimer is HAB ðqA , qB Þ ¼ HA ðqA Þ þ HB ðqB Þ þ VAB ðqA , qB Þ

ð5Þ

where the VAB(qA,qB) term in the Hamiltonian represents the interhydrogen bond interactions. In the ground state of the two normal vibrations of a single hydrogen-bonded oxindole dimer, the vibrational wave function may be written as: ΨG0 ðqA , qB Þ ¼ ϕ0 ðqA Þϕ0 ðqB Þ

ð6Þ

When one of the X
H bonds is in its first excited state, the total vibrational wave function takes a more general form: ΨE1 ðqA , qB Þ ¼ αϕ1 ðqA Þϕ0 ðqB Þ þ βϕ0 ðqA Þϕ1 ðqB Þ

ð7Þ

where α and β are the developing coefficients, ϕA1 and ϕA0 are the eigenfunctions of the vibrational Hamiltonian of the A-proton stretching vibrations in their first excited and in the ground state, respectively, ϕB1 and ϕB0 are the eigenfunctions of the vibrational Hamiltonian of B-proton stretching vibrations in their first excited and the ground state, respectively. 12156

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To determine the developing coefficients in ref 19 let us multiply the vibrational Schr€odinger equation: HAB ðqA , qB ÞΨE1 ðqA , qB Þ ¼ EΨE1 ðqA , qB Þ

and βHH The developing coefficients, αHH i i , for ΔHH > 0, for the proton vibrations in the model dimer are ΔHH
XHH ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, αHH 1 ½4CHH 2 þ ðΔHH
XHH Þ2 

ð8Þ

first from the left side by the ϕ1(qA)ϕ0(qB) product function and, next, by ϕ0(qA)ϕ1(qB). Let us integrate the two equations obtained in this way over the two normal vibration coordinates, qA and qB. By introducing the matrix notation for the two-equation system, we obtain the following matrix equation: " #" # " # CHH α α EA1 þ EB0 , ¼E ð9Þ CHH , EA0 þ EB1 β β

2CHH ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βHH 1 ½4CHH 2 þ ðΔHH
XHH Þ2  where XHH = (ΔHH2 + 4CHH2)1/2, and ΔHH þ XHH αHH ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, 2 ½4CHH 2 þ ðΔHH þ XHH Þ2 

where the symbols EA1 , EA0 , EB1 , EB0 and CHH are defined as follows: EA1

¼

EA0

¼

ÆϕA1 jTosc ðqA Þ ÆϕA0 jTosc ðqA Þ

þ þ

UðqA ÞjϕA1 æqA , UðqA ÞjϕA0 æqA

ð10Þ

EB1 ¼ ÆϕB1 jTosc ðqB Þ þ UðqB ÞjϕB1 æqB , EB0 ¼ ÆϕB0 jTosc ðqB Þ þ UðqB ÞjϕB0 æqB

2CHH ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βHH 2 ½4CHH 2 þ ðΔHH þ XHH Þ2 

ð11Þ

ð12Þ

Finally, the matrix eq 9 takes the form 2 3 3 1 " # " # pωA þ pωB , CHH 6 7 2 62 7 α ¼E α 4 5 β 1 3 β pωA þ pωB CHH , 2 2

H ¼

CHH 0

ð19Þ

HH A B þ A B PHH = ÆϕA0 ϕB0 jμ ~jðαHH 2 ϕ1 ϕ0 þ β2 ϕ0 ϕ1 ÞæqA , qB

ð20Þ

H

H

H

H

þ PHH = jαHH M BA þ βHH M BB j2 , 2 2

H

A M BA ¼ ÆϕA0 jμ ~H A jϕ1 æqA ,

H D On assuming that ΔHH = pωH A
pωB (and ΔDD = pωA
D pωB for the deuterium-bonded oxindole), the energy matrix is

ΔHH , CHH ,

HH A B
A B = ÆϕA0 ϕB0 jμ ~jðαHH PHH 1 ϕ1 ϕ0 þ β1 ϕ0 ϕ1 ÞæqA , qB


PHH = jαHH M BA þ βHH M BB j 2 1 1

ð13Þ

"

CHH
E

H

B M BB ¼ ÆϕB0 jμ ~H B jϕ1 æqB

ð22Þ

H

H

H

HH
BB j cos k = fjαHH M BA j2 þ 2αHH BA jj M PHH 1 1 β1 j M

#

H

M BA j 2 g þ jβHH 1

ð14Þ

ð23Þ H

H

HH þ BB j cos k = fjαHH M BA j2 þ 2αHH BA jj M PHH 2 2 β2 j M

The secular equation ΔHH
E, CHH ,

ð21Þ

H H where μ BA and μBB are the vibrational transition moment vectors for the moieties A and B. After transformations the formulas for the transition probability values are as follows:

H

"

ð18Þ

Now we define the vibrational transition moments corresponding to the excitation to the mixed excited states of the two mutually coupled vibrations in the dimer:

and CHH ¼ CÆϕA0 ϕB1 jVAB jϕA1 ϕB0 æqA , qB

ð17Þ

#

H

¼0

ð15Þ

gives the following solution: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ¼ ðΔHH
ΔHH 2 þ 4CHH 2 Þ, EHH 1 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 EHH ¼ ðΔHH þ ΔHH 2 þ 4CHH 2 Þ 2 2

ð16Þ

where ΔHH . 0, the E1HH symbol denotes the frequency of the proton stretching normal vibration in the “A” hydrogen bond, while the E2HH symbol denotes the corresponding value for the “B” hydrogen bond.

M BB j 2 g þ jβHH 2

ð24Þ

BBH. where k is the angle between the vectors M BAH and M The system of the coupling parameters, ΔHH and CHH, governing the νN
H band shapes in the crystalline spectra, cannot be precisely derived from the first principles. Although hypothetically the ΔHH parameter value might be calculated by ab initio methods, because the proton stretching frequency depends on the hydrogen bond length,45
47 the parameter value obtained in this way would be highly uncertain. Let us remind that this parameter is defined as a difference of two calculated proton vibration frequencies, each characterizing an individual hydrogen bond in a dimer. On the other hand, the CHH parameter cannot be derived from the first principles anyway. This parameter represents the vibrational exciton interactions in the model dimers. The mechanism of these interactions is 12157

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The Journal of Physical Chemistry A

ARTICLE

extremely complex, namely, of a vibronic nature. Therefore, it is beyond the reach of the ab initio calculations. The Born
Oppenheimer approximation is the basic assumption in the quantum-chemical theories. The relation between both parameter values can be approximately derived from the experimental spectra. C. H/D Isotopic Effect in the Spectra. The replacement of protons by deuterons in oxindole dimers modifies the coupling mechanism, involving the vibrating protons in the two nonequivalent hydrogen bonds. This is due to the fact that the basic coupling parameters, ΔHH and CHH, in the model are hydrogen atom mass-dependent. The following relations between ΔHH and ΔDD are satisfied: pffiffiffi ΔHH ¼ 2 ΔDD ð25Þ For the CHH and CDD parameters, their mutual relation is probably more complex: In the limits of the dipole
dipole exciton interaction model,6,7 the ratio of the parameters is equal to H

D

BA = M BA Þ2 ¼ 2:0 CHH =CDD ¼ ð M

ð26Þ

In practice, the ratio of the CHH and CDD parameters may be considerably larger because the two parameters are also dependent on electronic coordinates of the hydrogen bonds. This means that the deuterium bonds in oxindole dimers are proportionally less effectively coupled when compared with the coupling energy magnitude of the hydrogen-bonded dimers.

V. SPECTRAL CONSEQUENCES OF THE MODEL From the considerations presented above, it results that in the deuterium-bonded oxindole dimers, the interdeuterium-bond vibrational exciton coupling is proportionally weaker than the coupling characterizing the hydrogen-bonded counterpart. The consequences of this statement can be found in the IR spectra of the oxindole “alpha” and “beta” polymorph crystals measured in the νN
H and νN
D band frequency ranges. The relation between the magnitude of the ΔHH and CHH parameter values determines the νN
H band characteristics in the IR spectra of the two polymorphs. In turn, the relation between the ΔDD and CDD parameter values strongly determines the characteristics of the νN
D bands. We will focus on the analysis of the νN
D band first. a The “alpha” phase νN
D band is of a doublet structure. This effect probably results from a relatively low coupling energy of the hydrogen bonds in the dimer characterized by a low CDD parameter value in comparison with the ΔDD parameter value, for the oxindole dimers with the N
H 3 3 3 O hydrogen bonds noticeably differing in their lengths (i.e. by ca. 0.18 Å). In these circumstances, each deuterium bond of a nonsymmetric dimer in the lattice retains its individual spectral properties. The νN
D band of a doublet structure is composed of two separated narrow bands of almost identical intensities. This is due to the fact that the exciton interaction energy is lower than the energy difference of the two different deuterium bond vibration fundamentals in the crystalline spectra. In this case, each sub-band is attributed to an individual deuterium bond. The lower-frequency component corresponds to the shorter N
D 3 3 3 O deuterium bond, whereas the higher-frequency one is attributed to the longer deuterium bond in the oxindole dimer in the “alpha” phase.

b For the “beta” phase spectra the νN
D band is of a narrow singlet structure. It is placed at the central part of the frequency range in which the νN
D band doublet appears in the spectrum of the “alpha” phase. This fact also finds its explanation in our model. In the “beta” phase, deuterium bonds in oxindole dimers, which constitute the lattice of this polymorph, exhibit much less differed lengths (ca. 0.02 Å). Thus, the frequencies of the deuterium stretching vibrations characterizing each individual deuterium bond differ only slightly from one another. The dimers are practically symmetric. Therefore, in this case the ΔDD parameter value characterizing the spectrum is relatively low when compared with the CDD parameter value. In these circumstances, a sufficiently effective vibrational exciton coupling takes place involving both deuterium bonds in a deuterium-bonded oxindole dimer in the “beta” polymorph. Consequently, the vibrational exciton is diffused throughout the entire dimer in the lattice. The νN
D band is much narrower, with a noticeably pronounced two-branch fine structure pattern, which is a typical property of the corresponding spectra of centrosymmetric hydrogen- or deuterium-bonded dimers.10,17
22 c The νN
D band contour measured for CCl4 solution of oxindole fairly resembles the relative band contour in the spectra of the “beta” phase. In a nonpolar solvent like CCl4, oxindole also forms cyclic dimers. There are no physical reasons for the dimers to exhibit a lower effective symmetry than the symmetric one. The ΔDD parameter is now equal to 0.0, whereas the νN
D band is typical for cyclic deuteriumbonded dimers.10,17
22 However the interpretation of the νN
H bands constitutes a much more complex case. This is due to the fact that the spectral effects observed in the νN
D bands find no counterparts in the spectra of isotopically neat hydrogen bonded oxindole. a The “beta” phase νN
H band is fairly similar to the νN
H band measured for the CCl4 solution of hydrogen-bonded oxindole. This means that in both cases symmetric hydrogen bond dimers are the bearers of the spectral properties of the systems. In these two cases the ΔHH parameter values are negligibly small in comparison with the CHH parameter magnitudes. The νN
H bands generated via this mechanism exhibit a characteristic two-branch fine structure pattern, which is typical for the spectra of centrosymmetric hydrogen-bonded dimeric systems. This pattern is also retained in spectra of samples isotopically diluted by deuterium. b The “alpha” phase νN
H band is wide and of a complex fine structure pattern. No doublet structure composed of subbands of identical intensities, like in the case of the νN
D band, can be observed for this band. The νN
H band is considerably wider than the νN
H bandwidth from the “beta” phase spectra and the νN
H bandwidth from the spectrum of the CCl4 solution. Its shape is an intermediate between the spectrum of the “beta” phase and the hypothetical doublet band structure whereas qualitatively it resembles the doublet structure of the νN
D band contour from the “alpha” phase spectra. The band properties can be qualitatively explained as follows: the exciton energy CHH parameter magnitude is comparable with the magnitude of the ΔHH parameter, in contrast to the relation between the ΔDD and CDD parameters characterizing the νN
D band. This is because the exciton interaction parameter CHH most probably depends strongly on the electronic coordinates. 12158

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The Journal of Physical Chemistry A Thus, a partial sharing of the vibrational exciton throughout the whole system takes place even in the extremely nonsymmetric hydrogen bonded dimer of the “alpha” phase. As a result of this partial “off-resonance” vibrational exciton coupling the spectrum takes an intermediate form, placed between a doublet form with two equivalent components and the spectrum of the symmetric hydrogen-bonded dimers characterized by a two-branch fine structure pattern. At the initial stage the proposed model neglected the anharmonic coupling involving the high-frequency proton stretching vibrations as well as the low-energy hydrogen bond stretching vibrational motion in each hydrogen bond. The coupling of this kind as in many other cases is responsible for the widening of the νN
H bands and for the appearance of the fine structure pattern of the band, which qualitatively resembles the Franck
Condontype progression appearing in the electronic spectra of aromatic molecules. In our approach, we only considered the basic nature of the strong variations of the spectra accompanying the phase transition in the solid state when the cyclic dimers constituting the structural units of the two different lattices are slightly changed. In this paper we have not analyzed the influence of the interhydrogen bond coupling in the nonsymmetric cyclic dimers of oxindole on the fine structure pattern of the bands because the quantitative interpretation of the spectra is an extremely complex problem to solve. However, we do not need the exact solution to this problem to understand the main source of the observed spectral phenomena accompanying the phase transition leading from the “beta” toward the “alpha” phase. The proposed spectra generation mechanism rather excludes the proton tunneling as the mechanism determining the main spectral properties of the oxindole two polymorphs. From the X-ray data it results that the proton positions remain unchanged during the phase transition.36,37 This fact proves, that regardless of the crystalline phase case, the potential energy curve for the protonic movement in the N 3 3 3 O hydrogen bridges is highly asymmetric with a deep potential well placed in the neighborhood of the nitrogen atoms. It means stabilization of the proton positions in the hydrogen bonds of the N
H 3 3 3 O form. There is no evidence that the proton transfer really occurs in the hydrogen-bonded dimers of oxindole. Therefore, the oxindole hydrogen-bonded dimers cannot be treated as proper model systems for the description of the proton transfer occurring in selected enzymes.48
52

VI. CONCLUSION The presented results of our studies have shown that Davydov-type vibrational exciton coupling is the essential factor determining the νN
H and νN
D band contour shapes in the crystalline spectra of the hydrogen bond in oxindole dimers, which differ from one another in their geometry parameters. These dimers constitute the structural units of the lattices of two different polymorph forms of oxindole. Evolution of the band shapes accompanying the hydrogen bond geometry changes in the dimers due to the phase transition, from the “beta” phase toward the “alpha” phase proves the existence of a mathematical relation between the exciton coupling energy and the difference of the proton vibrations in the dimers. Due to geometry changes in the dimers, from the symmetric to the nonsymmetric form, the primarily mutually exciton coupled hydrogen bonds in dimers of the “beta” phase practically decouple in the “alpha” phase dimers. This induces strong changes in the spectra of the hydrogen bond

ARTICLE

in the oxindole crystals accompanying the phase transition. Such effects are beyond the Fermi resonance formalism. It has been shown that the hypothetical Fermi resonance mechanism, which basically only concerns single hydrogen bonds, is not the key factor responsible for the spectra generation. They originate from the collective properties of the systems related to the interhydrogen bond exciton couplings in the cyclic dimers.

’ AUTHOR INFORMATION Corresponding Author

*Phone: +48 32 3591598. Fax: +48 32 2599978. E-mail: flakus@ ich.us.edu.pl.

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