Effects of Dynamical Couplings in IR Spectra of the Hydrogen Bond in

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Effects of Dynamical Couplings in IR Spectra of the Hydrogen Bond in N-Phenylacrylamide Crystals Henryk T. Flakus,*,† Anna Michta,† Maria Nowak,‡ and Joachim Kusz‡ † ‡

Institute of Chemistry, University of Silesia, 9 Szkolna Street, Pl-40-006 Katowice, Poland Institute of Physics, University of Silesia, 4 Uniwersytecka Street, Pl-40-006 Katowice, Poland ABSTRACT: This article presents the investigation results of the polarized IR spectra of the hydrogen bond in N-phenylacrylamide crystals measured in the frequency range of the proton and deuteron, νN
H and νN
D, stretching vibration bands. The basic spectral properties of the crystals were interpreted quantitatively in terms of the “strong-coupling” theory. The proposed model of the centrosymmetric dimer of hydrogen bonds facilitated the explanation of the welldeveloped, two-branch structure of the νN
H and νN
D bands as well as the isotopic dilution effects in the spectra. The vibronic mechanism of the generation of the long-wave branch of the νN
H band ascribed to the excitation of the totally symmetric proton vibration was elucidated. The complex fine structure pattern of νN
H and νN
D bands in N-phenylacrylamide spectra in comparison with the spectra of other secondary amide crystals (e.g., N-methylacetamide and acetanilide) can be accounted for in terms of the vibronic model for the forbidden transition breaking in the dimers. On the basis of the linear dichroic and temperature effects in the polarized IR spectra of N-phenylacrylamide crystals, the H/D isotopic “self-organization” effects were revealed.

1. INTRODUCTION Infrared spectroscopy is still considered to be one of the most powerful tools applied in the research of the hydrogen bond formed in molecular systems. This is due to the fact that hydrogen bonding strongly influences IR spectra of the associated molecules. The most spectacular changes concern the characteristics of the X
H bond stretching vibration bands (the band assignment νX
H) in the X
H 3 3 3 Y hydrogen bonds.1
5 These bands are extremely susceptible to the diverse influences exerted by inter-and intra-molecular interactions. Strong changes in the νX
H characteristics accompany the changes in the condensation state of matter.1
5 Over the last 50 years the researchers have mainly focused on the νX
H band properties as well as on the band fine structure patterns. Contemporary quantitative theories based on IR spectra of hydrogen bonded systems have treated the problem of the generation of the νX
H bands as a purely vibrational one.6
12 The quantitative theoretical models derived from IR spectra of the hydrogen bonded systems, subsequently developed over the last four decades, aimed to reconstitute the intensity of the distribution in the spectra of single hydrogen bonds as well as in the spectra of more complex hydrogen bond systems. At first, centrosymmetric hydrogen bond dimers were assumed. Despite the indisputable success achieved in interpreting the dimeric system spectra in terms of the “strong-coupling” theory6
9 and recently, with the use of the so-called “relaxation” theory,10
12 it seems that a number of serious theoretical problems still remain unsolved. Currently, particular attention is paid to IR spectra of molecular crystals due to the rich diversity of hydrogen bond r 2011 American Chemical Society

arrangements present in their lattices that seem to be responsible for a variation of interhydrogen bond interactions in these systems. This should allow us to solve in the future the problem of the relation between the crystal X-ray structure and the spectral properties of the hydrogen bonds in IR in the frequency range of the νX
H bands. However, the solid state itself is responsible for the introduction of some unique spectral effects connected with intermolecular interactions in the lattice. Measurements of the IR spectra of spatially oriented hydrogenbonded molecular crystals with the help of polarized radiation enables a deeper insight into the nature of intra-as well as the inter-hydrogen-bond interactions in the lattices. Up to the 1990s such studies were extremely rare in literature.13
18 Quantitative interpretation of IR spectra of the hydrogen bond in molecular crystals poses a great challenge for the theoretical models regarding the description of crystal spectral properties. Over the last four decades this field has developed due to the so-called “strongcoupling” theory. During this time numerous spectacular successes were achieved in the interpretation of IR spectra of crystals characterized by diverse space-symmetry groups.19
22 Also several trials of the quantitative interpretation of IR spectra of a selected group of hydrogen-bonded crystals, with cyclic hydrogen bond dimers as the lattice structural units, were undertaken in terms of the novel “relaxation” theory.12,23,24

Received: July 29, 2010 Revised: November 24, 2010 Published: April 06, 2011 4202

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The Journal of Physical Chemistry A It appeared that the basic problem in performing a successful quantitative interpretation of the IR spectra of the hydrogen bond in a molecular crystal is not simply connected with the choice of the proper theoretical model. Our systematic studies of polarized crystalline IR spectra have proved that some yet unidentified inter-and intra-hydrogen bond interaction mechanisms strongly affect the IR spectra of associated molecular systems. These mechanisms contribute to the spectra generation of even such simple hydrogen bond aggregates like dimers and of molecular crystals. Investigation of IR spectra of isotopically diluted crystals allowed us to reveal the so-called H/D isotopic “self-organization” effects, connected with a nonrandom distribution of protons and deuterons in the hydrogen bond lattices. This peculiar H/D isotopic recognition mechanism was ascribed to dynamical co-operative interactions, which are common in hydrogen bond systems.25
27 It is the source of the invariability of the νX
H and νX
D band contours in IR spectra of isotopically diluted crystals, regardless of the H/D isotopic exchange rates characterizing these crystals.26,27 According to our latest estimations based on the quantitative analysis of the IR spectra of the hydrogen bond in diverse isotopically diluted crystalline systems dynamical cooperative interactions involving hydrogen bonds seem to be common in nature. Dynamical cooperative interactions result from dynamical couplings between the proton stretching motions and the electronic movement. They remain beyond the Born
Oppenheimer approximation. This term covers the nonadditive effects concerning the physicochemical constants characterizing hydrogen bonds. This newly revealed mechanism substantially differs from the familiar mechanism of static cooperative interactions, which resulted from quantum-chemical calculations performed within the limits of the Born
Oppenheimer approximation. The details of the theory of dynamical cooperative interactions in hydrogen bond dimeric systems have been described only recently.27 In the case of cyclic hydrogen bond dimers the H/D isotopic self-organization always occurred. No system contradicting this rule was found. For crystals with chain systems of hydrogenbonded molecules a considerable diversity of the spectral properties attributed to the dynamical cooperative interactions was found. This remains in a relatively simple relation to the electronic properties of the associated molecules in crystals. When the molecules contain easily polarizable “π”-electronic systems, directly linked to the hydrogen bond forming atoms, the strongest dynamical cooperative interactions involve the adjacent hydrogen bonds in a fragment of an individual hydrogen bond chain. This evokes the H/D isotopic self-organization process in these domains, e.g., in pyrazole,19 imidazole,20 and 4-thiopyridone22 crystals. This means that identical hydrogen isotope atoms are grouped together in fragments of the hydrogen bond chains (domains). On the other hand, in the case of molecular systems that do not possess large π-electronic systems a random distribution of protons and deuterons in the hydrogen bond systems was deduced from the IR spectra of the isotopically diluted crystals (e.g., decyl alcohol crystals28,29). IR spectra of secondary amide crystals (N-methylacetamide30 and acetanilide27 and N-methylthioacetamide31) exhibit an intermediate behavior. Although in these associated molecular crystals no large π-electronic systems exist, nevertheless some unique H/D isotopic self-organization effects in the spectra of the isotopically diluted crystals were identified. Quantitative analysis of the spectra allowed us to prove that in this case the strongest dynamical cooperative interactions usually involved the

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closely-spaced hydrogen bond pairs, in which each moiety belonged to a different chain of the associated molecules penetrating a unit cell of the lattice.19,21 Therefore, investigation of polarized IR spectra of crystals with chain arrangements of hydrogen bonds in their lattices may provide data facilitating the explanation of the mechanism of dynamical cooperative interactions. These studies may also help to elucidate the physical factors responsible for the observed diversity occurring during the H/D isotopic self-organization processes in the isotopically diluted crystals. Crystals of diverse secondary amides due to the mutual arrangement of the N
H and CdO bonds in their molecules seem to be particularly promising systems for such investigations. These molecules are predestinated to form chain N
H 3 3 3 OdC bonded associates. Indeed, in the majority of amide crystals the associate amide molecules are linked together, thereby forming infinite chains. This type of hydrogen-bonded associates is widespread in nature (e.g., the R-helix in biological systems). The secondary amide crystals are suitable model systems for the interpretation of protein properties, since the N
H 3 3 3 OdC bond lengths in the crystals are very close to those found in proteins. From our recent estimations it results that the electronic structure of amide and thioamide molecules, additionally modified by diverse atomic substituent groups linked to the amide or thioamide fragment, undoubtedly affects the way in which the H/D isotopic self-organization processes occur in diverse amide and thioamide crystals. However, our knowledge in this matter is still incomplete. Therefore, for our study of this problem a suitable molecular system should be chosen, i.e., one for which the effects of the substituent groups on to the electronic properties of the associating molecules appear to be extreme. We have chosen N-phenylacrylamide (in an abbreviated notation PAM), since in molecules of this compound two atomic groups with easily polarizable electrons on π-orbitals (i.e., the phenyl and the acryl groups) are linked to the two opposite sides of the amide fragments. Electrons of these groups are expected to couple effectively with the electronic and the proton stretching motions of the N
H 3 3 3 O hydrogen bonds in the crystal. In this paper we present the results of our studies on polarized IR spectra of the hydrogen bond in PAM crystals. By measuring and quantitatively interpreting the IR polarized crystalline spectra and the H/D isotopic effects in the spectra, we endeavored to answer the following questions: How strong are dynamical cooperative interactions involving hydrogen bonds in the lattice? Which hydrogen bonds from an individual unit cell participate in the H/D isotopic self-organization mechanism in the crystal? Do the electrons of the substituent groups, namely of the phenyl and the acryl group, couple effectively with the hydrogen bonds in the crystal, and thereby affect the crystal spectral properties? To what extent are the PAM crystal spectra similar to the relevant spectra of acetanilide27 and N-methylacetamide30 crystals?

2. EXPERIMENTAL SECTION PAM used for our studies was a commercial substance (SigmaAldrich) and was used without further purification. The deuterium-bonded crystals were obtained by evaporation of D2O solutions of the compound under reduced pressure at room temperature. The deuterium substitution rate for different studied crystalline samples varied in a relatively wide range (10
90%). 4203

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Table 1 (a) Crystal Data of PAM

Figure 1. Symmetry-independent molecule of PAM, showing the atomnumbering scheme. Displacement ellipsoids are drawn at the 50% probability level, and H atoms are shown as small spheres of arbitrary radii.

C9H9NO

V = 1578.6 (5) Å3

Mr = 147.17

Z=8

orthorhombic, Pbca

Mo KR radiation, λ = 0.710 73 Å

a = 9.6621 (19) Å

μ = 0.08 mm
1

b = 9.7317 (19) Å

T = 100 K

c = 16.788 (3) Å

0.6  0.18  0.02 mm (b) Data Collection

Oxford diffraction diffractometer with Sapphire3 CCD detector

1025 reflections with I > 2σ(I)

9453 measured reflections

Rint = 0.053

1396 independent reflections (c) Hydrogen-Bond Geometry (Å, deg)

Figure 2. View along the b axis of the N
H 3 3 3 O hydrogen-bonded chains of PAM molecules.

Single crystals of PAM, as well as its deuterium isotopomer, were obtained by crystallization from melted samples (melting point: 103
106
C), occurring between two closely spaced CaF2 windows. In this way, thin enough crystals were prepared, characterized by their maximum absorbance close to 0.5 at the νN
H band frequency range. From the crystalline mosaic, suitable monocrystalline fragments were selected and then spatially oriented, using a polarization microscope. Next, these selected single crystals were exposed for the experiment by placing them on a metal plate diaphragm with a 1.5 mm diameter hole. It was found that the PAM crystals most frequently developed the ab or ac plane of the lattice. The IR spectra of selected crystals were recorded with the FTIR Nicolet Magna 560 spectrometer by the transmission method with 2 cm
1 resolution. Measurements of the spectra were performed in the temperature range from 293 K to the temperature of liquid nitrogen for two different orientations of the electric field vector E. For crystals with the ac or ab face developed, the spectra were recorded for the E vector parallel to the a axis of the lattice, and in the other case, for the one perpendicular to it, i.e., parallel to the c or b identity period. For each isotopomer case the measurements were repeated for ca. 10 different single crystals.

D—H 3 3 3 A

D—H

H3 3 3A

D3 3 3A

D—H 3 3 3 A

N1—H1 3 3 3 O1i

0.868 (17)

1.991 (18)

2.8522 (18)

171.1 (16)

The Raman spectra of polycrystalline samples of PAM were measured at room temperature with the use of the Raman Accessory for the Nicolet Magna 560 spectrometer. 2.1. Crystal Structure of N-Phenylacrylamide. The crystal structure of PAM was unknown at the moment of initiation of the studies; therefore, the spectral studies were preceded by the X-ray studies. Crystals suitable for performing the crystal structure determination were obtained by crystallization from ethanol/acetone (50/50) solution. The X-ray diffraction experiments were done at 100 K. It was estimated that crystals of PAM belong to the orthorhombic system, space symmetry group is Pbca = D15 2h. The crystal lattice constants are a = 9.6621(19) Å, b = 9.7317(19) Å, and c = 16.788(3) Å. There is one independent molecule in an asymmetric unit cell (Figure 1). Each unit cell contains 8 molecules (Z = 8). The associated molecules form hydrogen-bonded chains were found to elongate along the a axis (Figure 2). Other data concerning the diffraction experiment and the geometry parameters of hydrogen bonds in the crystal were collected in Table 1. In the three crystalline lattices associating amide molecules, PAM, N-methylacetamide, and acetanilide, form infinite hydrogen-bonded chains. Moreover, the space-symmetry groups of PAM and acetanilide crystals are identical. In each different crystalline system the hydrogen bonds, belonging to two neighboring chains from a unit cell, are related to one another by the inversion center operation. The difference between the two different amide crystals is in the influence of the molecular electronic properties on to the hydrogen bond IR spectral properties.

3. RESULTS AND DISCUSSION 3.1. IR Spectra of the Hydrogen Bond in Amide Crystals: The State of the Art. Molecular structure of secondary amides

like acetanilide and N-methylacetamide as well as the amide group geometry is fairly similar to the corresponding geometry of polypeptides; therefore, studies of these molecular systems are interesting from the point of view of biochemistry and biophysics. IR spectra of amide crystals have been described only in 4204

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Figure 3. IR spectra of the polycrystalline samples of PAM, dispersed in the KBr pellets, measured at two different temperatures. To identify the νC
H bands, the Raman spectra measured at room temperature are also drawn.

several monographs.32
39 The authors of these papers introduced their own nomenclature for the two bands observed in the frequency range of the N
H bond stretching vibrations, proposing their assignment as “amide A” and “amide B”.32,38 The following theories elaborated for the description of IR spectra of secondary amide crystals may be divided into two groups: 1. Theories of the first group tried to explain the mechanism of the generation of the CdO group stretching vibration bands in the IR spectra of peptides. The subsequent versions of Davydov’s Solution theory belong to this group. In these models excitations were obtained as polaronic-type solutions of a Hamiltonian describing the interaction of the amide I νCdO vibration quanta with low-frequency lattice modes.40
44 2. Theories of the other group comprise models focused on the generation mechanisms of the fine structure pattern of the νN
H proton stretching vibration bands in IR spectra of hydrogen-bonded amide crystals. A wide spectrum of theories was proposed from the models assuming Fermi resonance mechanism involving the proton stretching vibrations and some other vibrations of the hydrogenbonded molecule to theories assuming vibrational exciton coupling occurring in the hydrogen bond system.34
41,45
47 Edller and Hamm noticed that the generation of the νN
H band fine structure pattern could not be explained in terms of the formalism of the Fermi resonance mechanism. On studying the temperature effects in polarized IR spectra of acetanilide (ACN) and acetanilide-d8 (D8-ACN) crystals and on the basis of the femtosecond infrared pump
probe experiments, they proposed the so-called “self-trapping” theory. In this model an exciton
phonon coupling plays an essential role that leads to the “vibrational self-trapping” state. Within this theory, the lower-frequency branch of the νN
H band is generated by the transition to a hypothetical “metastable” excited state of the proton stretching vibrations in the hydrogen bond lattice of the crystal, which anharmonically couple with the low-frequency N 3 3 3 O hydrogen bridge stretching vibrations. As the result of such a coupling, the absorption spectra in the νN
H band frequency range exhibit shapes qualitatively resembling typical Franck
Condon-type progressions, composed of one vibrational excitation quantum and several quanta of phonon excitation.46,47 This theory has been

Figure 4. Impact of temperature on the polarized spectra of the most intense components of the PAM crystal: (a) the ac plane case; (b) the ab crystalline face case.

proposed recently and is highly intuitive as well as being only of a qualitative character. The model of the metastable state within the self-trapping theory is totally abstracted from the “state-of-art” in the quantitative theories of the IR spectra of the hydrogen bond dimers and hydrogen-bonded crystals. The authors of the selftrapping theory have not considered the H/D isotopic effects in the IR spectra of the hydrogen bond of amide crystals. This approach also does not explain the differences in the νN
H band shapes characterizing crystals of diverse secondary amide systems. Moreover, to the authors’ knowledge no monograph dealing with the quantitative interpretation of IR spectra of PAM crystals has been published so far.46,47 3.2. Initial Studies of Vibrational Spectra of PAM Crystals. The νN
H band in the IR spectra of PAM crystal (the frequency range 2900
3350 cm
1) consists of several intense, wellresolved spectral lines. In Figure3 IR spectra of polycrystalline samples of the compound measured at 293K and 77 K are presented. Also the Raman spectrum is shown to identify the lines attributed to the C
H bond stretching vibrations (the line frequencies 3095, 3069, 3054, 3024, and 2984 cm
1). The C
H bond stretching vibration lines facilitate identification of crystal faces developed during crystallization from melt. In the spectra of the PAM crystal the νN
H band shift toward the lower frequencies, accompanying the formation of the hydrogen bond, is ca. equal to 250 cm
1. This fact indicates that hydrogen bonds are relatively strong. An identical conclusion can be drawn from the geometry of hydrogen bonds in the crystal (the N 3 3 3 O bond length is equal to 2.8522 Å).48 4205

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Figure 6. IR spectra of polycrystalline samples of PAM, N-methylthioacetamide and acetanilide dispersed in the KBr pellets.

Figure 5. Polarized IR spectra of PAM crystal measured at 77 K in the νN
H frequency range. (a) IR beam of normal incidence with respect to the ac crystal plane. The polarized component spectra were obtained for two orientations of the electric field vector E: (I) E II a and (II) E II c. (b) IR beam of normal incidence with respect to the ab crystal plane. The polarized component spectra were obtained for two orientations of the electric field vector E: (I) E II a and (II) E II b.

3.1. Temperature Effects in IR Spectra of PAM. In Figure 4

the temperature effect in the spectra of the two forms of PAM crystals is shown. From these spectra it results that on a temperature decrease the higher-frequency branch of the νN
H band (3350
3200 cm
1) remains almost unchanged. In these circumstances, the intensity of the band lower-frequency branch increases. The temperature effects in the crystal spectra seem to be very complex. This effect probably is connected with the averaging of the bent structure of the hydrogen bridges toward the axial symmetry at growing temperatures. On the other hand, the equilibrium geometry of the hydrogen bonds is temperature dependent (this results from X-ray studies of hydrogen-bonded crystals). This fact poses a problem for the theoretical models describing spectra of crystals with hydrogen bonds. 3.3. Linear Dichroic Effects in the Spectra. Polarized IR spectra of the hydrogen bond in PAM crystals measured in the frequency range of the νN
H band for two individual crystal forms, each having developed another crystal plane, are shown in Figure 5. Spectra of the two different crystal forms differ from one another by the intensities of their lower-frequency νN
H band branches and by relative intensities of the C
H bond stretching vibration lines. Although in the spectra of the two crystal forms some splitting effects accompanied by slight local linear dichroic effects can be

Figure 7. IR spectra of the polycrystalline samples of D-PAM (80% D in the sample), dispersed in the KBr pellets, measured at two different temperatures and in the νN
H and νN
D ranges.

found, no general differentiation of the polarization properties of the two opposite spectral branches of the νN
H band occurs. Therefore, the PAM crystal spectra in regard to these properties fairly resemble significantly the spectra of N-methylthioacetamide31 and acetanilide crystals27 measured earlier. In Figure 6 IR spectra of polycrystalline samples of PAM, N-methylthioacetamide, and acetanilide, measured in the frequency range of the νN
H band, are shown. 3.4. Isotopic Dilution Effects in the Crystalline Spectra. Replacement of protons by deuterons in the hydrogen bonds of PAM crystals causes the appearance of a new band in the 2300
2500 cm
1 range, attributed to the N
D bond stretching vibrations (band symbol νN
D). In Figure 7 IR spectra of partially deuterated polycrystalline samples of PAM, measured in the frequency range of the “residual” νN
H and νN
D bands are given. As shown above, the νN
D band is practically reduced to one intense and narrow spectral branch. The temperature effect in the polarized IR spectra of the two crystal forms, recorded in the frequency range of the residual νN
H and νN
D bands, is shown in Figure 8. From these spectra it results that the νN
D band in the whole band range homogeneously responds to the changes in temperature. On the other hand, the temperature effect in the residual νN
H band is fairly similar to the one found in the spectra of isotopically neat crystals. This is due to the stepwise change of the band intensity caused by temperature decrease. 4206

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Figure 8. Impact of temperature on the νN
H and νN
D bands in D-PAM crystal spectra (60% D in the sample) for both crystalline faces: (a) the ac plane; (b) the ab plane.

Figure 9 presents the polarized IR spectra of partially deuterated PAM crystals. They were measured in the residual νN
H and νN
D bands at 77 K for two orientations of the electric field vector of the incident beam of the IR radiation with respect to the oriented crystal lattice. The observed homogeneous linear dichroic properties of the crystalline spectra in the νN
D band range prove that the band consists of only one spectral branch. It remains in an approximate relation by the 21/2 factor with the frequency of the higherfrequency branch of the residual νN
H band. Next the almost homogeneous polarization properties of the residual νN
H band were also measured. The shape of the band remained practically unchanged in spite of the replacement of the major part of the hydrogen bond protons by deuterons. The residual νN
H bands of the two crystal forms remain unchanged while the corresponding bands of the isotopically neat crystals differ to some extent.

4. QUANTITATIVE MODEL FOR THE DESCRIPTION OF THE CRYSTAL SPECTRA PROPERTIES 4.1. Choice of Model for the Spectra Interpretation. We will show that all the discussed spectral properties of the PAM crystals can be quantitatively described in terms of a model by assuming that a centrosymmetric dimer of the N
H 3 3 3 O hydrogen bonds is the bearer of the basic crystal spectral properties. This means that from a unit cell of a crystal the model selects only those translationally independent pairs of hydrogen bonds that are most strongly excitoncoupled. The exciton coupling involves the pairs of the N
H 3 3 3 O

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Figure 9. Polarized spectra in the νN
H and νN
D band frequency range of isotopically diluted PAM crystals measured at 77 K: (a) the ac plane, 60% D-PAM and 40% PAM; (b) the ab plane, 60% D-PAM and 40% PAM.

hydrogen bonds that are connected with the symmetry center inversion operation. Moreover, each hydrogen bond belongs to another, translationally nonequivalent chain of the associated molecules (see Figure 2). Indeed, such dimeric systems of the hydrogen bonds are considered responsible for the isotopically diluted crystal spectra. The relatively weak exciton coupling in the unit cell, involving these two translationally nonequivalent dimers are only responsible for the negligibly small splitting of the spectral lines. This effect differentiates the spectra measured for the two different crystallographic faces. These latest fine spectral effects seem to be attributed to the couplings seem to concern the adjacent hydrogen bonds in each chain. Then we will prove that the contour shapes of the residual νN
H and νN
D bands can be quantitatively reproduced by the model calculations based on the formalism of the strong-coupling theory of the IR spectra of a centrosymmetric dimeric hydrogen bond system.6
8 4.2. Model Calculations of the νN
H and νN
D Band Contour Shapes. Model calculations, aiming at reconstituting the residual νN
H and νN
D band shapes, were performed within the limits of the strong-coupling theory,6
8 for a model centrosymmetric N
H 3 3 3 O hydrogen bond dimeric system. We assumed that the main νN
H and νN
D band shaping mechanism involved a strong anharmonic coupling, including the high-frequency proton (or deuteron) stretching vibrations and the low-frequency N 3 3 3 O hydrogen bridge stretching vibrational motions. According to the consequences of the strong-coupling model for centrosymmetric 4207

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Figure 10. Theoretical reconstruction of the νN
H band from the PAM spectra, measured at 77 K. The νN
H band shape simulation in the limits of the “strong-coupling” model: (I) the “plus” dimeric band reconstituting the symmetry-allowed transition band, (II) the “minus” dimeric band reproducing the forbidden transition band, (III) the superposition of the “plus” and “minus” bands with their statistical weight parameters Fþ and F
taken into the account. The coupling parameter values were bH = 1.5, C0 = 1.4, C1 =
0.3, Fþ = 0.75, F
= 1.0, and ΩN 3 3 3 O = 50 cm
1. The corresponding experimental spectrum is presented in the inset.

dimers, the νN
H and νN
D band contour fine structures were treated as a superposition of two component bands. They corresponded to the excitation of the two kinds of proton stretching vibrations, each exhibiting a different symmetry. For the Ci point symmetry group of the model dimer, the proton totally symmetric “in-phase” vibration normal coordinate belongs to the Ag representation when the nontotally symmetric “out-of-phase” vibration coordinate belongs to the Au representation. The excitation of the Ag vibrations in the dimer generates the lower-frequency transition branch of the νN
H band when the Au vibrations are responsible for the higher-frequency band branch. According to the formalism of the strong-coupling theory, the νN
H band shape of a dimer depends on the following system of dimensionless coupling parameters: (i) on the distortion parameter, bH, and (ii) on the resonance interaction parameters, CO and C1.6
8 The bH parameter describes the change in the equilibrium geometry for the low-energy hydrogen bond stretching vibrations, accompanying the excitation of the high-frequency proton stretching vibrations νN
H. The CO and C1 parameters are responsible for the exciton interactions between the hydrogen bonds in a dimer. They denote the subsequent expansion coefficients in the series on developing the resonance interaction integral C with respect to the normal coordinates of the νN 3 3 3 O low-frequency stretching vibrations of the hydrogen bond. This is in accordance with the formula C ¼ CO þ C 1 Q 1 where Q1 represents the totally symmetric normal coordinate for the low-frequency hydrogen bridge stretching vibrations in the dimer. This parameter system is closely related to the intensity distribution in the dimeric νN
H band. The bH and C1 parameters are directly related to the dimeric νN
H component bandwidth. The CO

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Figure 11. Theoretical reconstruction of the νN
D band from the D-PAM spectra, measured at 77 K. The νN
D band shape simulation in the limits of the “strong-coupling” model: (I) the “plus” dimeric band reconstituting the symmetry-allowed transition band, (II) the “minus” dimeric band reproducing the forbidden transition band, (III) the superposition of the “plus” and “minus” bands with their statistical weight parameters Fþ and F
taken into account. The coupling parameter values were bH = 0.85, C0 = 1.0, C1 =
0.1, Fþ = 1.0, F
= 0.0, and ΩN 3 3 3 O = 50 cm
1.The corresponding experimental spectrum is given in inset.

parameter determines the splitting of the component bands of the dimeric spectrum corresponding to the excitation of the proton vibrational motions of different symmetries, Ag and Au.6
8 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: pffiffiffi BH ¼ 2BD For the CO and C1 resonance interaction parameters the theory predicts the isotopic effect expressed by the 1.0 to 21/2-fold reduction of the parameter values for D-bonded dimeric systems. Figure 10 shows the results of model calculations, which quantitatively reconstitute the νresidual νN
H band contour shapes from the spectra of PAM crystals, isotopically diluted by deuterium. The theoretical spectrum was treated as a superposition of the “plus” and “minus” component bands taken with their appropriate statistical weight parameters, Fþ and F
, respectively. The spectrum was calculated for the following coupling parameter values: bH = 1.5, C0 = 1.4, C1 =
0.3, Fþ = 0.75, F
= 1.0, ΩN 3 3 3 O = 50 cm
1. Quantitative reproduction of the residual νN
D band contour shapes from the spectra of the PAM crystals, isotopically diluted by hydrogen, is presented in Figure 11. The coupling parameter values used for calculation of the theoretical spectrum were bD = 0.85, C0 = 1.0, C1 =
0.1, Fþ = 1.0, F
= 0.0, and ΩN 3 3 3 O = 50 cm
1. When the corresponding calculated spectra and the experimental spectra are compared, it can be noticed that a satisfactorily good reconstitution of the two analyzed band shapes has been achieved. The results also remain in agreement with the linear dichroic effects measured in the crystalline spectra. Moreover, no Fermi resonances48,49 were necessary to achieve this result. When the νN
H band 4208

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contour shapes are reconstituted, the so-called dimeric “minus” subband, corresponding to the in-phase proton vibrations, reproduce the lower-frequency branches of the band. The higher-energy branches of the νN
H bands are reproduced by the so-called “plus” dimeric subband related to the out-of-phase proton vibrations. The calculation results have suggested that the two dimeric component sub-bands, “minus” and “plus”, contributed to the results with their comparable statistical weights, represented by the appropriate F
and Fþ parameter values. However, it was found that the “minus” band, theoretically forbidden by the symmetry rules for dipole vibrational transitions, appeared in the IR spectra of a centrosymmetric dimer. The explanation of this effect is given in the next section of this article.

5. VIBRATIONAL DIPOLE SELECTION RULE BREAKING IN THE IR SPECTRA OF CENTROSYMMETRIC HYDROGEN BOND DIMERS

approximation50 for the Ψn(q,Q) electronic function. The expansion takes into the account a linear term dependence of the electronic wave-function of nth electronic state upon the normal coordinate of the proton stretching vibration. In the limits of the adiabatic approximation the electronic function is as follows: ψn ðq;Q Þ ¼ ψ0n
¼ ψ0n þ

ðΔE0nn Þ
1 Æψ0n jðDHel =DQ Þ0 jψ0n æψ0n þ 3 3 3 ∑ n 6¼ n 0

0

0

0

∑ ºÆψn jðD=DQ Þjψnæß0 ψ0n Q 0

0

n0 6¼ n

ð7Þ

where ψ0n are the electronic functions In the “crude adiabatic approximation” and ΔE0nn0 symbols denote the energy differences between different electronic states of the model hydrogen bond, n and n0 . In an abbreviated notation the adiabatic electronic wave function is ψn ðq;Q Þ ¼ ψ0n þ

5.1. Single Hydrogen Bond. In this section we will analyze

C0nn ψ0n Q ∑ n 6¼ n 0

0

0

ð8Þ

the problem of the activation of the symmetry-forbidden transition in IR, which is responsible for the generation of the lowerfrequency νN
H band branch in the crystalline spectra of PAM. For this purpose let us assume a simplified model of a single N
H 3 3 3 O hydrogen bond, in which the proton stretching vibration couples with electronic motions. The vibronic Hamiltonian of the system is as follows:

where C0nn0 is a Herzberg
Teller expansion coefficient. The ψ0n “crude-adiabatic” electronic functions of the nth states relate to the equilibrium configuration of the proton taken from the ground electronic state of the system. They are the eigenfunctions of the Hamiltonian (Hel)0, which is the first term in the HT expansion:

H ¼ TN ðQ Þ þ Tel ðqÞ þ Uðq;Q Þ

Hel ðq;Q Þ ¼ ðHel Þ0 ðq;Q 0 Þ þ ðDHel =DQ Þ0 Q

ð1Þ

where the symbols q and p denote the coordinates and the momenta of electrons, whereas the Q and P symbols represent the normal coordinate of the proton stretching vibration and the momentum conjugated with it. TN, Tel, and U subsequently denote the kinetic energy operator of the proton vibration, the energy operator of the electrons, and the potential energy operator for a single hydrogen bond. The total vibronic wave function of the model hydrogen bond satisfies the Schr€odinger equation: HΨðq;Q Þ ¼ EΨðq;Q Þ

ð2Þ

where E is the energy eigenvalue. For the vibronic function an adiabatic approximation is assumed Ψðq;Q Þ ¼ φðQ Þ ψðq;Q Þ

ð3Þ

where φ denotes vibrational wave-function and ψ is the electronic wave function. Both functions are defined by the following equations: Hel ψn ðq;Q Þ ¼ εn ðQ Þ ψn ðq;Q Þ

where the “0” subscript denotes the equilibrium configuration of the proton. On discussing vibrational transitions in IR, the ψ0 adiabatic electronic function of the ground electronic state ought to be considered. However, it is enriched by contributions originating from the crude-adiabatic electronic functions of upper electronic levels: ψ0 ¼ ψ00 þ

½TN ðQ Þ þ εn ðQ Þφnm ðQ Þ ¼ Enm φnm ðQ Þ

ð6Þ

and

The n and m indexes define the electronic and the vibrational states of the model hydrogen bond, respectively. For the formal description of vibronic effects in the IR spectra of the hydrogen bonds let us assume the Herzberg
Teller (HT)

ð10Þ

∑

þ

where ð5Þ

∑ C00i ψ0i Q

i6¼ 0

For a single hydrogen bond the vibrational transition in IR, responsible for the generation of the νX
H band may be treated as a transition occurring between the φ00(Q) ψ0(q,Q) and φ01(Q) ψ0(q,Q) vibronic states. Under these assumptions the following formula for the vibronic transition moment for the excitation of the proton stretching vibration in IR can be obtained:   *     C00i ψ0i Q Þφ00 ðQ Þ! μ ðqÞðψ00 M B01 ¼ ðψ00 þ   i6¼ 0 +

ð4Þ

Hel ¼ Tel ðqÞ þ Uðq;Q Þ

ð9Þ

C00j ψ0j Q Þφ01 ðQ Þ ∑ j6¼ 0

ð11Þ q;Q

where μB(q) is the dipole moment operator depending on the electronic coordinates. 5.2. Centrosymmetric Dimer of Hydrogen Bonds. Let us consider a centrosymmetric dimeric system composed of two identical N
H 3 3 3 O hydrogen bonds labeled by the A and B symbols. The vibronic Hamiltonian of the dimer may be written as Hdim ¼ HA ðqA ;QA Þ þ HB ðqB ;QB Þ þ VAB ðqA ;qB ;QA ;QB Þ ð12Þ 4209

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where the HA and HB symbols denote the vibronic Hamiltonians of the individual hydrogen bonds in the model system and VAB is the operator of the interhydrogen bond interactions. In the ground vibrational state the vibronic wave function of the dimer is ΨGDIM ¼ π0 ðQA ;QB Þ ψ0 ðqA ;QA Þ ψ0 ðqB ;QB Þ

ð13Þ

π0 ðQA ;QB Þ ¼ φA00 ðQA Þ φB00 ðQB Þ

ð14Þ

where ^h ðqA ;qAR Þ ¼ A DHelA ðqA ;QA Þ DQA

When one of the hydrogen bonds in the dimer is vibrationally excited, the total vibronic wave function takes the following form: ΨEdim ¼ πA1 ðQA ;QB Þ ψ0 ðqA ;qB ;QA ;QB Þ ð15Þ

where πA1 ¼ φA01 φB00

πB1 ¼ φA00 φB01

ð16Þ

and the ψ0 (qA,qB;QA,QB) and ψ00 (qA,qB;QA,QB) symbols denote the electronic functions, which in this case indicate the developing coefficients. These functions should be estimated by applying the following procedure. For this purpose we multiply the vibronic Schr€odinger equation of the dimer for its excited vibrational state Hdim ΨEdim ¼ EΨEdim

ð17Þ

πA1

in the first case by and in the second case by and then integrate over the vibrational coordinates QA and QB. This approach allows for the elimination of the vibrational coordinates in the procedure of the determination of the electronic functions in (4). In an abbreviated notation the following system of two differential equations can be obtained: πB1

AB ^ 0 ψ 0 þ Δ^hA ðqA Þψ0 þ ^vðqA ;qB Þψ00 ¼ Eψ 0 H ^ 0AB ψ 00 þ Δ^hB ðqB Þψ 00 þ ^vðqA ;qB Þψ 0 ¼ Eψ 00 H

0

Δ1H 6¼ 0

^ BN ðQB Þ þ H ^ B ðqB ;QB0 ÞjφB01 æQ ^ 0B ðqB Þ ¼ ÆφB01 jT H el0 B A ^ A B ^ B ^ V ðqA ;qB Þ ¼ Æπ1 jV AB jπ1 æQ Q ¼ Æπ1 jV AB jπ1 æQ Q ^vðqA ;qB Þ ¼

^hA ðqA Þ ¼ ^hB ðqB Þ ¼

A

B

¼ ! ^ Ael DH

ψ00 ðqA ;qB Þ ¼ ÆπB1 ðQA ;QB Þjψ00 ðqA ;qB ;QA ;QB ÞjπB1 ðQA ;QB ÞæQA QB

ð23Þ

0 ! B

^ el DH DQB

ð22Þ

ψ0 ðqA ;qB Þ ¼ ÆπA1 ðQA ;QB Þjψ0 ðqA ;qB ;QA ;QB ÞjπA1 ðQA ;QB ÞæQA QB

ÆπB1 jV^ AB jπA1 æQA , QB

DQA

ð21Þ

0

In the equation system (18) the physical sense of the electronic wave-functions has changed since they are no longer dependent on the vibrational coordinates. The symbols ψ0 and ψ00 denote electronic functions averaged over the vibrational coordinates in the excited state of the proton stretching vibrations.

^ AN ðQA Þ þ H ^ 0A ðqA Þ ¼ ÆφA01 jT ^ A ðqA ;QA0 ÞjφA01 æQ H el0 A

B

0

Δ0H ¼ ÆφA00 jQA jφA00 æQA ¼ ÆφB00 jQB jφB00 æQB ¼ 0 Δ1H ¼ ÆφA01 jQA jφA01 æQA ¼ ÆφB01 jQB jφB01 æQB

ð18Þ

AB ^ 0A ðqA Þ þ H ^ 0B ðqB Þ þ V^ ðqA ;qB Þ ^ 0 ðqA ;qB Þ ¼ H H

A

!

The electronic operators ^hA(qA,qAR) and ^hB(qB,qBR) in (21) are considered as a sum of contributions introduced subsequently by the individual hydrogen bonds themselves as well as by their molecular surroundings (especially aromatic rings or other π-electronic systems). The operators introduced above have a strictly defined ^ A0 and H^ B0 are the Hamiltonians of the physical meaning: H individual hydrogen bonds in the dimer, when each operator is averaged with respect to the vibrational coordinates. The symbol ^V denotes the potential energy operator for the inter-hydrogen-bond interactions in the excited vibrational state in the dimer. The^v symbol is the resonance interaction operator averaged with the respect to the proton vibration normal coordinates in the excited vibrational state in the dimer. Δ1H is the average value of the proton displacement in the excited state of the proton vibration. On assuming a strong anharmonicity of the proton stretching vibrational motions in the dimer hydrogen bonds we obtain:

where the component operators in (18) are defined as

ÆπA1 jV^ AB jπB1 æQA , QB

0

DHelA ðqAR ;qA ;QA Þ  þ DQA 0 ! B B DH ðq ;q ;Q Þ B B el R ^hB ðqB ;qB Þ ¼ R DQB 0 ! ! B B B DHel ðqB ;QB Þ DHel ðqR ;qB ;QB Þ  þ DQB DQB

where

þ πB1 ðQA ;QB Þ ψ00 ðqA ;qB ;QA ;QB Þ

!

! DHelA ðqA ;qAR ;QA Þ DQA

0

Δ1H ¼ ÆφA01 jQA jφA01 æQA ¼ ÆφB01 jQB jφB01 æQB

ð19Þ

and

The equation system (18) may be written in a more compact form in the matrix notation using the familiar Pauli matrices δ1 and δ3: ! ! ψ0 ψ0 ^ ¼E ð24Þ η ψ00 ψ00 where

HelA ðqA ;qAR Þ



    ^ 0AB 1 þ 1 Δ1H ^hA þ ^hB 1 þ 1 Δ1H ^hA
^hB δ3 þ ^ ^ ¼H η ν δ1 2 2 ð25Þ

HelA ðqA Þ þ HelA ðqAR Þ

HelB ðqB ;qBR Þ  HelB ðqB Þ þ HelB ðqBR Þ

ð20Þ 4210

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The Journal of Physical Chemistry A and

" δ1 ¼

0 1

1 0

#

" δ3

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1 0

0
1

#

where ^η is the 2  2 matrix electronic Hamiltonian of the model dimer. Now we introduce new, symmetrized vibrational coordinates (normal coordinates) of the dimer, which belong to two different irreducible representations of the Ci group, Ag and Au: A

Q1 g ¼ 2
1=2 ðQA þ QB Þ Q2Au ¼ 2
1=2 ðQA
QB Þ

ð26Þ

We also introduce new symmetrized base wave functions for the excited state of the proton vibrations in the dimer: πþ ðA u Þ ¼ 2
1=2 ðπA1 þ πB1 Þ π
ðA g Þ ¼ 2
1=2 ðπA1
πB1 Þ

ð27Þ

For this basis the matrix Hamiltonian transforms to the new, equivalent form:     ^ 0AB 1 þ 1 Δ1H ^hA þ ^hB 1 þ 1 Δ1H ^hA
^hB δ1 þ ^ν δ3 η^0 ¼ H 2 2 ð28Þ It satisfies the Schr€odinger equation with new electronic functions depending only on the electronic coordinates: ! ! ψþ ψþ 0 ¼E ð29Þ η^ ψ
ψ
Then, the total vibronic wave function of the dimer takes the following form: þ

ΨEdim ¼ πþ ψ þ π
ψ




ð30Þ

0

The Hamiltonian η^ is a purely electronic operator of the dimer. It relates to its averaged geometry in the first excited state of the proton vibrations in conditions of a strong anharmonicity of the motion. 5.3. Spectral consequences of the model. The electronic Hamiltonian η^0 describes the mixing of the proton vibrational states of the dimer, belonging to different irreducible representations of the Ci group. The purely electronic wave-functions ψþ and ψ
may be treated as the developing coefficients of vibrational functions in eq 30. They can be estimated by applying variational methods and by assuming the following approximation for each function: ψþ ¼ ψ
¼

n

n

∑ ∑ Cþij A ψoi B ψoj i¼0 j¼0 n

n

A oB o C
∑ ∑ kl ψk ψl k¼0 l¼0

ð31Þ


where the developing coefficients Cþ ij and Ci0 j0 can be obtained by solving the suitable secular equation whereas the n index relates to the highest electronic level taken into account. For the sake of reliability the choice of the functional basis in (31) should be safely restricted to the lowest electronic states of the hydrogen bond systems, mainly to those which most strongly couple with the protonic motions.

The Δ1H parameter value may be estimated from the potential energy surface parameters of the protonic motion in the single hydrogen bond, which in turn may be derived from spectroscopic data or from quantum-chemical calculations. However, the main problem concerns the estimation of the matrix elements of the ^hA, ^hB, and^νoperators. Therefore, a precise solution of the matrix 00 eq 29 does not seem feasible. Schrodinger On the other hand, to prove an effective mixing between the excited vibrational states πþ (Au) and π
(Ag) via the vibronic mechanism a precise solution of eq 29 is not necessary. The functions ψþ, ψ
yield the non-zero nondiagonal elements of the energy matrix. It means that an effective mixing involving the protonic vibrational states of different symmetry may take place, since both functions ψþ, ψ
are simultaneously different from zero. Therefore, the forbidden vibrational transition to the Ag state in the IR for the centrosymmetric hydrogen-bond dimer can “borrow” its intensity from the allowed vibrational transition to the Au state.

6. DISCUSSION The presented model considers the vibronic coupling mechanism as well as the anharmonicity of the proton stretching vibrations in their first excited state as the main sources of the vibrational selection rule breaking in IR spectra of centrosymmetric hydrogen bond dimers. Formally, this mechanism is a kind of reverse of the familiar Herzberg
Teller mechanism, which was originally proposed for the interpretation of the UV
vis spectra of aromatic molecules.50 In this case, the dipole-forbidden transition to the Ag state of the proton vibrations in the dimer is allowed due to the vibronic coupling involving the protonic and electronic motions in the system. As a result, the forbidden vibrational transition “borrows” the intensity from the symmetry-allowed transition to the Au state. The fundamental equation (18) describing the electronic movement in the dimer was obtained by averaging over the vibrational coordinates. Such an approach in its spirit is a kind of reverse of the separation of the vibrational and electronic movements in molecules in terms of the Born
Oppenheimer approximation. Changes in the electronic motions induced by the excited proton vibrations in the hydrogen bonds are small. However, even such small effects are important when the vibronic mechanism of IR transitions for hydrogen bond dimeric systems is discussed.51,52 On analyzing the vibronic coupling mechanism in the centrosymmetric dimers and the reason for the dipole selection rule breaking in their IR spectra, one should jointly discuss the molecular geometry and the symmetry of the electronic charge distribution. The electronic contribution to the dynamics of the hydrogen bond atoms is responsible for the appearance of an effective asymmetry in the dimer geometry. This remark mainly concerns the proton positions in the dimers. This seems to be the main source of the vibrational selection rule breaking in the IR spectra. The proton stretching vibrations are most strongly coupled with the movements of electrons occupying the nonbonding orbitals of the proton-acceptor atoms in the hydrogen bonds. Also couplings of protons with electrons on the π-orbitals in molecular skeletons of the associating molecules should be considered. In the case of aliphatic carboxylic acid dimers in which only the “hard-core” electrons exist the closest molecular environment of the hydrogen bonds should have a relatively small impact on to the vibronic coupling mechanism (see eqs 7 4211

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The Journal of Physical Chemistry A and 18). On the other hand, aromatic carboxylic acid dimers should be characterized by stronger vibronic coupling effects of the Herzberg
Teller-type. Therefore, in their IR spectra the forbidden transition spectrum, activated via the vibronic promotion mechanism, should be more intense than the intensity of the corresponding spectrum of aliphatic carboxylic acids. This conclusion is supported by experiment.13,23,24,53
55 From our analysis of polarized IR spectra of the PAM crystal it results that centrosymmetric dimeric N
H 3 3 3 O hydrogen bond systems are the bearers of the crystal spectral properties. This is due to the fact that the strongest vibrational exciton couplings involve the closely-spaced hydrogen bonds, each from a different chain of the associated molecules in the lattice. In the crystalline spectra the lower-frequency branch of the νN
H is attributed to the forbidden transition leading to the Ag excited state of the dimer. The transition is activated by the vibronic promotion mechanism presented above involving nonadiabatically coupled proton vibrations and the electronic motions in the hydrogen bond centrosymmetric dimeric systems in the crystal. Consequently, the normal vibrations of the protons in the dimers exhibit no precisely defined symmetry properties. Therefore, the dipole selection rules become weakened and the forbidden vibrational transition in IR is activated. From our previous studies it results that the integral intensity of the lower-frequency branches of the νX—H bands in IR spectra of centrosymmetric hydrogen bond dimeric systems strictly depends on the electronic structure of the associated molecules. In the case of the polarized IR spectra of the PAM crystal the effect of the selection rule breaking seems to be strong since the lower-frequency branch of the νN
H band is extremely intense in comparison with the corresponding spectra of other amide crystals. This spectral branch intensity is most probably the result of the coupling of the protonic motions with electrons of not only the hydrogen bridge atoms but also those of the substituent groups linked to the amide fragment (mainly of the phenyl and the acryl group π -electrons). In the case of amide crystals the linking of the acryl group to the carbonyl group significantly enhances the polarization properties of the proton acceptor in the N
H 3 3 3 OdC hydrogen bonds. They reach the level characteristic for the N
H 3 3 3 SdC hydrogen bonds found in N-methylthioacetamide crystals.31 The mechanism of the PAM crystal spectra generation, including the anomalous H/D isotopic effect in the crystalline spectra, fairly resembles the mechanism of the spectra generation of some rare molecular system cases, e.g., 2-mercaptobenzothiazole56 and N-methylthioacetamide31 crystals. Thus the above evidence seems to point to the fact that the spectral properties of the PAM crystals result from the strong influence of the electronic effects on the mechanisms of the generation of the centrosymmetric dimer system IR spectra of the N
H 3 3 3 O hydrogen bonds in the crystal lattice. The influence of both the phenyl and acryl groups on the electronic properties of the hydrogen bonds in the crystal is also manifested in the X-ray structure of PAM molecules. The C7
N1 bond (1.346 Å) is shorter than a typical C
N bond (1.47 Å).57 Nevertheless, it is longer than a typical CdN bond (i.e., 1.28 Å).57 This structural effect is the consequence of the conjugation, which involves the fragment with the N1, C7, O2, C8, C9 atoms as well as the phenyl ring. The presented above model of the vibrational selection rule breaking also explains the effect of the strong narrowing of the νN
D band observed in the IR spectra of the deuterium-bonded

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derivative of the compound. From our model calculations aiming at reproducing the νN
H and νN
D band shapes it results that the forbidden transition band intensity in the νN
D band is negligibly small. The νN
D band is practically formed by the allowed transition band. The explanation of this effect can also be found in our model. The promotion mechanism is strongly hydrogen atom mass-dependent since the deuteron vibrations in the N
D 3 3 3 O deuterium bonds are characterized by a lower anharmonicity than the proton vibration anharmonicity in the N
H 3 3 3 O hydrogen bonds in the crystal. The magnitude of this effect depends on the potential energy surface shape of the proton (and deuteron) stretching vibrations in the crystal. This shape is formed by the vibronic coupling mechanism. Similar H/D isotopic effects were observed in the IR spectra of the hydrogen bond in molecular crystals with the N
H 3 3 3 S bonds in their lattices. They characterize, for instance, the IR spectra of 2-mercaptobenzothiazole (with centrosymmetric dimers as the lattice structural units)56 and N-methylthioacetamide (with infinite chains of hydrogen bonded molecules)31 crystals. On the other hand, the identical H/D isotopic effect is the attribute of the spectra of 2-hydroxybenzothiazole crystals (with cyclic dimers of N
H 3 3 3 O hydrogen bonds).56

7. H/D ISOTOPIC SELF-ORGANIZATION EFFECTS IN THE SPECTRA The invariance of the residual νN
H band contour shapes in the spectra of isotopically diluted PAM crystals, along with the increasing D/H exchange rate value, prove that the distribution of protons and deuterons in the lattice of the hydrogen bonds is not random. This effect, namely the so-called H/D isotopic self-organization effect,19
25,27,30,31 is the result of dynamical cooperative interactions25
27 occurring in the hydrogen bond systems of molecular crystals. However, a similar vibronic coupling mechanism that takes place in the ground state of the proton vibrations in centrosymmetric dimeric systems of hydrogen bonds, is the source of the dynamical cooperative interactions in the hydrogen bond lattices in the crystals.26,27 These interactions are responsible for the grouping of identical hydrogen isotope atoms, i.e., protons or deuterons in systems of adjacent hydrogen bonds in the lattice (domains). Such a nonrandom arrangement of protons and deuterons in the lattice is energetically privileged.25
27 The spectral effects accompanying the isotopic dilution prove the influence of the dynamical cooperative interactions in hydrogen bond systems on the hydrogen bond energy of molecular complexes. In this case the strongest dynamical cooperative interactions involve the closely-spaced translationally nonequivalent hydrogen bonds. Moreover, each moiety belongs to a different chain of the associated molecules of PAM penetrating a unit cell of the lattice. The “domains” occupied by the residual protons elongate transversely to the molecular chain direction in an isotopically diluted crystal. A similar way of occurrence of the H/D isotopic self-organization effect was deduced earlier from the IR spectra of the hydrogen bond in N-methylacetamide30 and acetanilide27 crystals. Most probably, the dynamical cooperative interactions occur in the same way in polypeptide molecules. In the case of biological systems placed in the heavy water environment, a partial annihilation of these interactions, due to the isotopic dilution, may take place. This leads to the folding of polypeptide structures of in the heavy water environment and in effect to loosing of their biological activity in such circumstances.58
61 4212

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8. CONCLUSION Hydrogen-bonded crystals of secondary amides and thioamides exhibit a rich diversity of their spectral properties in the IR frequency range of the νN
H proton stretching vibration bands. In the literature it has been accepted that the νN
H band is composed of two sub-bands of different frequency assigned as “amide A” and “amide B”.32,37 In the crystalline IR spectra of acetanilide27 and PAM the νN
H bands are characterized by a more complex intensity distribution pattern when the lowerfrequency branch of the band for the latter compound is ca. 3 times more intense. Our studies have identified the mechanism of the νN
H band contour generation as an exciton one, strongly influenced by the vibronic coupling in the spatially-ordered hydrogen bond system. The vibrational exciton coupling involving hydrogen bonds forming a centrosymmetric dimeric system in which each moiety belongs to a different chain of the associated molecules is responsible for the generation of the fine structure of the νN
H bands in the majority of amide crystals. The observed diversity of the spectral behavior of amide crystals is strongly dependent on the electronic structure of amide molecules, which is modified by substituent groups linked to the amide fragment of the molecules. In the case of IR spectra of the PAM crystal an extremely large magnitude of the vibrational selection rule breaking effect was obtained. This was manifested by an extremely high intensity of the lower-frequency branch of the band. This effect is of a vibronic nature. It is strengthened by the coupling between the proton vibrations and the movement of the electrons on the π-orbitals of both the phenyl rings and the acryl groups. ’ AUTHOR INFORMATION Corresponding Author

*E-mail address: fl[email protected]. Telephone number: þ48 323591598. Fax number: þ48 322599978.

’ REFERENCES (1) Pimentel, C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman and Co.: San Francisco, CA, 1960. (2) Schuster, P.; Zundel, G.; Sandorfy, C. The Hydrogen Bond; North-Holland: Amsterdam, 1976; Tom I, II, III. (3) Hofacker, G. L.; Marechal, Y.; Ratner, M. A. The dynamical aspects of hydrogen bonds. In The Hydrogen Bond, Recent Developments in Theory and Experiment; Schuster, W. P., Zundel, G., Sandorfy, C., Eds.; North-Holland: Amsterdam,1976; Vol. 1, p 295. (4) Had_zi, D. Theoretical Treatments of Hydrogen Bonding; John Wiley & Sons Ltd.: Chichester, 1997. (5) Marechal, Y. The Hydrogen Bond and The Water Molecule, The Physics and Chemistry of Water, Aqueous and Bio Media; Elsevier: Amsterdam, Oxford, 2006. (6) Witkowski, A. J. Chem. Phys. 1967, 47, 3645. (7) Marechal, Y.; Witkowski, A. J. Chem. Phys. 1968, 48, 3697. (8) Flakus, H. T. Chem. Phys. 1981, 62, 103. (9) Fisher, S. F.; Hofacker, G. L.; Ratner, M. A. J. Chem. Phys. 1970, 52, 1934. (10) Henri-Rousseau, O.; Blaise, P. The infrared density of weak hydrogen bonds within the linear response theory. In Advances in Chemical Physics; Prigogine, I., Rice, S. A., Eds.; John Wiley & Sons Inc.: New York, 1998; Vol. 103. (11) Henri-Rousseau, O.; Blaise, P. The νX
H lineshapes for centrosymmetric cyclic dimers involving weak hydrogen bonds. Advances in Chemical Physics; John Wiley & Sons Inc.: New York, 2008; Vol. 139, Chapter 5, p 245.

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