Spectroscopic evidence for Davydov-like solitons in acetanilide

Detailed measurements of infrared absorption and Raman scattering on crystalline acetanilide [(CH3CONHC6H5)„] at low temperature show a new band close to the conventional amide I band. Equilibrium properties and spectroscopic data rule out explanations based on a conventional assignment, crystal defects, Fermi resonance, and upon frozen kinetics between two different subsystems. Thus we cannot account for this band using the concepts of conventional molecular spectroscopy, but a soliton model, similar to that proposed by Davydov for a-helix in protein, is in satisfactory agreement with the experimental data.


I. INTRODUCTION
Acetanilide, (CH&CONHCsHs)"or ACN, is an organic solid in which two close chains of hydrogen-bonded amide groups run through the crystal. It is an interesting system because the nearly-planar amide groups display bond distances which are close to those found in polypeptides (see Fig. 1). Both synthetic and natural polypeptides are made of several chains of such hydrogen-bonded amide groups: the infinite number of parallel chains displayed by the P sheet and the three coiled chains of the a-helix being better known examples. Since the physical properties of hydrogen-bonded amide systems are very sensitive to bond distances, we expect ACN to be a useful model system in the search for new physical features of extended polypeptides and perhaps even natural proteins.
A characteristic feature of the amide group (CONH) in polypeptides is the amide I mode, mainly involving CO stretching. This mode is observed as an ir-absorption peak at about 1665 cm ' in ACN and near that value in a wide variety of materials containing the amide group. Ten years ago some details of the ir and Raman spectra for ACN were reported showing that a new amide I band appears at low temperature. ' This new band, which we shall refer to here as the unconventional amide I band, is red shifted from the primary band (amide I) by about 15 wave numbers to 1650 cm '. It was suggested that the unconventional band could be related to a cooperative interaction between the hydrogen-bonded proton and the first excited state of amide I, but no quantitative theory was available at that time. A reformulation of this problem has been presented in a recent note, and the purpose of this paper is to present the experimental basis for our assignment of the unconventional band. The theory of our assignment is discussed in detail in the fo11owing paper, but a simplified version is presented here to facilitate interpretation of the experimental results. To appreciate the qualitative features of our theory consider that the effect of introducing localized amide I bond energy is to displace the ground states of other lowfrequency vibrations. These displacements can act as a potential well to trap amide I bond energy and prevent its dispersion via dipole-dipoleinteraction effects. The idea 1984 The American Physical Society of self-trapping in condensed matter physics is not new.
A half century ago Landau suggested that an electron in a crystal should be self-trapped in the potential well caused by its polarization field.
Self-trapping of vibrational quanta was introduced ten years ago by Davydov in the context of a-helix in protein as a means for the storage and transport of biological energy.
Since that time Davydov and his co-workers have discussed many aspects of this mechanism and biochemical implications have been described in a recent book.
To conform with current usage we shall use the generic term "soliton" for all self-trapped states.
Since this paper is primarily experimental we begin with a discussion of our methods followed by a presentation of our raw experimental results. In the next section we assign the observed bands and show that the abovementioned 1650-cm ' band has no conventional interpretation. This is followed by a simple version of the soliton theory which contains the main features of the problem but does not treat details of the crystal structure. Finally we discuss the intensity of the soliton line and present conclusions.

A. Materials
Different sources of ACN have been employed including Merck, Test proanalysis, and zone refined 99.99% by Aremco Products, Briarcliff Manor, New York. N' isotropic substitution (95%) was obtained from the Pro-Chem, Rome, Italy, 1977, special product. p-Cl-ACN was from Fluka AG, Hauppauge, New York, purum 99%. The purchased material displays a broad band in the 1700-cm ' region of about 5 -10% of the intensity of the amide I band at 1660 cID '. p-Cl-ACN was dissolved in trifluoroacetic acid and then recrystallized. This procedure removes the spurious band at 1700 cm ' after crystallization and reproducible results were obtained. NN' (diacetyl esamethylene diamide) and nylon-6, 6 were a gift of the SNAM Progetti Laboratory, San Donato, Italy. Be, Pi (picolinamide), and Ni were obtained from the BDH Lab, England (British Drug House, Ltd. ), reagent grade, no less than 98.5% purity. (The symbols for these materials are defined in the caption of Fig. 9.) Oriented crystals of ACN for ir-absorption measurements were obtained by cooling a thin layer of melted ACN between two Irtran-II windows. The control of the thickness was obtained by applying pressure during cooling. By touching the melted ACN at the edge of the window, large areas of uniform orientation were produced.
The normal habit is tabular on 100 and thus the polarized spectrum with the E vector parallel and perpendicular to the b axis was measured.
Samples of polycrystalline ACN were prepared by mixing ACN crystalline powder with ir grade KBr. Pellets of -, ' -in. diameter were obtained using 10 kbar of pressure.
Amorphous ACN samples were prepared by vacuum deposition on Irtran-II windows of evaporated ACN material. The ACN microcrystals were placed in a small heater with a carefully controlled temperature. At a temperature of about 100 C the ACN material sublimates under vacuum. The evaporated material was deposited in a form of a homogeneous thin layer on a cool Irtran-II window until the desired optical density was achieved.
The spectra of this deposited sample were measured. To achieve annealing of the amorphous sample, low heating was then applied until melting of the thin layer was obtained. Upon cooling, the crystalline properties were recovered. On occasion this annealing procedure was repeated for several cycles. B. Instrumentation ir spectra were obtained using three different ir spectrophotometers.
For the study of the temperature dependence of the amide I region, a Nicolet (Madison, Wisconsin) model no. 7000 Fourier-transform ir spectrophotometer was used. Spectra were collected for 100 scans using a bandwidth of 0.5 cm '. The sample was thermostated using a closed-cycle helium refrigerator from Lake Shore Cryotronics, Inc. (Columbus, Ohio), equipped with calcium-fluoride windows.
N' and p-Cl-ACN experiments were performed using a Perkin-Elmer model no. 180 grating spectrophotometer equipped with a digital interface. Data were collected at 1-cm ' resolution and stored in a Laben model no. 70 minicomputer for further analysis. Polarized spectra of single crystal and spectra of the series of amide crystal were obtained with a Beckman model no. IR9 spectrophotometer using Beckman gold wire polarizers.
Far-ir-absorption spectra were measured using a Michelson interferometer (model no. 720) equipped with a Golay cell. Samples consist of pellets obtained from a mixture of grounded ACN and polyethylene powder.
Pure polyethylene pellets were used to measure background transmission. Raman spectra were excited by a Coherent Radiation model no. 52 argon ion laser operating at 4880 A or 5145 A, with stabilized output power of 20 -200 mW. Incident light was filtered by proper choice of interference filters (in order to avoid plasma lines) and its intensity was monitored using a beam-splitter and a silicon photocell. Scattered light was analyzed by a Jarrel-Ash model no. 25-300 Raman spectrometer and detected by an ITT (Fort Wayne, Indiana) model no. FW-130 cooled photomultiplier using photon counting electronics. Spectral resolution was 1 cm ' and wave-number accuracy was +2 cm ' from 10 to 3500 cm '. Samples consist of pellets and small-size crystals of ACN and derivatives and were placed on a copper sample holder at an angle of about 30' from the laser direction (in a reflecting geometry). The holder was located in a modified Cryo-Tip (Waltham, Massachusetts) refrigerator operating down to 20 K. To reduce laser heating on sample surface, a flow of prerefrigerated helium gas was admitted into the sample chamber. The sample-holder temperature was monitored with a platinum resistor placed inside the copper block while actual sample temperature was evaluated from the intensity ratio between Stokes and anti-Stokes Raman lines.
La'ttice parameters for powdered ACN have been measured by a conventional vertical Philips (Eindhoven, The Netherlands) x-ray diffractometer equipped with a proportional counter, a copper target, and a nickel filter. The sample holder, consisting of a small copper plate with a cavity where the powdered sample was pressed, was supported by a cold tip. Fine alignment of the sample holder was performed by using the shadow of the x-ray beam scattered through this cavity, thus reaching an angular accuracy of +0.01'. Since 15 relevant reflections (in part overlapping) fall in the small range of 12' to 13', the computation of the lattice parameters gave a standard deviation of 0.005 A for a and 0.001 A for b and c, where a, b, and c are the lattice parameters. After several runs, a Inore realistic standard deviation has been estimated to be 0.012 A for a and 0.006 A for b and c.
To measure the specific heat of crystalline ACN

B. Specific heat
The specific heat of powdered crystalline ACN has been measured from liquid nitrogen to room temperature. A major change upon cooling appears in the amide I region where a new band at 1650 cm ' appears. All other bands of the spectrum above 300 cm ' show maximum shifts on the order of 5 -10 cm ', and at low temperature the width is generally decreased. In the low-frequency region below 200 cm ' where phonon modes dominate, there is a general shift toward higher frequencies on cooling and a sharpening of all bands.
A detailed temperature study of the amide I region is l.5-Results of three runs obtained with different heating powers W (in units of W) are reported in Table II. Data were fitted using the equation C~(T) =4.59X10 'T+1.505 (3.1) in units of Jg 'K ' where T is the temperature rneasured in 'C, to facilitate a comparison with similar data reported in the literature.
In Fig. 3 the value of the specific heat as a function of temperature is plotted.  7). Other amide bands are also shifted, in particular, the amide II at 1560 -1570 cm The band at 1650 cm ' is weak in the amorphous material at 87 K ( Fig. 8). Also, the crystal splitting displayed by many of the phenyl-ring frequencies is not present in the amorphous material, as can be seen for the modes at 1600, 1500, and 1420 cm '. The amide II band is at 1560 cm ' in the amorphous sample. After anneal-  cm ' increases on cooling without apparent change in frequency and shape. Instead, the amide I absorption at 1667 cm ' decreases in intensity, shifts to higher frequency, and becomes sharper. The peak intensities of the 1650-cm ' band as a function of temperature are reported in Table III.
Polarized ir spectra clearly show that the polarization direction of the band at 1667 cm ' and of the band at 1650 cm . ' are the same (Fig. 6). N' isotropic substitu- bod 'ng we present in Fig. 9 Fig.  13. The qualitative behavior is similar to that observed in the ir spectrum of the same band. The Raman spectrum for the low-frequency region from 180 to 20 cm ' for 300 and 50 K of temperature values is reported in Fig. 14. As a general observation, there is an increase of the peak frequencies upon cooling and a narrowing of the bands. tonic temperature dependence is displayed for C~(T) (Fig.   3) and for V(T} (Fig. 2). At high temperature, the specific heat of ACN increases linearly with temperature with a slope of 0.00459 J/g, to be compared with 0.00353 in o-chlorobenzoic acid (C7H5C102) and 0.003 57 in onitrobenzoic acid (C7H5NO4}, the two substances with seven carbon atoms where Cz(T) data have been reported. The volume expansion V(T) observed here for ACN is quite close to that reported for urea, a hydrogen-bonded o~3 . (where a is in the range 0.01 to 0.1 cm '/K), typical of anharmonic coupling, and the usual sharpening of bandwidths, which may exceed 20 cm ' at 300 K (for a single mode) and reduces to less than 2 cm ' at 35 K. Moreover, it is noteworthy that all spectral changes induced by temperature in low-frequency vibrations are continuous, confirming the absence of a crystal phase transition, at least in the range 35 -350 K, in agreement with x-ray diffraction and specific-heat results.

Internal phenyl modes
The phenyl ring, possessing 30 internal degrees of freedom, accounts for most of the vibrational features above 200 cm ' in the ir and Raman spectra of ACN. For band assignments we can use accurate vibrational analyses of the benzene ring, ' ' taking into account the following relevant effects: (i) the linkage with the acetamide group reduces the symmetry from D21, to C~, shifts vibrational frequencies (up to 50 cm ' or more), and allows ir and Raman vibrational modes which are strongly forbidden in the full D21, symmetry; (ii) the coupling between aromatic rings in the unit cell introduces a further splitting mechanisrn of intramolecular vibrations (Davydov splitting); and since the strongest interaction is expected for phenyl groups belonging to nearest molecules in different hydrogen-bonded chains, we expect at least a doubling of the phenyl-ring frequencies. These considerations can be applied, for instance, to CC stretching modes in the 1600cm ' region, which represent a main feature of both ir and Raman spectra. Vibrational bands in this region correspond to the e2s mode of the benzene molecule which appears at 1599 cm ' in the vapor-phase Raman spectrum. Symmetry lowering of phenyl group in ACN makes this mode active also in ir and splits the original vibrational frequency to about 1620 and 1605 cm '. Each component is further split by the crystal field and typical multiplets appear at low temperature separated by about 5 cm '. A tentative assignment of some phenyl-group fre-quencies (CC stretching modes, CH stretching and bending modes, breathing modes, etc.), has been performed and results are shown in Table IV. In all cases, a conclusive test for vibrational assignment has been the insensitivity of vibrational frequencies to isotopic substitutions in the amide moiety.
Temperature dependence of these bands is quite usual: frequency shifts between room temperature and 50 K are within 5 cm ' and bandwidths decrease on cooling by only a few wave numbers (phenyl bands are sharp also at room temperature). Only the doublets in the. Raman spectra (at 610 -615 cm ' and 1494 -1505 cm ') exhibit some changes (which are of uncertain origin) as temperature decreases.

Amide modes
Much effort has been devoted to characterization of vibration of the CONH group in model amides and peptides' ' and principal associated frequencies are usually classified as follows: (i) amide I, occurring in the range 1630 -1680 cm, which involves mainly CO stretching and displaces upon deuteration (COND); (ii) amide II, at about 1520 -1570 cm ', corresponding to coupling between NH bending and CN stretching vibrations, which shifts downward (&80 cm ') upon deuteration and is sensitive to N substitution; (iii) amide III, around 1300 cm ', containing a large percentage of NH bending and shifts on deuteration to 900 -1000 cm '; (iv) amide IV to amide VII, at frequencies below 800 cm ', corresponding to out-of-plane vibrations of the CONH group, sensitive to deuteration and strongly coupled to vibration of nearby groups; (v) amide A and amide 8, in the high-frequency region between 3000 and 3300 cm ', arising from a Fermi resonance between NH stretching and the amide I overtone and very sensitive to both H and N isotopic substitution. Following these criteria and comparing spectra with different isotopic substitution we made the assignment of amide frequencies in ir and Raman spectra of ACN as shown in Table V. As was previously reported, dramatic  between 16 rnolecules belonging to two nearby hydrogenbonded chains in three adjacent unit 'cells. A Ramanactive mode with As symmetry is found at a frequency 20. 1/x cm ' above a mode that is both Raman and ir active (where~is the effective value of the relative dielectric constant). Furthermore, we note that modes B&s, B2s, and 83g generate components a"~, a~, and a""respectively, ' in the polarizability tensor defined by temperature effects are observed in the amide I region, which will be analyzed in detail below. Temperature effects are much less relevant in other amide bands, for example, the amide II Raman band (Fig. 12), which is broad (half-width of about 15 cm '} an'd symmetrical at room temperature and becomes strongly asymmetrical at low temperature, shifting the peak about 15 cm ' upward but remaining quite broad.
C, Amide I region

Tentative assignments of amide I vibrations
At room temperature two principal vibrational frequencies appear in the amide I region: at about 1677 cm ' in the Rarnan spectrum and around 1665 cm ' in both Raman and ir spectra. From the low-temperature (10 K) ir spectrum in Fig. 5, it is evident that the 1665-cm band is composed of three vibations at 166S, 1662, and 1659 cm '. Since these measurements were made on microcrystalline powder, it is expected that the three ir-active modes (B3", Bz", and B~") will have intensities proportional to the components of the amide I transition dipole moment along the three crystal axes (a, b, and c or x, y, and z ? All of these tentative assignments must be confirmed by detailed measurements of polarized ir and Raman spectra, but it is clear that there is no conventional assignment available for the 1650-cm ' frequency. There are four conventional amide I Raman-active As already reported, the main change observed on cooling in the vibrational spectra of ACN crystalline samples is the growth of a new band at 16SO cm '. The integrated intensity of this band increases steadily with decreasing temperature from 350 to 4 K, without an appreciable change in peak frequency. Apart from this ternperature behavior, the 1650-cm ' band exhibits many similarities with the 1665-cm band, which is dominant at room temperature. In particular, we note the following similarities. (i) The two bands are active in both ir absorption and Raman scattering.
(ii) Polarized Raman experiments in oriented crystal samples (currently being conducted at Los Alamos) show the same polarization behavior for both bands.
(iii) On N' isotopic substitution the frequencies of the 1665and 1650-cm ' bands shift at 1661 and 1647 cm respectively. The parallel small shift in both vibrations of 3 -4 cm ' is in agreement with a small NH bending content and corresponds to the typical amide I mode shift reported in the literature.
(iv) On deuterium substitution of the amide proton, the frequencies of the 1665 and 1650-cm ' bands are both affected. To quantify this effect, a detailed spectral analysis is necessary, and an extensive study of the deuteration effect will be reported later.
3. Conventional interpretation of the 1650 crn t b-and 'i he presence and behavior of the 1650-cm ' band does not have a simple interpretation in terms of usual molecular or solid-state effects. To show this, we discuss some possible conventional explanations and the evidence against them.
(i) Despite the behavior on N' and deuterium substitution, the 1650-cm ' band cannot be considered an additional linear vibrational component of amide I because its polarization behavior is not distinct from that at the 1665-cm ' band, as is required by this hypothesis.
(ii} Another effect that might explain the unconventional band in a conventional manner is as follows. The 1650-cm frequency might be coincident with a peak in the density of states of amide I vibrations away from zero wave vector spectroscopically activated by the presence of low-temperature defects in the crystal structure. Similar mechanisms have been reported in some organic solids.
Although the presence of crystal defects cannot be completely ruled out in ACN, our crystallographic, calorimetric, and spectroscopic results at low frequency do not show the presence of a density of defects as large as required for relaxing wave-vector selection rules.
Moreover, the 1650-cm ' band exhibits the same behavior both after repeated temperature cycles and in samples prepared by different methods, and such repeatibility is unlikely to occur when crystal defects play a major role. In particular, it is noteworthy that the 1650-cm ' band appears in low-temperature ir spectra of amorphous ACN prepared by vacuum deposition of sublimated ACN (where many defects are expected) with an intensity much lower than in crystal samples, but its intensity can be fully recovered after annealing treatments which induce crystallization.
(iii) The 1650-cm ' band might also be explained by an intramolecular process (Fermi resonance) arising from anharmonic interaction between the 1665-cm ' mode and a combination mode of the same symmetry and nearly the same frequency. We note that since the 1665-cm ' mode is not totally symmetric, the interacting mode cannot be a first overtone which in D2t, symmetry is always totally symmetric. Because of the complexity of the vibrational spectrum of ACN, however, an accidental quasidegeneracy between two frequencies cannot be ruled out, but a strict correlation should be observed between the splitting of the two interacting modes and their ir intensities, In our case, the zero-order intensity of the amide I fundamental can be assumed much stronger than that of the combination mode. Thus, the following approximate relationship should hold at the fir'st perturbative order: I(1665)+I (1650) I(1665) -I(1650) (4.2) where b.v and hvo are first-order and zero-order separations of the two interacting modes and the I s are ir intensities. Since the intensity of the 1650-cm band strongly increases at low temperature, one should observe a corresponding increase of the frequency separation. This frequency separation remains nearly constant (within +2 cm ') so the occurrence of a Fermi resonance seems to be excluded.  Table VI. Actually Me-ACN cannot be compared to ACN either for the molecular configuration or for the crystal structure.
For instance, while in ACN the angle between the aromatic ring plane and the amide plane is about 18, in Me-ACN this angle is about 90. The C=IO distance in Me-ACN is 0.044 A longer than in ACN; no hydrogen-bond network is present in Me-ACN and the crystal cell is considerably smaller than in ACN. Moreover, x-ray diffrac-where p, D, and E are the transition moments, the density of states, and the energies of the two configurations, respectively If w. e assume pz --p~, Dtt --10D&, and (Eti E~)/k =3-60 K, Eq. (4.3) agrees reasonably well with the experimental result reported in Table III in the temperature range 300 to 100 K, but fails at lower temperature. In particular, at 20 K the predicted value for Iz /Iz is 2 orders of magnitude lower than the experimental one. This failure can be attributed to the presence of a potential wall which at low temperature strongly reduces the transition rate from B to A and thus, on the time scale experimentally accessible, freezes the system in nonequilibrium conditions. We can disregard this hypothesis following the results of the thermal cycles performed using widely different cooling rates.
Of course (4.3) can be used to fit the experimental results if we assume strongly temperature-dependent parameters, but there are no physical reasons for such temperature dependence of the process. In fact (see Fig. 2), the thermal expansion coefficient below 100 K is nearly zero. p-Cl-ACN is an interesting substance because the molecules are hydrogen bonded as in ACN, although only along single chains and not in double chains as in ACN. In p-Cl-ACN there are two such chains per unit cell, running parallel to the c axis, and the N 0 distance reported in the literature is lower than ACN. On the other hand, the ir spectrum of the NH stretching mode region (see Fig. 11), which is a very sensitive test for the hydrogen-bonding distance N. 0, does not show the broad red-shifted band of the strongly hydrogen-bonded systems.
Since the reported C=O distances in p-Cl-ACN and in ACN are quite close, one should expect a similar behavior for both substances in the amide I region.
This is indeed the case, as shown in Fig. 10 The first contribution (5.2a) represents the amide I excitation energy in the nth molecule, Eo being the energy of the uncoupled transition dipole, J being the strength of dipole-dipole interaction between nearest neighbors and B ", B"creation and annihilation operators, respectively, for the amide I excitation.
The second term (5.2b} represents the energy of the low-frequency vibrations that are responsible for selftrapping. As was noted in Ref. 2, we believe that these vibrations involve the hydrogen-bonding proton but here we avoid a suggestive notation. For analytic convenience we represent all of the low-frequency vibrations by a single classical harmonic oscillator along the coordinate q"(t) with frequency co and elastic constant W. A more detailed  E"i Ep X /2W . ---(5.14) The energy shift between a fully delocalized exciton (5.10) and a strongly localized soliton (5.14) is therefore = x' hE=E,"-E, ] ---2J . To check that this value is of acceptable order of magnitude, we assume X to be the value 6.2&(10 " N obtained from (3.2). This implies W=4. 8 N/m which is reasonable for a force constant related to hydrogen bonding.
At this point the reader might be tempted to raise the following objection to a soliton interpretation for the 1650-cm ' line in Fig. 5. A soliton is generally considered to be a long-lived phenomenon, yet the width of the 1650-cm ' line is of the same order of magnitude as that of the conventional 1665-cm ' line. Thus the lifetime should be about the same for both excitations.
To answer this objection we note that the above analysis has, for clarity of presentation, neglected interaction of localized amide I vibrational energy with acoustic phonons which was the basis for Davydov where b is the distance between molecules and A, is the wavelength of incident radiation. Since the number of ir-active excitons per unit distance in the beam direction is b /1, times the corresponding number of amide I vibrations, the total absorption from a beam is the same whether one considers it to be caused by excitons or by individual amide I bands. Therefore the intensity of the soliton line relative to that of the exciton line should depend primarily on the inner product of the ground-state wave function for the low-frequency vibration before soliton absorption to that after absorption. Thus we return to (5.5b) and note that before soliton absorption, the ground state of the low-frequency vibration 1s ACETANILIDE DAVYDOV-LIKE SOLITONS IÑ~~ (   6 2 Table III. VII. CONCLUSIONS From the above discussion we draw the following conclusions. (i) The unconventional amide I absorption described in Sec. III is a well-established experimental fact.
(ii) As discussed in Sec. IV, conventional concepts in molecular spectroscopy offer no acceptable explanation for the unconventional amide I band.
(iii) The soliton hypothesis sketched in Secs. V and VI provides a straightforward explanation for both the red shift and the intensity of the 1650-cm ' band.
Thus we suggest that the soliton described here is a new member of the growing family of self-trapped states that have been detected in condensed matter and the first example in an organic solid which is a suitable model for proteins. Perhaps the most important finding of our work is that a soliton on a network of hydrogen-bonded amides can be created by infrared light. Although we are aware of the biological relevance of a light-sensitive soliton, we choose not to discuss those aspects in this paper because they are more appropriate for biochemical journals.