Fine structure of the amide i band in acetanilide

,


INTRODUCTION
Recently there has been much experimental'   and theoretical interest in crystalline acetanilide (ACN), a model system for proteins, with emphasis on the temperature-dependent ir absorption band at 1650 cm This is a rather narrow band, detached from the general amide I vibrational excitation, and it has been identi6ed as a highly trapped soliton state ' in the Davydov model or as a vibronic analog of a small Holstein polaron.'   The more recent theoretical work suggests that the shift 6 of this polaron frequency from the unperturbed amide I mode is due to coupling with both acoustic and optical longitudinally polarized lattice modes.Moreover, acous- tic coupling is found to contribute to about half of the to- tal observed shift (b =15 cm ') and to dominate the temperature dependence of the absorption strength of the polaron peak.This last theoretical result prompted us to look at the fine structure of the unpolarized absorption spectrum in the amide I region, where the absorption proNe shows the presence of temperature-dependent unresolved bands in the shoulder of the 1650 cm ' peak (see Fig. 5 of Ref. 2, reprinted as Fig. 2 in Ref. 7).

MATKRIAI. S AND METHODS
Acetanilide, from Sigma Chemicals (St.Louis), was dis- solved in reagent-grade ethanol, filtered, and recrystallized.The crystals were then zone re6ned in a homemade oven.Two methods were exnployed for obtaining single crystals suitable for ir absorption experiments.A small amount of the zone-re6ned powder was sealed under 0.8 bar of CO& gas in a glass envelope which had a square cross section.The glass envelope was placed on one side on a hot plate set.at 80'C.The powder sublimated and condensed on the top cold face, and long needles and Sakes of ACN crystals were formed.The glass envelope was then carefully opened and the Sakes, of about 0.5)&0.5 cm, were removed and mounted in a holder made of aluminum foil.The crystal holder was clamped to a cell made from oxygen-free high-conductivity copper mounted on a closed-cycle helium refrigerator (Lake Shore Cryotonics, Inc. , Columbus, Ohio) equipped with calcium fluoride windows.
Single crystals were also grown by melting some ACN powder between two pressed Istran II or CaF2 windows.Upon cooling, the material crystallized into several wedge-shaped single crystal 6ngers.The larger single crystal was selected by masking the rest of the material.Abbott and Elliott have shown that this procedure results in crystals preferentially grown along the c axis.Crystals obtained with this procedure were generally thinner than the crystal Aakes, and they were more suitable for the study of the a- direction polarization.Instead, the absorption in the b direction was very weak.Partially deuterated samples were prepared by dissolving ACN in deuterated methyl alcohol and then recrystallized.The amount of water ab- sorbed from the air during the crystallization process was generally sufficient to obtain a low H/D ratio.The deu- terium content was estimated from the ratio of the N-0 to the N-H stretching-band integrated absorption.
A Mattson 5000 (Cleveland, Ohio) Fourier transform infrared spectrometer equipped with a Perkin Elmer gold-grid polarizer was used for the measurement of the polarized spectra.At least 1000 scans at a resolution of 1.0 cm were collected for each polarization direction.
The polarizer was then turned 10 and a new spectrum was collected.The intensity of the bands were plotted versus the polarizer angle to determine the direction of the crystal axes with respect to the polarizer vertical.

FITTING PRGCEDURK
In the spectral region from 1630 to 1680 cm ', four I orentzian bands were fitted to the measured ir spee- Qc1988 The American Physical Society TABLE I. Four-band decomposition using a sum of Lorentzians.the center (cm '), and 8'the FWHM (cm ').(n -U -1) Analysis of the amide I bands using Lorentzian components An analysis of the 1665-and 1650-cm ' bands in terms of superposition of Lorentzian components was per- formed on the same set of data already reported in Fig. 5 of Ref. 2. Ai least two components were necessary to de- scribe the shape of the 1650-cm ' baod in the entire tem- where j (1 -50) corresponds to the number of data points used, U is the number of free parameters, the index i (1-4) corresponds to the four difFerent Lorentzians, v is the fre- quency in wave numbers, and the D 's and o J are the di- gitized values of the spectrum and the error at each wave number in the region 1630-1680 cm '.To start the fitting routine, the initial values of the four center fre- quencies and the width of the bands were fixed at the values obtained by inspection of the low-temperature spectrum.Then the amplitudes only were fitted.Once a good fit for the amplitude was obtained, the band's center, amplitude, and width were simultaneously fitted.
For temperatures higher than 70 K the width of the four bands was assumed to be the same in order to reduce the number of independent parameters.The effective num- ber of parameters was 9 at each temperature.The values of the X were close to 1, except at 20 K, where the X was about 2 due to the presence of a small band near 1656 cm ' not included in the 5it.perature range investigated.
The decomposition of the band centered at 1665 cm ' required also at least two components, but at low temperature the deviation from the recovered shape using two components was quite high, and probably three components must be used (from Fig. 5 of Ref. 2 three components can be distinguished in the region 1655-1667 cm ').The result of the analysis at several different temperatures [center, amplitude, and full width at half maximum (FWHM) of each of the com- ponents] is reported in Table I.The position of the center of the bands did not change with temperature, whereas the width and intensity were temperature depen- dent.In calculating the area of the bands (Table II), as the product of the FWHM times the amplitude, we first recognized that the total integrated intensity, i.e. , the sum of the areas of the four component bands, remained fairly constant in the temperature range from 20 to 300 K.The integrated intensity of the two Lorentzian com- ponents in which we decomposed each band had diferent temperature behavior.The component bands at 1665 cm ' and at 1645 cm ' had similar, but complementary temperature behavior and the total area change due to the sum of these two bands was about 10% of the total area over all the temperature range.Instead, the in- tegrated intensity of the two components bands at 1661 and 1650 cm ' had complementary behavior.The sum of their integrated intensity was constant in the tempera- ture range from 300 to 20 K, but each of them had a strong temperature dependence (Fig. 1).The integrated intensity of each of these two subbands changed about fivefold from 20 to 300 K.

Partially deuterated samples
As we earlier reported, fully deuterated samples display a difkrent behavior with respect to the unusual temperature dependence of the polaron (or soliton) band at 1650 cm '.In the experiments reported here, we  1.Temperature behavior of the integrated intensity of the 1650-(O ) and 1662-cm ' () bands and the sum (scale g -, ' )   of the integrated intensities of the two bands ( X ).
prepared partially deuterated samples in which the ratio D/H was about 90%.Upon cooling, some spectral features characteristic of the undeuterated sample appeared in the amide i region.In the partially deuterated sample, we were able to distinguish four small bands at 1667, 1662, 1650, and 1645 cm ' (Fig. 2), in exact correspondence with the position of the components bands obtained by decomposing the spectrum of the non- deuterated polycrystalline sample using four Lorentzians.
Polarized ir spectra of single crystal of ACN To further investigate the origin of the component bands in the amide I region, we performed a series of ir absorption experiments using polarized light with the aim of detecting whether there was a different polarization direction of the component bands.The polarization ex- periments have shown that there was a strong depen- dence of the band intensity upon the polarization direction, but we were unable to assign uniquely a different po- larization direction to the component bands.Due to the sample preparation technique employed, only one crystal orientation was investigated, while in the microcrystalline samples used for the band analysis in terms of Lorentzian components, presumably all the crystal orientations were equally represented.
To determine the crystal orientation, we followed the Abbott and Elliott argument.
A band at 1570 cm ', as- signed to the C -N vibration mode, has a transition- moment direction along the b axis of the crystal.This band is 100% polarized in our samples, indicating that the crystal orientation has the c axis parallel to the direc- tion of the incident radiation and the b axis at 0 with respect to the vertical direction of the polarizer.
The ir spectrum in the 1000-1800 cm ' region for po- larization direction along the a axis and b axis is dÃerent.In the a direction, which roughly corresponds to the alignment along the hydrogen-bonded chain, all the ab- I 1650 WAVE NUMBER (cm ')   FIG.
2. ir spectra of powder sample of partially deuterated ACN in the temperature range from 10 to 300 K. sorption bands associated with amide vibrations have a large intensity.In contrast, the spectrum in the b direc- tion shows weak absorption bands for the amide modes.The same characteristic features were observed in several diferent samples of different thickness and size.
Inspection of the amide i region from 1600 to 1700 cm ' (see Fig. 3) shows the characteristic absorptions of the amide I in ACN at 1665 and 1650 cm '.These bands are well resolved in the b direction.In the a direction, broader bands are observed centered at around 1665 and 1650 cm ' with FWHM on the order of 3 cm ' at 60 K.
In the b direction a small red shift of about 1 cm ' was   observed with respect to the a direction for the band at was much larger than in the b direction" in agreement with the room temperature experiments of Abbott and Elliot t. 8   In our previous work, we tentatively assigned the component bands at 1665, 1662, and 1659 cm ' (partially resolved in the low-temperature spectrum of Fig. 5 of Ref. 2) to the ir-active modes Bi",8,", and Bs", respec- tively.These modes should be polarized along the crystal's a, b, and c directions, respectively.%'e already cautioned that this assignment was not supported by calculations based on dipole-dipole interactions.'o The po- larization experiments reported here further point out the inadequacy of this explanation.The decomposition of the amide I region into four Lorentzian bands may be questionable.
However, the low-temperature spectrum clearly shows a peak at 1667 cm ' and two shoulders at 1662 and 1660 cm '.In this spectral region we used only two components.At high temperature, the bands are not resolved, and we arbitrarily impose, as a starting point for the fitting procedure, the existence of two bands of Lorentzian shape with the same center position as determined from the low-temperature spectrum.The fitting program then adjusted the position of the bands to give the best fit.In the region from 1650 to 1645 cm the low-temperature spectrum shows only one band which is clearly nonsymmetric.
The use of a symmetric Lorentzian shape forced the fitting algorithm to include a band at 1645 cm ' to account for the nonsymmetry of the spectral shape.However, due to the small contribu- tion of this band (less than 10%) to the total intensity and due to the small temperature variation, we have not in- cluded this band in the discussion.On the basis of our band decomposition and single-crystal polarized spectra, we observe that the temperature dependence of the in- tegrated area of the band at 1666 cm ' shows a change between 300 and 100 K, but then levels o8' at lower tern- perature, while the band at 1661 cm ' shows a much larger and continuous decrease of the integrated intensity as the temperature is lowered (Fig. 1).According to the present proposed explanation for the origin of the 1650- cm ' band, the intensity of these two subbands should have the same temperature dependence.
The band analysis shows that this is not the case and a modification of the proposed model must be introduced for the under- standing of the behavior of the ACN ir spectrum in the amide I region.One possibility that can qualitatively account for the existence of subbands is the existence of a double well structure, which arises from the nonplanarity of the amide group.Two equivalent positions for the N -H bond, corresponding to a deviation of about 0.1 rad from the planar geometry of the amide group, have been proposed by Fillaux and deLoze" to explain the fine structure of the soft-mode region shown in the Raman spectrum of X-methylacetamide.The asymmetry due to the double well potential could be the origin for the non- linear coupling between the C=O vibration and the N -H bending, which was proposed to explain the amide I anomalous behavior.A Raman doublet at approximate- ly 120 cm ' was identified in the low-temperature spec- trum of X-methylacetamide and assigned to the torsional mode along the C -N bond.Recently Fillaux suggest- ed' that the nonharmonic potential in which the N -H proton is moving is responsible for the formation of the soliton at 1650 cm ', following Scott's argument.As a matter of fact, disregarding the weak and temperature-dependent 1645-cm ' band, one could sup- pose that the normal amide I band in ACN is split into two components with absorption at 1662 and 1666 cm because of this double well." This splitting can arise be- cause of tunneling between the two wells, and only the component at 1662 cm ' gives rise to the anomalous band at 1650 cm '.This interpretation is based on the sum law shown in Fig. 3 for the 1650-and 1661-cm bands.
As a second possibility to account for the fine structure of the amide I bands in ACN, one can postulate that the band at 1650 cm ' is due to a soliton which is stable at high temperature (an excited polaron state in the phonon Seld, visually a deformation of the trapped charge cloud).Then, still disregarding the weak band at 1645 cm ', the observed nearly constant intensity of the sum of the band at 1650 and 1662 cm ' could arise from the competition of the two soliton energy levels during the ir absorption.This model requires a treatment of the temperature dependence of the soliton band(s) diff'erent from the one initially proposed by Scott et aI.
FIG. 1. Temperature behavior of the integrated intensity of FIG.3.Polarized ir spectra of a single crystal of ACN in the amide I region at 10 K. a, direction of polarization; b, direction of polarization.The e axis was parallel to the radiation beam.

TABLE II .
Integrated intensities of the component bands.