J. Phys. Chem. B 2010, 114, 11703–11708
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Prediction of Vibrational Spectra of PolysaccharidessSimulated IR Spectrum of Cellulose Based on Density Functional Theory (DFT) Søren Barsberg* Faculty of Life Sciences, UniVersity of Copenhagen, RolighedsVej 23, DK-1958 Frederiksberg C, Denmark
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ReceiVed: May 9, 2010; ReVised Manuscript ReceiVed: July 28, 2010
The continuing developments of electronic structure methods may provide insight into the vibrational spectroscopy of polysachharides, which was not accessible to older works on this subject. The present work shows for the first time how main features of cellulose infrared spectra can be predicted and assigned using simple single chain models of cellulose combined with density functional theory prediction of their vibrational properties. The results provide a more informed basis for assigning cellulose IR bands and may resolve some of the challenges associated with the molecular origin of “marker” bands, which are commonly used to measure properties such as crystallinity or crystalline forms. The theoretical approach can be seen as a first-order approximation, which can be further improved. Introduction Vibrational spectroscopy of polysaccharides provides basic knowledge on their structure, properties, and interactions with the environment. Among the polysaccharides, cellulose accounts for most of the biomass in the plant kingdom. The ultrastructure of its crystalline forms is a highly complex subject. Here, we point out its main features with emphasis on natural cellulose I. For more details, the reader can consult several reviews on the subject and the references contained herein.1-3 The polyglucan chains, which make up cellulose, are synthesized in parallel at the cell surface and associate noncovalently to form microfibrils. Their transverse dimension varies depending on the source from 2-3 nm up to 20 nm in algal and tunicate samples, whereas the longitudinal dimension is much larger. Cellulose I is thus a semicrystalline arrangement of parallel polyglucan chains and is (from a crystallographic viewpoint) practically of infinite dimension only in the chain direction. In addition, various treatments are capable of modifying this arrangement and lead to the polymorphs cellulose II, III, and IV, which differ in characteristics such as chain directions (e.g., antiparallel for cellulose II) and/or arrangement within the unit cell. Cellulose I occurs in two different crystal forms (allomorphs) IR and Iβ both assembled from parallel chains in flat-ribbon conformation with alternating glycosyl units locked in opposite orientation by two intramolecular hydrogen bonds. One of these is enabled by the rotational tg position of the hydroxymethyl group (O6C6 relative to O5C5 and C4C5), which brings the O6 in close proximity to O2 of the neighboring residue. The chains are held together edge to edge in flat sheets by intermolecular hydrogen bonds. The IR and Iβ forms differ in the way chains are organized and here mainly in the stacking and relatively weak bonding of chain sheets to form the microfibrils. This leads to a triclinic single chain unit cell for IR, whereas Iβ forms a monoclinic unit cell of two crystallographic independent center and origin chains. The IR form can be converted to the thermodynamically more stable Iβ form by thermal activation or (in principle) by shear forces. For each * Phone: +45 35 33 15 00. Fax: +45 35 33 15 08. E-mail: sbar@ life.ku.dk.
of these three types of chain sheets (IR, Iβ center, and Iβ origin), the hydroxyl rotational positions can be described in terms of two different hydrogen bonding networks, which both organize the sheet. Thus, the sheets which stack to form cellulose I can be organized in either of these six (three by two) “sub-forms” based on qualitatively the same single-chain heavy atom organization. Thus, for cellulose, IR spectroscopy can provide information on the ratio of IR/Iβ forms,4-6 degree of crystallinity,7 molecular orientation in plant cells,8,9 and interactions with water.10,11 For native cellulose, present day interpretation of IR spectroscopy results are largely based on older works on the assignments of its vibrational bands.12-16 These works could not take advantage of more recent developments of basic electronic structure methods and their implementation by ever growing computational resources. A more recent work is notable in its thorough attempt to assign cellulose IR bands from the perturbations induced by EM field polarization, H/D exchange, and controlled heating.17 Still, the capabilities of electronic structure methods to provide valuable complementary information have to the best of the author’s knowledge not been explored within this field. The present work demonstrates for cellulose I how the vibrations of polysaccharide crystals can be predicted and assigned from density functional theory (DFT) calculations. Cellulose IR bands are predicted from single chain models of finite degree of polymerization (DP) of the pyranose unit. These simple models do in principle not distinguish between the IR and Iβ forms, which would require several chains in crystal models, but do reflect the distinction in terms of hydrogen bond networks. Thus, the single chain cellulose I models adopt two possible orientational states of the hydroxyl groups, which are truncated representations (as intermolecular bonds are not modeled) of the corresponding hydrogen bond networks. It will be shown that such single chain models capture the essential features of the cellulose IR spectrum and provide valuable information on the nature of corresponding vibrations (normal modes). A refined description, which is not explicitly considered in the present work, would obtain the IR or Iβ spectra by considering at an appropriate lower level of theory how the single chain spectrum is perturbed by intermolecular couplings, i.e., mainly Via hydrogen bonding, to neighboring chains within
10.1021/jp104213z 2010 American Chemical Society Published on Web 08/20/2010
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J. Phys. Chem. B, Vol. 114, No. 36, 2010
a chain sheet or full crystal model. In order to model single chain based cellulose IR bands, the well documented B3LYP functional and a relatively small basis set was chosen (details are found below). A critical point is how the vibrations of cellulose itself, consisting of orderly arranged molecular chains of DP ∼ 103-104, can be modeled by DFT which in present day implementations usually handle at most ∼102 atoms (or DP ∼ 5-10 depending mainly on basis set and hardware). Thus, a method to approximate the vibrations of a DP > 103 system from DP < 101 systems is needed. Such a method must at least address the covalent intrachain interactions which are relatively strong and essential for predicting the vibrations as compared to the weaker noncovalent interchain interactions. In the present work, interchain interactions and chain arrangements in the crystallographic unit cell are, as explained above, not explicitly considered. Since this work focuses on proof of principle rather than an exhaustive assignment work, we limit the considerations to the 1500-600 cm-1 “fingerprint” interval. It will be shown that such single chain modeling captures most of the features of the cellulose IR spectrum in this interval. Rather than studying simulated spectra of limited DP ) 2, 3, etc., model systems, which all contain significant contributions from vibrations located at or near the ends of the models, the method focuses on the differences or increments of one simulated spectrum for a model with DP ) n to the next obtained for a model with DP ) n + 1. Thus, for n ) 4, the incremental spectrum, which is a simple subtraction of the spectrum of the n ) 4 model from that of the n ) 5 model, effectively displays the vibrations pertaining to the middle residue in the DP ) 5 model structure as the contributions from the penultimate and terminal residues are minimized (subtracted). It is shown that for several simulated bands displayed in the incremental spectra a practical convergence of position and IR band strength is obtained for the limited size (DP) models used. Such converged or extrapolated simulated spectral features are representative of DP ∼ ∞ cellulose within the premises and limitations of the oVerall model. The results show that this procedure is a reasonable, firstorder approximation. Its usefulness is exemplified by showing how cellulose IR, Iβ and crystallinity “marker” bands can be qualitatively related to the nature of corresponding predicted vibrations. It is also found that not all vibrational modes lend themselves to simple interpretation. Methods Microcrystalline cellulose (from Merck), which is derived from wood sources and mainly consists of the Iβ form, was used as cellulose reference material. A cellulose spectrum was obtained as the average of three spectra (100 scans, 4 cm-1) obtained using a dry air purged Nicolet 6700 FT-IR spectrometer equipped with an ATR (Golden Gate) unit maintained at T ) 30 °C. Dispersion effects were corrected for by the spectrometer software using cellulose refractive index n ) 1.46 obtained by (exponential decay) extrapolation of n(λ) to the mid-IR range.18 This corrects both for the wavelength dependence of penetration depth and for dispersion induced shifts of band positions. The Gaussian 03W (Rev. D.01) and Gaussview 3.0 software were used for the calculation of vibrational properties and displaying the vibrational nature of normal modes, respectively.19 All DFT calculations employed the default (75, 302) grid, and tight geometry convergence criteria (
