Letter pubs.acs.org/JPCL
Quantum Mechanical Calculations of Vibrational Sum-FrequencyGeneration (SFG) Spectra of Cellulose: Dependence of the CH and OH Peak Intensity on the Polarity of Cellulose Chains within the SFG Coherence Domain Christopher M. Lee,†,§ Xing Chen,‡,§ Philip A. Weiss,‡ Lasse Jensen,*,‡ and Seong H. Kim*,† †
Department of Chemical Engineering and Materials Research Institute, and ‡Department of Chemistry, The Pennsylvania State University, State College, Pennsylvania 16802, United States S Supporting Information *
ABSTRACT: Vibrational sum-frequency-generation (SFG) spectroscopy is capable of selectively detecting crystalline biopolymers interspersed in amorphous polymer matrices. However, the spectral interpretation is difficult due to the lack of knowledge on how spatial arrangements of crystalline segments influence SFG spectra features. Here we report time-dependent density functional theory (TD-DFT) calculations of cellulose crystallites in intimate contact with two different polarities: parallel versus antiparallel. TD-DFT calculations reveal that the CH/OH intensity ratio is very sensitive to the polarity of the crystallite packing. Theoretical calculations of hyperpolarizability tensors (βabc) clearly show the dependence of SFG intensities on the polarity of crystallite packing within the SFG coherence length, which provides the basis for interpretation of the empirically observed SFG features of native cellulose in biological systems.
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TD-DFT calculations were carried out using the NWChem package with the B3LYP functional and 6-311G basis set.10 The computational details are described in the Supporting Information, and only brief descriptions are provided here. In our previous DFT study, the cellulose crystal structures were simulated with periodic boundary conditions and a plane wave basis set, giving vibrational frequencies comparable with the experimental data.11,12 However, simulations of spectral intensities are needed for more detailed comparison with the experimental spectra, but could not be done with DFT. Thus, we used TD-DFT to simulate the SFG intensities in this work. Here the cellulose crystal structure was modeled with truncated dimeric units to facilitate TD-DFT calculations using Gaussian basis sets and hybrid density functionals. The cellulose chains in a single crystalline domain were represented with four glucose dimers (Figure 1a,c) with the initial positions of H, C, and O atoms corresponding to the experimentally determined unit cells of cellulose Iβ and Iα.8,9 Both ends of the glucose dimers (O1 and C4) were terminated with hydrogen atoms. During the energy minimization of the model structure, only H atoms covalently bonded to the C and O atoms were allowed to relax, while the chain backbones containing C and O atoms were held fixed at the experimentally determined positions. This prevented the displacement of the C and O lattice atoms from the experimentally determined
ibrational sum frequency generation (SFG) spectroscopy is well-known for the superior selectivity and sensitivity in detection of molecular species at two-dimensional (2D) interfaces.1 SFG is a second-order nonlinear optical process which requires noncentrosymmetry in the medium. The surface sensitivity originates from the inherent noncentrosymmetry of the interface breaking the randomness or inversion symmetry of two bulk phases. The same principle can be employed for the selective detection of noncentrosymmetric crystalline domains interspersed in amorphous matrices. This noncentrosymmetryspecific detection capability of SFG has been demonstrated for crystalline biological polymers such as cellulose,2 amylose,3 chitin,4 and collagen.5 However, compared to the 2D interfacial applications of SFG, which have been studied extensively, the spectral interpretation in SFG analyses of 3D crystalline domains has not been well established. One of the challenges for SFG study of biological polymers in bulk samples is the lack of good single crystalline samples to use as a reference to generate the data set needed for structural interpretation of the SFG responses of crystalline segments dispersed in amorphous matrices. In such situations, theoretical calculations of spectral features for given molecular structures and orientations could be helpful.6,7 In this study, we conducted time-dependent density functional theory (TD-DFT) calculations to attain a theoretical understanding of the relative SFG intensities of alkyl and hydroxyl stretching modes of cellulose crystals for which the unit cell parameters are available.8,9 Especially, the effect of crystallite polarityparallel versus antiparallelwas studied. © XXXX American Chemical Society
Received: November 9, 2016 Accepted: December 8, 2016 Published: December 8, 2016 55
DOI: 10.1021/acs.jpclett.6b02624 J. Phys. Chem. Lett. 2017, 8, 55−60
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The Journal of Physical Chemistry Letters where
∂αab ∂Q q
and
∂ μc ∂Q q
are the derivatives of polarizability and
dipole with respect to the normal mode, respectively; ωSFG, ωVIS, and ωIR are frequencies of SFG signal, visible input, and IR input beams; Γq is the damping associated with the lifetime of vibrational transition, which was fixed to 10 cm−1 in this work. In order to produce the second-order susceptibility tensor (χ(2) XYZ), the βabc was transformed from the molecular frame (a, b, c) into the laboratory coordinates (X, Y, Z): (2) χXYZ = N ∑ ⟨RXaRYbRZc⟩βabc abc
(2)
where N is the number density of the SFG active moieties, and ⟨RXaRYbRZc⟩ is the Euler transform matrix. In the model shown in Figure 1, the cellulose chain axes are within the laser incidence (XZ) plane. In the absence of preferential packing, all crystallites rotated arbitrarily about the chain axis are equally probable. Therefore, theoretical SFG intensities were calculated by averaging the product of complex conjugates of effective second-order susceptibility for multiple domains generated by rotating the truncated models shown in Figure 1 along the X-axis with a 1° interval from 0° to 360°: (2) 2 I ∝ |χeff | ∝
positions during the energy minimization. In our previous work, such constraints were shown to improve the accuracy in vibrational peak position calculations.11 Two sets of these truncated crystallites were stacked along the a-axis direction, and the chain direction (C4−C1) aligns with the c-axis. To simulate the antiparallel packing, the bottom crystallite was rotated around the Z axis by 180° with respect to the top crystallite. Figures 1b and 1d represent the parallel and antiparallel packing of cellulose Iβ and Iα crystallites, respectively, within the SFG coherence domain. For the energy-minimized geometry, the stretch modes of the C−H and O−H groups and their frequencies (ωq) were calculated. The polarizability and dipole derivatives with respect to the mass-weighted normal mode coordinates were obtained using three-point numerical differentiation.13 Under the Placzek approximation ignoring vibronic resonances,14 the hyperpolarizability is written as βabc (ωSFG , ω VIS , ωIR ) ⎞ ∂αab ∂μc ⎛ 1 ⎜⎜ ⎟ 2ωq ∂Q q ∂Q q ⎝ ωIR − ωq + Γq ⎟⎠
∑ −ℏ q
360 ° (2) χ (2) * ∑ χXYZ (i) XYZ(i) i
(3)
where M is the total number of domains counted in the simulations. Figure 2 shows the simulated SFG spectra for parallel- and antiparallel-packed crystallites of cellulose Iβ and Iα at ssp, ppp, and psp polarization combinations (the three-letter notation represents the polarizations of three beams in the order of SFG, visible, and IR). The ssp and ppp combinations are sensitive to achiral modes, and the psp combination is sensitive to chiral modes. The vibrational peaks of the artificially introduced OH and CH2 groups at both ends of the dimer (O1 and C4) were manually removed. The free OH groups at the (110) and (11̅0) surfaces of the crystallites were also removed. So, only the OH groups highlighted in yellow in Figure 1a,c are included in the simulation result. It should be noted that the vibrational modes of cellulose are delocalized throughout the entire crystallites;11,12 in other words, they involve stretching motions of many C−H or O−H groups in the crystallites (see Figures S1 and S2 in the Supporting Information). Due to this coupling, the contributions from vibrational modes of the C−H groups at the (200) surface could not be removed manually. Regardless of the polymorphic structure (Iβ and Iα) or the polarization combinations (ssp, ppp, and psp), the simulated spectra in Figure 2 show that the OH SFG peaks are about 10 times stronger than the CH SFG peaks in the parallel packing, while they are smaller than the CH peaks in the antiparallel packing. The overall SFG intensities of the CH stretch modes are relatively insensitive to the crystallite polarity. The polarity dependence originates from the relative strength of the secondorder susceptibility tensor (χ(2) ijk ) contributing to the specific polarization combination of the probe beams. Based on the structure depicted in Figure 1, the ssp spectrum probes the (2) combination of χ(2) YYX and χYYZ terms, while the ppp spectrum (2) (2) (2) (2) measures the contributions from χ(2) XXX, χXXZ, χXZX, χXZZ, χZXX, (2) (2) (2) (2) χZXZ, χZZX, and χZZZ terms. For the psp combination, χXYX, χ(2) XYZ, (2) χ(2) ZYX, and χZYZ components are involved. Figure 3 compares how the magnitudes of these 14 components of χ(2) ijk for the selected C−H and O−H peaks vary with the polarity for one
Figure 1. Computational models of (a,b) cellulose Iβ and (c,d) cellulose Iα. Panels a and c show the top view of single crystalline domains, whereas b and d show the side-view of two domains stacked with the parallel and antiparallel polarity for each allomorph. In (b), the (200), (110), and (11̅0) surfaces of cellulose Iβ are marked. In the laboratory frame, the laser incident plane lies in the XZ plane. So, the p-polarization has electric fields in the X and Z directions, while the spolarization has an electric field in the Y direction, which is parallel to the b-axis.
=
1 M
(1) 56
DOI: 10.1021/acs.jpclett.6b02624 J. Phys. Chem. Lett. 2017, 8, 55−60
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Figure 2. Simulated SFG spectra of uniaxially aligned cellulose Iβ (a−f) and cellulose Iα (g−l) at ssp, ppp, and psp polarization combinations. The spectra in panels a−c and g−i are for parallel packing of two crystallites, and those in panels d−f and j−l are for antiparallel packing of two identical crystallites. Note the scale difference between the parallel-packed spectra and the antiparallel-packed spectra. The C−H and O−H normal modes are presented with blue and red, respectively. In the unit of the SFG intensity, e, a, and Eh are electron charge, Bohr radius, and Hartree energy, respectively. (2) (2) (2) (2) (2) (2) Similarly, the χ(2) YYX, χXXX, χXZZ, χZXZ, χZZX, χXYX, and χZYZ terms of the CH modes have nonzero values in the parallel packing and become zero in the antiparallel packing. However, unlike the OH modes, the magnitudes of the dominant CH terms do not change. So, the net change in the CH SFG intensity upon switching the crystallite polarity is insignificant. Overall, the TD-DFT calculations show that the SFG spectra of cellulose are governed by the χ(2) ijk terms containing X (2) components (along the chain axis; for example, χ(2) YYX in ssp, χXXX (2) in ppp, and χXYX in psp) in the parallel packing of crystallites and those containing Z components (perpendicular to the (200) (2) (2) plane; χ(2) YYZ in ssp, χZZZ in ppp, and χXYZ in psp) in the antiparallel packing of crystallites. The magnitudes of the dominant χ(2) ijk terms in each polarization are plotted in Figures S3−S4 in the Supporting Information. The magnitude and directionality of the derivatives of polarizability and dipole for the selected C−H and O−H normal modes are shown in Figures S5−S7 in the Supporting Information. These data show
specific orientation where the (200) plane of cellulose crystallite is in the XY plane, and its chain axis is along the X direction. Numerical values are presented in Tables S1−S4 in the Supporting Information. (2) (2) In both allomorphs (Iβ and Iα), the χ(2) YYX, χXXX, and χXYX terms are dominant in the ssp, ppp, and psp spectra of the OH modes, respectively, when all cellulose chains are parallel. Contributions from other terms are minor compared to these three terms. When one crystallite is rotated around the Z axis by 180° (X → −X, Y → −Y, and Z → Z) to make the overall polarity of cellulose chains antiparallel, the χ(2) ijk terms containing the odd number of X and Y components in ssp, ppp, and psp become zero due to the symmetry cancellation. For example, (2) (2) (2) (2) the χ(2) YYX term in ssp, the χXXX, χXZZ, χZXZ, and χZZX terms in ppp, (2) (2) as well as the χXYX and χZYZ terms in psp are zero. By contrast, the magnitudes of other χ(2) ijk terms do not change upon switching from parallel to antiparallel packing. 57
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Figure 3. Second-order susceptibility tensors of the 14 selected normal modes of contributing to the ssp, ppp, and psp polarization SFG spectra of cellulose Iβ (a,b) and cellulose Iα (c,d) with the (200) plane in the XY plane. The magnitude is given in the atomic unit, e3a3o /E2h, where e, a, and Eh are electron charge, Bohr radius, and Hartree energy, respectively. The color code for the C−H and O−H normal modes are in blue and red, respectively.
Figure 4. Experimental SFG spectra collected with the ssp polarization combination for (a) uniaxially and randomly packed cellulose Iβ crystallites (isolated from the tunicate), (b) cross-lamellar packing of cellulose Iβ (native tunic of Halocynthia) and randomly packed cellulose II (produced by NaOH treatment of Avicel), and (c) randomly packed cellulose Iα (pellicle of Gluconacetobacter; contains about 80% Iα and 20% Iβ) and randomly packed cellulose II (produced by NaOH treatment of the same sample). The spectra shown in panels a, b, and c are reproduced from refs 15, 2, and 24, respectively.
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measuring piezoelectric responses of woody tissues as well as engineered samples containing cellulose crystallites.17−22 However, without careful control and precise characterization of the polar assembly of cellulose crystallites, the measured piezoelectric coefficient cannot be interpreted meaningfully. The reason for the suppression of the OH signal upon antiparallel packing of cellulose crystallites (Figures 2 and 3) can also be applied to explain the difference in OH SFG intensities between the naturally produced cellulose (Iβ and Iα) and the regenerated cellulose II. When cellulose crystals are treated with 4 M NaOH solution, then cellulose Iβ and Iα are converted to cellulose II where two adjacent cellulose chains are running antiparallel within the unit cell.2,23 The SFG spectra of cellulose II show very weak OH peaks at 3450 and 3480 cm−1 (Figure 4b,c). The weakness of the OH signal in the SFG spectra of cellulose II is due to the symmetry cancellation of the OH dipoles pointing the opposite directions in the two adjacent chains in the unit cell.2,23,24 The small peak at 3320 cm−1 in the SFG spectra of cellulose II in Figure 4b,c must be due to incomplete conversion of cellulose Iβ and Iα. In previous studies, the 2944 cm−1 peak in the ssp SFG spectra of cellulose in secondary cell walls and Avicel (produced from pulps) was tentatively attributed to the CH2 asymmetric stretch mode.2,25 TD-DFT simulations show that the χ(2) YYZ component would be the dominant term in the ssp spectra of the antiparallel packed crystallites (Figure 2b). In the cellulose Iβ structure, the CH2 asymmetric stretch dipole is expected to have a larger contribution in the Z direction (normal to the (200) plane) than the CH2 symmetric stretch dipole. However, the coupling with the axial CH stretch (Figures S1b and S2b) makes it difficult to determine the exact contribution from the CH2 asymmetric stretch. In summary, the insights obtained from TD-DFT calculations of SFG spectra for the parallel- and antiparallel-packed cellulose systems provide theoretical explanations for several empirical trends observed in SFG analysis of biological samples. The CH/OH SFG intensity ratio can be correlated with the overall polarity of cellulose crystallites or microfibrils within the SFG coherence length that is estimated to be hundreds of nanometers (i.e., mesoscale in length). The degree of the symmetry cancellation of the χ(2) YYX term in ssp spectra and the χ(2) XXX term in ppp spectra would vary with the intercrystallite distance. This is a very important feature of SFG that is not found in other characterization techniques used in structural analysis of cellulose such as IR and Raman spectroscopy, nuclear magnetic resonance, and X-ray diffraction. These conventional techniques cannot provide the chain polarity information. Since the CH modes are not sensitive to the cellulose packing polarity, the total intensity of the CH modes could be related to the total amount of cellulose in the sample.26 Also, the symmetry cancellation of OH SFG peaks of cellulose can be used to unambiguously determine the symmetry of the crystal unit cell.2 The similar principle could be extended to other crystalline biopolymers.3,4 Overall, these features make SFG unique and useful for nondestructive and selective characterization of the unit cell symmetry and mesoscale packing of crystalline biopolymers inside biological samples and engineered biomaterials.
that the dipole derivatives of the OH modes are the most sensitive to the packing polarity because the dipoles of OH groups are mostly within the XY plane (Figure 1). Even though the exact peak positions and shapes of the simulated SFG spectra of the truncated dimeric crystals are somewhat different from the experimental SFG spectra of cellulose, the simulation results reveal an important insight useful for interpretation of experimental data. Figure 4a compares the ssp SFG spectra of highly crystalline cellulose Iβ isolated from the tunicate.15 The direct comparison of the relative intensities and peak positions of experimental and simulated SFG spectra are shown in Figure S8 and Tables S5− S6 in the Supporting Information. The uniaxially aligned crystallites exhibit a weak OH SFG peak at 3320 cm−1, much smaller than the CH SFG peak at 2944 cm−1. Since the uniaxial alignment was made from the randomly dispersed crystallite solution, the polarity of the aligned crystallites must be random. In other words, the number of crystallites pointing upward along the alignment axis is statistically equal to that pointing downward. This situation is equivalent to the antiparallel packing in average over the SFG coherence length. Thus, the experimental spectrum in Figure 4a is consistent with the CH/ OH intensity ratio calculated for the antiparallel-packed case in Figure 2d. When the cellulose Iβ crystallites are randomized, the symmetry cancellation of the χ(2) YYX terms of the OH stretch modes is abated, resulting in the enhancement of the OH intensity relative to the CH intensity (Figure 4a). The CH/OH peak intensity ratio is not as small as the parallel-packed case shown in Figure 2a since the crystallites are random. The CH/OH SFG intensity ratios of the cellulose microfibrils in secondary cell walls of land plants are similar to that of the uniaxially aligned cellulose Iβ shown in Figure 4a, while those of cellulose in primary cell walls are close to that of the randomly aligned cellulose Iβ in Figure 4a.15 Native cellulose in tunicates (Figure 4b), algal cell walls, and bacterial pellicles (Figure 4c) also show SFG spectra with CH/OH intensity ratios similar to the randomly aligned crystallites.15 Based on high-resolution electron microscopy images and statistical mechanics arguments, it was hypothesized that cellulose microfibrils in the secondary cell walls must be packed antiparallel in average over the SFG coherence length, while microfibrils in the primary cell walls, algal cell walls, and tunicates are not antiparallel, but either cross-lamellar or random.15 The simulation spectra shown in Figure 2 provide theoretical justification for this hypothesis. The confirmation of the random polarity (which is equivalent to antiparallel) along the cellulose microfibril axis in secondary cell walls is important in plant biology as well as biomaterial engineering. It was recently reported that the cellulose microfibrils in the induced secondary cell wall of Arabidopsis are deposited by the concerted movement of a group of cellulose synthase complexes along one-dimensional path associated with microtubules.16 The ensembles moving up and down the path are almost the same, which will results in the deposition of microfibrils with the overall antiparallel polarity. Since the 1950s, it has been hypothesized that the native cellulose crystals can have piezoelectric properties based on the noncentrosymmetry of the crystal structure.17 Recently, this hypothesis was theoretically tested.18 The piezoelectric response must be related to the deformation of hydrogen bond lengths within the cellulose Iβ crystal under a strong electric field. There were several experimental attempts
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02624. 59
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(10) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; et al. NWChem: A Comprehensive and Scalable Open-source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477−1489. (11) Lee, C. M.; Kubicki, J. D.; Fan, B.; Zhong, L.; Jarvis, M. C.; Kim, S. H. Hydrogen-Bonding Network and OH Stretch Vibration of Cellulose: Comparison of Computational Modeling with Polarized IR and SFG Spectra. J. Phys. Chem. B 2015, 119, 15138−15149. (12) Lee, C. M.; Mohamed, N. M. A.; Watts, H. D.; Kubicki, J. D.; Kim, S. H. Sum-Frequency-Generation Vibrational Spectroscopy and Density Functional Theory Calculations with Dispersion Corrections (DFT-D2) for Cellulose Iα and Iβ. J. Phys. Chem. B 2013, 117, 6681− 6692. (13) Reiher, M.; Neugebauer, J.; Hess, B. A. Quantum Chemical Calculation of Raman Intensities for Large Molecules: The Photoisomerization of [{Fe‘S4’(PR3)}2(N2H2)] (‘S4’2−= 1, 2-bis(2-mercaptophenylthio)-ethane (2−)). Z. Phys. Chem. 2003, 217, 91−104. (14) Bishop, D. M.; Kirtman, B.; Champagne, B. Differences between the exact sum-over-states and the canonical approximation for the calculation of static and dynamic hyperpolarizabilities. J. Chem. Phys. 1997, 107, 5780−5787. (15) Lee, C. M.; Kafle, K.; Park, Y. B.; Kim, S. H. Probing Crystal Structure and Mesoscale Assembly of Cellulose Microfibrils in Plant Cell Walls, Tunicate Tests, and Bacterial Films Using Vibrational Sum Frequency Generation (SFG) Spectroscopy. Phys. Chem. Chem. Phys. 2014, 16, 10844−10853. (16) Li, S.; Bashline, L.; Zheng, Y.; Xin, X.; Huang, S.; Kong, Z.; Kim, S. H.; Cosgrove, D. J.; Gu, Y. Cellulose Synthase Complexes Act in a Concerted Fashion to Synthesize Highly Aggregated Cellulose in Secondary Cell Walls of Plants. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 11348−11353. (17) Fukada, E. Piezoelectricity of Wood. J. Phys. Soc. Jpn. 1955, 10, 149−154. (18) García, Y.; Ruiz-Blanco, Y. B.; Marrero-Ponce, Y.; SotomayorTorres, C. Orthotropic Piezoelectricity in 2D Nanocellulose. Sci. Rep. 2016, 6, 34616. (19) Hirai, N.; Sobue, N.; Date, M. New Piezoelectric Moduli of Wood: d31 and d32. J. Wood Sci. 2011, 57, 1−6. (20) Gindl, W.; Emsenhuber, G.; Plackner, J.; Konnerth, J.; Keckes, J. Converse Piezoelectric Effect in Cellulose I Revealed by Wide-angle XRay Diffraction. Biomacromolecules 2010, 11, 1281−1285. (21) Csoka, L.; Hoeger, I. C.; Rojas, O. J.; Peszlen, I.; Pawlak, J. J.; Peralta, P. N. Piezoelectric Effect of Cellulose Nanocrystals Thin Films. ACS Macro Lett. 2012, 1, 867−870. (22) Abas, Z.; Kim, H. S.; Zhai, L.; Kim, J.; Kim, J. H. Possibility of Cellulose-based Electro-active Paper Energy Scavenging Transducer. J. Nanosci. Nanotechnol. 2014, 14, 7458−7462. (23) Langan, P.; Nishiyama, Y.; Chanzy, H. X-ray Structure of Mercerized Cellulose II at 1 Å Resolution. Biomacromolecules 2001, 2, 410−416. (24) Park, Y. B.; Lee, C. M.; Kafle, K.; Park, S.; Cosgrove, D. J.; Kim, S. H. Effects of Plant Cell Wall Matrix Polysaccharides on Bacterial Cellulose Structure Studied with Vibrational Sum Frequency Generation Spectroscopy and X-Ray Diffraction. Biomacromolecules 2014, 15, 2718−2724. (25) Barnette, A. L.; Bradley, L. C.; Veres, B. D.; Schreiner, E. P.; Park, Y. B.; Park, J.; Park, S.; Kim, S. H. Selective Detection of Crystalline Cellulose in Plant Cell Walls with Sum-FrequencyGeneration (SFG) Vibration Spectroscopy. Biomacromolecules 2011, 12, 2434−2439. (26) Barnette, A. L.; Lee, C. M.; Bradley, L. C.; Schreiner, E. P.; Park, Y. B.; Shin, H.; Cosgrove, D. J.; Park, S.; Kim, S. H. Quantification of Crystalline Cellulose in Lignocellulosic Biomass Using Sum Frequency Generation (SFG) Vibration Spectroscopy and Comparison with Other Analytical Methods. Carbohydr. Polym. 2012, 89, 802−809.
Computational details of TD-DFT calculations and visualizations of selective vibration modes along with a comparison of the polarizability tensor and dipole moment vectors (PDF)
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (L.J.). *E-mail:
[email protected] (S.H.K.). ORCID
Seong H. Kim: 0000-0002-8575-7269 Author Contributions §
C.M.L. and X.C. contributed equally.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The design and data interpretation of this work were supported by the Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-16-1-0062). The SFG data were collected with the support by The Center for Lignocellulose Structure and Formation, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award Number DE-SC0001090. The TD-DFT computations were carried out with support from the National Science Foundation (Grant No. CHE1414466).
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REFERENCES
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