Sum-frequency-generation (SFG) vibration spectroscopy selectively detects noncentrosymmetric vibrational modes in crystalline cellulose inside intact lignocellulose. However, SFG peak assignment in biomass samples is challenging due to the complexity of the SFG processes and the lack of reference SFG spectra from the two crystal forms synthesized in nature, cellulose I alpha and I beta. This paper compares SFG spectra of laterally aligned cellulose I alpha and I beta crystals with vibration frequencies calculated from density functional theory with dispersion corrections (DFT-D2). Two possible hydrogen-bond networks A and B (Nishiyama et al. Biomacromolecules 2008, 9, 3133) were investigated for both polymorphs. From DFT-D2 calculations the energetically favorable structures for cellulose I alpha and I beta had CH2OH groups in tg conformations and network A hydrogen bonding. The calculated frequencies of C-H stretch modes agreed reasonably well with the peak positions observed with SFG and were localized vibrations; thus, peak assignments to specific alkyl groups were proposed. DFT-D2 calculations underestimated the distances between hydrogen-bonded oxygen atoms compared to the experimentally determined values; therefore, the OH stretching calculated frequencies were similar to 100 cm(-1) lower than observed. The SFG peak assignments through comparison with DFT-D2 calculations will guide the SFG analysis of the crystalline cellulose structure in plant cell walls and lignocellulose biomass.