Solid-state nuclear magnetic resonance (CP/MAS C-13 NMR) spectroscopy has often been used to study cellulose structure, but some features of the cellulose NMR spectrum are not yet fully understood. One such feature is a doublet around 84 ppm, a signal that has been proposed to originate from C4 atoms at cellulose fibril surfaces. The two peaks yield different T-1, differing by approximately a factor of 2 at 75 MHz. In this study, we calculate T-1 from C4-H4 vector dynamics obtained from molecular dynamics computer simulations of cellulose I beta-water interfacial systems. Calculated and experimentally obtained T-1 values for C4 atoms in surface chains fell within the same order of magnitude, 3-20 s. This means that the applied force field reproduces relevant surface dynamics for the cellulose-water interface sufficiently well. Furthermore, a difference in T-1 of about a factor of 2 in the range of Larmor frequencies 25-150 MHz was found for C4 atoms in chains located on top of two different crystallographic planes, namely, (110) and (1 (1) over bar0). A previously proposed explanation that the C4 peak doublet could derive from surfaces parallel to different crystallographic planes is herewith strengthened by computationally obtained evidence. Another suggested basis for this difference is that the doublet originates from C4 atoms located in surface anhydro-glucose units with hydroxymethyl groups pointing either inward or outward. This was also tested within this study but was found to yield no difference in calculated T-1.