Diffraction Pattern Simulation of Cellulose Fibrils using Distributed and Quantized Pair Distances

Intensity simulation of X-ray scattering from large twisted cellulose molecular fibrils is important in understanding the impact of chemical or physical treatments on structural properties such as twisting or coiling. This paper describes a highly efficient method for the simulation of X-ray diffraction patterns from complex fibrils using atom-type-specific pair-distance quantization. Pair distances are sorted into arrays which are labelled by atom type. Histograms of pair distances in each array are computed and binned and the resulting population distributions are used to represent the whole pair-distance data set. These quantized pair-distance arrays are used with a modified and vectorized Debye formula to simulate diffraction patterns. This approach utilizes fewer pair distances in each iteration, and atomic scattering factors are moved outside the iteration since the arrays are labelled by atom type. This algorithm significantly reduces the computation time while maintaining the accuracy of diffraction pattern simulation, making possible the simulation of diffraction patterns from large twisted fibrils in a relatively short period of time, as is required for model testing and refinement. A diffraction pattern simulation of cellulose fibrils is presented, using a modification of the Debye formula in cylindrical coordinates. Pair distances are labelled by atom type and quantized using a two-dimensional histogram, which greatly decreases the computation time and maintains a smaller R factor.