DFT energy optimization of a large carbohydrate: cyclomaltohexaicosaose (CA-26)

CA-26 is the largest cyclodextrin (546 atoms) for which refined X-ray structural data is available. Because of its size, 26 D-glucose residues, it is beyond the scope of study of most ab initio or density functional methods and to date has only been computationally examined using empirical force fields. The crystal structure of CA-26 is folded like a figure "8" into two 10 D-glucoses long antiparallel left-handed V (Verkleisterung)-type helices with a "band-flip" and "kink" at the top and bottom of the helices. DFTr methods were applied to CA-26 to determine if a carbohydrate molecule of this size could be geometry optimized and if it would show structural variances from application of dispersion and/or solvation. The DFTr reduced basis set method developed by the authors uses 4-31G on the carbon atoms of the glucose rings and 6-31+G* on all other atoms. B3LYP is the density functional used to successfully optimize CA-26, and other density functionals were then applied, including a self-consistent charge density functional tight binding (SCC-DFTB) method and the B97D (dispersion-corrected) and B97D-PCM (dispersion + implicit solvent) methods. Heavy atom coordinates were taken from one X-ray structure, fitted with hydrogen atoms, and geometry optimized using PM3 followed by B3LYP/6-31+G*/4-31G optimization. After optimization, the heavy atom rms deviation of the optimized DFTr (B3LYP) structure to the crystal structure was 0.89 Å, the rmsd of the B97D optimization was 1.38 Å, that for B97D-PCM was 0.95 Å, and that for SCC-DFTB was 0.94 Å. These results are very good considering that no explicit water molecules were included in the computational analysis and there were ~32-38 water molecules around each CA-26 molecule in the crystal structure. Tables of internal coordinates and puckering parameters were compared to the X-ray structures, and close correspondence was found.