A Cyclic Periodic Wave Function Approach for the Study of Infinitely Periodic Solid-State Systems: II. Application to Helical Polysaccharides

Abstract

The cyclic periodic wave function (CPWF) approach is applied at the AM1 and PM3 semiempirical levels of approximation to two infinitely periodic polymer systems in the solid state. The two polysaccharides of interest here are (1→3)-β- d -glucan and (1→3)-β- d -xylan. Our calculated results show excellent agreement with the available data for the two polysaccharides and demonstrate that the use of the CPWF approach at the AM1 and PM3 levels of approximation provides a convenient and reliable method for the study of infinitely periodic bonds of two different types: moderately strong O–H···O hydrogen bonding and strong C–O–C covalent bonding.

Development of a Cyclic Periodic Wave Function Approach for the Study of Infinitely Periodic Solid-State Systems

“…Longer-range interactions are at least partially recovered by the use of our Madelung correction scheme, which corrects both the individual Fock matrix elements as well as the total energy by approximately recovering all interactions between farther neighbors . We have found that using N = 4 suffices for most solid-state systems, , as long as the intermonomer interactions are weaker than covalent interactions. Even when covalent interactions occur between monomers, we have found that N = 4 often suffices, though using N = 6 in the direction of the covalent interaction will provide greater accuracy for some systems.…”

“…Second, it is a chemically intuitive approach. The repeat units are chosen to be either the individual molecules within molecular solids or the individual monomer units within polymers, , and are placed at their exact translationally periodic positions, as found in the infinitely periodic crystal, without any built-in periodic boundary conditions (PBCs). For chemists, it is a more intuitive way to study large organic crystals.…”

“…Because our wave functions use individual molecules or monomers as the repeat unit, instead of the unit cell of the crystal, , and because our wave functions are cyclically periodic, instead of translationally periodic, our method is origin independent and does not depend in any way upon how the repeat unit is chosen. The CPWF approach builds the symmetry relations between identical molecules or monomers directly into the wave functions, ensuring that the electron density at each individual molecule within the infinite system is identical.…”

“…Finally, the CPWF approach is applied at the AM1 and PM3 semiempirical levels of approximation to study different three-dimensional infinitely periodic solid-state systems stabilized by different kind of weak interactions between repeat units, all intra- and intermonomer geometry parameters are optimizable in this CPWF method. , Thus, our approach leads to complete flexibility in the determination of the three-dimensional geometry of the solid-state system.…”