Ab-initio wave-function approach to aperiodic helical lattices

As a model system, a chain of hydrogen atoms is embedded onto a cylinder and its electronic ground-state is numerically investigated. The resulting helix is periodic in the curved cylindrical space, but the periodicity in the Cartesian space is not guaranteed. Aperiodic helices exist and can be generated by irrational rotations, akin to the Penrose tiling [1]. To address such systems with microscopic precision, integrals of localized functions are calculated in a given supercell, while the Hartree-Fock is formulated in the Fourier space associated to the helical symmetry. Second order perturbative corrections are limited to pair excitations (pair-MP2). The method is thoroughly benchmarked on finite rings against coupled cluster theory [2]. The 1D thermodynamic limit is reached by extrapolation. The issue of a slow (1/R) saturation of the Coulomb field is overcame by approximating the contributions from the tails of the chain, i.e. the far-field, by a fast multipole expansion (FMM) that utilizes merely one-body properties.

[1] C. Corduneanu, Almost periodic functions (Chelsea Pub. Co, New York, N.Y, 1989)

[2] M. Motta et. al,Physical Review X 7 (2017), 10.1103/physrevx.7.031059.