Study on the behavior of energy convergence in ab initio crystal orbital calculations

Abstract

This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N0). The energy convergence behavior with respect to N0 depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C2H4 unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N0 a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N0 = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N0 ⩽ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.