Extended metal atom chains (EMACs) are promising candidates for molecular wires but their band structures remain to be explored. As a quasi-one-dimensional (Q1D) system, the incommensurate helical nature of EMACs hinders such calculations. In this work, we resolved this issue via explicit implementation of helical symmetry. Moreover, the pattern of metal d bands was rationalized by a systematic investigation on a series of related Q1D helical systems. Two critical factors, helical ligand field and chemically asymmetric ligand field, are proposed and identified. We found that the symmetry and ligand fields of the system dominate the pattern of the metal d bands, instead of specific chemical composition of ligands. The presented method and rationale are applicable to not only EMACs but also related Q1D helical systems.