  Deterministic band gap in quasi-one-dimensional nanoribbons is prerequisite
for their integrated functionalities in high-performance molecular-electronics
based devices. However, multiple band gap values commonly observed in the same
width of graphene nanoribbons fabricated in same slot of the experiments
remains unresolved, and raise a critical concern over scalable production of
pristine and/or hetero-structure nanoribbons with deterministic properties and
functionalities for plethora of applications. Here, we show that a modification
in the depth of potential wells in the periodic direction of a supercell on
relative shifting of passivating atoms at the edges is the origin of multiple
band gap values for the same width of nanoribbons in a crystallographic
orientation, although they carry practically the same ground state energy. The
results are similar when calculations are extended from planar graphene to
buckled silicene nanoribbons. Thus, the findings facilitate tuning of the
electronic properties of quasi-one-dimensional materials such as bio-molecular
chains, organic and inorganic nanoribbons by performing edge engineering.
