A general algorithm based on the line symmetry group theory is proposed for ab initio modeling of one-dimensional (1D) helical nanoobjects using computer codes designed for periodic structure calculations. The key point of the algorithm is the interpolation between the properties of a sequence of periodic structures to obtain the properties of 1D helical nanoobjects without translational periodicity. A special selection of periodic structures avoids excessively long periods, thereby providing control over computational costs. The developed approach gives an opportunity to simulate the continuous dependences of mechanical and electronic properties on the torsional strain for any helical 1D nanoobject using high-level quantum chemical methods. The superposition of torsional and axial deformations can be used to generate the two-parameter maps of the desired properties. The proposed algorithm is applied to obtain the structure and properties of selected nanohelicenes, which are the helicenes infinitely continued along the helical (screw) axis direction. The CRYSTAL17 computer code based on atomic basis set has been used for this purpose. The main advantage of this program in comparison with other widely available ab initio simulation codes is the built-in accounting for helical symmetry operations in 1D periodic systems. Performed calculations show that nanohelicenes have several local minima of potential energy, differing in the order of the helical axis. The irrational order of the helical axis found at all energy minima indicates the absence of translational symmetry in these structures. Two-parameter electronic band gap maps and the dependences of Young's moduli on the torsion angle for the selected nanohelicenes are calculated and discussed.