A density matrix based soft-computing solution to the quantum mechanical problem of computing the molecular electronic structure of fairly long polythiophene (PT) chains is proposed. The soft-computing solution is based on a random mutation hill climbing scheme which is modified by blending it with a deterministic method based on a trial single-particle density matrix [P(0)(R)] for the guessed structural parameters (R), which is allowed to evolve under a unitary transformation generated by the Hamiltonian H(R). The Hamiltonian itself changes as the geometrical parameters (R) defining the polythiophene chain undergo mutation. The scale (γ) of the transformation is optimized by making the energy [E(γ)] stationary with respect to γ. The robustness and the performance levels of variants of the algorithm are analyzed and compared with those of other derivative free methods. The method is further tested successfully with optimization of the geometry of bipolaron-doped long PT chains.