A [1,5]-dinitro-anthracene molecule performs a NOR or AND digital logic function depending of the polarity of the bias voltage applied to the molecule. Its design is based on the fact that a quantum system can demonstrate a Boolean like dependent Rabi oscillation frequency while this frequency is controlled by well unidentified parameters of its Hamiltonian therefore used as logic inputs for the logic gate. This quantum Hamiltonian computing (QHC) approach permits a systematic design of quantum driven classical logic gates whose quantum structure can be mapped on the electron pi system of a polyaromatic molecule. The output of such molecule logic gate is encoded in the tunnelling current I passing through the board of the molecule. Supposed to be interconnected to two semi-infinite metallic atomic wires, our NOR (AND) dinitro-anthracene molecule presents a two orders of magnitude difference between its logic levels '1' and '0' as demonstrated by calculating its full low current I(theta(1), theta(2)) logic surface where theta(1) and theta(2) are the NO2 conformation angles encoding for a classical '0' or '1' logic input on the molecule. (C) 2009 Elsevier B. V. All rights reserved.