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The latest development of Pettifor's bond-order approach - the analytic bond-order potentials (ABOPs) - represents a significant improvement over the empirical potentials of the Abell-Tersoff Brenner type. This article aims at a critical evaluation of this promising novel scheme for the hydrocarbon system and assesses its applicability to realistic large-scale atomistic simulations. It is shown that ABOP reproduces the underlying orthogonal tight-binding model accurately for both hydrocarbon molecules and carbon crystalline phases in their ground-state configurations. However, in order to reproduce also non-equilibrium configurations it is necessary to extend the sigma bond-order expression to account for the non-negligible sp atomic energy level separation of carbon. While the Brenner hydrocarbon potential exhibits several deficiencies in the description of amorphous hydrocarbon films, the extended ABOP model comes closer to results of accurate non-orthogonal tight-binding calculations. Remaining discrepancies of ABOP can be traced back to the limitations of the underlying orthogonal tight-binding model and its parameterization.