Homologous gene shuffling between DNA molecules promotes genetic diversity and is an important pathway for DNA repair. For this to occur, homologous genes need to find and recognize each other. However, despite its central role in homologous recombination, the mechanism of homology recognition has remained an unsolved puzzle of molecular biology. While specific proteins are known to play a role at later stages of recombination, an initial coarse grained recognition step has, however, been proposed. This relies on the sequence dependence of the DNA structural parameters, such as twist and rise, mediated by intermolecular interactions, in particular, electrostatic ones. In this proposed mechanism, sequences that have the same base pair text, or are homologous, have lower interaction energy than those sequences with uncorrelated base pair texts. The difference between the two energies is termed the "recognition energy." Here, we probe how the recognition energy changes when one DNA fragment slides past another, and consider, for the first time, homologous sequences in antiparallel alignment. This dependence on sliding is termed the "recognition well." We find there is a recognition well for anti-parallel, homologous DNA tracts, but only a very shallow one, so that their interaction will differ little from the interaction between two nonhomologous tracts. This fact may be utilized in single molecule experiments specially targeted to test the theory. As well as this, we test previous theoretical approximations in calculating the recognition well for parallel molecules against MC simulations and consider more rigorously the optimization of the orientations of the fragments about their long axes upon calculating these recognition energies. The more rigorous treatment affects the recognition energy a little, when the molecules are considered rigid. When torsional flexibility of the DNA molecules is introduced, we find excellent agreement between the analytical approximation and simulations.