In this study we present an effective Potential of Mean Force (PMF) designed for Lagrangian and Quaternion Molecular Dynamics (LQMD) of DNA. The DNA model is built from pseudoatoms as well as rigid and pseudo-elastic bodies described by a limited number of selected Cartesian and internal degrees of freedom. Phosphate groups, deoxyribose rings and nucleic acid bases are represented by pseudoparticles, some of them with internal degrees of freedom. PMF is defined as the sum of effective bonded and long-range potentials. The potentials were fitted to numerical free energy surfaces. Over 50 free energy surfaces, each depending on a conformational variable (pseudobond length, angle or dihedral angle) and the pseudorotation phase of the nearest neighbour deoxribose ring, were computed. The numerical free energy surfaces were obtained from probability distributions derived from a 1.5 ns conventional, microscopic MD simulation of the d(GpC)₉ double helical DNA molecule. An umbrella sampling method was used to simulate transitions between the A and B DNA forms, and PMF reproduces these transitions.