We present and implement in this paper a novel spin-free valence-universal multi-reference coupled cluster (VU-MRCC) formalism for energy differences which can capture orbital relaxation and correlation relaxation to all orders. Unlike in the traditional normal ordered cluster Ansatz for computing energy differences, this cluster expansion formalism allows contractions between various valence excitation operators with valence spectator lines. These contractions simulate the orbital relaxation and correlation relaxation effects for the ionized/excited states via Thouless-like exponential type of operators. Generally such operators are non-commuting. To ensure that each distinct excitation generated by contracted composites formed by these operators appear only once in the wave-operators, the factors accompanying these composites have to be judiciously chosen. Hence, the combinatoric factors accompanying such contracted composites are not taken to be 1/n! for nth-power, but rather the inverse of the automorphic factor (the number of ways the n operators can be connected in various permutations generating the same composite). It is shown that this Ansatz leads to a set of VU-MRCC equations for the valence cluster amplitudes, in which all the cluster operators are attached to the hamiltonian by at least one non-spectator line (a strongly connected series). The series is thus terminating at the quartic power. Illustrative applications are presented by computing electron affinity of neutral doublet radicals (viz., NH 2 , OH, F, BO and CN), where the orbital relaxation effect attendant on the anion formation is considerable. Several basis-sets capable of describing the anions have been studied. It has been found that aug-cc-pVTZ basis gives the best overall results, while aug-cc-pVQZ overestimates the electron affinity, presumably because of an imbalance in describing the neutral radicals. The method performs consistently much better then the one with the traditional normal ordered Ansatz.