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Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range 0.0−0.3 au, where is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm-1for the E12and E23seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm-1occurring at 0.3 au. The characteristic parameters gIJand hIJare also predicted to great accuracy, even at large , with the error growing to only 10−15% at 0.3 au. [ABSTRACT FROM AUTHOR]