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Variation of the precession K along the torsion C2-C6 BCP bond-path of fulvene for the S 0 (left panel) and S 1 (right panel) electronic states for a series of values of the torsion θ = 0.0° (Franck-Condon) to θ = 64.3° (conical intersection). Bond critical points (BCP s) are located at a distance = 0.0 a.u along the bond-path. • Determined the precessions K of the path-packets for the S 0 and S 1 states of fulvene. • The precessions K of the path-packets quantified the bond rigidity and flexibility. • An asymmetry is found for the S 1 state variation in the bond-path rigidity with torsion. • The S 1 state at torsion θ = 0.0° possesses maximum bond-rigidity along the entire bond. • The S 1 state possessed a higher degree of bond-anharmonicity than the S 0 state. Here we have determined the precessions K and K' of the { p , p ′} and { q , q ′} path-packets for the excited state deactivation reaction of fulvene in terms of bond-flexing, bond-torsion and bond-anharmonicity that includes the tendencies towards bond-path-rigidity and bond-path-flexibility. An asymmetry is found for the S 1 state resulting in an unpredictable variation in the direction of the bond-path-rigidity as a function of the torsion coordinate. Uniquely, the S 1 state at torsion θ = 0.0° possesses the possible maximum bond-path-rigidity, along the entire bond-path but then drops lower than for the S 0 state at the conical intersection indicating photo-excitation facilitates the torsion. [ABSTRACT FROM AUTHOR]