Quantum mechanical holonomy of molecular vibration has firstly been formulalted.

Selected Publications:

"Complete Molecular Hamiltonian Based on the Born-Oppenheimer Adiabatic Approximation," A. Tachibana and T. Iwai, Phys. Rev. A, 33, 2262-2269 (1986).

"Reaction Holonomy and the Geometric Phase of Quantum Evolution in Chemical Reaction Systems," A. Tachibana, J. Mol. Structure (Theochem), 310, 1-11 (1994).

"Role and Treatment of Zero Eigenvalues of Rotation in the Cartesian Force Constant Matrix along Reaction Path," A. Tachibana and T. Iwai, in "The Reaction Path in Chemistry: Current Approaches and Perspectives," Ed. by D. Heidrich (Kluwer, Dordrecht, 1995), pp. 77-94.

"A Simple Algorithm for Conservation of Invariants of Motion in Reaction Dynamics Calculations: Application to the NH3+ + NH3 System,"  A. Tachibana and M. Fuju, J. Chem. Phys., 110, 2323-2331 (1999).

"Differential Geometry in Chemical Reaction Dynamics," A. Tachibana, in "The Transition State - A Theoretical Approach," Ed. by T. Fueno (Kodansha, Tokyo; Gordon and Breach, Amsterdam, 1999), pp. 217-247.

"The Geometry and Mechanics of Multiparticle Systems," T. Iwai and A. Tachibana, Ann. Inst. Henri Poincare, 70, 525-559 (1999).