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Instead of the Cooper pair of BCS theory, we incorporate the chemical structural effects of pairwise movement by using $geminals1$ (two-electron wavefunctions), rather than the simple orbital (one-electron wavefunction) model. Instead of the nearest-neighbor antisymmetric-type vibronic interaction of Bipolaron Theory, we emphasize the distant neighbor's opposing vibrations in doped systems. Besides the Jahn-Teller effect of second-order energy, we propose Renner-Teller effect for crystals other than lincar molecules, and obtain first-order energy of degenerate vibronic geminal $states2,3$ by using the Herzberg-Teller expansions of vibronic states of the Hamiltonian.