The parameter-dependent fermion states for molecules with symplectic symmetry

Under a certain kind of similarity transformation, a parameter-dependent (abbreviated as PD) symplectic group chain Sp(2M) ⊃ Sp(2M - 2) ⊃ ⋯ ⊃ Sp(2) that is characterized by a set of pairing parameters is introduced to build up the PD antisymmetrized fermion states for molecules with symplectic symmetry, and these states will be useful in carrying out the optimization procedure in quantum chemistry. In order to make a complete classification of the states, a generalized branching rule associated with the symplectic group chain is proposed. Further, we are led to the result that the explicit form of the PD antisymmetrized fermion states is obtained in terms of M one-particle operators and M geminal operators.