| Abstract: | Neutral, ionic, and complete alternant systems are studied using the alternancy symmetry adapted (ASA ) approach. This approach is based on an explicit construction of ASA operators that are up to the sign invariant with respect to the particle-hole symmetry transformation. These operators serve as building blocks of alternant systems, and they determine their characteristic properties. All Hamiltonians describing neutral alternant systems are explicitly constructed. Up to some minor restrictions, all Hamiltonians describing ionic and complete alternant systems are also explicitly constructed. Inversely, given a Hamiltonian ? in a second quantization notation, one can easily check whether or not this Hamiltonian describes a neutral (ionic, complete) alternant system. All linear properties characteristic to neutral (ionic, complete) alternant systems are obtained. In particular, all one- and two-particle properties are derived in an explicit form. The properties obtained substantially generalize “classical” properties of alternant systems such as, in the case of neutral alternant systems, uniform charge density distribution, vanishing bond orders between atomic sites of the same parity, and alternancy selection rules for the electric dipole transitions. |
