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First, a new approach to treat the strongly correlated conjugated-circuit model on two-dimensional networks is made with computational effort comparable to that for corresponding tight-binding models. Toward this end a translationally symmetric arrow assignment is used to construct an antisymmetrically signed ‘‘adjacency’’ matrix for two-dimensional networks. Then symmetry blocking is used to manipulate this ‘‘adjacency’’ matrix, and make the associated conjugated-circuit computations. Second, a series of two-dimensional translationally symmetric structures related to graphite is constructed by means of a kind of local rearrangement on the graphite lattice. A consequent detailed description of π-electron resonance energy via conjugated-circuit computations is presented for these novel two-dimensional nets as well as several other regular and semiregular nets with vertices of degree 3. Approximate energy estimates indicate that resonance stability depends dominantly on the local topology of the networks, and in particular on the fraction of faces which are hexagonal.

The coupled-cluster (CC) equations in the work of Coester, Kümmel, Čižek, Paldus, and others are inhomogeneous, nonlinear and algebraic in the cluster operators to be determined. If taken to all orders, they are equivalent to complete configuration–interaction (CI) equations, except for states orthogonal to the reference state Φ. However, if taken only to nth order, they are not equivalent to the nth order CI equations, and due to their nonlinear form, the existence and the number of the solutions is not guaranteed. Also, the reality of the associated energy values is not certain since these values do not arise as eigenvalues of a Hermitian operator. We show that the equations can be cast in the form of perturbed CI equations, with the ’’perturbations’’ being non-Hermitian and nonlinear in the CI-like coefficients to be calculated. In the case of a finite number of single-particle states, we construct the solutions to the CC equations by analytic continuation from the CI solutions. Singularities peculiar to the method are identified and studied, and conditions for reality and the maximum multiplicity of solutions are given. In general, the energy will be real, and the number of solutions equals that of the associated CI problem. Singularities or instabilities in the coupled-cluster equations can be traced to unphysical assumptions in the basis set Hamiltonian, or a poor description to highly excited states.