Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. III. Rules for the Singlet Stability of Hartree–Fock Solutions of π-Electronic Systems

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Abstract
The singlet stability conditions for closed‐shell electronic systems, which ensure that the Hartree–Fock (HF) determinant with doubly occupied orbitals minimizes the energy expectation value, are applied to the symmetry adapted HF solutions of linear polyacenes, using the Pariser–Parr–Pople‐type semi‐empirical Hamiltonian. It is found that the symmetry adapted HF solutions for linear polyacenes containing an even number of benzene rings are always singlet stable, while the HF solutions for linear polyacenes having an odd number of benzene rings may exhibit singlet instability if the coupling constant is large enough. For cases where singlet instability was found, we have also calculated new HF solutions having lower energy than the symmetry adapted HF solutions. These new HF solutions violate the space symmetry conservation laws as usual. Furthermore, the qualitative rules for the existence of singlet stability of the symmetry adapted HF solution of π‐electronic systems with conjugated double bonds are derived. These rules are formulated through the simple symmetry properties of possible Kekulé structures of the studied system. These rules are used to explain the results of stability calculations for linear polyacenes as well as further illustrated on other examples.

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