High‐spin behavior of molecular crystals and extended π systems

Abstract

The qualitative rules for the existence of high-spin ground states in extended systems and molecular crystals are examined here on a firmer theoretical footing. Extended systems have been categorized into three groups, namely, type I, type II, and type III, depending on the type of bonding interactions. The general form of the spin Hamiltonian operators have been written down. The active spaces have been restricted to the minimum size for each of these three types of spin systems. The zeroth-order state vectors and the Hartree–Fock ground-state energies have been identified for unit species of each type. The extended system Hamiltonian operators are further truncated in such a way that only the nearest-neighbor interactions are retained. Expressions have been derived for the energy gap from a molecular orbital approach. The relatively small effects of electron correlation on the energy gaps have been estimated for the type I systems, which belong to the systems of solid-state physics. In particular, it has been shown that for the type I systems the singlet–triplet gap, and hence the ferromagnetic coupling constant, primarily depends upon the difference of one-electron kinetic energies and not on the two-electron exchange integrals. This result agrees with the concept of kinetic exchange that was introduced in the context of a resonating valence-bond formalism. Type II systems are exemplified by extended systems that can be prepared from conjugated molecules while organic molecular crystals form examples of type III species. For these systems, however, the Coulomb exchange interaction has been shown to dominate the energy gap. A quick review of the Heisenberg spin Hamiltonian for the H2 molecule is sufficient to point out that the sign of the calculated ferromagnetic coupling constant depends on the method of calculation, the nature of the basis set, and the bond length. This is amply supported by ab initio calculations on this species. Numerical data have also been obtained from computations on m-phenylene-coupled nitroxy radicals and stacks of α-nitronyl nitroxide, but these calculations have been based on a semiempirical quantum chemical methodology (INDO) since some of the species involved are exceedingly large. Computed energy gaps are in good agreement with experimental and other theoretical (AM1, PM3) results. Nevertheless, for the dimer, trimer, tetramer, and pentamer of the type II specimen, the important π orbitals are far from being degenerate. The quantitative results clearly deviate from the criterion of degeneracy that was suggested from qualitative theories for the existence of a high-spin ground state. Therefore, the criteria for the existence of high spins have been reformulated in terms of the monomer orbitals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 308–324, 2000