Spin and Pseudo Spins in Theoretical Chemistry. A Unified View for Superposed and Entangled Quantum Systems

A unified picture for magnetism, superconductivity, quantum optics and other properties of molecule-based materials has been presented on the basis of effective model Hamiltonians, where necessary parameter values have been determined by the first principle calculations of cluster models and/or band models. These properties of the matetials are qualitatively discussed on the basis of the spin and pseudo-spin Hamiltonian models, where several quantum operators are expressed by spin variables under the two level approximation. As an example, ab initio broken-symmetry DFT calculations are performed for cyclic magnetic ring constructed of 34 hydrogen atoms in order to obtain effective exchange integrals in the spin Hamiltonian model. The natural orbital analysis of the DFT solution was performed to obtain symmetry-adapted molecular orbitals and their occupation numbers. Several chemical indices such as information entropy and unpaired electron density were calculated on the basis of the occupation numbers to elucidate the spin and pair correlations, and bonding characteristic (kinetic correlation) of this mesoscopic magnetic ring. Both classical and quantum effects for spin alignments and singlet spin-pair formations are discussed on the basis of the true spin Hamiltonian model in detail. Quantum effects are also discussed in the case of superconductivity, atom optics and quantum optics based on the pseudo spin Hamiltonian models. The coherent and squeezed states of spins, atoms and quantum field are discussed to obtain a unified picture for correlation, coherence and decoherence in future materials. Implications of theoretical results are examined in relation to recent experiments on molecule-based materials and molecular design of future molecular soft materials in the intersection area between molecular and biomolecular materials.