Symmetry and broken-symmetry in molecular orbital descriptions of unstable molecules. 3. The nature of chemical bonds of spin frustrated systems.
Symmetry and broken symmetry in the molecular orbital description of spin frustration systems have been investigated in relation to the resonating valence bond (RVB) theory of the spin liquid state and non-BCS superconductivity. Broken symmetry (BS) and resonating BS (RBS) molecular orbital (MO) methods have been employed to obtain resonating valence bond (RVB)-type explanations of spin frustrated systems. RBS MO solutions are expanded using the localized molecular orbitals (LMO) to elucidate a universal MO-VB description. The BS and RBS MO descriptions of triangular spin frustrated systems corresponding to transition structures for exchange-forbidden radical insertions were investigated in comparison with the RVB-type explanations of such systems. The BS and RBS calculations by the use of three different axial (SDW) solutions or three noncollinear GSO (helical SDW) solutions of a triangular hydrogen cluster were performed to obtain potential curves with and without resonance (quantum) effects. The resonating GSO (noncollinear) state responsible for short-range correlation was found to be the most stable for the system. The reliability of the approximate spin projection (AP) procedure to eliminate the high-spin component was also elucidated, comparing with the AP BS and RBS potential curves. The BS GSO (GHF) computations of several triangular systems, N(CH(2))(3), (CH(2))(3), and Mn(II)(3)O(4), were performed to obtain total energies and total spin angular momentums and effective exchange integrals (J) between local spins, which are crucial for construction of effective spin Hamiltonian models. The exact diagonalization of the Heisenberg models was also performed to depict the energy levels and magnetic susceptibility curves for triangular and kagome lattices to elucidate spin frustration effects and related quantum spin behaviors. Implications of the computational results have been discussed in relation to magnetic properties of several triangular and kagome systems synthesized recently and the superconductivity of triangular systems discovered recently.
Kawakami
T
T
Department of Chemistry, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
Takeda
R
R
Nishihara
S
S
Saito
T
T
Shoji
M
M
Yamada
S
S
Yamanaka
S
S
Kitagawa
Y
Y
Okumura
M
M
Yamaguchi
K
K
D000588:Amines / Q000737:chemistry; D001554:Benzene / Q000737:chemistry; D006859:Hydrogen / Q000737:chemistry; D008958:Models, Molecular; D008968:Molecular Conformation; D011789:Quantum Theory; D028561:Transition Elements / Q000737:chemistry
D000588:Amines; D028561:Transition Elements; D006859:Hydrogen; D001554:Benzene