Symmetry and broken symmetries in molecular orbital descriptions of unstable molecules II. Alignment, flustration and tunneling of spins in mesoscopic molecular magnets

Abstract

As an extention of previous work [Yamaguchi K (1983) J Mol Structure (Theochem) 103:101], our theoretical eorts toward molecular materials are brie¯y reviewed. Axial, helical and general (cone, tetrahedron, etc) spin structures of carbon clusters, manganese oxide clusters and iron-sulfur clusters were investigated using the classical Heisenberg model and generalized HartreeFock theory. The spin¯ustrations in the clusters were also studied in relation to theoretical descriptions of the magnetism and the chemical bonds in active sites of several enzymes. The macroscopic quantum tunneling and coherence of spins in the manganese oxide clusters were analyzed using the instanton model, and the tunneling rate of spins was calculated by the coherent state path integral method. The spin transitions induced by an external magnetic ®eld were studied by the path integral Monte Carlo method. The theoretical results were explained in terms of the symmetry and broken symmetry of the wavefunctions in the mesoscopic molecular systems, which are intermediate in the scale factor. The results were also applied to molecular design of mesoscopic clusters of clusters in the intermediate and strong correlation regime. The active control of spins is ®nally discussed from the viewpoint of functionalities in molecular and biological materials, and technological applications of mesoscopic molecular magnets are discussed with regard to quantum computing.

Structural and Electronic Responses to the Three Redox Levels of Fe(NO)N2S2‐Fe(NO)2

“…Consistent with the diamagnetism of complex 1 + + ,c omputations predict as inglet ground state with the broken-symmetry [34] (BS) singlet, 2.0 kcal mol À1 more stable than the triplet and 10.0 kcal mol À1 more stable than the closed-shell( CS) singlet. The BS singlet features anti-ferromagnetically coupled {Fe(NO)} 7 and {Fe(NO) 2 } 9 spin centers [19] with the iron atoms separated by 2.834 .…”

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

“…37 However, precisely these spin correlations are at the core of the chemical and physical properties of these compounds. Methodologies and schemes to partially circumvent the limitations in BS-DFT have been discussed extensively by Yamaguchi and co-workers, 38,39 with noncollinear schemes being closer to the accurate description of the non-local nature of spin correlations. [40][41][42][43][44] Exact ab initio wave functions, instead, allow for such correlations, but their applicability is hindered by the exponential scaling of the many-body wave function with respect to the number of unpaired electrons.…”

A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock

“…Applying this to eqs. (18) and (19), we see that in the present case, ⟨S y ⟩ is 0, as are the two-electron parts of ⟨S x S y ⟩, ⟨S y S x ⟩, ⟨S y S z ⟩, and ⟨S z S y ⟩. Therefore, in this case, A xy = A yx = A yz = A zy = 0, i.e.…”

“…Generalized Hartree Fock (GHF) should be used. GHF has been researched for a long time, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and while it has only rarely been used, it is gaining momentum. For example, GHF has recently been used to obtain interesting new perspectives on a variety of fullerenes.…”