Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.
Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.
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DOI：
10.1002/chem.201705897
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发表时间：
2018-03
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影响因子：
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通讯作者：
Shadan Ghassemi Tabrizi;A. Arbuznikov;M. Kaupp
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文献类型：
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作者：
Shadan Ghassemi Tabrizi;A. Arbuznikov;M. Kaupp
交换耦合分子自旋团簇（如单分子磁体）的热力学和光谱数据通常用两种不同的模型来解释：多自旋哈密顿量（MSH）明确考虑单个自旋中心之间的耦合，而巨自旋哈密顿量（GSH）将系统视为单个集体自旋。当各向同性交换耦合较弱时，由于局部零场分裂（ZFS）相互作用（S-mixing）混合了自旋多态，两个自旋哈密顿模型之间的物理兼容性成为一个严重的问题。到目前为止，这种使得映射MSH→GSH（“自旋投影”）非平凡的效应，只被摄动（直到三阶）处理过，有明显的局限性。在此，基于MSH的精确对角化，应用经典有效哈密顿理论构建了一个GSH，该GSH与包含有效自旋多重子的相关（2S+1）态的能量完全匹配。为了比较，最近开发的有效（“伪自旋”）哈密顿量的独特推导策略，现在通常用于单核系统的从头计算，适用于自旋投影问题。用不可约张量算子（或史蒂文斯算子）展开零场哈密顿算子和磁矩，得到有效自旋中所有k阶（直至k=2S）的项。利用已发表的MSH参数进行的计算表明，研究充分的[Ni(hmp)(dmb)Cl]4 （'Ni4 '）单分子磁体具有精确的自旋投影，显示出弱各向同性交换（dmb=3,3-二甲基-1-丁醇，hmp-是2-羟甲基吡啶的阴离子）。所得的GSH在有限域中的性能是根据EPR共振和恶魔点来评估的。导致Ni4中快速隧穿的S=4多重子的M=±4地重态中的大隧穿是由具有八重旋转对称的Stevens算符引起的，这标志着自旋簇中k=8项的首次量化。对于弱耦合系统，MSH→GSH的唯一和精确映射具有普遍的重要性；它代表了将理论预测（例如从量子化学计算）与光谱拟合的ZFS，超精细或g张量进行比较的强制性最终步骤。
Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]4 ('Ni4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.