核磁共振屏蔽常数的新一代相对论方法
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摘要
核磁共振光谱参数(如屏蔽张量)的非相对论和相对论理论计算已经有很长历史了。然而,令人吃惊的是,磁性质的最高理论-四分量完全相对论方法还很不成熟,远远滞后于其它近似准相对论方法的发展和应用,这与四分量完全相对论方法对电性质的计算已趋完善形成鲜明的对比。其根本原因是磁场微扰与电场微扰不同,前者能强烈地耦合Dirac旋量的大小分量,导致负能态对磁性质的贡献是O(c~0)而不是电性质中的O(c~(-4))。也就是说,如果忽略负能态的贡献,我们将得不到逆磁项,甚至连正确的非相对论极限都得不到。因此,关键问题是如何在四分量相对论理论中有效地考虑负能态的贡献。标准的线性响应理论虽然形式上很简单,但因没有明显考虑磁平衡条件,在实际计算中需要用很大的基组才能得到稳定的结果。为了解决这一问题,本论文发展了几种全新的明显考虑磁平衡与动态平衡条件的精确方法,包括轨道分解方法、依赖于外场的酉变换算符方法和依赖于全场的酉变换矩阵方法,后两者是对适用于单一非奇异磁场的Kutzelnigg方法的推广。通过系统地忽略负能态量级为O(c~(-2))或O(c~(-4))的贡献,我们还提出了上述方法的近似形式,使计算进一步简化。上述所有方法都可以很容易地推广到其它磁性质的计算,因此可以说,磁性质的相对论理论已得到解决!事实上,四分量完全相对论对磁性质的计算已经变得和电性质一样简单了-用标准的triplezeta基组就能得到好的结果。
Theoretical calculations, nonrelativistic or relativistic, on NMR spectroscopic pa-rameters such as shielding tensors have a long history. Surprisingly, however, the mostrelativistic method, four-component relativistic theory, for magnetic properties has notbeen developed to the same level of sophistication as for electric properties. The un-derlying reason is that, compared to an electric perturbation, a magnetic perturbationhas a much stronger in?uence on the coupling of the large and small components ofthe Dirac spinor, leading to the fact that the contributions of negative energy statesto magnetic properties are of O(c~0) instead of O(c~(-4)) as for electric properties. Thatis, if the contributions of negative energy states are neglected, the entire diamagneticterm will be missed, even at the nonrelativistic limit. The key issue is therefore howto account for such contributions in a four-component relativistic treatment. Standardlinear response theory is just painful for practical use: It requires una?ordable largebasis sets of high angular momenta to compensate for the lack of the magnetic bal-ance condition. Here we propose several novel schemes to take explicitly into accountthe magnetic balance condition, in addition to the kinetic balance condition. Theseinclude the orbital decomposition approach, external-field dependent unitary transfor-mation at operator level, and the full-field dependent unitary transformation but atmatrix level. The latter two are generalizations of Kutzelnigg’s original formulationfor a single regular field. The corresponding approximate variants are also obtained byconsistent neglect of negative energy states, leading to errors of O(c~(-2)) or O(c~(-4)). Allthe variants can readily be extended to other magnetic properties. It can therefore beclaimed that relativistic theory for magnetic properties has been solved. As a matter offact, four-component relativistic theory for magnetic properties has become as easy asfor electric properties-A standard triple-zeta basis set already leads to decent results!
Theoretical calculations, nonrelativistic or relativistic, on NMR spectroscopic pa-rameters such as shielding tensors have a long history. Surprisingly, however, the mostrelativistic method, four-component relativistic theory, for magnetic properties has notbeen developed to the same level of sophistication as for electric properties. The un-derlying reason is that, compared to an electric perturbation, a magnetic perturbationhas a much stronger in?uence on the coupling of the large and small components ofthe Dirac spinor, leading to the fact that the contributions of negative energy statesto magnetic properties are of O(c~0) instead of O(c~(-4)) as for electric properties. Thatis, if the contributions of negative energy states are neglected, the entire diamagneticterm will be missed, even at the nonrelativistic limit. The key issue is therefore howto account for such contributions in a four-component relativistic treatment. Standardlinear response theory is just painful for practical use: It requires una?ordable largebasis sets of high angular momenta to compensate for the lack of the magnetic bal-ance condition. Here we propose several novel schemes to take explicitly into accountthe magnetic balance condition, in addition to the kinetic balance condition. Theseinclude the orbital decomposition approach, external-field dependent unitary transfor-mation at operator level, and the full-field dependent unitary transformation but atmatrix level. The latter two are generalizations of Kutzelnigg’s original formulationfor a single regular field. The corresponding approximate variants are also obtained byconsistent neglect of negative energy states, leading to errors of O(c~(-2)) or O(c~(-4)). Allthe variants can readily be extended to other magnetic properties. It can therefore beclaimed that relativistic theory for magnetic properties has been solved. As a matter offact, four-component relativistic theory for magnetic properties has become as easy asfor electric properties-A standard triple-zeta basis set already leads to decent results!
引文
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