关于关联变换方法的研究
Studies on the Transcorrelated Method
AI总结：
本文基于双变分原理开发关联变换方法，通过二阶矩最小化优化哈密顿矩阵，为闭壳层原子和类氦离子提供高精度能量，并图形化分析关联子对尖点的影响。
摘要：
我们研究了使用关联变换哈密顿量来描述电子关联的可能性。基于双变分原理的数学框架，开发了一种获得关联变换波函数的方法。这涉及构造一个有效的关联变换哈密顿矩阵，该矩阵可以自洽地求解。我们使用一种称为二阶矩（SOM）最小化的方法对此进行优化，为一些闭壳层原子和类氦离子提供了高精度的能量。我们还以图形方式检查了某些关联子项对电子-电子和电子-核尖点描述的影响，并将一些关联变换波函数与近乎精确的Hylleraas波函数进行了比较。
英文摘要：
We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This involves the construction of an effective transcorrelated Hamiltonian matrix which can be solved in a self-consistent manner. This was optimised using a method we call Second Order Moment (SOM) minimisation to give highly accurate energies for some closed-shell atoms and helium-like ions. The effect of certain correlator terms on the description of electron-electron and electron-nuclear cusps were also examined graphically and some transcorrelated wavefunctions were compared against near-exact Hylleraas wavefunctions.
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