Development of transcorrelated coupled cluster methods using automatic implementation for calculating highly accurate ground and excited state energies and properties

耦合团簇体系是著名的收敛速度非常快，没有强电子关联的系统的确切结果。然而，高度精确的相对能量要求相对于基组收敛。显式相关的框架允许加快基组收敛，但对于高于两倍的激发是麻烦的。互相关形式主义修改了哈密顿量，因此直接适用于任何激发能级。最近，它与全组态相互作用量子蒙特-卡罗结合在一起，产生了非常精确的原子电离能。此外，互相关的方法已被证明可以减少强相关系统的哈伯德模型的例子的激发水平的要求。设计和优化互相关因子需要大量的计算以及使用大基组的基准计算。因此，从方法论的观点来看，将联合收割机与耦合集团方法结合起来是非常重要的。由于相互关联，哈密顿量包含三体项，而不是厄米算符。因此，传统的代码不容易使用。我们将采用自动生成的程序，结合我们已有的张量框架，实现基于互关联哈密顿量的高阶耦合团簇方法，并利用线性响应形式将该方法扩展到激发态和分子性质的计算，并将其应用于有机金属化合物自旋态分裂的研究.

The coupled cluster hierarchy is famous to converge very quickly to exact results for systems without strong electron correlation. However, the highly accurate relative energies require convergence with respect to the basis set. The explicitly correlated framework allows to speed up the basis set convergence, but is cumbersome for higher than doubles excitations. The transcorrelation formalism modifies the Hamiltonian and is therefore directly applicable to any excitation levels. Very recently, it has been combined together with the Full Configuration Interaction Quantum Monte-Carlo yielding extremely accurate ionization energies of atoms. Additionally, the transcorrelated methods have been shown to reduce the excitation-level requirements for strongly correlated systems on the example of the Hubbard model. This makes them extremely appealing in the context of the coupled cluster methods.Designing and optimizing the transcorrelation factor requires many calculations together with benchmark calculations using large basis sets. Therefore, from the methodological point of view, it is very important to combine the formalism with the coupled cluster methods.Due to the transcorrelation the Hamiltonian contains three-body terms and is not Hermitian. Therefore the conventional codes cannot be easily used. We will employ an automatic code generation, which will be combined with our existing tensor framework, in order to implement high-order coupled-cluster methods based on the transcorrelated Hamiltonian.Linear response formalism will be used to extend the methods to excited states and molecular properties calculations.The methods will be applied in the context of spin-state splittings of organometallic compounds.