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

对于没有强电子相关性的系统，耦合簇层次以收敛得非常快而著称。然而，高度精确的相对能量要求对基集收敛。显式相关框架允许加速基集收敛，但对于高于双激励是麻烦的。反相关形式修正了哈密顿量，因此直接适用于任何激励水平。最近，它与全构型相互作用量子蒙特卡罗结合在一起，得到了非常精确的原子电离能。此外，在哈伯德模型的例子中，跨相关方法已被证明可以降低强相关系统的激励水平要求。这使得它们在耦合集群方法的上下文中非常有吸引力。设计和优化相关因子需要大量的计算和使用大基集的基准计算。因此，从方法论的角度来看，将形式主义与耦合聚类方法结合起来是非常重要的。由于反相关，哈密顿量包含三体项而不是厄米量。因此，传统的编码不容易使用。我们将采用自动代码生成，它将与我们现有的张量框架相结合，以实现基于超相关哈密顿量的高阶耦合聚类方法。将使用线性响应形式将方法扩展到激发态和分子性质的计算。这些方法将应用于有机金属化合物的自旋态分裂。

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.