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

• Applicant: Dr. Daniel Kats
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 455145945

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.

• DFG Programme: Research Grants