Relativistic coupled cluster method

Ephraim Eliav

Hermann G. Kümmel

Simen Kvaal

The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrödinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.

Bruce H. J. McKellar

Jan Brandejs, Jakub Višňák, Libor Veis +3 more

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Alexander V. Oleynichenko, Artem S. Rumiantsev, Andrei V. Zaitsevskii +1 more

The efficiency of the Tucker decomposition of amplitude tensors within the single-reference relativistic coupled cluster method with single and double excitations was studied in a series of benchmark calculations for (AuCl)n chains, Aun clusters, and the cluster model of solid YbCl2. The 1 kJ/mol level of accuracy for correlation energy estimates of moderate-size systems and typical reaction energies can be achieved with relatively high compression rates of amplitude tensors via rejecting singular values smaller than ∼10-4. For the most extensive system studied (the YbCl7 cluster used for modeling of the ytterbium center in the ytterbium dichloride crystal), only ∼3% of compressed double amplitudes were shown to be significant. Thus, the rank reduction for the relativistic coupled cluster method with single and double theory, improving its computational scaling, is feasible. The advantage (if not necessity) of using the Goldstone diagrammatic technique rather than the "antisymmetrized" Brandow one is underlined. The proposed approach is promising for high-precision modeling of relatively large systems with heavy atoms.