The coupled-cluster method with full inclusion of single, double and triple excitations applied to high sectors of the Fock space

Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

“…These diagrams for the (0p, 0h), (0p, 1h), and (0p, 2h) Fock space sectors are presented on Figure 2. Numerous approximate techniques reducing the overall computational cost of the CCSDT model have been proposed during recent decades, both within the single-reference [51][52][53][54][55] and multi-reference CC frameworks [37,40,[56][57][58][59][60][61][62]. The most widely used approximations are CCSD(T) and CCSDT-1, the former is often referred as the "gold standard" of quantum chemistry [63].…”

“…During recent decades the relativistic Fock Space CC approach in both effective and intermediate Hamiltonian formulations proved its efficiency and high accuracy in challenging calculations of heavy atomic and molecular systems with dense spectra, especially in cases when both d and f atomic orbitals become valence (see also recent reviews [26,29,36]). In the non-relativistic realm the pilot implementation of the FS-CC method accounting for triple excitations and allowing the treatment of up to six valence electrons sectors was pioneered by Hughes and Kaldor in earlier 1990s; they reported calculations of electronic states of light atoms in rather modest basis sets [37][38][39]. Later the more advanced non-relativistic implementation of the IH-based full FS-CCSDT approach (and some its effective approximations) to excitation spectra of some light atomic and molecular systems has been published by Musiał and co-authors [24,25,40].…”

Study of Actinides by Relativistic Coupled Cluster Methods

“…The main shortcoming is the limitation to states obtained from a closed shell configuration by adding and/or removing two electrons at most. We hope to continue previous efforts [36] and extend the scope of the method to higher sectors of the Fock space. Other work in progress includes further development of the Hilbert-space and mixed-sector IHCC [37], as well as the double FSCC formalism mentioned in the introduction, which will include higher QED terms and make possible the treatment of highly ionized species.…”

“…The sector (m, n) of the Fock space includes all states obtained from the reference determinant by removing m electrons from designated occupied orbitals, called valence holes, and adding n electrons in designated virtual orbitals, called valence particles. The practical current limit is m + n ≤ 2, although higher sectors have also been tried [36]. The excitation operator S, defined by the exponential parametrization of Ω, is partitioned into sector operators S = m≥0 n≥0 S (m,n) .…”

Relativistic Fock space coupled cluster study of bismuth electronic structure to extract the Bi nuclear quadrupole moment

“…Up to now, the applications of FS-RCC were limited to the systems with no more than two "valence" electrons (unpaired electrons over the Fermi vacuum state) [15,16]. The attempts to extend the scope of applicability of its non-relativistic counterpart to systems with three or even more (up to six) electrons were made by Hughes and Kaldor in early 1990s [17][18][19][20][21] and recently by Meissner and co-authors [22]. Though the reported pilot applications were restricted to atoms and simple molecules of second-and third-row elements, the results have clearly shown that the inclusion of contributions of triple excitation operators is inevitable to achieve a highly accurate modelling.…”