Intermediate Hamiltonian coupled cluster method

A. Landan, E. Ehav, and U. Kaldor, Intermediate Hamiltonian Fock-Space Coupled-Cluster Method and Applications. In R. F. Bishop, T. Brandes, K. A. Gernoth, N. R. Walet, and Y. Xian (Eds.) Recent Progress in Many-Body Theories, Advances in Quantum Many-Body Theories, Vol. 6. (World Scientific, Singapore, 2002), pp. 355-364 and references therein. 

A. Landau, E. Eliav, U. Kaldor, Intermediate Hamiltonian Fock-space coupled-cluster method, Chem. Phys. Lett. 313 (1999) 399. 

The basic relativistic equations are described in Sec. 2, and the Fock-space coupled cluster method is discussed in Sec. 3. The recently developed intermediate Hamiltonian approach is described and illustrated by several... 

A particular variant of the coupled cluster method, called Fock-space or valence-universal [49,50], gave remarkable agreement with experiment for many transition energies of heavy atoms [51]. This success makes the scheme a useful tool for reliable prediction of the structure and spectrum of superheavy elements, which are difficult to access experimentally. A brief description of the method is given below. A more flexible scheme with higher accuracy and extended applicability, the intermediate Hamiltonian Fock-space coupled cluster approach, is shown in the next section. 

A major advantage of the intermediate Hamiltonian approach is the flexibility in selecting the model space. This has been a major problem in applying the Fock-space scheme, as described at the beginning of this section. While in the Fock-space coupled cluster method one may feel lucky to find any partitioning of the function space into P and Q with convergent CC iterations, the intermediate Hamiltonian method makes it possible for the first time to vary the model space systematically and study the effect upon calculated properties. An example is given in Table 3, which shows the dependence of the calculated electron affinity of Cs on the model spaces Pm and Pi [55]. 

Excitation energies of atomic barium and radium were calculated in 1996 using the Fock-space coupled cluster method [57]. The model space in the 2-electron sector included all states with two electrons in the 5d, 6s and 6p orbitals, except the 6p states inclusion of the latter led to intruder states and divergence, so that incomplete model spaces had to be employed. In the intermediate Hamiltonian approach all these states (including 6p ) were in Pm, Pi was defined by adding states with occupied 7s-10s, 7p-10p, 6d-... 

On the performance of the intermediate Hamiltonian Fock-space coupled-cluster method on linear triatomic molecules The electronic spectra of NpOj, NpOj, and PuQ2+. /. Chem. Phys., 125 (2006) 074301. 

The Fock-space and intermediate Hamiltonian coupled cluster methods were applied to the ground and excited levels of the second actinide element, thorium, and its heavy homo-logue eka-thorium (E122) [60], Two Fock-space schemes are used. The first starts with the NT + ion, with a closed-shell stmcture corresponding to a rare gas, and adds two electrons. 

A. Landau, E. Eliav, and U. Kaldor, Intermediate Hamiltonian Fock-space coupled-cluster Method, Chem. Phys. Lett. 313,399 (1999) A. Landau, E. Eliav, and U. Kaldor, Intermediate Hamiltonian Fock-space coupled-cluster method, Adv. Quantum Chem. 39, 172 (2001). 

E. Ehav and U. Kaldor, Transition energies of Rn- and Fr-like actinide ions by relativistic intermediate Hamiltonian Fock-space coupled-cluster methods, Chem. Phys. 392, 78 (2012). 

Recent developments include exact [12-14, 44, 90, 91] and approximate [14, 90, 92-94] iterative schemes to determine Hg, the intermediate Hamiltonian method [21, 24, 95], the use of incomplete model spaces [43, 44] and some multireference open-shell coupled-cluster (CC) formalisms [16-20, 96, 97]. Only some eigenvalues of the intermediate Hamiltonian H, are also eigenvalues of H. The corresponding model eigenvectors of H, are related to their true counterparts as in Bloch s theory. Provided effective operators a are restricted to act solely between these model eigenvectors, the possible a definitions from Bloch s formalism (see Section VI.A) can be used. 

Coupled Cluster based size-extensive intermediate hamiltonian formalisms were developed by our group [33-35] by way of transcribing a size-extensive CC formulation in an incomplete model space in the framework of intermediate hamiltonians. In this method, there are cluster operators correlating the main model space. There are no cluster operators for the intermediate space. This formulation thus is conceptually closer to the perturbative version of Kirtman... 

Comparing the different methods with the experimental data of Kaufman and Radziemski [88], the excitation energies of the U + ion appear to be best described by the XIHFSCCSD scheme (extrapolated Intermediate Hamiltonian Fock-Space Coupled Cluster Singles Doubles excitations), which within the large UBS basis set gives an MAE relative to the experimental data of 1,650 cm without and 651 cm with the Breit interaction. 

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