Fock space coupled cluster methods

The relativistic coupled cluster method starts from the four-component solutions of the Drrac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. The Fock-space coupled-cluster method yields atomic transition energies in good agreement (usually better than 0.1 eV) with known experimental values. This is demonstrated here by the electron affinities of group-13 atoms. Properties of superheavy atoms which are not known experimentally can be predicted. Here we show that the rare gas eka-radon (element 118) will have a positive electron affinity. One-, two-, and four-components methods are described and applied to several states of CdH and its ions. Methods for calculating properties other than energy are discussed, and the electric field gradients of Cl, Br, and I, required to extract nuclear quadrupoles from experimental data, are calculated. 

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. 

U. Kaldor, Theor. Chim. Acta, 80, 427 (1991). The Fock Space Coupled Cluster Method Theory and Application. 

Equations for the Fock space coupled cluster method, including all single, double, and triple excitations (FSCCSDT) for ionization potentials [(0,1) sector], are presented in both operator and spin orbital form. Two approximations to the full FSCCSDT equations are described, one being the simplest perturbative inclusion of triple excitation effects, FSCCSD+T(3), and a second that indirectly incorporates certain higher-order effects, FSCCSD+T (3). 

In the Fock space coupled cluster method, the Hartree-Fock solution for an iV-electron state, 0), is used as the vacuum. The Fock space is divided into sectors, (m,n), according to how many electrons are added to and removed from 0). Thus, the vacuum is in the (0,0) sector, single ionizations are in the (0,1) sector, one-electron attached states are in (1,0), and (1,1) are single excitations relative to 0). The orbitals are also divided into active, which can change occupation, and inactive, for which the occupation is fixed. All possible occupations of the active orbitals in all possible sectors constitute the multireference space for the system. 

D. E. Bernholdt, Triple Excitation Effects in the Fock-Space Coupled Cluster Method, PhD thesis, University of Florida, Department of Chemistry, Gainesville, FL 32611, 1993. 

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 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 polarizability of T1 and element 113 has been calculated using the fully relativistic ab initio Dirac-Coulomb Fock-space coupled-cluster method and the finite field procedure. For Tl, the theoretical value is in good agreement with experiment. In group 13, the atomic polarizability increases from A1 to Ga, attains a maximum for In and then decreases towards Tl and furthermore towards element 113. So, element 113 presents the smallest polarizability, which results from the large relativistic contraction and stabilization of the 7pi/2 orbital. These values have then been used to estimate the adsorption enthalpies of Tl and element 113 on polyethylene and teflon surfaces and have shown that the difference of enthalpy attains 6 kJ/mol, which should be enough to separate and identify them. 

S. R. Hughes and U. Kaldor, Relativistic coupled cluster calculations for closed shell atoms, Chem. Phys. Lett. 194, 95 (1992) The coupled cluster method with full inclusion of single, double and triple excitations applied to high sectors of the fock space, ibid. 204, 339 (1993) Fock-space coupled-cluster method The (1,2) sector, Phys. Rev. A 47, 4705 (1993) The Fock-space coupled cluster method Electron affinities of the five halogen elements with consideration of triple excitations, J. Chem. Phys. 99, 6773 (1993) The coupled cluster method in high sectors of the Fock space, Intern. J. Quantum Chem. 55, 127 (1995). 

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). 

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