Coupled states method

The most accurate theoretical results for positronium formation in positron-helium collisions in the energy range 20-150 eV are probably those of Campbell et al. (1998a), who used the coupled-state method with the lowest three positronium states and 24 helium states, each of which was represented by an uncorrelated frozen orbital wave function... 

Similar coupled-state methods, both with and without the inclusion of positronium terms, have been applied to the excitation of other alkali atoms. The results of McAlinden, Kernoghan and Walters (1994, 1997) and Hewitt, Noble and Bransden (1994) for the dominant resonant excitation cross sections for sodium, rubidium and caesium all exhibit a similar energy dependence to that for lithium. Also, the neglect of positronium terms in the expansion, as in the work of McEachran, Horbatsch and Stauffer (1991), again has the effect of increasing the low energy excitation cross sections over those obtained when such terms are included. 

There is a variation on the coupled cluster method known as the symmetry adapted cluster (SAC) method. This is also a size consistent method. For excited states, a Cl out of this space, called a SAC-CI, is done. This improves the accuracy of electronic excited-state energies. 

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

The use of Cl methods has been declining in recent years, to the profit of MP and especially CC methods. It is now recognized that size extensivity is important for obtaining accurate results. Excited states, however, are somewhat difficult to treat by perturbation or coupled cluster methods, and Cl or MCSCF based methods have been the prefen ed methods here. More recently propagator or equation of motion (Section 10.9) methods have been developed for coupled cluster wave functions, which allows calculation of exited state properties. 

The spin contamination makes the UCC energy curves somewhat too high in the intermediate region, but the infinite nature of coupled cluster methods makes them significantly better at removing unwanted spin states as compared to UMPu methods (Figure 11.8). 

Stanton JF, Bartlett RJ (1993) The equation of motion coupled-cluster method - a systematic biorthogonal approach to molecular-excitation energies, transition-probabilities, and excited-state properties. J Chem Phys 98 7029... 

As was already noted in [9], the primary effect of the YM field is to induce transitions (Cm —> Q) between the nuclear states (and, perhaps, to cause finite lifetimes). As already remarked, it is not easy to calculate the probabilities of transitions due to the derivative coupling between the zero-order nuclear states (if for no other reason, then because these are not all mutually orthogonal). Efforts made in this direction are successful only under special circumstances, for example, the perturbed stationary state method [64,65] for slow atomic collisions. This difficulty is avoided when one follows Yang and Mills to derive a mediating tensorial force that provide an alternative form of the interaction between the zero-order states and, also, if one introduces the ADT matrix to eliminate the derivative couplings. 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

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. 

Figure 4. Ground-state potential energy curves of Hs from 2-RDM and wavefunction methods are shown. MP2 and MP4 denote second- and fourth-order perturbation theories, while CCSD and CCSD) represent coupled cluster methods.

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