Hamiltonian structure constants

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order o , where a is the fine-structure constant) and correlation effects (all products smd powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 md 111. Molecular applications are also presented. 

The V" includes the effect of the finite nuclear size, while some finer effect, like QED, can be added to the hDCn perturbatively. The DCB Hamiltonian in this form contains all effects through the second order in a, the fine-structure constant. 

A couple of new quasi-relativistic Hamiltonians have been proposed and the methods have been implemented and tested on some one-electron atoms. The calculations show that the energies obtained with the present quasi-relativistic Hamiltonians are in fairly good agreement with the corresponding Dirac energies. The discrepancy between the quasi-relativistic and the Dirac energies scales with a Z, where Z is the the nuclear charge and a is the fine structure constant. 

This spin-spin constant, a, should not be confused with the fine-structure constant a = e2/fic. The direct spin-spin contribution to the A doubling, a, cannot be separated from a second-order spin-orbit term. All contributions are combined in the ov parameter, which is the coefficient of the term in the effective Hamiltonian (Brown et al. 1979 Brown and Merer, 1979) with a AE = -AA = 2 selection rule,... 

As shown in [6.6] the LMTO-ASA Hamiltonian matrix may be transformed into the two-centre form [6.7] where the hopping integrals are products of potential parameters and the canonical structure constants. This result was already stated in Sect.2.5. A less accurate two-centre approximation based upon the KKR-ASA equations will be presented in Sect.8.1.2. The canonical structure constants which, after multipiication by the appropriate potential parameters, form the two-centre hopping integrals are 1 isted in Table 6.1. The... 

Although the proper point of departure for relativistic atomic structure calculations is quantum electrodynamics (QED), very few atomic structure calculations have been carried out entirely within the QED framework. Indeed, almost all relativistic calculations of the structure of many-electron atoms are based on some variant of the Hamiltonian introduced a half century ago by Brown and Ravenhall [1] to understand the helium fine structure. By decoupling the electron and radiation fields in QED to order a (the fine-structure constant) using a contact transformation. Brown and Ravenhall obtained a relativistic momentum-space Hamiltonian in which the electron-electron Coulomb interaction was surrounded by positive-energy projection operators. Owing to the fact that contributions from virtual electron-positron pairs are automatically projected out of... 

By using atomic units (ft = 1, Wc = I, c = a a being fine structure constant) and spherical coordinates the one-particle Hamiltonian becomes... 

Compute explicitly, starting from the fine-structure constants D and E of the anthracene molecule (Table 7.3), the fine-structure constants D and F and the orientation of the principal axis of the triplet excitons in the anthracene crystal (Fig. 7.15). Hint First derive the spin Hamiltonian in the form = SFqS. Here, S = s"i -1- S2 is the sum of the spin operators of the two electrons 1 and 2, and... 

Here, h r) is a one-particle Dirac Hamiltonian for electron in a field of the finite size nucleus and y is a potential of the interelectron interaction. In order to take into account the retarding effect and magnetic interaction in the lowest order on parameter a (a is the fine structure constant), one could write [23]... 

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