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Dirac-Fock-Breit

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. [Pg.161]

Heavy atoms exhibit large relativistic effects, often too large to be treated perturba-tively. The Schrodinger equation must be supplanted by an appropriate relativistic wave equation such as Dirac-Coulomb or Dirac-Coulomb-Breit. Approximate one-electron solutions to these equations may be obtained by the self-consistent-field procedure. The resulting Dirac-Fock or Dirac-Fock-Breit functions are conceptually similar to the familiar Hartree-Fock functions the Hartree-Fock orbitals are replaced, however, by four-component spinors. Correlation is no less important in the relativistic regime than it is for the lighter elements, and may be included in a similar manner. [Pg.161]

The no-pair DCB Hamiltonian (6) is used as a starting point for variational or many-body relativistic calculations [9], The procedure is similar to the nonrelativistic case, with the Hartree-Fock orbitals replaced by the four-component Dirac-Fock-Breit (DFB) functions. The spherical symmetry of atoms leads to the separation of the one-electron equation into radial and spin-angular parts [10], The radial four-spinor has the so-called large component the upper two places and the small component Q, in the lower two. The quantum number k (with k =j+ 1/2) comes from the spin-angular equation, and n is the principal quantum number, which counts the solutions of the radial equation with the same k. Defining... [Pg.163]

Molecules are more difficult to treat accurately than atoms, because of the reduced symmetry. An additional complication arises in relativistic calculations the Dirac-Fock-(-Breit) orbitals will in general be complex. One way to circumvent this difficulty is by the Douglas-Kroll-Hess transformation [57], which yields a one-component function with computational effort essentially equal to that of a nonrelativistic calculation. Spin-orbit interaction may then be added as a perturbation, implementation to AuH and Au2 has been reported [58]. Progress has also been made in the four-component formulation [59], and the MOLFDIR package [60] has been extended to include the CC method. Application to SnH4 has been described [61] here we present a recent calculation of several states of CdH and its ions [62], with one-, two-, and four-component methods. [Pg.170]

In Table 6.3, the values of De for RfCU are compared with those obtained within various approximations using relativistic effective core potentials (RECP) Kramers-restricted Hartree-Fock (KRHF) (Han et al 1999), averaged RECP including second-order M0ller-Plesset perturbation theory (AREP-MP2) for the correlation part (Han et al. 1999), RECP coupled-cluster single double (triple) [CCSD(T)] excitations (Han et al. 1999), and a Dirac-Fock-Breit (DFB) method (Malli and Styszynski 1998). The AREP-MP2 calculation of De gives 20.4 eV, while the RECP-CCSD(T) method with correlation leads to 18.8 eV. Our value of De of 19.5 eV is just between these calculated values. [Pg.223]

Here frs and (7 s tu) are, respectively, elements of one-electron Dirac-Fock-Breit and antisymmetrized two-electron Coulomb-Breit interaction matrices over Dirac four-component spinors. The effect of the projection operators A+ is now taken over by normal ordering, denoted by the curly braces in (16), which requires annihilation operators to be moved to the right of creation operators as if all anticommutation relations vanish. The Fermi level is set at the top of the highest occupied positive-energy state, and the negative-energy states are ignored. [Pg.88]

Y. Ishikawa. Atomic Dirac-Fock-Breit Self-Consistent Field Calculations. Int.. Quantum Chem., Quantum Chem. Symp., 24... [Pg.681]

Y. Ishikawa, H. M. Quiney, G. L. MaUi. Dirac-Fock-Breit self-consistent-field method Gaussian basis-set calculations on many-electron atoms. Phys. Rev. A, 43(7) (1991) 3270-3278. [Pg.681]

Y. Ishikawa, G. L. MaUi, A. J. Stacey. Matrix Dirac-Fock-Breit SCF calculations on heavy atoms using geometric basis sets of Gaussian functions. Chem. Phys. Lett., 188(1,2) (1992) 145-148. [Pg.681]

E. Eliav, LI. Kaldor, Y. Ishikawa. Open-sheU relativistic coupled-duster method with Dirac-Fock-Breit wave functions Energies of the gold atom and its cation. Phys. Rev. A, 49(3) (1994) 1724-1729. [Pg.681]

G. L. MaUi, J. Styszynski. Ab initio aU-electron fully relativistic Dirac-Fock-Breit... [Pg.681]

G. L. MaUi, A. B. F. Da Silva, Y. Ishikawa. Universal Gaussian basis functions in relativistic quantum chemistry atomic Dirac-Fock-CoulQmb and Dirac-Fock-Breit calculations. Can. J. Chem., 70 (1992) 1822-1826. [Pg.697]

M. S. KeUey, T. Shiozaki. Large-scale Dirac-Fock-Breit method using density fitting and 2-spinor basis functions. J. Chem. Phys., 138 (2013) 204113. [Pg.697]

Main, G.L., Styszynski, J. Ab initio all-electron fully relativistic Dirac-Fock-Breit calculations for molecules of the superheavy transactinide elements rutherfordium tetrachloride. J. Chem. Phys. 109, 4448-4455 (1998)... [Pg.232]


See other pages where Dirac-Fock-Breit is mentioned: [Pg.167]    [Pg.167]    [Pg.314]    [Pg.320]    [Pg.327]    [Pg.260]    [Pg.266]    [Pg.64]    [Pg.64]    [Pg.81]    [Pg.82]    [Pg.191]    [Pg.352]    [Pg.161]    [Pg.167]    [Pg.682]    [Pg.189]    [Pg.317]    [Pg.146]    [Pg.309]    [Pg.31]   
See also in sourсe #XX -- [ Pg.162 , Pg.260 ]

See also in sourсe #XX -- [ Pg.352 ]




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Dirac-Fock

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