Coupled perturbed Dirac-Hartree-Fock

The expression above now contains the response of the wave function to the perturbation Q which can be accomplished by solving the coupled-perturbed Dirac-Hartree-Fock equations (CPDHF) yielding a different set of MO-coefficients for the molecular wave function [138] according... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

If effects from electron correlation on parity violating potentials shall be accounted for in a four-component framework, the situation becomes more complicated than in the Dirac Hartree-Fock case. This is related to the fact, that in four-component many body perturbation theory (MBPT) or in a four-component coupled cluster (CC) scheme the reduced density matrices on the respective computational level are required in order to determine the parity violating potentials. Since these densities were not available in analytic form, Thyssen, Laerdahl and Schwerdtfeger [153] used a finite field approach to compute parity violating potentials in a four-component framework on a correlated level. This amounts to adding the parity violating operator with different scaling factors A to the... 

The 5s manifold shows great complexity. For the lowest state S23.4(5s) = 0.37. This value is considerably lower than many structure calculations predict, but the perturbation calculation of Kheifets and Amusia (1992) obtains 0.384. The orbital energy ess (11.18) is 27.6+0.3eV, which is to be compared to the Dirac—Fock value 27.49 eV. The Hartree—Fock value is 25.70 eV. The criterion for the strength of the perturbation, given by the ratio of the standard deviation to the mean of the 5s manifold is 0.18. The ratios S29.i(5s) S23.4(5s) and S23.4(5s) Z/S/(5s) are compared at different momenta in fig. 11.10. The condition for the validity of the weak-coupling binary-encounter approximation is completely satisfied within experimental error. 

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. 

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