Dirac-Fock code

Dreams is a program that has evolved as a Dirac-Fock code (Dyall 1994c Dyall et al. 1991a) and has been extended to the RMP2 approach for the estimation of correlation energies for closed and open-shell systems (Dyall 1994a). 

P. IndeRcato, E. lindroth, J. P. Desclaux. Nonrelativistic limit of Dirac-Fock codes The role of BriHouin configurations. Phys. Reo. Lett, 94 (2005) 013002. 

Desclaux has developed a numerical Dirac-Fock code for atoms which can be used to obtain relativistic numerical allelectron four-component spinor wavefunctions for any atom in the periodic table. The relativistic four-component wave-functions for all the atomic orbitals could then be used for the construction of pseudo-orbitals and relativistic effective core potentials. The resulting relativistic potentials would also have four component spinor forms. 

Full Dirac-Fock calculations are often performed using the GRASP code [18]. Exact criteria for the optimisation procedure depend somewhat on the accuracy required (for further details, see [15]. 

Fig. 5.18. Spin-orbit splittings for the nf series of Ba+, showing that good agreement is obtained between g Hartree and experimental values. For comparison, Dirac-Fock (labelled DHF) and multiconfigurational Dirac-Fock (labelled MCDF) curves computed from the same code are also shown (after J.-P. Con-nerade and K. Dietz [230]).

Desclaus has developed a computer code to solve the many-electron Dirac-Rock equation for atoms in a numerical self-consistent method. In this method, the relativistic Hamiltonian is approximated within the Dirac-Fock method, ignoring the two-electron Breit interaction. The Breit interaction is introduced as a first-order perturbation to energy after self-consistency is achieved. Relativistic wavefunctions and energies calculated this way are available for a number of atoms. ... 

Both, SE and VP, corrections are calculated, in the GRASP2K code, as the first order contributions to the Dirac-Fock-Coulomb energy. 

DIRAC is a relativistic quantum chemistry code for solving Dirac-Fock calculations based on a Dirac-Coulomb Hamiltonian. It is capable of... 

The development of fully relativistic molecular Dirac-Fock (DF)-LCAO codes including correlation effects is still underway and calculations are usually restricted to molecules with very few atoms. In contrast to nonrelativistic calculations, large basis sets are needed to describe accurately the inner... 

Tupitsyn, I. I. HFDB 2003. Program for atomic finite-difference four-component Dirac-Hartree-Fock-Breit calculations written on the base of the hfd code [110]. 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

The relativistic theory and computation of atomic structures and processes has therefore attained some sort of maturity and the various codes now available are widely used. Those mentioned so far were based on ideas originating from Hartree and his students [28], and have been developed in much the same way as the non-relativistic self-consistent field theory recorded in [28-30]. All these methods rely on the numerical solution, using finite differences, of the coupled differential equations for radial orbital wave-functions of the self-consistent field. This makes them unsuitable for the study of molecules, for which it is preferable to expand the radial amplitudes in a suitably chosen set of analytic functions. This nonrelativistic matrix Hartree-Fock method, as it is often termed, was pioneered by Hall and Lennard-Jones [31], Hall [32,33] and Roothaan [34,35], and it was Roothaan s students, Synek [36] and Kim [37] who were the first to attempt to solve the corresponding matrix Dirac-Hartree-Fock equations. Kim was able to obtain solutions for the ground state of neon in 1967, but at the expense of some numerical instability, and it seemed at the time that the matrix Dirac-Hartree-Fock scheme would not be a serious competitor to the finite difference codes. 

Figure 1. Total nonrelativistic multi-configuration Hartree-Fock energy, relativistic corrections (estimated as the difference between the multi-configuration Dirac-Hartree-Fock and Hartree-Fock energies) and correlation contributions (estimated from correlation energy density functional calculations) for the group 4 elements. The multi-configuration treatments were carried out with the atomic structure code GRASP [78] and correspond to complete active space calculations with the open valence p shell as active space. The nonrelativistic results were obtained by multiplying the velocity of light with a factor of 10 .

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