Dirac-Hartree

The Dirac equation can be readily adapted to the description of one electron in the held of the other electrons (Hartree-Fock theory). This is called a Dirac-Fock or Dirac-Hartree-Fock (DHF) calculation. 

There are several ways to include relativity in ah initio calculations more efficiently at the expense of a bit of accuracy. One popular technique is the Dirac-Hartree-Fock technique, which includes the one-electron relativistic terms. Another option is computing energy corrections to the nonrelativistic wave function without changing that wave function. 

DHF (Dirac -Hartree-Fock) relativistic ah initio method DHF (derivative Hartree-Fock) a means for calculating nonlinear optical properties... 

Figure 4.13 Excitation energies for the s-d and s-p gaps of the Group 11 elements. Experimental (Cu, Ag and Au) and coupled cluster data (Rg) are from Refs. [4, 91]. For the s-p gap of Rg we used Dirac-Hartree-Fock calculations including Breit and QED corrections.

Figgen, D., Rauhut, G., Dolg, M. and StoD, H. (2005) Energy-consistent pseudopotentials for group 11 and 12 atoms adjustment to multi-configuration Dirac-Hartree-Fock data. Chemical Physics, 311, 227-244. 

Apparently, a large number of successful relativistic configuration-interaction (RCI) and multi-reference Dirac-Hartree-Fock (MRDHF) calculations [27] reported over the last two decades are supposedly based on the DBC Hamiltonian. This apparent success seems to contradict the earlier claims of the CD. As shown by Sucher [18,28], in fact the RCI and MRDHF calculations are not based on the DBC Hamiltonian, but on an approximation to a more fundamental Hamiltonian based on QED which does not suffer from the CD. At this point, let us defer further discussion until we review the many-fermion Hamiltonians derived from QED. 

The partition (2) is quite arbitrary, since one could with equal validity absorb all one-body relativistic effects of order Zaf into the mean-field energy of the Dirac-Hartree-... 

Table 6 Matrix Dirac-Hartree-Fock (Edhf) and Hartree-Fock (Ehf) energies calculated using BERTHA. The Gaussian exponential parameters are those of the non-relativistic sets derived by van Duijenveldt and tabulated in Poirier et al [36]. Thejirst-order molecular Breit energy, Eb, v as calculated using methods described in [12] relativistic corrections to Ehf collected in the column labelled E energies are in atomic units.

In Table 6, we present a series of calculations ofthe molecular structures of N2, CO, BF, andNO+ using sets of published Gaussian basis set parameters [36]. The relativistic Dirac-Hartree-Fock electronic energies, and the non-relativistic Hartree-Fock... 

Table 7 Estimates of total relativistic correction, E, and the first-order Breit energy correction,, obtained by combining the atomic or ionic contributions indicated by the second column. They may be compared with the values of the total relativistic correction, Ek. and thefirst-order Breit interaction, Eb, obtained directly from matrix Dirac-Hartree-Fock and Hartree-Fock calculations of the molecular structure using BERTHA [12], Only the results of the Iis7p2d atom-centred basis sets for Ek and Eb are quoted. All energies in atomic units.

Dirac-Hartree-Fock-Breit (DHFB) calculations of atoms and molecules across the Periodic Table. 

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]. 

These (see Chapter 2) may be obtained utilizing the relativistic analogue of the Hartree-Fock method, normally called the Dirac-Hartree-Fock method [176-178], The relevant equations may be found in an analogous manner to the non-relativistic case, therefore here we shall present only final results (in a.u. let us recall that X = nlj, X = nl j) ... 

Relativistic X-Ray Scattering Factors for He Through Ar from Dirac-Hartree-Fock Wave Functions. 

The relativistic or non-relativistic random-phase approximation (RRPA or RPA)t is a generalized self-consistent field procedure which may be derived making the Dirac/Hartree-Fock equations time-dependent. Therefore, the approach is often called time-dependent Dirac/Hartree-Fock. The name random phase comes from the original application of this method to very large systems where it was argued that terms due to interactions between many alternative pairs of excited particles, so-called two-particle-two-hole interactions ((2p-2h) see below) tend to... 

Relativistic Dirac-Hartree-Fock from Reference 32. 

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