Dirac-Fock method

The parameters X of Eq. (9.3) and M of Eq. (9.5) are determined by the electronic structure of the molecule. They were calculated in 1997 for the ground 0+ state of TIE by Parpia [89] and by Laerdahl, Saue, Faegri Jr., and Quiney [88] using the Dirac-Fock method with gaussian basis sets of large sizes (see Table 4). Below we refer to paper [127] with the calculations presented in details and not to the brief communication [88] of the same authors. There was also a preliminary calculation of electronic structure in TIF performed by Wilson et al. in [128]. In paper [19] the first calculation of accounts for correlation effects was performed (see also [129]... 

R(q) is momentum-dependent. Both the extended-average-level and the optimal-level multiconfiguration Dirac—Fock methods were tried. The results are illustrated in fig. 11.12. The sensitivity of electron momentum spectroscopy is shown by the fact that the former calculation is completely... 

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-... 

Uncovering two-step autoionisation involved a combination of techniques the photoabsorption spectrum of Ba was obtained using synchrotron radiation and classical spectroscopy of high dispersion [358]. The analysis was performed using the multiconfigurational Dirac-Fock method, which allowed the limits to be identified [359]. The doubleionisation spectrum was obtained by photoion spectroscopy using syn-... 

Indeed, as the pi/2 orbitals differ in behaviour from the ps/2 orbitals, it is obvious that the six electrons of a p orbital will not be equivalent when hybridization is involved to form bonding molecular orbitals including heavy atoms. As an illustration, we display in Fig. 7 the transition from LS to jj coupling down the Group 14 column of the Periodic Table as given by the Dirac-Fock method. 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

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. ... 

Pyykko and Desclaux (1978) (see also Desclaux and Pyykko 1974,1976) have used the one-center Dirac-Fock method to study diatomic hydrides containing very heavy atoms. In particular, the work of Pyykko (1987) on several lanthanide hydrides is worth citing. We will describe the results of these calculations subsequently. It should be stated that the one-center DF method is applicable only to diatomic hydrides. A critical comparison of the properties computed by this method with the state-of-the-art ab initio method suggests that the properties obtained by the one-center method are not always in good agreement with more accurate procedures. Also, the properties of the excited states have not been computed using this method. 

P. Indelicato, J. P. Desclaux. Projection Operator in the Multiconfiguration Dirac-Fock Method. Phys. Scr., T46 (1993) 110-114. 

Visscher, L. Post-Dirac-Fock methods. In Sehwerdtfeger, P. (ed.) Relativistic Electronic Structure Theory, Part I, pp. 291-331. Elsevier, Amsterdam (2002)... 

Another attractive future experiment could be an attempt to reduce Sg(VI) to Sg(IV) in 0.1 M HCl/0.1 M HF and to distinguish the two oxidation states on an anion-exchange column where the reduced species, in contrast to the oxidized species, is being eluted [115]. Standard reduction potentials of Sg in acid solutions have been calculated by Pershina et al. [116] (see Redox Potentials ) using the multiconfiguration Dirac-Fock method predicting that the reduction of Sg(VI) to Sg(lV) should be feasible experimentally. 

Saue, T. (2002). Post Dirac-Fock-methods - Properties. In P. Schwerdtfeger (Ed.)> Relativistic electronic structure theory. Part 1. Fundamentals (p. 332). Amsterdam Elsevier. 

The 4p —4p 5s transitions of these ions have been identified in the spectra of laser produced plasmas (2x10 W/cm irradiation power) and energy predictions by the DIrac-Fock method supported the identifications [9]. The accuracy of the levels reported in Table 2/93 is about 160 cm which makes them in very good agreement with earlier theoretical values obtained by the Slater-Condon method [6]. The oscillator strengths of 4p—5s transitions are given In [9] and the probabilities of forbidden transitions within 4s 4p in [6]. Slater and spin-orbit energy parameters are reported in [6, 9]. 

The configuration sharing on the basis 4s4p2+4s24d+4s25s has been evaluated by means of the Slater-Condon parametric method. The spin-orbit constants derived from experiment are compared with ab initio (Hartree-Fock) and with semiempirical predictions [4]. The ground term splitting has been also calculated by means of the Dirac-Fock method [7]. 

In absence of experimental results on these Ions, the 27 energy levels of the three configurations 3s 3p , 3s3p , and 3s 3p3d are studied for all Ions by the Dirac-Fock method. The Breit interaction and Lamb shift are calculated perturbatively and all configurations of the (n = 3) complex are included in this multiconfiguration calculation. Selected results are tabulated below [7] ... 

These ions emit in different spectral regions according to the type of transition. Their spectra have neither yet been observed in any region for Os and Ir, nor in the vacuum ultraviolet for platinum. In the bromine-like, gallium-like, and zinc-like isoelectronic sequences, the fine structures of the lowest P terms have been predicted by the Dirac-Fock method with semiempirical corrections added [1]. The level energies E (in cm ) are ... 

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