Breit-Pauli approximations

Breit-Pauli Approximation for Evaluating Line Strengths for Spin-Forbidden Transitions Application to NF. 

The spin-orbit operator in the Breit-Pauli approximation is given by (49,71)... 

The leading order of DPT is equivalent to the Breit-Pauli approximation [21], provided that the nonrelativistic wave function is exact. Otherwise... 

It is important to note that (473) - which is equivalent to (472) or (469) - is a better approximation to the leading relativistic correction than that given by the Breit-Pauli approximation. The latter is equivalent to the former expressions only if is the exact non-relativistic wave function, or if the last term in (473) vanishes for some other reason [10]. 

Relativistic corrections to density functional (DFT) calculations by means of DFT have successfully been evaluated by van Wiillen [94], with application e.g. to transition metal carbonyls, unfortunately only at the level of the lowest order relativistic correction 0 c ) to the energy (i.e. slightly better than with the Breit-Pauli approximation). For a comparison of this method with a combination of DFT and ZORA see Ref. [95],... 

In the calculations in terms of Gaussian geminal wave functions [10, 96] an interesting observation was made. While generally the DPT results converge much faster with extension of the basis than the results from the Breit-Pauli approximation, only small differences between the two ap-... 

The leading order of DPT is superior to the Breit-Pauli approximation. 

Most applications to molecules that do not contain heavy atoms (beyond Br in the periodic table) have been based on the Breit-Pauli Hamiltonian which consists of six terms and operates on ordinary nonrelativistic wave functions. In the Breit-Pauli approximation, the total Hamiltonian is defined as... 

For atoms from the first row of the periodic table and molecules containing them, the Breit-Pauli approximation appears to afford an accurate description of relativistic effects. The most important of these effects is usually the spin-orbit coupling... 

A more unified description of relativistic effects, which can be used for systems containing atoms from the second row of the periodic table and beyond, is described in Section VIII where the Breit-Pauli approximation is avoided. 

Here is given in parentheses for the nonrelativistic states and the iE carry the E = E ov E" representations of the Cg double group. The relativistic wave functions, kE, A = 1—3 and E = E or E", are the eigenfunctions of in this basis. The spin-orbit operator is described within the Breit-Pauli approximation. ... 

As discussed by Dyall [720] for the NESC method, the so-called Breit-Pauli approximation to the matrix representation of the X-operator, which is used to construct the relativistic transformation matrix according to Eq. (14.29), is... 

S. J. Havriliak, D. R. Yarkony. On the use of the Breit-Pauli approximation for evaluating line strengths for spin-forbidden transitions Application to NF. J. Chem. Phys., 83(3) (1985) 1168-1172. 

As a second example, we illustrate the influence of relativistic effects - in the Breit-Pauli approximation - on the density function of the Be-like O " atom, by comparing the densities of the flne-structure states Is l p and From... 

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