General Self-Consistent-Field Equations and Atomic Spinors

General Self-Consistent-Field Equations and Atomic Spinors 

What remains is the calculation of the two radial functions Fn,K,(t) and Qn,)c, ( )- For this task the coupled first-order differential SCF equations have to be solved. The explicit form of these equations depends on the many-electron Hamiltonian used to calculate the total electronic energy. For the Dirac-Coulomb Hamiltonian in combination with the general multi- 

These SCF equations contain the r variable only and are therefore onedimensional, which makes them particularly accessible by numerical solution methods. The corresponding Dirac-Coulomb-Brrif SCF equations [201] can be obtained in an analogous way from the energy expression that includes the Breit term. It is, however, interesting to note that some of the Breit potential energy terms enter the qff-diagonal and are therefore added to (r). This is a 

The inhomogeneous SCF Eqs. (9.105) for all shells may be cast into the form of a homogeneous multiparameter super-equation. Its solution, however, is not as straightforward as the sequential solution of the individual inhomogeneous equations [477,478]. 

The Cl expansion coefficients, which enter the structure factors 7 and r,y)t/, are obtained as eigenvectors of the Cl eigenvalue problem introduced in section 8.7 for a Cl-type wave function. 

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General Self-Consistent-Field Equations and Atomic Spinors 359 configuration wave function these equations turn out to read [351]... 

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