Selfconsistent field calculations

MCSCF multiconfiguration selfconsistent field calculation. Q(v) total cross section. 6 Gengenbach et al. (1973b). c Gengenbach et al. (1973c). 

A different approach is chosen when the screening of nuclear potential due to the electrons is incorporated in /z . Transformation to the eigenspinor basis is then only possible after the DHF equation is solved which makes it more difficult to isolate the spin-orbit coupling parts of the Hamiltonian. Still, it is also in this case possible to define a scalar relativistic formalism if the so-called restricted kinetic balance scheme is used to relate the upper and lower component expansion sets. The modified Dirac formalism of Dyall [24] formalizes this procedure and makes it possible to identify and eliminate the spin-orbit coupling terms in the selfconsistent field calculations. The resulting 4-spinors remain complex functions, but the matrix elements of the DCB Hamiltonian exhibit the non-relativistic symmetry and algebra. 

Roos, B.O. (1987.) The complete active space selfconsistent field method and its applications in electronic stmcture calculations, in Ah initio Methods in Quantum Chemistry—II (ed. K. Lawley), John Wiley Sons, Ltd., Chichester. 

Equation (1-180) can be obtained from a variational calculation of the energy of the dimer with a wave function that is product of determinantal wave functions of the monomers constructed from the optimal (selfconsistent) orbitals. Unfortunately, the optimization of the orbitals of one monomer in the electrostatic field of the other does not prevent the unphysical transfer of electrons from one system to the other, since the antisymmetry of the wave function of the dimer is not preserved, and consequently, the Pauli principle is not satisfied. This may lead to some unphysical results in the short range260. It should also be stressed that the interaction part of Eq. (1-180) cannot be obtained, as proposed in Ref. (261), by taking the expectation value of the interaction operator V with the product of determinantal wave functions of the monomers constructed from the optimal (selfconsistent) orbitals. This would result in an overcounting of the induction terms, already in the second order. 

Eq. (3.2.1.61) shows that for the selfconsistent calculation of the full interlayer multiple diffraction, we have again to invert a matrix, now in plane-wave representation of the wave field. The dimension of the matrix is correlated to the number of visible beams, which is determined by the request that — (iko — g ) is... 

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