Electronic states self-consistent field method

Thus, the state of each electron in a many-electron atom is conditioned by the Coulomb field of the nucleus and the screening field of the charges of the other electrons. The latter field depends essentially on the states of these electrons, therefore the problem of finding the form of this central field must be coordinated with the determination of the wave functions of these electrons. The most efficient way to achieve this goal is to make use of one of the modifications of the Hartree-Fock self-consistent field method. This problem is discussed in more detail in Chapter 28. 

The electronic spectrum of aniline has been analyzed, using wave-mechanical methods, by various authors - . The self-consistent field method which has been presented in section I and used in section II to describe the ground state of this molecule can also be used to represent its electronically excited states. For practical reasons it is necessary to introduce the lcao approximation and either the Hiickel or the Pariser and Parr method is used. Furthermore, the virtual orbitals approximation is added. Let us consider the eigenfunctions 77j of the self-consistent field operator A " corresponding to the ground state of aniline in the lcao approximation. They obey the equation... 

There is far less reported experience for the HF studies of electronic excited states (ESs). Especially, highly, doubly and core hole excited (ionized) states are not often studied. It is clear that existing ground state self-consistent field (SCF) methods cannot be directly applied to excited states of the same symmetry or of the same spin multiplicity as a lower state because of the so-called variational collapse i.e., the optimization procedure will find only the lowest solution of a given symmetry or a given spin multiplicity. Therefore, such calculations for ES cannot be considered as routine. The most powerful scheme for accurate treatment of ESs is based on multireference methods [2-8]. They typically provide an accuracy of about 0.1 eV but require the expense of much computational cost. Thus, it can be quite difficult to carry out the corresponding calculations. Such methods are, however, indispensable to study systems where... 

In 1926, he began studying radiative transitions in Hj, and in so doing, he examined Heisenberg s ideas of symmetric and antisymmetric two-electron states in helium. When Douglas Hartree introduced the self-consistent field method for the electronic structure of atoms in 1928, Slater saw the connection with Heisenberg s two-electron states. Slater published a major paper the next year. It described a theory of complex spectra, and in it he showed that with a determinantal many-electron wavefunction (the Slater determinant) one could achieve a self-consistent field wavefunction and also have the proper symmetry for electron systems (antisymmetric with respect to particle exchange). 

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

It is also possible to employ highly correlated reference states as an alternative to methods that employ Hartree-Fock orbitals. Multiconfigu-rational, spin-tensor, electron propagator theory adopts multiconfigura-tional, self-consistent-field reference states [37], Perturbative corrections to these reference states have been introduced recently [38],... 

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