Nonrelativistic states electron configuration

Element Major relativKStic electron configuration J Ref. Major nonrelativistic electron configuration State Ref. 

Many chemical problems can be discussed by way of a knowledge of the electronic state of molecules. The electronic state of a molecular system becomes known if we solve the electronic Schrodinger equation, which can be separated from the time-independent, nonrelativistic Schrodinger equation for the whole molecule by the use of the Bom-Oppenheimer approximation D. In this approximation, the electrons are considered to move in the field of momentarily fixed nuclei. The nuclear configuration provides the parameters in the Schrodinger equation. 

Figure 1. The radial parts of the large component of the 6pi/2 bispinor and the corresponding pseudospinor obtained in equivalent Dirac-Fock and 21-electron GRECP/SCF calculations for the state averaged over the relativistic 65 /26 1/2 configuration of thallium. Their difference is multiplied by 1000. The GRECP is generated for the state averaged over the nonrelativistic 6s 6p 6d configuration.

When the single-configuration HF energy is subtracted, the energy (16a) represents 46% of the total electron correlation nonrelativistic energy of Be S, which is 1.19 eV. Nevertheless, it will be used in Section 9 for the calculation of excitation energies of low-lying excited states of Be, whose wavefunctions are also truncated appropriately. 

Approximate many-electron wave functions are then constructed from the Hartree-Fock reference and the excited-state configurations via some sort of expansion (e.g., a linear expansion in Cl theory, an exponential expansion in CC theory, or a perturbative power series expansion in MBPT). When all possible excitations have been incorporated (S, D, T,. .., for an -electron system), one obtains the exact solution to the nonrelativistic electronic Schrodinger equation for a given AO basis set. This -particle limit is typically referred to as the full Cl (FCI) limit (which is equivalent to the full CC limit). As Figure 5 illustrates, several WFT methods can, at least in principle, converge to the FCI limit by systematically increasing the excitation level (or perturbation order) included in the expansion technique. 

Both direct and indirect effects act on all shells of an atom, however to a different extent. For the valence shells of a many-electron atom one typically observes a contraction and stabilization of the s and p shells and an expansion and destabilization of the d and f shells. The consequences for the ground state configurations of the lanthanide and actinide atoms are depicted in Figure 16.6. Note for example, that at the nonrelativistic Hartree-Fock (HF) level of theory the ground state configurations of Ce and Th are 4f 6s and 51 7s, ... 

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