Of multielectron atoms

Electron Spin and the Pauli Exclusion Principle Orbital Energy Levels in Multielectron Atoms Electron Configurations of Multielectron Atoms Electron Configurations and the Periodic Table... 

A. Scrinzi, Ionization of multielectron atoms by strong static electric fields, Phys. Rev. A 61 (4) (2000) 041402. 

In case of multielectron atoms the energies of various orbitals depend not only upon the nuclear charge but also upon the other electrons present in the atom. It is impossible to calculate the exact energies of various orbitals in a multielectron atom. However, approximate values of their energies can be obtained from the special data. Relative order of energies of various orbitals in all multielectron atoms is same and is illustrated in following figure. 

The quantum numbers that describe states of multielectron atoms are defined as follows ... 

To this point in the discussion of multielectron atoms, the spin and orbital angular momenta have been treated separately. In addition, the spin and orbital angular momenta couple with each other, a phenomenon known as spin-orbit coupling. In multielectron atoms, the S and L quantum numbers combine into the total angular momentum quantum number J. The quantum number J may have the following values ... 

The problem of the searching for the optimal one-electron representation is one of the oldest in the theory of multielectron atoms. Three decades ago, Davidson had pointed the principal disadvantages of the traditional representation based on the self-consistent field approach and suggested the optimal natural orbitals representation. Nevertheless, there remain insurmountable calculational difficulties in the realization of the Davidson program (see, e.g. Ref. [12]). One of the simplified recipes represents, for example, the DPT method [18,19]. Unfortunately, this method does not provide a regular refinement procedure in the case of the complicated atom with few quasiparticles (electrons or vacancies above a core of the closed electronic shells). For simplicity, let us consider now the one-quasiparticle atomic system (i.e., atomic system with one electron or vacancy above a core of the closed electronic shells). The multi-quasiparticle case does not contain principally new moments. In the lowest second order of the QED PT for the A , there is the only one-quasiparticle Feynman diagram a (Fig. 12.1), contributing the ImAZ (the radiation decay width). 

Quantum Numbers of Multielectron Atoms 409 TABLE 11.3 Examples of Atomic States (Free-lon Terms) and Quantum Numbers... 

In a previous section, we presumed that the wavefunctions of multielectron atoms can be approximated as products of hydrogen-like orbitals ... 

In addition to the conditions for the electronic structures of multielectron atoms established by the monoelectronic wave functions and their relative energies mentioned above, other restrictions should also be considered. One of them is the Pauli principle stating that no two electrons can have the same quantum numbers. Thus one orbital can contain a maximum of two electrons provided they have different spin quantum numbers. Other practical rules or restrictions refer to the influence of interelectronic interactions on the electronic structures established by Hund s rules. The electrons with the same n and / values will occupy first orbitals with different nti and the same rris (paired spins). 

The aufbau principle is used to build up the electronic structures of multielectron atoms by adding protons and electrons to the hydrogen atom. According to this principle electrons are placed in hydrogen-like orbitals filling them in the order of decreasing stability (energy of the orbital and interelectronic... 

The energy levels of multielectron atoms can be characterized by orbital and spin angular momentum values in the Russell-Saunders approximation. 

There are several commonly used approximation schemes that can be applied to the electronic states of multielectron atoms. The first approximation scheme was the variation method, in which a variation trial function is chosen to minimize the approximate ground-state energy calculated with it. A simple orbital variation trial function was found to correspond to a reduced nuclear charge in the helium atom. This result was interpreted to mean that each electron in a helium atom shields the other electron from the full charge of the nucleus. A better variation trial function includes electron correlation, a dependence of the wave function on the electron lectrcm distance. ... 

Homonuclear diatomic molecules have two nuclei of the same element. We base our discussion of these molecules on the LCAO molecular orbitals of the molecule ion in much the same way as we based our discussion of multielectron atoms on the hydrogen-like atomic orbitals. 

This is rarely applied to organometallic species in part because laser irradiation can cause complexes to decompose, but the method is in principle useful for detecting nonpolar bonds, which do not absorb, or absorb only weakly in the IR. Tlie intensity of the Raman spectrum depends on the change of polarizability of the bond during the vibration. One of the earliest uses was to detect the Hg-Hg bond in the mercurous ion [y(Hg-Hg) = 570 cm ], a case where the polarizability change is large as a result of multielectron atoms being involved. Unlike IR spectroscopy, the method is compatible with measurements in aqueous solution. 

In the previous section, we pointed out that the interpretation of atomic line spectra posed a difficult problem for classical physics and that Bohr had some success in explaining the emission spectrum for the hydrogen atom. However, because his model was not correct, he was unable to explain all features of the hydrogen emission spectrum and could not explain the spectra of multielectron atoms at all. A decade or so after Bohr s work on hydrogen, two landmark ideas stimulated a new approach to quantum mechanics. Those ideas are considered in this section and the new quantum mechanics— wave mechanics—in the next. 

In Section 8-10 and in Chapter 24, we will see that orbital energies of multielectron atoms also depend on the quantum numbers and m. ... 

Describe two ways in which the orbitals of multielectron atoms resemble hydrogen orbitals and two ways in which they differ from hydrogen orbitals. 

Realistic values of can be obtained from an analysis of the wave functions of multielectron atoms, as described in Are You Wondering 9-1. Values of Zgg for the valence electrons for the first 36 elements are shown in Figure 9-7. The following points can be established by careful examination of these values. 

These estimates come from an analysis of the wave functions of multielectron atoms. An exact solution of the Schrodinger equation can be obtained for the H atom, but for multielectron atoms, only approximate solutions are possible. The principle of the calculation is to assume each electron in the atom occupies an orbiM much like those of the hydrogen atom. However, the functional form of the orbital is based on another assumption that the electron moves in an effective or average field dictated by all the other electrons. With this assumption, the complicated multielectron Schrodinger equation is converted into a set of simultaneous equations—one for each electron. Each equation contains the unknown effective field and the unknown functional form of the orbital for the electron. The approach to solving such a set of equations is to guess at the functional forms of the orbitals, calculate an average... 

Multiplying numerator and denominator by /Tq and comparing the expression obtained with eq. (5.2.7), we shall find the molar magnetic susceptibility of multielectron atoms... 

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