Atoms, electronic structures

To return to our main line of thought, the development of variational techniques for valence theory, there is an obvious parallel between the use of the usual (complex) AOs for the calculation of atomic electronic structures and the hybrid AOs for the molecular case ... 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

The various areas of atomic spectroscopy will be discussed in more detail in the experimental and applications sections of this chapter. However, in order to better appreciate the ranges of applicability and limitation of the various atomic spectroscopic methods, it is in order to proceed next to a consideration of the features of atomic electronic structure which form the basis for atomic line spectra and to the processes which result in the production of atomic absorption or emission spectra. 

Orbitals, States, and the Complexities of Atomic Electronic Structure... 

L. Visscher, K. G. Dyall, Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions, At. Data Nucl. Data Tables 67 (1997) 207-224. 

Hartree-Fock (table), 534 Herman and Skillman (table), 50f for optical absorption, 100 significance, 53,450f use of Hartree-Fock, 451,454 values, 50f, and Solid State Table Atoms, electronic structure, 81T, 29pr Augmented Plane Wave method, 433... 

The Englishman, Hartree (1,60) the Russian, Fock (2,3) and the American, Slater (5-7), in the early development of modern quantum mechanics, pioneered the calculation of atomic electronic structure. Hartree based his method on the variation principle and this led naturally to the development of the self-consistent field method, which is at the heart of the design of modem molecular orbital programs. 

Suppose that we can make a guess at theJo7m of the orbitals which minimise eqn (2.1) and further suppose that this functional form of each of the approximate orbitals depends on a number of parameters. An obvious example is the case of the electronic structure of atoms which are all the same shape and there is a familiar model for the electronic structure the hydrogen atom. The parameters on which this model of atomic electronic structure might depend are the effective nuclear charges of each orbital i.e. replacing the hydrogenic Zjn by... 

In the usual restricted model of atomic electronic structure the opposite choice is made, since the symmetry-adapted functions are complex. 

Is hybridization a useless concept, flien No, it is not. It serves as a first indicator (when calculations are not yet performed) of what happens to a local atomic electronic structure, if the atomic configuration is tetrahedral, trigonal, etc. For example, the trigonal hybrids describe the main features of flie electronic configuration in flie benzene molecule (see Fig. 8.31). 

GFMC does not have time-step error but its requirements for computational time are higher than DMC. This makes GFMC a less common choice for treatment of molecular or atomic electronic structure problem. 

The values for single-zeta STOs, the i, 2 C and C2 values for double-zeta STOs, and the VSIP values can be taken from results of atomic electronic structure calculations using the Hartree-Fock method [49, 50]. There... 

One of our goals in this chapter has been to determine the electronic structures of atoms. So far we have seen that quantum mechanics leads to a very elegant description of the hydrogen atom. The hydrogen atom, however, has only one electron. How must our description of atomic electronic structure change when we consider atoms with two or mote electrons (a inany-electrcm atom) To describe these atoms, we must consider not only the nature of orbitals and their relative energies but also how the electrons populate the available orbitals. 

X-ray and ultraviolet photoelectron spectroscopy XPS UPS Electron emission from atoms Electronic structure and oxidation state of surface atoms and adsorbed species... 

---