The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion

Abstract

The methods of solution of the wave equation for a central field given in the previous paper are applied to various atoms. For the core electrons, the details of the interaction of the electrons in a single nk group are neglected, but an approximate correction is made for the fact that the distributed charge of an electron does not contribute to the field acting on itself (§2).For a given atom the object of the work is to find a field such that the solutions of the wave equation for the core electrons in this field (corrected as just mentioned for each core electron) give a distribution of charge which reproduces the field. This is called the self-consistent field, and the process of finding it is one of successive approximation (§ 3).Approximations to the self-consistent field have been found for He (§ 4), Rb+ (§ 5), Na+, Cl− (§ 9). For He the energy parameter for the solution of the wave equation for one electron in the self-consistent field of the nucleus and the other corresponds to an ionisation potential of 24·85 volts (observed 24·6 volts); this agreement suggests that for other atoms the values of the energy parameter in the self-consistent field (corrected for each core electron) will probably give good approximations to the X-ray terms (§4).The most extensive work has been carried out for Rb+. The distribution of charge given by the wave functions in the self-consistent field is compared with the distribution calculated by other methods (§ 6). The values of X-ray and optical terms calculated from the self-consistent field show satisfactory agreement with those observed (§ 7).The wave mechanical analogue of the case in which on the orbital model an internal and an external orbit of the same energy are possible is discussed (§ 8).

Extending the Characteristic Polynomial for Characterization of C20 Fullerene Congeners

“…The geometries were built at the Hartree-Fock (HF) [3][4][5][6] 6-31 G [36] level of theory and calculated properties (namely, area and volume) were extracted from these calculations. Two different structures proved stable for bbbb (see Figure 9) and both were included in the analysis, resulting in a sample of 46 compounds.…”

“…The generic name of the files was stored as dd_R1R2R3R4, where dd is the number of the compound in the set and R1-R4 are the atoms on layers 1-4 (e.g., 02_bbbn.chp is the second compound in the sample and has boron of the first three layers and nitrogen on the last layer). The geometries were built at the Hartree-Fock (HF) [3][4][5][6] 6-31 G [36] level of theory and calculated properties (namely, area and volume) were extracted from these calculations. Two different structures proved stable for bbbb (see Figure 9) and both were included in the analysis, resulting in a sample of 46 compounds.…”

“…The second extension of the ChP was found by Hartree [3,4] and Fock [5,6] by going in a different direction with the approximation of the wavefunction treatment. They actually found the same older eigenvector-eigenvalue problem ( §20 in [7]; T1 in [8]) in Slater's treatment [9,10] of molecular orbitals.…”

New analytical independent-particle model potential for atoms

“…The HF method, proposed in the 1930's [1,2], is a good approximation to the atomic and molecular problem. The computational complexity of the HF method increases when the exchange effects of elec-and Horton [10] proposed the optimized effective potential (OEP) method as a variation on Slater's method [4].…”

Comparison of Variational Solutions of the Thomas-Fermi Model in Terms of the Corrected Ionization Energy

“…It is well known that the Thomas-Fermi (TF) model [1] of many electrons atom, as it stands, shows poor predictions if com pared to the Hartree approxim ation [2], the quantum mechanical equiv alent of the TF theory [3].…”