scholarly journals NO Detoxification Reaction in Heme of Truncated Hemoglobin N of Tubercle Bacillus from the Point of View of the Multiconfigurational Theory of the Self-Consistent Field

2020 ◽  
Author(s):  
K.V. Simon ◽  
A.V. Tulub
Keyword(s):  
Point Of View ◽  
The Self ◽  
Tubercle Bacillus ◽  
Truncated Hemoglobin ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

scholarly journals Self-consistent field, with exchange, for Cu +

1936 ◽  
Vol 157 (892) ◽  
pp. 490-502 ◽  
Keyword(s):  
Complete Solution ◽  
Point Of View ◽  
Wave Functions ◽  
The Self ◽  
Radial Wave ◽  
Electron Atom ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field

Solutions of Fock’s equations for the self-consistent field of a many-electron atom, including exchange effects, have already been carried out for several atoms by Fock and Petrashen and the present authors. The heaviest atom for which results of such calculations have previously been published is Cl - ; Cu + was selected as the next atom for which to attempt the solution of Fock’s equations, for the following reasons. As already pointed out in Paper IV, the results of the solution of Fock’s equations are most interesting for atoms for which exchange effects are large; the self-consistent field without exchange, which is an almost necessary preliminary to the solution of Fock’s equation, had already been worked out for Cu + , and from this work it was known that the (3 d ) 10 group of Cu + is very sensitive to the atomic field, so that it is likely to be con­siderably affected by the inclusion of exchange terms in the equations. Further, in view of the interest of Cu from the point of view of metal theory, it is desirable to have as good wave functions for Cu + as possible, particularly for the outer groups, which are those likely to be most affected by the inclusion of exchange terms in the equation from which they are determined. The number of radial wave functions involved in the normal con­figuration of Cu + is perhaps almost the largest for which a complete solution of Fock’s equations is practicable, for the following reason.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

Sign in / Sign up

Export Citation Format

Share Document