Localization of the 4f wave-function in cesium

1996 ◽  
Vol 74 (9-10) ◽  
pp. 565-567
Author(s):  
B. N. Onwuagba
Keyword(s):  
Wave Function ◽  
Field Potential ◽  
Local Spin Density Approximation ◽  
Energy Term ◽  
Radial Part ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Kinetic Energy Term ◽  
Insight Into

The local spin density approximation is used in the study of the localization of the 4f wave function in cesium, by superimposing the radial part of the kinetic-energy term on the self-consistent field potential VSCF(r). The results obtained show a collapsed 4f wave function in Cs+, but not in neutral Cs, which compares favourably with the previous findings and provide good insight into the understanding of the collapsed 4f wave function in cesium.

Atomic wave functions for gold and thallium

1955 ◽  
Vol 51 (3) ◽  
pp. 486-503 ◽  
Author(s):  
A. S. Douglas ◽  
D. R. Hartree ◽  
W. A. Runciman
Keyword(s):  
Wave Function ◽  
Absorption Edge ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Independent Variable ◽  
Independent Calculation

Before the war, self-consistent field calculations for the Au+ ion had been carried out by W. Hartree but were left still unpublished at his death (see prefatory note in (5)). These results have been used by Brenner and Brown (1) in a relativistic calculation of the K-absorption edge for gold, and they were also used in obtaining initial estimates for the partial self-consistent field calculations for thallium of which results are given in §§3–5 of the present paper. In the meantime an independent calculation for Au+ has been carried out by Henry (6), and his results agree closely with those of W. Hartree. However, it still seems desirable to publish the latter, since they give directly the radial wave function P(nl; r) at exact values of r, whereas Henry used log r as independent variable, as had been done for similar calculations for Hg(4), and has tabulated r½P(nl; r) which is the natural dependent variable to use with log r as independent variable (2); in some applications it is more convenient to have the radial wave functions themselves.

scholarly journals A generalization of the equations of the self-consistent field for two-electron configurations

1937 ◽  
Vol 160 (903) ◽  
pp. 588-604 ◽  
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Configuration Interaction ◽  
The Self ◽  
Angular Function ◽  
Radial Functions ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
General Method

The most successful general method so far devised for dealing with many- electron atoms is th a t of the self-consistent field (abbreviated in what follows to “ s. c. f.” ). If greater accuracy is required than is obtainable with the method as ordinarily used (either with or without exchange), either the so-called “ configuration interaction ” must be taken into account —usually a very laborious procedure—or else more complicated (varia­tional) methods must be used, which must be designed separately for each particular case, and in which the concept of each electron being assigned to its own “ orbit” is usually abandoned. It would seem desirable, therefore, to have, if possible, some general method which will increase the accuracy of the calculations without taking into account configuration interaction, and which will still allow the conceptual features of the s. c. f. method (i. e. the assignment of “ orbits” ) to be retained. In this paper such a method is developed for the case of two-electron configurations in Russell-Saunders coupling. The method consists in assuming a form for the wave function which is similar to that used in the s. c. f. method, except that the proper spatial symmetry is allowed for (which is not so in the case of the s. c. f. equations without exchange), and further, an adjustable function of Θ, the angle between the radii vectores to the two electrons, is inserted as a multiplying factor. The usual varia­tional method is then applied, and yields differential equations for the two radial functions which are similar to those of the ordinary theory, together with an equation for the angular function.

Quadratic response functions for a multiconfigurational self‐consistent field wave function

1992 ◽  
Vol 97 (2) ◽  
pp. 1174-1190 ◽  
Author(s):  
Hinne Hettema ◽  
Hans Jo/rgen Aa. Jensen ◽  
Poul Jo/rgensen ◽  
Jeppe Olsen
Keyword(s):  
Wave Function ◽  
Response Functions ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Quadratic Response ◽  
Field Wave

Self-consistent-field potential energies for the ground negative-ion and neutral states of HeH, ArH, and ArCl

1978 ◽  
Vol 17 (5) ◽  
pp. 1568-1574 ◽  
Author(s):  
R. E. Olson ◽  
B. Liu
Keyword(s):  
Field Potential ◽  
Negative Ion ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

scholarly journals Self-consistent field with exchange for potassium and argon

1938 ◽  
Vol 166 (927) ◽  
pp. 450-464 ◽  
Keyword(s):  
Wave Function ◽  
Sufficient Accuracy ◽  
Wave Functions ◽  
The Self ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Difference

As already mentioned in a previous paper on the calculation of the self- consistent field with exchange for calcium (D. R. and W. Hartree 1938), wave functions more accurate than those calculated without exchange are required both for K + and for Ar, and the calculations for calcium were carried out partly in the hope that it would be possible to interpolate with sufficient accuracy the difference between the wave functions calculated with and without exchange for K + and Ar from the corresponding differences for Cl - and Ca ++ . The results showed that for the (I s ), (2 s ) and (2 p ) wave function this interpolation would probably be satisfactory, but for the (3 s ) and (3 p ) wave functions it was not as straightforward as had been hoped, though even for the latter wave functions, estimates of the differences could be made which, while rather uncertain, would probably give appreciably better wave functions than those calculated without exchange and taken without modification.

Hexaborane(10). Self-consistent field wave function, localized orbitals, and relations to chemical properties

1971 ◽  
Vol 10 (1) ◽  
pp. 171-181 ◽  
Author(s):  
William N. Lipscomb ◽  
Irving R. Epstein ◽  
John A. Tossell ◽  
Eugene Switkes ◽  
Richard Morton Stevens
Keyword(s):  
Wave Function ◽  
Chemical Properties ◽  
Localized Orbitals ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Field Wave
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