ACCURATE ANALYTICAL SELF-CONSISTENT-FIELD (SCF) HARTREE–FOCK (H–F) WAVE FUNCTIONS FOR SECOND-ROW ATOMS

1966 ◽  
Vol 44 (12) ◽  
pp. 3121-3129 ◽  
Author(s):  
Gulzari L. Malli
Keyword(s):  
Wave Functions ◽  
Atomic Systems ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Consistent Field ◽  
Shielding Constants ◽  
Self Consistent Field ◽  
F Wave ◽  
Expansion Coefficients ◽  
Orbital Exponents

Analytical H–F SCF wave functions have been calculated for the second-row atoms in their ground and lowest excited states. Expectation values for the various one-electron operators evaluated by using these wave functions are also presented. Tables of the basis-function orbital exponents, expansion coefficients, and the orbital energies of all the occupied atomic orbitals are given. Nuclear magnetic shielding constants and the magnetic susceptibilities for these atomic systems are also calculated.

Accurate Numerical Hartree–Fock Self-Consistent-Field Wave Functions for La+, Tm+, and Yb+

1972 ◽  
Vol 50 (7) ◽  
pp. 708-709 ◽  
Author(s):  
K. M. S. Saxena
Keyword(s):  
Rare Earth ◽  
Virial Theorem ◽  
Wave Functions ◽  
Rare Earth Ions ◽  
Radial Wave ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Field Wave

Accurate numerical Hartree–Fock (HF) self-consistent-field (SCF) wave functions have been obtained for La+(4ƒ16S)3F and 1F, Tm+(4ƒ136S)3F and 1F, and Yb(4ƒ146S)2S rare-earth ions. In general, the total energy values have an accuracy of seven figures, the virial theorem is satisfied to seven significant digits, and the radial wave functions are self-consistent and without tail oscillations to three decimals. Several Hartree–Fock parameters are also evaluated with these functions.

APPROXIMATE WAVE FUNCTIONS OF Pb+++ BY THE METHOD OF SELF-CONSISTENT FIELD WITHOUT EXCHANGE

1959 ◽  
Vol 37 (9) ◽  
pp. 983-988 ◽  
Author(s):  
J. F. Hart ◽  
Beatrice H. Worsley
Keyword(s):  
Common Point ◽  
Wave Functions ◽  
The Self ◽  
Decimal Digit ◽  
Hartree Fock ◽  
The Core ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Approximate Wave

The FERUT program previously described for calculating Hartree–Fock wave functions by the method of the self-consistent field has been adapted to the configuration Pb+++. Although the exchange factors were omitted, the program was extended beyond its original scope in other respects, and an assessment of the difficulties so encountered is made. It might be noted, however, that, except in the case of the 4ƒ wave function, it was possible to begin all the integrations at a common point. Initial estimates were made from the Douglas, Hartree, and Runciman results for thallium. The estimates for the core functions were not assumed to be satisfactory. The errors in the final wave functions are considered to be no more than one or two units in the second decimal digit.

Radial wave functions with exchange for Va 2+ , Kr and Ag +

1958 ◽  
Vol 247 (1250) ◽  
pp. 390-399 ◽  
Keyword(s):  
Wave Functions ◽  
Initial Slope ◽  
Radial Wave ◽  
University Of Toronto ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Physical Approximation ◽  
Self Consistent Field ◽  
The University

A generalized program for calculating atomic radial wave functions with exchange has been prepared for the Ferranti computer (FERUT) at the University of Toronto, and is described in a separate paper. This program has now been applied to V 2+ , Kr and Ag + . The wave functions for these atoms, together with the energy and initial slope parameters, are presented to the accuracy justified by the physical approximation of the Hartree–Fock formulation. The configurations of Kr and Ag + are considerably larger than any which have previously been treated by the self-consistent field process with exchange.

Accurate Numerical Hartree–Fock Self-Consistent-Field Wave Functions for Rare-Earth Ions having 4fN6s Configuration

1971 ◽  
Vol 49 (20) ◽  
pp. 2619-2620 ◽  
Author(s):  
K. M. S. Saxena ◽  
Gulzari Malli
Keyword(s):  
Rare Earth ◽  
Virial Theorem ◽  
Wave Functions ◽  
Rare Earth Ions ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Significant Figures ◽  
Field Wave

Accurate numerical Hartree–Fock (HF) self-consistent-field (SCF) wave functions have been obtained for Ce+(4f26s)4H, Pr+(4f36s)5I, Nd+(4f46s)6I, Pm+(4f56s)7H, Sm+(4f66s)8F, Eu+(4f76s)9S, Gd+(4f86s)8F, Tb+(4f96s)7H, Dy+(4f106s)6I, Ho+(4f116s)5I, and Er+(4f126s)4H rare-earth ions. In general, total energy values have an accuracy of seven significant digits. The virial theorem is satisfied to the minimum of six significant digits and the Pnl wave functions are self-consistent to at least five significant figures. Several HF parameters are also evaluated with these wave functions.

A simple quality test for self-consistent-field atomic orbitals

1993 ◽  
Vol 71 (2) ◽  
pp. 175-179 ◽  
Author(s):  
N. Desmarais ◽  
G. Dancausse ◽  
S. Fliszár
Keyword(s):  
Basis Functions ◽  
Quality Test ◽  
Linear Combinations ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Consistent Field ◽  
Valence Region ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Finite Linear

A quality test is proposed for SCF atomic orbitals, [Formula: see text] approximated as finite linear combinations of suitable basis functions [Formula: see text] The key is in a function, readily derived from the Hartree–Fock equation [Formula: see text] which is identically zero for true Hartree–Fock spin orbitals and not so for approximate orbitals. In this way, our test measures how closely approximate orbital descriptions approach the true Hartree–Fock limit and thus provides a quality ordering of orbital bases with respect to one another and with respect to that limit, in a scale uniquely defined by the latter. Moreover, this analysis also holds for atomic subspaces of our choice, e.g., the valence region. Examples are offered for representative collections of Slater- and Gaussian-type orbital expansions.

Sign in / Sign up

Export Citation Format

Share Document