English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This work presents the formalism for evaluating molecular SCF equations, asadapted to four$-$component Dirac spinors, which in turn reduce toSlater$-$type orbitals with non$-$integer principal quantum numbers in thenon$-$relativistic limit. The "catastrophe" which emerges for a charge numbers$Z>137$, in solving the Dirac equation with a potential corresponding to apoint$-$charge is avoided through using Slater$-$type spinor orbitals in thealgebraic approximation. It is observed that, ground$-$state energy ofhydrogen$-$like atoms reaches the negative$-$energy continuum $\left(-mc^2\right)$ while critical nuclear charge $Z_{c}$, about $Z_{c}=160$. Thedifficulty associated with finding relations for molecular integrals overSlater$-$type spinors which are not$-$analytic in the sense of complex analysisat $r = 0$, is eliminated. Unique numerical accuracy is provided by solving themolecular integrals through Laplace expansion of Coulomb interaction andprolate spheroidal coordinates. New convergent series representation formulaeare derived. The technique draws on previous work by the author and the generalformalism is presented in this paper.

On the use of Slater-type spinor orbitals in Dirac-Hartree-Fock method. Results for hydrogen-like atoms with super$-$critical nuclear charge