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

The random phase approximation (RPA) to the correlation energy is extended tofractional occupations and its performance examined for exact conditions onfractional charges and fractional spins. RPA satisfies the constancy conditionfor fractional spins that leads to correct bond dissociation and no staticcorrelation error for H$_2$ but massively fails for fractional charges, with anenormous delocalization error even for a one-electron system such as H$_2^+$.Other methods such as range-separated RPA can reduce this delocalization errorbut only at the cost of increasing the static correlation error. None of theRPA methods seem to have the discontinuous nature required to satisfy bothexact conditions and the full unified condition, emphasizing the need to gofurther than just smooth functionals of the orbitals.

Failure of the random phase approximation correlation energy