The exact exchange-correlation (xc) kernel ${f}_{\text{xc}}(x,{x}^{\ensuremath{'}},\ensuremath{\omega})$ of linear response time-dependent density functional theory is computed over a wide range frequencies for three canonical one-dimensional finite systems. Methods used to ensure the numerical robustness ${f}_{\text{xc}}$ are set out. frequency dependence found be largely due its analytic stru...

Most approximate exchange-correlation functionals used within density-functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have b...

The adiabatic-connection fluctuation-dissipation theorem (ACFDT) provides a formal frame work to treat the exchange-correlation energy. Under the random phase approximation (RPA), the effect of the exchange-correlation kernel is neglected, leading to the so-called EXX/RPA method. It has been shown that EXX/RPA yields overall a good description of structural properties of materials with differen...

A theoretical methodology for exploring the conventional Bardeen–Cooper–Schrieffer (BCS) pairing instability superconductivity from a correlated normal phase all possible degrees of many-body correlation has been developed. The Gutzwiller projection scheme with parameter was made use in generating BCS state. variational thereafter implemented, leading to self-consistent equation superconducting...