Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

Abstract

The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange–correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of a range of local interpolation models against accurate exchange–correlation energy densities. The importance of the strictly correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models, and prospects for future approximations based on the local adiabatic connection are discussed.

Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy

“…The reference w 1 ( r ) are obtained at the full-CI and CCSD level of theory, as in refs (14 and 48), by using the aug-cc-pCVTZ and aug-cc-pV6Z basis sets 56 for Ne and H – , respectively. Insets show the absolute error of approximate energy densities, δw 1 ( r ) = w 1 – w 1 apx ( r ).…”

“…Reference energy densities and those obtained with the LB local interpolation scheme are from ref (14). …”

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

“…The adiabatic connection has been employed in various density functional theory studies. First, the method described above has been extended to range‐dependent and local adiabatic connection . A potential driven adiabatic connection has also been proposed to construct new approximations in density functional theory.…”

“…First, the method described above has been extended to range-dependent [30] and local adiabatic connection. [31] A potential driven adiabatic connection [32] has also been proposed to construct new approximations in density functional theory. Exchangecorrelation potential and the local energies were also obtained using nonlinear adiabatic connections.…”

Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection

“…28,45 3 Different formulas that interpolate between the limits of eqs 7 and 8 are available in the literature . 23,24,26,28,46 As in the Padé example of eq 6, when these interpolation formulas are inserted in eq 1 they give an XC energy that is a nonlinear function of the 4 ingredients (or a subset thereof) W 0 [ρ], W 0 [ρ], W ∞ [ρ], W ∞ [ρ] appearing in eqs 7-8.It is clear from these examples that we can write a general XC functional obtained by modeling the adiabatic connection aswhere f ACM is a non-linear function that results from the integration [via eq1] of the given adiabatic connection model (ACM), and W[ρ] = {W 1 [ρ], ..., W k [ρ]} is a compact notation for the k input ingredients that have been used. Then we have N i=1…”