Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories

Abstract

Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+fcDFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+fcDFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+fcDFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+fcDFT scheme are discussed in light of these results.

Synergy between pair coupled cluster doubles and pair density functional theory

“…The problem affects pCCD+f DFT because pCCD excludes correlations of the active orbitals that break electron pairs [42]. This issue of the scaling factor holds for other MR+f DFT methods (albeit for different reasons), such as CAS+f DFT and PHF+f DFT, where it typically is related to core orbitals with n k ≈ 2 [17,26]. In pCCD+f DFT, orbitals with small n k may also be affected given that it is unlikely to get occupations numbers that are exactly zero due to the structure of the pCCD density matrix (although exact zeros by symmetry are possible).…”

“…Nevertheless, we note that despite this issue our results for pCCD+f PBE are quite satisfactory, suggesting that the effect of this problem is not too dramatic. In addition, as noted above, this problem can be alleviated by simply relaxing the threshold on n k for orbitals to contribute to ref (r), or by the various improvements of the scaling factor that have been proposed in the literature [16,17,26]. For example, increasing the threshold on n k to 1×10 −5 for the Be series leads to ca.…”

“…We do not employ the pCCD+f LDA variant because LDA provides correlation energies that are too large in magnitude; this problem is not so severe in hybrid schemes due to error cancellation with the LDA exchange. This is a wellknown feature of LDA functionals, which are not recommendable for MR+DFT combinations with 100% MR exchange [15,26]. Figure 3 shows the energy profiles for the symmetric dissociation of an H 4 chain, an H 6 chain (both linear), and the water molecule [ (HOH) = 104.474…”

“…[12], a simple way (n, ∞) and the DFT correlation energy density. The f (r) used here is an adaptation for pCCD from the one developed for CAS-DFT by Miehlich et al [15], analogous to the adaptation for PHF in our PHF+f DFT method [26]. To compute f (r), we first construct a reference density where ψ k (r) are the natural orbitals and the sum runs over all ψ k (r) with nonzero occupation numbers n k .…”

“…Most MR methods have a poor scaling (typically combinatorial), which ultimately hinders their applicability, and further suffer from sizeextensivity and size-consistency problems. This motivated us to develop combinations of DFT with a meanfield projected Hartree-Fock [35,36] (PHF) methodology in place of a traditional MR wavefunction [25,26]. Our PHF+DFT schemes were relatively successful; however, they are also limited by the lack of size-extensivity and size-consistency of PHF, and the fact that PHF does not always capture all of the static correlation.…”