arXiv subjects

Erik Verzijl

Publications and source records attributed to Erik Verzijl.

2 recordsLinked to original sources

arXiv2026

Static Effective Hamiltonians for Molecular Systems through RPA-based Downfolding

Green's function-based downfolding methods construct effective Hamiltonians of reduced dimension that capture dynamical correlations of an electronic environment through effective potentials acting on the active space only. Using methods based on the constrained random phase approximation (cRPA) and moment RPA (mRPA), we construct static effective Hamiltonians that include screening through the environment. We derive expressions for the energy contribution from the environment and for the effective one- and two-body terms, taking into account double-counting corrections. cRPA requires additional consideration due to its frequency dependence, while mRPA provides a static Hamiltonian by construction. For the ground state energy of benzene and bond dissociation curves, we discuss the differences and similarities between the different flavors of RPA-based screening. We show that downfolding using cRPA describes both dynamical and strong correlation well, while mRPA and cRPA restricted to screening the particle-hole matrix elements can fail to describe bond dissociation due to a dominating dynamical correlation term. In the static limit, these two methods are shown to be almost indistinguishable.

physics.chem-ph↗

arXiv2026

$GW$ reduced density matrix from iterated linearized Dyson equation

Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's $GW$ approximation. The non-iterated $GW$ based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).

physics.chem-ph↗