Ghost Embedding Bridging Chemistry and One-Body Theories

Abstract

Phenomenological rules play a central role in the design of chemical reactions and materials with targeted properties. Typically, these are formulated heuristically in terms of non-interacting orbitals and bands, yet show remarkable accuracy in predicting the complex behavior of intrinsically interacting many-body systems. While their non-interacting formulation makes them easy to interpret, it potentially hinders the development of new rules for systems governed by strong correlation, such as transition metal-based materials. In this work, we present a rigorous framework that allows bridging between fully interacting, even strongly correlated, systems and an effective one-body picture in terms of quasiparticles. Further, we present a computational strategy to efficiently and accurately access the main components of such a description: the embedding approximation of the ghost Gutzwiller Ansatz. We illustrate the capabilities of this quasiparticle formulation on the Woodward-Hoffmann rules, and apply their reformulated version to toy ``reactions'' which exemplify the main scenarios covered by them.

Figures (9)

• Figure 1: Toy example of Woodward-Hoffmann forbidden reaction for H$_4$ cluster in sto-6g basis. a) Schematic of reaction. b) Non-interacting orbital energies as a function of the reaction coordinate $x$, marking the orbital parity with respect to the $\sigma_{xz}$ mirror plane. c) Logarithm of the absolute value of the determinant of the exact Green's function, with Hartree-Fock orbital energies shown as dashed gray lines. Poles of the green's function appear as bright linese, zeros as dark ones. Note that the crossing of a pair of even/odd non-interacting orbitals at $x = 1/2$ in the corresponds to the crossing of zeros in the interacting Green's function.
• Figure 2: Symmetry analysis of $\mathrm{log}[|\mathrm{det}(G)|]$ for the ED Green's function of the H$_4$ reaction in the sto-6g basis. We compare the total Green's function determinant with its components in the four irreducible representation of the $C_{2v}$ point group.
• Figure 3: Logarithm of the absolute value of the determinant of the Green's function for the H$_4$ reaction in sto-6g basis, as computed with ghost Gutzwiller with different numbers of ghosts $N_g$. The Hartee-Fock orbital energies are shown as dashed gray lines.
• Figure 4: Quasiparticle eigenvalues within the ghost Gutzwiller treatment of the H$_4$ reaction in 6-31g basis, as computed with different numbers of ghosts $N_g$. We indicate the irreducible representation of the $\mathrm{C_{2v}}$ group to which each quasiparticle state corresponds with a different color/marker.
• Figure 5: Toy H$_4$ reaction in non-minimal sto-6g basis. Left panel shows the quasiparticle eigenvalues within a ghost Gutzwiller treatment with 4 ghosts per orbital. We indicate the irreducible representation of $\mathrm{C_{2v}}$ to which each quasiparticle state corresponds with a different color/marker. Right panel show the logarithm of the absolute value of the exact determinant. Note that in this non-minimal basis model, the crossing of zeros does not happen at zero energy.