Analysis of Electron Correlation Effects in Strongly Correlated Systems (${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$) by applying DMRG and Quantum Information Theory

Abstract

The dissociation of ${\mathrm{N}}_2$ and ${\mathrm{N}}_2^{+}$ has been studied by using the \emph{ab initio} Density Matrix Renormalization Group (DMRG) method. Accurate Potential Energy Surfaces (PES) have been obtained for the electronic ground states of ${\mathrm{N}}_2$ (${\mathrm{X}}^1{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) and ${\mathrm{N}}_2^{+}$ (${\mathrm{X}}^2{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) as well as for the ${\mathrm{N}}_2^{+}$ excited state ${\mathrm{B}}^2{\mathrm{\Sigma }}_{\mathrm{u}}^{+}$. Inherently to the DMRG approach, the eigenvalues of the reduced density matrix ($\rho$) and their correlation functions are at hand. Thus we can apply Quantum Information Theory (QIT) directly, and investigate how the wave function changes along the PES and depict differences between the different states. Moreover by characterizing quantum entanglement between different pairs of orbitals and analyzing the reduced density matrix, we achieved a better understanding of the multi-reference character featured by these systems.

35 pages, 13 figures

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