Abstract
We employ tensor network methods for the study of the seniority quantum number – defined as the number of unpaired electrons in a many-body wave function – in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the \mathbf{D_{6h}}D6h symmetry of benzene.
Highlights
The quantum mechanical characterization of molecular systems is highly nontrivial due to its many-body character
We find that doubly occupied configuration interaction (DOCI) ground state wave functions have in general lower entanglement than their corresponding full configuration interaction (FCI) ground state wave function; accurate results for DOCI can be obtained with a much lower bond dimension
For DOCI calculations, we can immediately implement the DOCI-projected quantum chemical Hamiltonian in Eq (11). This results in a very fast tensor network calculation, partly because of the simpler Hamiltonian, partly because the correlations in the seniority-zero subspace for molecular systems are captured by tensor networks; even for very large systems, a bond dimension of less than 100 suffices for energies within chemical accuracy of the exact DOCI energy
Summary
The quantum mechanical characterization of molecular systems is highly nontrivial due to its many-body character. For molecular systems dominated by singlet-pairs bond structures, it was shown that most of the strong static correlation in a system can already be captured in the subspace spanned by all determinants with zero seniority (no unpaired electrons) [24,25,26,27,28,29,30]. This tremendously reduces the dimension of the Hilbert space at hand, finding the exact doubly occupied configuration interaction (DOCI) wave function is still an exponentially scaling problem. We will present results for the nitrogen dimer (Section 3.1), benzene (Section 3.2) and the neon dimer (Section 3.3), to discuss higher-seniority properties of dynamical correlation, symmetry breaking/restoration and dispersion respectively
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