Near exact excited states of the carbon dimer in a quadruple-zeta basis using a general non-Abelian density matrix renormalization group algorithm

TL;DR

This paper enhances the density matrix renormalization group algorithm to incorporate non-Abelian symmetries, enabling highly accurate calculations of excited states of the carbon dimer with improved efficiency and precision.

Contribution

The authors develop a flexible non-Abelian symmetry implementation in DMRG that generates tensor operators dynamically, allowing precise excited state calculations for complex molecules.

Findings

Achieved near-exact energies for C$_2$ dimer within 0.01 mE$_h$ residual error.

Computed potential energy curves for twelve states with 0.1 mE$_h$ accuracy.

Demonstrated the method's efficiency and accuracy surpassing previous quantum Monte Carlo and extrapolation methods.

Abstract

We extend our previous work [J. Chem. Phys, \textbf{136}, 124121], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group (DMRG) algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C$_2$ dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10$^{12}$ many-body states. While our calculated energy lies within the 0.3 mE$_h$ error bound of previous initiator full configuration interaction quantum Monte Carlo (i-FCIQMC) and correlation energy extrapolation by intrinsic scaling (CEEIS) calculations, our estimated residual error is only 0.01 mE$_h$, much more accurate than these previous estimates. Further, due to the additional efficiency afforded by the algorithm, we compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations $^1\Sigma^+_g$, $^1\Sigma^+_u$, $^1\Sigma^-_g$ and $^1\Sigma^-_u$, to an estimated accuracy within 0.1 mE$_h$ of the exact result in this basis.