A general non-Abelian density matrix renormalization group algorithm with application to the C₂ dimer

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group 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 C₂ dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10¹² 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 and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE_h, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T_e) of eight lowest lying excited states: a³Π_u, b³Σ_g⁻, A¹Π_u, c³Σ_u⁺, B¹Δ_g, B^′1Σ_g⁺, d³Π_g, and C¹Π_g are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations ¹Σ_g⁺, ¹Σ_u⁺, ¹Σ_g⁻, and ¹Σ_u⁻, to an estimated accuracy of 0.1 mE_h of the exact result in this basis