Attacking the integral transformation bottleneck: A fast orbital-optimization algorithm with sub-cubic computational cost for arbitrary seniority-zero wavefunctions

An orbital-optimization algorithm is devised for finding stationary points of seniority-zero wavefunctions applied to quantum-chemical Hamiltonians of full seniority. The algorithm is agnostic to peculiarities of the seniority-zero method, requiring only the availability of its one- and two-electron reduced density matrices. Their simpler structure is exploited to avoid the computationally demanding four-index two-electron integral transformation; instead, intermediary rank-three tensors are constructed, which greatly reduce the consumption of computational resources. In combination with the spatial locality of atomic and molecular orbitals, as well as the sparsity of the seniority-zero density cumulant, the algorithm achieves sub-cubic scaling with system size. A direct inversion in the iterative subspace scheme is applied to accelerate orbital-optimization convergence. Using pECCD as the seniority-zero wavefunction, it is demonstrated that the algorithm succeeds in optimizing large linear oligomer chains and hydrogen 2D/3D clusters with up to 1391 orbitals on modest computer hardware. The method is subsequently applied to predict molecular properties of ozone, the rotational barrier in ethylene, and isomerization energies of organic reactions, where it is benchmarked against conventional quantum-chemical methods.