Analytical gradients of variational reduced-density-matrix and wavefunction-based methods from an overlap-reweighted semidefinite program

Analytical gradients of variational two-electron reduced-density matrix (2-RDM) methods are derived by transforming the atomic-orbital reduced-density matrices to remove the dependence of the N-representability conditions on the orbital-overlap matrix. The transformation, performed through a Cholesky decomposition of the geminal-overlap matrix, generates a Hellmann-Feynman-like expression for the gradient that only depends on the derivative of the transformed reduced Hamiltonian matrix. The formulation is applicable not only to the variational 2-RDM method but also to variational wavefunction methods like the full configuration interaction and complete active-space self-consistent-field. To illustrate, we apply the analytical gradients to perform geometry optimizations on several transition metal complexes, octahedral and trigonal prismatic CrF₆ as well as the (ethylene-1,2-dithiolato)nickel, or Ni(edt)₂, complex.