## Chapter 12

Random Phase Approximation Calculations: Energy and First-Order Properties

Ground state energies and analytic first-order properties (e.g., ’gradients’ for structure
optimizations) can be computed within the random phase approximation (RPA) using the rirpa
module. Theory and development of the rirpa module is published in references [151,152] for
the energy and reference [153] for the first-order properties. In case of two-component
relativistic RPA energy calculations see reference [154]. For energy and gradients, the
resolution-of-the-identity (RI) approximation is used to approximate the two-electron repulsion
integrals in the correlation treatment and is combined with an imaginary frequency
integration. The RI approximation is also employed by default for the computation of the
Coulomb integrals for the HF energy. For the energy, it is optional to use RI for the Fock
exchange integrals (’RI-K’), while RI-K for the gradients is not available yet. Open shell
systems and the frozen core approximation may be used in RPA energy calculations
but are not presently available in gradient calculations. Two-component RPA energy
calculations are only possible for Kramers-restricted closed-shell systems. ECPs are
presently not compatible with RIRPA gradients. Neither RPA energy nor gradients
support symmetry at the moment. The gradients may be used together with the scripts
jobex (for structure optimizations) and NumForce (for numerical harmonic vibrational
frequencies).