Oscillator strengths of electronic excitations with response theory using phase including natural orbital functionals

del Campo J. Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation

In this work, we explore the use of Piris natural orbital functionals (PNOFs) to calculate excited-state energies by coupling their reconstructed second-order reduced density matrix with the extended random-phase approximation (ERPA). We have named the general method PNOF-ERPA, and specific approaches are referred to as PNOF-ERPA0, PNOF-ERPA1, and PNOF-ERPA2, according to the way the excitation operator is built. The implementation has been tested in the first excited states of H2, HeH+, LiH, Li2, and N2 showing good results compared to the configuration interaction (CI) method. As expected, an increase in accuracy is observed on going from ERPA0 to ERPA1 and ERPA2. We also studied the effect of electron correlation included by PNOF5, PNOF7, and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where GNOF achieves better results. Overall, the extension of PNOF to excited states has been successful, making it a promising method for further applications.

Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization

Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.