Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree

Abstract

We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), where the excitation degree (with respect to a given reference determinant) and the seniority number (i.e., the number of unpaired electrons) are combined in a single hierarchy parameter. The key appealing feature of hCI is that each hierarchy level accounts for all classes of determinants whose number shares the same scaling with system size. By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or, at least, parallels that of excitation-based CI. For higher orders of hCI and excitation-based CI, the additional computational burden related to orbital optimization usually does not compensate the marginal improvements compared with results obtained with Hartree–Fock orbitals. The exception is orbital-optimized CI with single excitations, a minimally correlated model displaying the qualitatively correct description of single bond breaking at a very modest computational cost.

State-Specific Configuration Interaction for Excited States

“…The inclusion of correlation at the ΔCISD level brings the excitation energy down to 6. 93 eV. An important question in butadiene concerns the energy gap between the 2 1 A g dark state and the lower-lying 1 1 B u bright state, whose correct ordering has only recently been settled.…”

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

“…Obviously, to fully exploit the potential of first-principle simulations, it is mandatory to select a reliable and robust protocol, ideally not requiring extensive computational resources. There is a vast computational spectroscopy literature covering a wide palette of aspects, including (i) – (iii) and suggesting strategies to select the most appropriate models for treating different types of states and compounds. − However, by and large, published works either treat these aspects separately or provide a detailed analysis for a selected dye or a small set of closely related compounds. The aim of the present contribution is to propose an efficient protocol to overcome some of these limitations and discuss the accuracy and reliability of electronic and vibrational structure methods for simulating vibrationally-resolved electronic absorption spectra, including nonempirical estimations of the inhomogeneous broadening.…”

Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality

“…By taking into account all single and double excitations, one gets CI with singles and doubles (CISD) with a computational cost scaling as scriptO false( N 6 false) (where N is the number of one-electron basis functions), while adding the triples yields CI with singles, doubles, and triples (CISDT) scaling as scriptO false( N 8 false) , and so on. Alternatively, one can systematically increase the seniority number (i.e., the number of unpaired electrons) or the hierarchy parameter (average of the excitation degree and half the seniority number). − Unfortunately, all these methods require considering a huge number of electronic configurations, most of them contributing very little to the energies and/or properties of interest.…”