Active Learning Configuration Interaction for Excited-State Calculations of Polycyclic Aromatic Hydrocarbons

We present the active
learning configuration interaction (ALCI)
method for multiconfigurational calculations based on large active
spaces. ALCI leverages the use of an active learning procedure to
find important electronic configurations among the full configurational
space generated within an active space. We tested it for the calculation
of singlet–singlet excited states of acenes and pyrene using
different machine learning algorithms. The ALCI method yields excitation
energies within 0.2–0.3 eV from those obtained by traditional
complete active-space configuration interaction (CASCI) calculations
(affordable for active spaces up to 16 electrons in 16 orbitals) by
including only a small fraction of the CASCI configuration space in
the calculations. For larger active spaces (we tested up to 26 electrons
in 26 orbitals), not affordable with traditional CI methods, ALCI
captures the trends of experimental excitation energies. Overall,
ALCI provides satisfactory approximations to large active-space wave
functions with up to 10 orders of magnitude fewer determinants for
the systems presented here. These ALCI wave functions are promising
and affordable starting points for the subsequent second-order perturbation
theory or pair-density functional theory calculations.