Active learning configuration interaction for excitation energies of organic molecules

To accurately predict the electronic excited states of organic molecules, multiconfigurational methods are needed for describing strong electronic correlations. Among various multiconfigurational methods, selected configuration interaction (SCI) theory has been developed due to its simplicity and considerably reduced computational cost compared to the full configuration interaction (FCI) theory. The key idea of the SCI is to sample energetically important configurations (or determinants), by performing an iterative selection procedure to select configurations. However, previous SCI approaches have mostly focused on small systems due to its limited capacity to identify important configurations efficiently. In this work, we developed the active learning configuration interaction (ALCI) protocol in which a binary classification machine learning (ML) model queries the machine (i.e., performing SCI calculations using GAMESS software) for important configurations to efficiently explore configuration space. Polyacenes and pyrene were selected as test materials, and all the bonding and antibonding π orbitals were selected as the active space. Various ML algorithms were compared such as kernel ridge classifier, k-nearest neighbor, random forest, XGBoost, Gaussian Process and artificial neural networks. The protocol starts by performing a restricted active space configuration interaction (RASCI) calculation with up to two holes in RAS1 (i.e., bonding π orbitals) and up to 2 electrons in RAS3 (i.e., antibonding π orbitals) for obtaining initial training data. Iterations are then carried out with constantly expanded configuration space by adding singly excited configurations from the important configurations identified in the previous step, and an ML model is trained with the updated data to predict important configurations for the next SCI calculation using GAMESS. The ALCI can compute accurate excitation energies for the first singlet excited state of the organic molecules compared to the complete active space configuration interaction (CASCI) results for systems up to 16 active electrons in 16 active orbitals.