Abstract
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.
Highlights
Electronic excited states of organic materials play a key role in photovoltaics,[1−3] light-emitting diodes,[4,5] and photochemistry.[6−8] The computational analysis of excited states of organic materials such as hydrocarbon molecules[9] and porous organic polymers[10,11] is important to rationalize the experimental spectroscopic results and make predictions
The following iteration parameters were tested to check the convergence of the active learning configuration interaction (ALCI) calculations: (i) maximum number of iterations for each selected CI (SCI) calculation (3, details are available in the Supporting Information (SI), Section S3.1), (ii) maximum sampling number of queries (2000, see the SI, Section S3.2), (iii) maximum level of excitations for each iteration (1), (iv) query sampling method, and (v) CI coefficient threshold for important configurations (0.01)
The excitation energies using ALCI and complete activespace configuration interaction (CASCI) are compared to experimental values in Figure 8.92 Before discussing our results, it should be noted that a direct comparison between experimental and computed excitation energies is often difficult because experimentally one measures band maxima, which are usually red-shifted with respect to the computed vertical excitations.[93]
Summary
Electronic excited states of organic materials play a key role in photovoltaics,[1−3] light-emitting diodes,[4,5] and photochemistry.[6−8] The computational analysis of excited states of organic materials such as hydrocarbon molecules (e.g., aromatic molecules and polyenes)[9] and porous organic polymers (e.g., conjugated organic polymers, hyper-cross-linked polymers, and covalent organic frameworks)[10,11] is important to rationalize the experimental spectroscopic results and make predictions. One flavor of SCI is to use perturbation theory to select important configurations, like in the configuration interaction using an iterative perturbative selection (CIPSI).[37] In the adaptive sampling CI approach,[38,39] the single and double excitations are generated only from configurations with the highest coefficients, and they are selected using the perturbation theory This method has been recently employed in combination with very large active spaces, up to (52e, 52o).[40] In the heat-bath CI (HCI) method, an approximation to the full expression of first-order perturbation is used to select configurations.[41] In Monte Carlo configuration interaction (MCCI),[42−44] configurations are stochastically chosen and only those with a coefficient higher than a certain threshold are retained in the wave function.
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