Development and Application of Efficient Data Analytic Methods in Quantum Chemistry

This work presents systematical approaches to improve both the application and theory of quantum chemical methods. Semi-empirical and ab initio quantum chemical methods are used to model fluorescent dyes for bio-imaging. A new approach to development of semiempirical quantum chemical methods is explored, and imitation learning is used to accelerate convergence of self consistent field calculations. The fluorescence of the SKC-513 dye is highly sensitive to the binding of K+ ion. Computations reveal that, in the absence of K⁺, excitation is to two nearly-degenerate states, a neutral (N) excited state with high oscillator strength and a charge-transfer (CT) state with lower oscillator strength. Binding of K⁺ raises the CT state far above the N state, shutting down a non-radiative pathway mediated by the CT state. This rationalizes the high sensitivity of the quantum yield to ion binding. Computations on a series of thiazole orange derivatives are used to successfully account for the observed spectral shifts through frontier orbital analysis. A means to take advantage of molecular similarity to lower the computational cost of electronic structure theory is explored, in which parameters are embedded into a low-cost, low-level (LL) ab initio model and adjusted to obtain agreement with results from a higher-level (HL) ab initio model. In the parametrized LL (pLL) model, selected matrix elements of the Hamiltonian are scaled by factors that depend on element types. Various approaches to scaling, including making parameters sensitive to atomic charges and bond orders, are explored. The models are trained on ethane and ethylene, substituted with -NH₂, -OH and -F, and tested on substituted propane, propylene and t-butane. The molecules are distorted and placed in electrostatic fields. Fitted properties include total and decomposed energies, frontier orbital energies, and interactions with test charges. The best-performing model forms reduce the root mean square (RMS) difference between the HL and LL energy predictions by over 85% on the training data and over 75% on the test data. Many computational methods, including self consistent field calculations in quantum chemistry, work by fixed-point iteration—repeatedly applying a given update function until convergence is achieved. A means to accelerate fixed-point iteration via imitation learning is explored. The approach is simple and needs only black-box access to the original update function. Experiments show that the approach successfully accelerates Hartree-Fock convergence, and that policies trained on one set of molecules transfer successfully to other molecules of the same general class. Imitation learning also leads to more-robust transfer than alternative methods that do not take into account the distribution of states induced by the learned policies.