On Developing Cost-Efficient Computational Solutions to Physical Chemistry Problems

Despite steady advances in the power of computer hardware, many computations on molecular systems remain computationally expensive, especially when high numerical
precision is required. The work presented here is aimed at reducing computational cost through advances in the algorithms used to solve physical chemistry problems. The studies span two subfields of computational chemistry, quantum chemistry and computational chemical kinetics.
In quantum chemistry, self-consistent field calculations are central to almost all modern approaches to the determination of a chemical system’s electronic structure.
Chapters 2 and 3 develop and test a least-squares commutator in the iterative subspace (LCIIS) scheme for accelerating self-consistent field (SCF) calculations.
LCIIS is similar to current direct inversion of the iterative subspace (DIIS) methods in that both approaches obtain the next iterate of the density matrix as a linear combination of past iterates. However, whereas DIIS methods find the linear combination by minimizing a sum of error vectors, LCIIS minimizes the Frobenius norm of the commutator between the density matrix and the Fock matrix. The two chapters
apply LCIIS to two fundamentally different SCF optimization algorithms, to demonstrate that LCIIS can be applied to multiple algorithm templates. LCIIS leads to faster convergence than other SCF convergence accelerating methods. In addition, numerical experiments on a variety of chemical systems, where self-consistent field convergence is problematic, show that LCIIS can increase the chance of finding low energy solutions for the ground electronic state. Another aspect of quantum chemistry addressed in this study is the development of semi-empirical quantum chemistry methods. These methods offer dramatic
reduction in computational cost, compare with their ab initio counterparts, while maintaining an acceptable level of accuracy on specific families of chemical compounds.
Chapter 4 reformulates density functional tight binding (DFTB) theory, a commonly used semiempirical Hamiltonian, as a layer for use in deep learning. Integration
with deep learning enables flexible models to be used for the semiempirical parameters and provides an efficient means to optimize these parameters on large datasets of molecular properties. In computational chemical kinetics, a software system is developed to automate the design of synthetic methods for specific polymer targets. The system has two
computational components, a polymer reaction simulator and a deep reinforcement learning (RL) agent. The reaction simulator mimics the kinetics of atom transfer radical polymerization (ATRP) and the RL controller is allowed to add chemical reagents to the simulation throughout the course of the reaction. When trained using an actor-critic algorithm, the RL controller is able to discover and optimize control policies that lead to a variety of target molecular weight distributions (MWDs) for the final product. The learned control policies are robust and transfer to similar but
not identical ATRP reaction settings, even under the presence of simulated noise. A number of ways to to increase the sample efficiency of the RL algorithm are explored, with the hope of transplanting the system from simulator to the physical lab. Overall, this is a new and computationally efficient approach to design of functional
materials that makes uses of modern advances in chemical kinetics simulation and deep reinforcement learning.