Development of photovoltaic and photoresponsive materials depends on properties of electronically excited states which can be determined from higher-energy solutions to self-consistent field calculations. However, obtaining these higher-energy solutions has proven difficult. Conventional methods such as steepest descent and the non-Aufbau method either do not converge to an excited state or have difficulties converging at all. An alternative method is the Maximum Overlap Method (MOM), which allows the prescription of a target state and ensures the calculation is guided to a solution near that target state. The aim of this project is to illustrate the mechanics of MOM using the RGB color space as an analogy for molecular orbital space. This analogy provides visual illustration for how MOM allows us to find excited state self-consistent field solutions. Additionally, we can easily test new ideas and compare methods without working through the full machinery of molecular orbital calculations. Using the color analogy we compare results of steepest descent, non-Aufbau, and MOM optimizations. Additionally, direct inversion in the iterative subspace (DIIS) is implemented to accelerate the convergence of MOM in RGB color space. This analogy has aided in the implementation of MOM into the DFTB+ package to assist the convergence of excited-state self-consistent charge calculations.

Color-based illustration of the maximum overlap method

253rd National Meeting (2017)

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