Algorithms Design Molecules for Better Laser Technologies

Nonlinear optical (NLO) materials underpin numerous photonic, telecommunication and laser technologies, but identifying molecules with superior NLO properties remains a significant computational hurdle owing to expansive chemical spaces and conflicting design goals. Dominic Mashak and Jacob Schrum, both from Southwestern University, alongside S. A. Alexander, present a comparative analysis of evolutionary algorithms for molecular design, addressing four key objectives: maximising the ratio of first-to-second hyperpolarizability, optimising the HOMO-LUMO gap and linear polarizability within desired ranges, and minimising energy per atom. Encoding molecules as SMILES strings and evaluating their properties via quantum chemical calculations, the researchers compared NSGA-II, MAP-Elites, MOME, a single-objective evolutionary algorithm, and simulated annealing. This work is significant because the quality diversity methods employed maintain archives across a measure space defined by atom and bond count, facilitating the discovery of structurally diverse molecules, and ultimately demonstrating that NSGA-II consistently achieves high performance across all objectives while MOME excels at exploring a broader range of molecular possibilities.

Designing molecules with specific optical properties has long relied on trial and error. Now, algorithms can automatically generate candidates with tailored characteristics, accelerating materials discovery. This new approach efficiently balances multiple, often conflicting, design goals to yield promising molecules for advanced technologies. Scientists are increasingly focused on designing molecules with specific nonlinear optical (NLO) properties for use in technologies like optical communication and computing.

Discovering materials with enhanced NLO characteristics presents a significant computational challenge, stemming from the enormous number of possible molecular structures and the need to balance multiple, often conflicting, design goals. Recent research has explored the application of evolutionary algorithms to this problem, seeking molecules that simultaneously maximise desirable properties while minimising undesirable ones.

These algorithms treat molecules as sequences of characters, specifically, SMILES strings, and assess their potential using quantum-chemical calculations. The investigation targeted four key objectives: maximising the ratio of first-to-second hyperpolarizability, optimising the HOMO-LUMO gap and linear polarizability within desired ranges, and minimising energy per atom to ensure stability.

By encoding molecules as SMILES strings and evaluating them with quantum-chemical methods, researchers aimed to identify compounds suitable for use in electro-optic modulators, devices that control light intensity. Simply achieving high hyperpolarizability is insufficient; an effective modulator demands a delicate balance between several factors. Linear polarizability must be high enough to encourage charge transfer, but not so high as to cause unwanted absorption or aggregation.

Similarly, the HOMO-LUMO gap requires careful tuning to avoid either excessive absorption or diminished NLO activity. These competing demands necessitate a search strategy capable of navigating a complex, multi-dimensional property space. The algorithms employed differ in their exploration strategies. Quality diversity methods, such as MAP-Elites and MOME, maintain archives of diverse molecular structures, defined by characteristics like atom and bond count, allowing for the discovery of a wider range of possibilities.

NSGA-II, a multi-objective optimisation algorithm, consistently achieves high scores across all objectives, producing high-quality molecules. However, MOME excels at exploring a broader range of molecular structures, resulting in higher global hypervolume and MOQD scores, indicating a more diverse and well-optimised population.

MOME demonstrates superior solution diversity and hypervolume in molecular optimisation

NSGA-II consistently achieved high scores across all four objectives used in the molecular design process, excelling in maximising the ratio of first-to-second hyperpolarizability (β/γ), optimising the HOMO-LUMO gap and linear polarizability within target ranges, and minimising energy per atom. While NSGA-II demonstrated strong performance, MOME proved more effective at exploring a broader range of molecular possibilities.

This exploration resulted in a higher global hypervolume and MOQD score for MOME, indicating a greater diversity of solutions. Molecules were encoded as SMILES strings and their properties were evaluated using quantum-chemical calculations. Examining the results, the global hypervolume metric, a measure of both quality and diversity, reached higher values with MOME than with NSGA-II.

Specifically, MOME achieved a markedly larger hypervolume, demonstrating its ability to identify a wider range of promising molecular structures. By contrast, NSGA-II, while producing high-quality molecules, focused on refining solutions within a narrower search space. Single-objective evolutionary algorithms prioritized maximising the first-to-second hyperpolarizability ratio, often at the expense of other objectives.

These algorithms showed a tendency to neglect optimisation of the HOMO-LUMO gap and linear polarizability. MAP-Elites fostered diversity by maintaining archives across a measure space defined by atom and bond count, allowing it to perform well across a wider range of objectives, even without explicit instruction. Under the conditions of this study, the diversity fostered by MAP-Elites allowed it to achieve a broader distribution of solutions, though not necessarily with the highest individual scores on each objective.

Beyond simply identifying high-performing molecules, MOME’s approach to exploring the chemical space resulted in a more thorough archive of structurally diverse candidates. Rather than focusing solely on optimisation, MOME prioritized maintaining a variety of solutions, which proved beneficial for overall performance as measured by hypervolume and MOQD scores.

Quantum Chemical Descriptors and Optimisation Algorithms for Molecular Nonlinearity

A quantum-chemical calculation pipeline underpinned this work, evaluating molecular properties directly from structural information. Molecules were encoded as Simplified Molecular Input Line Entry System (SMILES) strings, a text-based notation allowing computational manipulation and representing molecular connectivity. These SMILES strings served as the genome for each candidate molecule within the evolutionary algorithms.

Property evaluation involved determining the first hyperpolarizability (β), second hyperpolarizability (γ), linear polarizability (α), the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap, and energy per atom using established quantum chemistry methods. Five distinct optimisation algorithms were implemented to explore the chemical space.

NSGA-II, a multiobjective evolutionary algorithm, competed alongside MAP-Elites, a quality diversity method that constructs an archive of solutions based on both performance and novelty. MOME, another quality diversity approach, was also tested, alongside a single-objective (μ+λ) evolutionary algorithm and simulated annealing. Quality diversity methods crucially maintain archives categorised by atom and bond count, a measure space designed to encourage structural diversity in the resulting molecules.

The selection of these algorithms was not arbitrary; evolutionary algorithms are well-suited to navigating complex, high-dimensional search spaces like that of molecular structures. Quality diversity methods were chosen to specifically promote the discovery of a broad range of molecular scaffolds, potentially uncovering solutions overlooked by traditional optimisation techniques.

Simulated annealing offered a complementary approach, providing a stochastic search method for comparison. To ensure a fair comparison, all algorithms were tasked with optimising four objectives simultaneously: maximising the ratio of first-to-second hyperpolarizability (β/γ), optimising both the HOMO-LUMO gap and linear polarizability to fall within specified target ranges, and minimising energy per atom. For each molecule generated, these properties were calculated, and the algorithms used these values to guide their search towards better solutions.

Evolutionary algorithms accelerate discovery of optimised nonlinear optical materials

Once a material science challenge seemed confined to painstaking laboratory synthesis and trial-and-error testing, the search for better nonlinear optical (NLO) materials now benefits from a computational revolution. For decades, progress in photonics, telecommunications, and laser technology has been hampered by the difficulty of designing molecules with precisely tuned optical properties.

The problem isn’t a lack of potential building blocks, it’s the sheer size of the chemical space, coupled with the need to balance multiple, often conflicting, objectives during the design process. Existing methods struggle to navigate this complexity, often getting stuck in local optima or failing to explore diverse structural possibilities. This work demonstrates a shift towards more intelligent exploration of that chemical space.

By employing evolutionary algorithms, researchers are effectively mimicking natural selection to breed molecules with desired characteristics. Rather than relying on human intuition or brute-force calculations, these algorithms learn from their successes and failures, gradually refining molecular designs to meet specific performance targets. Although NSGA-II showed consistent high performance, the ability of MOME to cast a wider net across potential structures is a valuable contribution, suggesting that diversity in the search process is as important as achieving peak performance in any single metric.

Assessing the true potential of these computationally designed molecules remains a significant hurdle. Predictions based on calculations must be validated through physical synthesis and characterisation, a process that can be time-consuming and expensive. The current focus on individual molecular properties overlooks the complexities of real-world applications, where factors like material stability, processability, and scalability become critical.

The field is poised to move beyond simply identifying promising molecules to engineering practical materials. Future efforts might explore combining these computational design methods with machine learning techniques to predict material properties more accurately and accelerate the discovery process. Automated synthesis and high-throughput testing could create a closed-loop system, where computational models are continuously refined based on experimental feedback, bringing us closer to a future where custom-designed NLO materials are readily available for a wide range of technological applications.