Benchmarking Hartree-Fock and DFT for Molecular Hyperpolarizability: Implications for Evolutionary Design

TL;DR

This work tackles the need for rapid, reliable fitness functions in evolutionary design of nonlinear optical materials by benchmarking Hartree-Fock and five DFT functionals across six basis sets against experimental hyperpolarizability values $β$ for five push–pull chromophores. The authors quantify absolute accuracy with $MAPE$ and assess the preservation of pairwise rankings, as well as computational cost, across 30 method combinations. A key finding is that HF with the modest 3-21G basis set achieves a favorable balance ($MAPE \approx 45.5\%$) and, crucially, all method combinations preserve perfect pairwise rankings, enabling robust evolutionary selection even if absolute errors vary. Basis-set size dominates accuracy, with Pareto-optimal options identifying HF/3-21G (and HF/STO-3G) as practical choices; these results offer evidence-based guidance for high-throughput design of NLO materials, although broader validation beyond simple push–pull systems remains necessary.

Abstract

Evolutionary algorithms for molecular design require computationally efficient yet accurate fitness functions. We systematically benchmark Hartree-Fock and density functional theory for predicting molecular first hyperpolarizability ($β$), evaluating five functionals (HF, PBE0, B3LYP, CAM-B3LYP, M06-2X) across six basis sets against experimental data from five organic push-pull chromophores. For this dataset, HF/3-21G achieves 45.5% mean absolute percentage error with perfect pairwise ranking in 7.4 minutes per molecule. All 30 tested combinations of functional and basis sets maintain perfect pairwise agreement, validating their use as evolutionary fitness functions despite moderate absolute errors. Larger basis sets yield a lower percentage error compared to the experimental values than the difference with the functional. The preservation of pairwise rankings across all combinations of functionals and basis sets provides crucial guidance for evolutionary optimization of nonlinear optical materials.

Figures (4)

• Figure 1: Distribution of percentage errors across all basis sets for each functional. Box boundaries indicate quartiles, orange lines show medians, and green dashed lines indicate means.
• Figure 2: (a) Mean wall time increases systematically with basis set size. (b) The Pareto frontier identifies optimal methods (red dots). Only HF/STO-3G and HF/3-21G achieve Pareto optimality.
• Figure 3: Calculated versus experimental hyperpolarizabilities for five representative functionals. Each panel shows one functional across all basis sets. Black dashed lines indicate regression fits; red solid lines show ideal $y=x$. All achieve R$^2 > 0.99$ with near-unity slopes.
• Figure 4: Performance heatmap showing MAPE for all 30 combinations. Colors indicate performance from green (low error) to red (high error). Dominant vertical structure confirms basis set choice has a greater impact than functional selection.