Expanding the Pareto Frontier of Electronic Structure Methods with Advanced Basis Sets

Abstract

Theoretical studies on vast molecular databases increasingly drive the rational design of drugs and materials, demanding highly efficient electronic structure methods. Density functional theory (DFT) remains the workhorse of computational chemistry, while semiempirical quantum mechanical (SQM) methods achieve speed-ups of three to four orders of magnitude at reduced accuracy. A key factor in balancing efficiency and accuracy is the Gaussian atomic orbital (AO) basis set, which dictates how the electronic wavefunction is represented. This thesis explores strategies to enhance electronic structure methods using advanced basis sets. <br/> ωB97X-3c lowers DFT’s computational cost by combining the newly developed polarized valence double-ζ basis set, vDZP, with the state-of-the-art density functional ωB97X-V. vDZP is variationally optimized for molecular environments and features a deep contraction to ensure well-suited AOs. Alongside large-core effective potentials and the D4 dispersion correction, ωB97X-3c extends the "3c" composite DFT series, outperforming conventional triple-ζ methods in cost-to-accuracy ratio. It is particularly effective for large systems where non-local Fock exchange is essential. <br/> The vDZP basis set is further utilized in the density matrix tight-binding (PTB) method, which incorporates two key advancements: <em>(i)</em> an SQM Hamiltonian expanded in a double-ζ basis set and <em>(ii)</em> a parameterization scheme aimed at reproducing the electron density of a converged ωB97X-3c DFT calculation. PTB predicts infrared and Raman spectral intensities with near-DFT accuracy and reliably computes atomic charges and bond orders with minimal deviations from the reference DFT method. <br/> However, developing a robust energy expression within this framework proved infeasible. To address this, the environment-adaptive single-ζ basis set, q-vSZP, is introduced. Retaining vDZP’s key features, q-vSZP dynamically contracts or expands based on atomic charge and the number of coordinating atoms, capturing effects typically requiring multiple-ζ expansions. <br/> Despite its single-ζ nature, q-vSZP achieves double-ζ accuracy in DFT thermochemistry benchmarks. The required atomic charges are computed via the Charge Extended Hückel (CEH) method, which achieves accuracy comparable to advanced SQM methods while being 10–20 times faster. <br/> This thesis proposes, develops, and tests electronic structure methods that expand the <em>Pareto front</em> of methods with optimal cost-to-accuracy balances and are consistently available across the periodic table. All advancements are implemented in accessible computational frameworks, primarily as open-source software. The q-vSZP basis set, together with insights from PTB and CEH, lays the foundation for next-generation SQM methods.