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We developed a new framework for creating density functional approximations (DFAs) by combining nonempirical (NE) constraints and empirical (E) data. This method uses B-splines for improved accuracy and transferability in chemical property predictions.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Density Functional Approximations (DFAs) are crucial for electronic structure calculations.
  • Current DFA construction involves either nonempirical (NE) constraint satisfaction or empirical (E) data-driven optimization.
  • A unified approach is needed to leverage the strengths of both methods.

Purpose of the Study:

  • To present a general framework uniting NE and E strategies for DFA construction.
  • To introduce the use of B-splines for constructing inhomogeneity correction factors (ICFs).
  • To demonstrate enhanced performance and physical rigor in DFAs.

Main Methods:

  • Employing B-splines for ICF construction, offering advantages over polynomial expansions.
  • Utilizing Tikhonov and penalized B-splines (P-splines) regularization for constraint enforcement and ICF smoothness.
  • Developing the CASE (constrained and smoothed empirical) framework as a proof-of-concept.

Main Results:

  • Successfully constructed a constraint-satisfying, data-driven global hybrid DFA.
  • The CASE framework enables explicit enforcement of linear and nonlinear constraints.
  • Demonstrated enhanced performance across a diverse set of chemical properties.

Conclusions:

  • The CASE approach generates DFAs with physical rigor and transferability of NE-DFAs.
  • Leverages high-quality quantum-mechanical data to improve DFA performance.
  • Reduces arbitrariness in ansatz selection for DFAs.