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Optimally Tuned Multiconfigurational Short-Range DFT for Linear Response Properties

Michał Hapka, Katarzyna Pernal, Ewa Pastorczak

Abstract

Multiconfigurational short-range density functional theory (MC-srDFT) rigorously combines ground state wavefunction theory with DFT. Unlike single-reference range-separated hybrid functionals, MC-srDFT has lacked theoretically grounded protocols for choosing the system-specific range-separation parameter. To address this problem, we introduce an optimal-tuning scheme based on enforcing the correct exponential decay of the electron density. We show that the range-separation parameter can be determined from the ionization potential given by the smallest-magnitude eigenvalue of the Extended Koopmans' Theorem matrix constructed for the model Hamiltonian. We validate this approach for static and dynamic dipole polarizabilities of ground-state molecular systems using MC-srDFT within both full linear response and its extended random phase approximation (ERPA) variant. Optimal tuning substantially improves polarizabilities relative to the commonly used universal $μ= 0.4\,\mathrm{bohr}^{-1}$ parameter.

Optimally Tuned Multiconfigurational Short-Range DFT for Linear Response Properties

Abstract

Multiconfigurational short-range density functional theory (MC-srDFT) rigorously combines ground state wavefunction theory with DFT. Unlike single-reference range-separated hybrid functionals, MC-srDFT has lacked theoretically grounded protocols for choosing the system-specific range-separation parameter. To address this problem, we introduce an optimal-tuning scheme based on enforcing the correct exponential decay of the electron density. We show that the range-separation parameter can be determined from the ionization potential given by the smallest-magnitude eigenvalue of the Extended Koopmans' Theorem matrix constructed for the model Hamiltonian. We validate this approach for static and dynamic dipole polarizabilities of ground-state molecular systems using MC-srDFT within both full linear response and its extended random phase approximation (ERPA) variant. Optimal tuning substantially improves polarizabilities relative to the commonly used universal parameter.
Paper Structure (9 sections, 24 equations, 2 figures, 5 tables)

This paper contains 9 sections, 24 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Range-separated multicofigurational DFT (MC-srDFT)
  4. Optimal range-separation parameter for MC-srDFT based on an exact condition
  5. Approximate dynamic linear response from MC-srDFT
  6. Performance of MC-srDFT response for polarizabilities
  7. Computational Details
  8. Results and Discussion
  9. Summary and Conclusions

Figures (2)

  • Figure 1: Mean error of static polarizabilities calculated in the aug-cc-pVDZ basis set. The area highlighted in red marks the range of tuned $\mu$ values for the studied systems, while the red dot marks the average tuned value $\bar{\mu}_{opt}=0.28\,\mathrm{bohr}^{-1}$. Pirydazine was excluded from the set due to poor convergence of the CASSCF wave function in this basis set. CAS$^*$ denotes that the larger active space was used, as described in Section \ref{['sec3a']}.
  • Figure 2: Violin plots of errors in static polarizability for range-separated methods with a standard value of the range-separation parameter ($\mu=0.4\,\mathrm{bohr}^{-1}$) vs. the optimally tuned values, $\mu_{opt}$.