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Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Mikael Scott1, Gabriel L S Rodrigues1, Xin Li2

  • 1Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden.

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|January 13, 2024
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A new variational formulation of multiconfigurational pair-density functional theory (MC-PDFT) offers accurate calculations for challenging molecules. This method, with reduced active space dependency and lower computational cost, is efficient for large systems.

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Area of Science:

  • Quantum chemistry
  • Computational chemistry
  • Theoretical chemistry

Background:

  • Traditional density functional theory (DFT) struggles with systems involving transition metals, open-shells, and strong electron correlation.
  • Multiconfigurational pair-density functional theory (MC-PDFT) combines a flexible multiconfigurational wave function with pair-density functionals to address static and dynamic correlation.
  • Existing MC-PDFT methods rely on post-hoc calculations following a multiconfigurational self-consistent field (MCSCF) step.

Purpose of the Study:

  • To develop a variational formulation of MC-PDFT through direct optimization of the wave function.
  • To derive and analyze the wave function gradient expressions for this new variational approach.
  • To assess the accuracy and computational efficiency of the variational MC-PDFT method.

Main Methods:

  • Developed a direct optimization approach for MC-PDFT, leading to a variational formulation.
  • Derived wave function gradient expressions analogous to standard MCSCF equations.
  • Applied the method to calculate singlet-triplet gaps and dissociation curves, and performed a large-scale calculation on a ferredoxin protein.

Main Results:

  • The variational MC-PDFT formulation is accurate, as shown by calculations of singlet-triplet gaps and dissociation curves.
  • MC-PDFT exhibits a reduced dependency on the size of the active space compared to traditional multiconfigurational methods.
  • Computational cost is potentially lower than MCSCF and comparable to Kohn-Sham DFT, demonstrated by a large protein calculation.

Conclusions:

  • The variational formulation of MC-PDFT provides an accurate and efficient method for electronic structure calculations.
  • This approach overcomes limitations of traditional DFT for complex molecular systems.
  • MC-PDFT offers a promising computational tool for studying challenging chemical problems, including large biomolecules.