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

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.