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Fully Internally Contracted Multireference Configuration Interaction Theory Using Density Matrix Renormalization

Masaaki Saitow1, Yuki Kurashige1,2,3, Takeshi Yanai1,2

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Summary

This study introduces an optimized multireference configuration interaction (MRCI) method combined with density matrix renormalization group (DMRG) for accurate electronic structure calculations. The enhanced DMRG-MRCI method favors the iron(IV)-oxo state, deeming the iron(V) electromer thermally inaccessible.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The multireference configuration interaction (MRCI) method combined with the quantum-chemical density matrix renormalization group (DMRG) offers a powerful approach for calculating dynamic electron correlation.
  • Previous DMRG-MRCI implementations faced computational scaling limitations (Nact^8 × N) with large active spaces, hindering further applications.
  • Accurate electronic structure calculations are crucial for understanding complex chemical systems, such as metalloporphyrins.

Purpose of the Study:

  • To develop an extended and computationally efficient implementation of the DMRG-MRCI method.
  • To investigate the relative stability of iron(IV)-oxo porphyrin and its iron(V) electronic isomer (electromer).
  • To resolve discrepancies in theoretical predictions regarding the accessibility of the iron(V) electromer.

Main Methods:

  • An extended optimization of tensor contractions was developed by incorporating rank reduction of the decomposed cumulant-approximated four-particle reduced density matrix (4-RDM).
  • This optimization reduces computational scaling to Nact^7 × N and mitigates cache-miss penalties.
  • Enhanced symbolic manipulation software was used to manage the complexity of tensor contraction terms involving decomposed 4-RDM objects.

Main Results:

  • The new DMRG-MRCI implementation was applied to iron(IV)-oxo porphyrin using an active space of (29e,29o).
  • The DMRG-cu(4)-MRCI+Q model determined the triradicaloid iron(IV)-oxo state as the lowest energy state.
  • The iron(V) electromer was characterized as thermally inaccessible, supporting prior experimental and density functional studies.

Conclusions:

  • The optimized DMRG-MRCI method provides a computationally feasible approach for high-level electronic structure calculations with large active spaces.
  • The study confirms the stability of the iron(IV)-oxo state over the iron(V) electromer in porphyrin systems.
  • These findings contradict previous restricted active-space second-order perturbation theory (RASPT2) calculations, highlighting the importance of accurate correlation treatment.