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Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix-Driven Complete Active-Space

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We developed a faster algorithm using CPUs and GPUs for calculating electronic structures. This method reveals polyradical characteristics in large polycyclic aromatic hydrocarbons, with periacenes showing the most unpaired electron density.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Accurate electronic structure calculations are crucial for understanding molecular properties.
  • Configuration-interaction-driven complete active-space self-consistent field (CASSCF) theory provides high accuracy but is computationally expensive.
  • Approximations are needed to make these calculations feasible for larger systems.

Purpose of the Study:

  • To develop a computationally efficient algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM).
  • To implement a heterogeneous Central Processing Unit (CPU) + Graphical Processing Unit (GPU) approach for this optimization.
  • To investigate the electronic structure and polyradical character of 3,k-circumacene and 3,k-periacene series.

Main Methods:

  • A heterogeneous CPU+GPU algorithm for variational 2RDM (v2RDM) optimization was developed.
  • This v2RDM approach enables a polynomially scaling approximation to CASSCF.
  • The algorithm was benchmarked, achieving a 3.7x speedup on a GPU+CPU combination compared to CPU-only execution for a 50-electron, 50-orbital system.

Main Results:

  • The GPU-accelerated v2RDM-CASSCF algorithm was applied to explore the electronic structure of 3,k-circumacene and 3,k-periacene molecules.
  • Larger circumacene and periacene molecules exhibit polyradical characteristics in their singlet states, similar to oligoacenes.
  • Periacenes show the earliest onset of polyradical behavior, followed by circumacenes and then oligoacenes, with periacenes displaying the highest unpaired electron density buildup.

Conclusions:

  • The developed heterogeneous algorithm significantly accelerates v2RDM-CASSCF computations.
  • This computational advancement allows for the study of larger polycyclic aromatic hydrocarbons.
  • Circumacene and periacene series display distinct polyradical characteristics, with implications for their electronic and magnetic properties.