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Fragment quantum embedding using the Householder transformation: A multi-state extension based on ensembles.

Filip Cernatic1, Emmanuel Fromager1, Saad Yalouz1

  • 1Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France.

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This study extends density matrix embedding theory (DMET) using the Householder transformation to describe multiple electronic states, including excited states. The novel ensemble embedding method accurately captures ground and excited states in various systems.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Materials science

Background:

  • Density Matrix Embedding Theory (DMET) has been reformulated using Householder transformations for fragment embedding.
  • Previous work focused on ground-state calculations using a non-interacting one-electron reduced density matrix.

Purpose of the Study:

  • To extend the Householder transformation-based DMET to describe multiple electronic states, including ground and excited states.
  • To develop an ensemble embedding method for accurate fragment embedding.

Main Methods:

  • Utilized an ensemble non-interacting density matrix as a reference.
  • Applied successive Householder transformations to generate an expanded set of bath orbitals.
  • Demonstrated the method in single-shot DMET calculations.

Main Results:

  • Achieved exact fragment embedding for multiple electronic states.
  • Proved that the number of additional bath orbitals scales with fractionally occupied natural orbitals.
  • Successfully described ground and first excited states in a Hubbard model and a hydrogen system.

Conclusions:

  • The ensemble embedding approach using Householder transformations is feasible for describing multiple electronic states.
  • The method provides a larger set of bath orbitals, enhancing accuracy.
  • Future work can focus on self-consistency to further improve ensemble embedding.