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Half-Projected σ Self-Consistent Field For Electronic Excited States.

Hong-Zhou Ye1, Troy Van Voorhis1

  • 1Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.

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We introduce half-projected sigma self-consistent field (HP σ-SCF) to improve calculations of electronic excited states. This method enhances accuracy and stability for singlet and triplet excitations, overcoming limitations of previous approaches.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Calculating electronic excited states is challenging due to their nature as energy saddle points, causing methods like Δ-SCF to collapse to the ground state.
  • The σ-SCF method addresses variational collapse but suffers from spin contamination and symmetry breaking in open-shell systems.

Purpose of the Study:

  • To develop an improved method for calculating electronic excited states that overcomes the limitations of σ-SCF.
  • To enhance the accuracy and stability of excited-state calculations, particularly for singlet and triplet excitations.

Main Methods:

  • Introduced a half-projection (HP) scheme to partially restore spin symmetry in σ-SCF solutions.
  • Employed a variation-after-projection (VAP) approach for optimizing orbitals of the projected wave function.
  • Developed the half-projected (HP) σ-SCF theory.

Main Results:

  • HP σ-SCF significantly improves the description of singlet and triplet excitations compared to the original σ-SCF method.
  • Numerical simulations show HP σ-SCF yields high-quality excited-state solutions with smooth potential energy surfaces across various geometries.
  • Local excitations calculated with HP σ-SCF demonstrate size-intensivity.

Conclusions:

  • HP σ-SCF effectively resolves spin contamination and symmetry breaking issues present in the original σ-SCF method.
  • The new method provides a robust and accurate approach for studying electronic excited states in molecules.
  • HP σ-SCF offers a promising tool for computational chemistry research, enabling reliable excited-state potential energy surface calculations.