Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Molecular Modeling

Background:

• Molecular Hamiltonians possess inherent rotational and parity symmetries.
• These symmetries are often compromised by fixed Gaussian basis sets in computational methods.
• This symmetry breaking leads to contamination in wave function calculations.

Purpose of the Study:

• To introduce a symmetry projection technique for nuclear-electronic Hartree-Fock wave functions.
• To restore and enforce rotational and parity symmetries in molecular calculations.
• To improve the accuracy of calculating molecular rotational states.

Main Methods:

• Symmetry projection onto representations of the special orthogonal group in three dimensions (SO(3)).
• Generating trial wave functions with correct symmetry properties.
• Calculating energies of low-lying rotational states using the projected wave functions.

Main Results:

• The symmetry projection technique successfully enforces rotational and parity symmetries.
• Wave functions become eigenfunctions of the angular momentum operator.
• Elimination of contamination from excited rotational states was observed.
• Accurate calculation of low-lying rotational state energies for H2 and H3+ was achieved.

Conclusions:

• The symmetry projection technique is an efficient method for accurate molecular symmetry enforcement.
• This approach enables precise targeting and calculation of specific molecular rotational states.
• The method significantly improves the reliability of nuclear-electronic Hartree-Fock calculations.