On the nodal structure of single-particle approximation based atomic wave functions

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Wave functions describe electron behavior in atoms and molecules.
• Different approximations exist for wave functions, such as restricted, unrestricted, and generalized valence bond methods.

Purpose of the Study:

• To investigate the equivalence of nodal structures across different atomic wave function types.
• To verify the findings using computational simulations.

Main Methods:

• Theoretical analysis of atomic wave function nodal structures.
• Fixed node-diffusion Monte Carlo simulations for atomic systems (up to Neon).
• Application to a molecular system (Li(2)) using multideterminantal generalized valence bond and restricted Hartree-Fock methods.

Main Results:

• Nodal structures of restricted, unrestricted, and generalized valence bond atomic wave functions are equivalent.
• Fixed node-diffusion Monte Carlo simulations support this equivalence for atoms up to Neon.
• For Li(2), a multideterminantal generalized valence bond wave function did not improve nodal surfaces over restricted Hartree-Fock.

Conclusions:

• The nodal topology is consistent across common atomic wave function approximations.
• Computational methods confirm the equivalence of these nodal structures.
• Advanced wave function methods may not always refine nodal surfaces for simple molecular systems.