Adiabatic projection: Bridging ab initio, density functional, semiempirical, and embedding approximations.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Modern electronic structure calculations rely on approximate Hamiltonians.
• Developing accurate and efficient computational methods is crucial for understanding molecular and material properties.

Purpose of the Study:

• Introduce the adiabatic projection formalism for formally exact corrections to approximate reference systems.
• Generalize existing methods like Kohn-Sham density functional theory (DFT) and explore new theoretical avenues.

Main Methods:

• Construct a reference system Hamiltonian by projecting operators onto selected states.
• Develop density functionals from adiabatic connections to correct differences between projected and unprojected energies.
• Apply the formalism to create corrections for coupled cluster theory and DFT.

Main Results:

• Demonstrate formally exact and systematically improvable analogues to embedding and DFT+U methods.
• Achieve accurate dimerization energies with a projected kinetic energy functional, correcting basis set errors in DFT.
• Show performance comparable to Boys-Bernardi counterpoise correction while addressing intramolecular errors.

Conclusions:

• The adiabatic projection formalism offers a powerful framework for enhancing the accuracy of electronic structure calculations.
• This method provides a pathway to systematically improve approximate theories and correct for common computational artifacts.
• The presented numerical results validate the potential of this formalism in practical applications.