Complete-active-space extended Koopmans theorem method.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Koopmans' theorem provides a simple approximation for ionization energies.
• Extended Koopmans' theorem (EKT) methods offer improved accuracy over the original theorem.
• Complete-active-space (CAS) methods are crucial for accurately describing electron correlation in quantum chemistry.

Purpose of the Study:

• To define and analyze the complete-active-space (CAS) extended Koopmans theorem (EKT) as a specific variant of EKT.
• To establish the relationship between CAS EKT and configuration interaction (CI) methods.
• To clarify the accuracy and limitations of CAS EKT for predicting first ionization energies.

Main Methods:

• Defining CAS EKT as a restricted form of EKT using a CAS configuration interaction (CI) reference state.
• Analyzing the electron removal operator's action restricted to active orbitals.
• Comparing CAS EKT predictions with full CI calculations for ionization energies.

Main Results:

• Demonstrated the equivalence between CAS EKT and a specific set of CI calculations involving hole-state configurations within the active space.
• Showed that CAS EKT ionization energies are generally not exact but can approach full CI accuracy.
• Established that CAS EKT can achieve arbitrary precision within finite basis sets.

Conclusions:

• CAS EKT is a valuable theoretical tool with properties analogous to the original Koopmans theorem.
• The method provides a transparent understanding of the accuracy of EKT for ionization energies.
• The findings reconcile disparate statements regarding EKT in existing scientific literature.