A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Complete Active Space Self-Consistent-Field (CASSCF) calculations are crucial for accurately describing electron correlation in molecules.
• Iterative orbital updates are a key step in CASSCF methods, but convergence can be slow.
• Existing methods often rely on iterative diagonalization of density matrices.

Purpose of the Study:

• To develop a novel perturbation theory-based algorithm for accelerating iterative orbital updates in CASSCF calculations.
• To present an alternative approach to constructing unitary orbital update matrices.
• To demonstrate the efficiency of the new algorithm when combined with DIIS.

Main Methods:

• Utilizes perturbation theory to evaluate the first-order contribution of singly excited configurations.
• Employs the Dyall Hamiltonian to define a zeroth-order Hamiltonian.
• Constructs a unitary orbital update matrix directly from single-excitation amplitudes.
• Combines the new orbital update strategy with Direct Inversion of the Iterative Subspace (DIIS).

Main Results:

• The proposed algorithm leads to very rapid convergence of the CASSCF iteration procedure.
• Single-excitation amplitudes vanish at convergence, consistent with the generalized Brillouin's theorem.
• The method provides an efficient alternative for orbital updates compared to iterative diagonalization.

Conclusions:

• The new perturbation theory-based algorithm significantly accelerates CASSCF calculations.
• This approach offers a computationally efficient and robust method for iterative orbital updates.
• The findings contribute to the advancement of quantum chemical calculation methods.