An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Evaluating high-order density matrices in perturbation theory is computationally intensive.
• The Dyall Hamiltonian is crucial for accurate electronic structure calculations.

Purpose of the Study:

• To develop a computationally efficient method for evaluating matrix elements in N-electron valence state perturbation theory.
• To avoid the bottleneck of explicit fourth-order density matrix evaluation.

Main Methods:

• Factorization of matrix elements of the Dyall Hamiltonian.
• Application of factorization to residual terms in approximate complete active space configuration interaction.
• Analogous factorization for complete active space second-order perturbation theory.

Main Results:

• Computational effort is reduced to be comparable to third-order density matrix construction.
• Avoidance of explicit fourth-order density matrix evaluation.
• Efficient evaluation of residual terms involving fifth-order density matrices.
• Significant computational gains in efficiency without compromising accuracy or stability.

Conclusions:

• The proposed factorization method offers a substantial improvement in computational efficiency for electronic structure calculations.
• This approach enables accurate calculations with reduced computational resources.