Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate prediction of molecular geometries is crucial in chemistry.
• Complete active space self-consistent field (CASSCF) methods are widely used but computationally intensive.
• Variational two-electron reduced-density-matrix (2-RDM) methods offer a potentially more efficient alternative.

Purpose of the Study:

• To develop and present analytic energy gradients for a variational 2-RDM-driven CASSCF method.
• To evaluate the performance of this new method against traditional CASSCF approaches for molecular geometry.
• To assess the accuracy of the variational 2-RDM-CASSCF method for predicting bond lengths.

Main Methods:

• Utilized a semidefinite programming (SDP) algorithm with an augmented Lagrangian formalism to determine the active-space 2-RDM.
• Derived analytic energy gradients, simplifying calculations due to Lagrangian stationarity.
• Compared variational 2-RDM (v2RDM)-CASSCF with configuration interaction (CI)-CASSCF for 20 small molecules.

Main Results:

• v2RDM-CASSCF optimized bond lengths showed minimal error (mean unsigned error of 0.0060 Å) compared to CI-CASSCF when enforcing two-particle N-representability conditions.
• Enforcing three-particle conditions further reduced errors to 0.0006 Å.
• Deviations from experimental bond lengths were comparable to CI-CASSCF, with v2RDM-CASSCF showing average deviations of 0.017 Å (two-particle) and 0.011 Å (three-particle).

Conclusions:

• The variational 2-RDM-driven CASSCF method provides accurate analytic energy gradients for molecular geometry optimization.
• The method demonstrates high accuracy in predicting bond lengths, comparable to established CI-CASSCF methods.
• This approach offers a promising alternative for electronic structure calculations, especially for systems where traditional CASSCF is computationally prohibitive.