Open-shell molecular electronic states from the parametric two-electron reduced-density-matrix method.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Electronic structure theory

Background:

• The two-electron reduced-density-matrix (2-RDM) method is crucial for accurately describing molecular electronic structure.
• Existing methods face challenges with open-shell systems and capturing multireference correlation.
• N-representability constraints are vital for ensuring the physical validity of the 2-RDM.

Purpose of the Study:

• To extend the parametric 2-RDM method for open-shell molecules and various spin states.
• To improve the accuracy of vertical excitation energy calculations.
• To enable efficient molecular geometry optimization using energy gradients.

Main Methods:

• Extension of the parametric variational 2-RDM method to handle open-shell systems (singlet, doublet, triplet).
• Modification of the 2-RDM using N-representability conditions to ensure size extensivity and approximate N-representability.
• Calculation of vertical excitation energies using a polarized valence triple-zeta basis set.
• Development and application of an energy gradient relation for molecular geometry optimization.

Main Results:

• The extended parametric 2-RDM method accurately treats closed- and open-shell molecules.
• Improved recovery of multireference correlation in singlet excited states leads to more accurate vertical excitation energies.
• Efficient molecular geometry optimization is achieved via a Hellmann-Feynman-like energy gradient relation.
• Application to HCN(+)<-->HNC(+) isomerization demonstrates accurate relative energies and barrier heights.

Conclusions:

• The extended parametric 2-RDM method offers a robust approach for electronic structure calculations, including excited states.
• The method demonstrates improved accuracy and efficiency for molecular property predictions.
• The computed 2-RDMs satisfy necessary N-representability conditions, validating the approach.