Molecular properties from variational reduced-density-matrix theory with three-particle N-representability conditions

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Calculating molecular ground-state energies and properties is crucial for understanding chemical systems.
• Traditional methods often rely on approximations or computationally expensive wave function calculations.
• Two-electron reduced density matrices (2-RDMs) offer an alternative pathway, but their accurate determination is challenging.

Purpose of the Study:

• To extend the use of 2-RDMs with three-positivity conditions for calculating molecular properties.
• To assess the accuracy of this method against full configuration interaction (FCI) benchmarks.
• To compare the three-positivity 2-RDM approach with other 2-RDM and wave function methods.

Main Methods:

• Constraining the two-electron reduced density matrix (2-RDM) to satisfy a complete set of three-positivity conditions for N representability.
• Calculating molecular ground-state energies and properties, including multipole moments and energy components.
• Comparing results with full configuration interaction (FCI) and other approximate methods.

Main Results:

• Molecular ground-state energies were computed within 0.3% of the correlation energy.
• Dipole, quadrupole, and octupole moments for various molecules (BeH2, BH, H2O, CO, NH3) were within 0.04% of FCI values.
• Accurate expectation values for kinetic energy, electron-nuclei potential, and electron-electron repulsion were obtained for N2.

Conclusions:

• The three-positivity conditions for 2-RDMs provide a robust and accurate method for determining molecular ground-state energies and properties.
• This approach offers a viable alternative to traditional wave function methods, achieving high accuracy without explicit wave function computation.
• The method shows promise for accurate electronic structure calculations across various molecular systems and properties.