Active-space two-electron reduced-density-matrix method: complete active-space calculations without diagonalization...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Electronic Structure Theory

Background:

• Molecular wave functions often require multiple electronic configurations.
• Traditional Complete-Active-Space Self-Consistent-Field (CASSCF) methods have exponential scaling, limiting their application to small active spaces.
• Accurate treatment of larger active spaces is crucial for understanding complex molecular systems.

Purpose of the Study:

• To develop a novel active-space variational two-electron reduced-density-matrix (2-RDM) method.
• To overcome the computational limitations of CASSCF for large active spaces.
• To enable accurate electronic structure calculations for systems previously inaccessible to CASSCF.

Main Methods:

• Developed an active-space variational 2-RDM method using semidefinite programming for optimization.
• Replaced expensive CASSCF diagonalization with a constrained variational 2-RDM calculation.
• Employed a two-step approach: variational 2-RDM calculation followed by Jacobi rotations for active orbital optimization.

Main Results:

• The active-space 2-RDM method exhibits polynomial scaling (r(a)^6) with the number of active orbitals, r(a).
• Successfully applied the method to molecules like HF, H2O, N2, and acene chains up to n=8.
• Demonstrated the method's efficiency compared to one-step 2-RDM approaches for large basis sets.

Conclusions:

• The active-space 2-RDM method significantly expands the scope of accurate electronic structure calculations.
• The method accurately captures the emergence of bi- and polyradical character in long acene chains.
• This approach provides a computationally feasible alternative to CASSCF for large and complex molecular systems.