Approximate Analytical Gradients and Nonadiabatic Couplings for the State-Average Density Matrix Renormalization...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Calculating electronic wave functions is crucial for understanding molecular behavior.
• State-average complete active space self-consistent-field (SA-CASSCF) methods are powerful but computationally intensive.
• Efficient calculation of analytical gradients and nonadiabatic couplings is essential for reaction dynamics.

Purpose of the Study:

• To present an approximate scheme for analytical gradients and nonadiabatic couplings.
• To develop a novel method for state-average density matrix renormalization group self-consistent-field (SA-DMRG-SCF) wave function calculations.
• To avoid computationally expensive sweep procedures in solving coupled-perturbed CASSCF (CP-CASSCF) equations.

Main Methods:

• Utilized a Lagrangian formalism based on the SA-CASSCF ansatz.
• Introduced a new definition for matrix product state (MPS) Lagrange multipliers using a single-site tensor.
• Employed a mixed-canonical form of the MPS to simplify calculations.
• Solved the CP-CASSCF equations without iterative sweeps.

Main Results:

• Successfully implemented an approximate scheme for analytical gradients and nonadiabatic couplings.
• Demonstrated the avoidance of sweep procedures in solving CP-CASSCF equations.
• Achieved arbitrary accuracy in reproducing SA-CASSCF results.

Conclusions:

• The new method provides an efficient and accurate approach for electronic structure calculations.
• This work advances the application of matrix product states in quantum chemistry.
• The developed scheme is suitable for optimizing challenging molecular systems, such as conical intersections.