Second-Order Self-Consistent-Field Density-Matrix Renormalization Group.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Matrix-product states (MPS) are powerful tools for representing quantum many-body systems.
• Density-matrix renormalization group self-consistent-field (DMRG-SCF) methods are essential for accurate electronic structure calculations.
• Achieving rapid convergence in DMRG-SCF is crucial for computational efficiency.

Purpose of the Study:

• To present a novel MPS-based DMRG-SCF algorithm.
• To achieve quadratically convergent energy calculations.
• To improve the efficiency of quantum chemical computations.

Main Methods:

• Developed a DMRG-SCF algorithm based on direct energy minimization.
• Incorporated a simultaneous optimization of MPS wave function and molecular orbitals.
• Utilized an energy expression correct to second order for orbital basis changes.

Main Results:

• The proposed DMRG-SCF algorithm demonstrates quadratic convergence.
• Energy convergence is typically achieved within two to four self-consistent cycles.
• The method surpasses the convergence scaling of previous Newton-Raphson and superconfiguration-interaction algorithms.

Conclusions:

• The novel MPS-based DMRG-SCF approach offers a significant improvement in computational efficiency.
• This method enables faster and more reliable electronic structure calculations.
• The direct minimization strategy is key to achieving rapid convergence.